5th sense math book

555Fifth SenseAccelerating Instruction for Grade 5 Math

Aligned to STAAROrganized into Focal Points

Acknowledgements:

Copyright © The blackline masters of this book may be reproduced by classroom teachers for their students only. No other part of the book may be reproduced or transmitted in any form or by any means, electronic or mechanical including photocopying and recording, or by any information storage or retrieval system without the prior written permission of Educaiton Service Center Region XIII. October 2011

Carol Gautier Project Coordinator for Curriculum Support ESC Region XIII Jerry Karacz Instructional Coach ESC Region XIII

Tamara Ramsey Coordinator Academic Services ESC Region XIII Natalie Brown Elementary Math Coach Del Valle ISD

Haley Stanfield Communication and Production Specialist ESC Region XIII

Resources given by permission from: Charles A. Dana Center University of Texas at Austin Austin, Texas www.utdanacenter.org Texas Education Agency 5th Grade TAKS Information Booklet (realigned to STAAR) 5th Grade TAKS Study Guide (realigned to STAAR) http://www.tea.state.tx.us

Table of Contents

Table of Contents: Focal Point 1: Using fractions and decimals to represent and compare quantities 5.1 (A) Use place value to read, write, compare, and order whole numbers through the 999,999,999,999

place.

5.1 (B) Use place value to read, write, compare, and order decimals through the thousandths place.

5.2 (A) Generate a fraction equivalent to a given fraction such as 1/2 and 3/6 or 4/12 and 1/3.

5.2 (B) Generate a mixed number equivalent to a given improper fraction or generate an improper fraction

equivalent to a given mixed number.

5.2 (C) Compare two fractional quantities in problem‐solving situations using a variety of methods, including

common denominators.

5.2 (D) Use models to relate decimals to fractions that name tenths, hundredths, and thousandths.

5.3 (A) Use addition and subtraction to solve problems involving whole numbers and decimals.

5.3 (E) Model situations using addition and/or subtraction involving fractions with like denominators

using concrete objects, pictures, words, and numbers.

5.12 (A) The student is expected to use fractions to describe the results of an experiment.

5.14 (all) The student applies Grade 5 mathematics to solve problems connected to everyday experiences and

activities in and outside of school.

5.15 (all) The student communicates about Grade 5 mathematics using informal language.

5.16 (all) The student uses logical reasoning.

Focal Point 2: Developing proficient use of whole‐number division algorithms 5.3 (B) Use multiplication to solve problems involving whole numbers (no more than three digits times two

digits without technology.

5.3 (C) Use division to solve problems involving whole numbers (no more than two‐digit divisors and three‐

digit dividends without technology), including interpreting the remainder within a given context.

5.3 (D) Identify common factors of a set of whole numbers.

5.4 (A) Use strategies, including rounding and compatible numbers to estimate solutions to addition,

subtraction, multiplication, and division problems.

5.5 (B) Identify prime and composite numbers using concrete objects, pictorial models, and patterns

in factor pairs.





Focal Point 3: Connecting measurement concepts to the use of measurement formulas to solve problems 5.5(A) Describe the relationship between sets of data in graphic organizers such as lists, tables, charts, and

diagrams.

5.10(B) Connect models for perimeter, area, and volume with their respective formulas.

5.10(C) Select and use appropriate units and formulas to measure length, perimeter, area, and volume.

Table of Contents





Focal Point 4: Collecting, organizing , displaying, and interpreting sets of data to solve problems 5.5 (A) The student is expected to describe the relationship between sets of data in graphic organizers such

as lists, tables, charts, and diagrams.

5.12 (B) The student is expected to use experimental results to make predictions.

5.12 (C) The student is expected to list all possible outcomes of a probability experiment such as tossing a

coin.

5.13 (A) The student is expected to use tables of related number pairs to make line graphs.

5.13 (B) The student is expected to describe characteristics of data presented in tables and graphs including

median, mode, and range.

5.13 (C) The student is expected to graph a given set of data using an appropriate graphical representation

such as a picture or line graph.





Focal Point 5: The student will demonstrate an understanding of probability and statistics. 5.4 (A) The student is expected to use strategies, including rounding and compatible numbers to estimate

solutions to addition, subtraction, multiplication, and division problems.

5.7 (A) The student is expected to identify essential attributes including parallel, perpendicular and

congruent parts of two‐ and three‐dimensional geometric figures.

5.8 (A) The student is expected to sketch the results of translations, rotations, and reflections on a Quadrant

I coordinate grid.

5.8 (B) The student is expected to identify the transformation that generates one figure from the other when

given two congruent figures on a Quadrant I coordinate grid.

5.10 (A) The student is expected to perform simple conversions within the same measurement system (SI

(metric) or customary).

5.11 (A) The student is expected to solve problems involving changes in temperature.

Introductory Experiences : Grade 5 TEKS:

5.6 (A) The student is expected to select from and use diagrams and equations such as y = 5 + 3 to represent

meaningful problem situations.

5.9 (A) The student is expected to locate and name points on a coordinate grid using ordered pairs of whole

numbers.

5.11 (B) The student is expected to solve problems involving elapsed time.

Teacher Tips

Teacher Tips: Strategies for Modifying Games/Activities

Allow students to work in pairs instead of individually to discuss strategies. (also provides for a safe environment for the student(s))

Assign a role to each person in the group.

Introduce activities in small chunks.

Use clues: verbal or physical

Ask students to repeat directions in their own words.

Ask questions to check for understanding of directions and vocabulary. (E.g., “What do we do first?”)

Adapt the game to fit the child’s ability. (E.g., Use one die instead of a pair of dice, limit the number of cards to manipulate at a time; add other pieces as students progress, etc.)

Allow the use of manipulatives for the tactile learner.

Provide ready‐made pieces for the activities.

Allow students to use a workmat. (E.g., 100’s chart, 10‐frame)

Simplify and limit the number of visuals.

Select appropriate difficulty level for the student when questioning.

Increase wait time for a response.

Grouping Patterns for Mathematics

There are many ways to group students. Grouping students successfully is the beginning of developing rich discovery, mathematical conversations, collaborative team work, the engagement into multiple strategies, experiences in various problem solving techniques, and valuable justification processes. Prior to grouping, teachers must know where their students’ strengths and weaknesses occur along the continuum of mathematics. Suggestions for assessing students are pre‐assessment testing, teacher observation during activities, daily conversation with students in the classroom, homework, quiz and classroom test performance, and district and state assessments. Once strengths and weaknesses in performance have been identified, keep a log on each student. This log could also include student input. It is important for you, as a teacher, to monitor student success; however, it is just as important for the student to see success.

Teacher Tips

Once targeted areas are determined for each student, use an appropriate grouping pattern that will benefit all students. Below are five examples of grouping patterns. Cooperative Grouping: Teacher will assign students to cooperative groups and will assign roles to each student or allow students to select a role that will be followed throughout the activity. If students have not been trained in cooperative grouping, this will need to be done first. Collaborative Grouping: Teacher will assign students to mixed ability groups. Members of mixed ability groups will assist each other in group activities to ensure success of all. Interest Grouping: Teacher will assign students to mixed ability groups based on similar interests of students. Teacher will survey the students’ prior to grouping. Paired Grouping: Teacher will assign each student with a partner (There are four types of pairs: weak/medium, weak/strong, medium/medium, medium/strong. It is not recommended to use weak/weak pairs.) Then two or three Partner Pairs will work together as one group. Paired grouping allows students to collaborate and builds confidence within a safe environment that fosters success. Special Need or Skill Grouping: Teacher will assign students to skill‐level groups based on a pre‐assessment of topic (weak/medium/high). Remember in all group situations, students will need some short instruction prior to arriving in their groups unless this is a repeated activity. It is not recommended to change group members daily because time is needed for students to begin to feel comfortable with other team mates. However, all students should be participating even on the first day. If a student is not participating, ask the student what the group is discussing or how the problem is being approached. If the student cannot answer immediately, inform the student you will be back in a few minutes and will ask the same question again. This should engage the student to ask questions and be prepared to answer. Remember, never tell “how to do the math” when working with groups; instead use questioning strategies to help the group reach an understanding, so they can be successful in their problem solving experiences.

ELL (English Language Learners) General Tips and Suggestions:

Make sure the correct language of instruction has been determined and is being used.

Make available native language and simplified English resources.

Textbooks are available in Spanish for 5th grade.

Allow for cooperative learning and many opportunities to talk About math concepts.

Problem solving for mathematics is full of cultural differences, including methods for division and showing work, etc.

Consider using this additional ELL Resource. Purchase at store.esc13.net.

Teacher Tips

Students w/Disabilities General Tips and Suggestions:

Presentation Techniques Practice Techniques Feedback Practices

Make learning visible and

explicit. Use clear, simple directions. Adjust pacing. Highlight key information. Reduce amount of

information/skills taught. Use study guides, semantic

maps, and graphic organizers.

Activate background knowledge.

Allow alternative ways to demonstrate learning.

Increase the amount of small‐group instruction weekly.

Change grouping from small groups.

Use peer and cross‐age

tutoring. Use games. Use manipulatives. Provide more frequent

practice on less information/fewer skills.

Use computer programs. Ensure mastery before

moving on to next skill. Provide a variety of practice

opportunities (e.g., manipulatives, problem‐solving, explanations).

Use prompts to help students notice, find, and/or fix errors and write responses.

Encourage students with prompts of encouragement.

Textbook/Materials Content Check for Understanding

Highlight key

points/concepts. Provide books on tape/CD‐

ROM with study guides. Reduce amount of reading. Use shared reading or have

peers read to students. Provide study guides. Highlight directions. Use high‐interest/low‐

vocabulary books. Use trade books/textbooks

written at various levels.

Use task analysis to divide

tasks into smaller steps. Identify and check to see if

students have prerequisite skills.

Teach the vocabulary of instruction (e.g., direction words).

Teach technical vocabulary. Relate concepts to each

other using graphic organizers, such as semantic maps.

Ask different levels of questions and encourage students to generate questions.

Use a variety of ways for students to respond.

Incorporate sufficient wait time.

Teach self‐monitoring, such as graphing progress.

Taken from the Instructional Decision‐Making Procedures for Ensuring Appropriate Instruction for Struggling Students Developed by UTCLRA and TEA, 2003

Consider using this additional Resource. Purchase at store.esc13.net.

Teacher Tips

Bibliography Ball, D. L. (1997). From the general to the particular: Knowing our own students as learners of mathematics. Mathematics Teacher, 90, 732‐737. Huling, L., & Beck, J. (2005). Mathematics for English language learners (MELL): Classroom practices framework (CPF). San Marcos, Texas: Texas State University. Instructional Decision‐Making Procedures for Ensuring Appropriate Instruction for Struggling Students Developed by UTCLRA and TEA, 2003 Marzano, R. J. (2003). What works in schools: Translating research into action. Alexandria, VA: Association for Supervision and Curriculum Development. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. Swanson, H. L., Hoskyn, M., and Lee, Carole, Interventions for Students with learning Disabilities: A Meta‐Analysis of Treatment Outcomes, The Guilford Press, New York, NY, 1999

Texas Education Agency. (2003). Texas assessment of knowledge and skills, 2003: Statewide Performance Results. Retrieved November 14, 2005 from http://www.tea.state.tx.us/student.assessment/reporting/results/swresults/taks/index.html Texas Education Agency. (2004). Texas assessment of knowledge and skills, 2004: Statewide Performance Results. Retrieved November 14, 2005 from http://www.tea.state.tx.us/student.assessment/reporting/results/swresults/taks/index.html Texas Education Agency. (2005). Texas assessment of knowledge and skills, 2005: Statewide Performance Results. Retrieved November 14, 2005 from http://www.tea.state.tx.us/student.assessment/reporting/results/swresults/taks/index.html

Van de Walle, J. (2004). Elementary and middle school mathematics: Teaching developmentally. Boston: Pearson Education, Inc.

Teacher Tips

Grade 5 Mathematics Chart

LENGTH

Metric Customary

1 kilometer = 1000 meters

1 meter = 100 centimeters

1 centimeter = 10 millimeters

1 mile = 1760 yards

1 mile = 5280 feet

1 yard = 3 feet

1 foot = 12 inches

CAPACITY AND VOLUME

Metric Customary

1 liter = 1000 milliliters

1 gallon = 128 ounces

1 quart = 2 pints

1 pint = 2 cups

1 cup = 8 ounces

MASS AND WEIGHT

Metric Customary

1 kilogram = 1000 grams

1 gram = 1000 milligrams

1 ton = 2000 pounds

1 pound = 16 ounces

Teacher Tips

TIME 1 year = 365 days

1 year = 12 months

1 year = 52 weeks

1 week = 7 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

Grade 5 Mathematics Chart

Perimeter

Square P = 4 × s

Rectangle P = (2 × l) + (2 × w)

Area

Square A = s × s

Rectangle A = l × w

Volume

Cube V = s × s × s

Rectangular prism V = l × w × h

Teacher Tips

Grid for Grades 4 and 5

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Teacher Tips

Hundreds Chart

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31 32 33 34 35 36 37 38 39 40

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Copyright©2011 ESC Region XIII 5.1A

STAAR Reporting Category 1: Numbers, Operations, and Quantitative Reasoning: The student will demonstrate an understanding of numbers, operations, and quantitative reasoning.

TEKS 5.1: The student uses place value to represent whole numbers and decimals.

Student Expectation: 5.1(A): The student is expected to use place value to read, write, compare, and order

whole numbers through the 999,999,999,999. Overview:

In this lesson, students and their partners will create numbers with 12 digits and then read, write, compare and order the numbers as a group.

Materials: Per group of two students

A spinner, labeled 0‐9 Student Sheet 5.1A: Activity 1 Student Sheet 5.1A: Activity 2 8 ½ x 11 piece of paper to make 4 sentence strips

Vocabulary: Ones, tens, hundreds, thousands, ten thousand, hundred thousand, millions, ten million, hundred million, billions, ten billion, hundred billion, period, place value, comma

Lesson: 1. Present this scenario: Today we are going to play “Hit the Target”. I will show you a twelve‐

digit target number. Your challenge is to hit the target or get as close as possible to the target using a spinner. You must use a spinner to help you.

Game Rules: 1. You must use a spinner

2. You must write the number into one of the twelve spaces.

3. You may not skip a turn.

4. You may work in pairs.

5. You may not move a number after you write it down.

To check for understanding, ask:

Which digits can you use to fill in the circles? (0‐9)

How are you going to generate the digits? (by spinning the spinner)

2. After all 12 places have been filled, have the students write the value of each digit in expanded form on the Student Sheet 5.1A: Activity 1. Tell them to find the sum of the numbers written in expanded form.

Is it possible to get a sum with fewer than 12 digits? What is the smallest possible number? What is the largest possible number? (It is possible to have a zero in the hundred billions place.)


What is the purpose of zeros? What would happen if you got rid of the zeros in your number? (Zeros are place holders. It would change the value.)

What symbol is used to group the numbers, and what is each group called? (Comma is used to separate the periods. “Each set of three numbers have something in common. The three places have the same last name like a family. E.g., the millions period”)

When you are reading a number and come to a comma, what should you say? (You should say the period word. E.g., billions, millions, and thousands.)

3. Have each pair read their numbers stressing the correct place value of each digit. 4. Have each student fold the sentence strip twice to create four equal rectangles. Have each

student write his or her number on the strip with each rectangle representing a different period. A strategy for students with disabilities is to highlight the periods with different colors.

5. Have the students arrange the sentence strips vertically beginning with the greatest number and compare/order the differences in sizes. Write the numbers into the place value chart, Student Sheet 5.1A: Activity 2.

Debriefing Questions:

Who has the highest ten thousands digit?

Who has the highest one billions digit?

What is the value of 0 in any place? (0)

Who made the greatest number?

Who made the least number?

How does your number fit into the place value chart?

Who came closest to the target number? (You may want to have a calculator available.)

What was the difference?

Billion Million Thousand Units

Hundred Ten One , Hundred Ten One , Hundred Ten One , Hundred Ten One


Guided Practice: Write the following numbers in the place value chart from least to greatest. 7,853,203,916 564,092,895 7,765,298,000 309,824,252

Billion Million Thousand Units Hundred Ten One , Hundred Ten One , Hundred Ten One , Hundred Ten One

Read the numbers, and we will decide together which number you would write in the

chart first. Remember, you are putting them in order from least to greatest. Write L to G out beside the chart.

How many digits does the smallest number have? (nine)

There are two nine‐digit numbers. Which one would you write first in the chart? (309,824,252 would be first in the chart. Yes, 3 < 5 )

After filling in the first two numbers, let’s look at the next two numbers. Do both of these numbers begin with the same digit? (yes)

Which digits do we compare next? (hundred millions place)

Tell me what you can about these two digits? (7 < 8)

Which number would be written next? (7,765,298,000)

Which number is the greatest? (7,853,203,916)

Assessment:

1. What does the digit 9 represent in 935,254,683,112? A. nine thousand B. nine billion C. nine hundred billion D. nine million

2. Which shows 693,000,000 written in words?

F. six hundred ninety‐three thousand G. six hundred ninety‐three billion H. six hundred ninety‐three million J. six hundred ninety‐three trillion

3. What is the value of the digit in the ten millions’ place in this number 1,593,615,902?

A. 10,000 B. 3,000,000 C. 90,000,000 D. 500,000,000

4. Which value is greater than seventy‐eight thousand, thirty but less than seventy‐nine thousand, ninety eight?

F. 70,000 + 9,000 + 80 + 9 G. 78,016 H. seventy nine thousand, one

hundred J. 70,000 + 800 + 40 + 9

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Student Sheet Activity 1 Reporting Category 1: TEKS 5.1(A) Name: ________________________________ Date: _____________

Target Number: ______________________________________________

_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

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Student Sheet Activity 2 Reporting Category 1: TEKS 5.1(A) Name: ________________________________ Date: _____________




Spinners for TEKS 5.1(A)

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Guided Practice: Reporting Category 1: TEKS 5.1(A)

Name: ________________________________ Date: _____________

Write the following numbers in the place value chart from least to greatest. 7,853,203,916 564,092,895 7,765,298,000 309,824,252



Read the numbers, and we will decide together which number you would write in the chart

first. Remember, you are putting them in order from least to greatest. Write L to G out beside the chart.

How many digits does the smallest number have? _________________

There are two nine‐digit numbers. Which one would you write first in the chart?

_________________________________________________________________

After filling in the first two numbers, let’s look at the next two numbers. Do both of these numbers begin with the same digit? _____________

Which digits do we compare next? ___________________

Tell me what you can about these two digits? _____________________________

Which number would be written next? _______________________________

Which number is the greatest? _______________________


Assessment: Reporting Category 1: TEKS 5.1(A)

Name: ________________________________ Date: _____________

1. What does the digit 9 represent in 935, 254, 683, 112?

A. nine thousand B. nine billion C. nine hundred billion D. nine million

2. Which shows 693,000,000 written in words? F. six hundred ninety‐three thousand G. six hundred ninety‐three billion H. six hundred ninety‐three million J. six hundred ninety‐three trillion

3. What is the value of the digit in the ten millions’ place in this number: 1,593,615,902? A. 10,000 B. 3,000,000 C. 90,000,000 D. 500,000,000

4. Which value is greater than seventy‐eight thousand, thirty but less than seventy‐nine thousand, ninety eight?

F. 70,000 + 9,000 + 80 + 9 G. 78,016 H. seventy‐nine thousand, one hundred J. 70,000 + 800 + 40 + 9

Copyright©2011 ESC Region XIII 5.1B


TEKS 5.1: The student uses place value to represent whole numbers and decimals.

Student Expectation: 5.1(B): The student is expected to use place value to read, write, compare, and order decimals through the thousandths place.

Overview:

This lesson will give students practice in reading, writing, and giving meaning to the value of digits. Students will also compare decimals through the thousandths place.

Materials: Per table group:

three sets of cards numbered from 0‐9 six decimal point cards chips to represent decimals set of Number Sentence Decimal grids decimal recording sheet

Vocabulary: Tenths, hundredths, thousandths, greater than, less than, equal, and (the word and should only be used to signify a decimal place). E.g., 24.17 twenty four and seventeen hundredths

Lesson: 1. Today we are going to play a game using decimals. I have written a secret number on

a sheet of paper. Let’s see who can create a number closest to mine. The teacher should write a number containing a decimal on a sheet of paper and place it face down. This activity is to be carried out in groups of four students. A student shuffles and deals 6 number cards to each student in the group of four. Put the extra cards aside.

2. Each member of the group selects one of the decimal grids and places his or her six cards face‐up on the grid.

3. The students must read their numbers aloud. Have each student record his or her numbers on his or her decimal recording sheet.

4. Each student should then compare his or her two numbers on the grid and describe how the two numbers compare using greater than (>) or less than (<) signs and write each number sentence in words.

5. After the students have compared their own two numbers, then the group of four students should order all eight numbers from least to greatest by arranging their number cards in a vertical line aligning the decimal points.


Example: Activity 1:

To extend this activity, put away the card grids. Add the six decimal point cards to the number cards; shuffle, and deal four cards to each student. Have students turn their cards over on their desks and read the number correctly. Cards are not allowed to be rearranged after turning them over. The decimal point could turn up anywhere or not at all. If any player has more than one decimal point card, have that player discard the extra decimal point card and draw another card to replace it. Have the students compare and order the numbers using symbols and number sentences in words.

Accommodation: Use a hundreds‐to‐hundredths place‐value chart with those students having difficulty with place names. Have students study the place names in the chart and ask why we use “th.” Practice pronunciation and listening skills for place values to the left versus the right of the decimal. It is difficult for ELL’s to distinguish between thousands & thousandths.

Extension: Have students record all four numbers at their table and write an ordering and comparing word problem using all four numbers.

Debriefing Questions: Ask students:

How does the placement of the zero affect the number?

Examples: 0.12

What does the zero in this number mean? (There are zero wholes.)

How do you read this number? (twelve hundredths)

What would this look like shaded on a 10 x 10 grid?

2 . 36

. 439

24 . 6


1.02

What does the zero in this number mean? (There are zero tenths.)

How do you read this number? (one and two hundredths)

What would this look like on a 10 x 10 grid?

1.20

What does the zero in this number mean? (The zero is holding the value of the hundredths.)

How do you read this number? (one and twenty hundredths or one and two‐tenths) Make sure students understand 1.20 hundredths is the same as 1.2.

What would this look like on a 10 x 10 grid?


What would my decimal grid need to look like if I wanted to write money amounts?

How do you use the word “and” when reading a number? (“And” refers to the decimal point within a number.)

The decimal point plays an important role in our number system. What do you think it could be? (The decimal point designates parts of a whole. The numbers to the right of the decimal point are less than one whole.)

How can you accurately compare a number with tenths along with a number with thousandths? (Line up the decimal points, and then begin to compare the numbers beginning with the far left place.)

Guided Practice: Use the place value chart to order these decimals to find the fastest skater.

The scores for the speed skating contest have been announced. Tamara’s time was 35.80 seconds while Angela’s time was 35.76 seconds. Evelyn had a time of 57.93 seconds, and Cynthia crossed the finish line with a time of 37.54 seconds. What was the fastest time? **Delete answer choices and make a griddable.**

Do all of the numbers have the same digit in the tens place? (Three numbers have a 3 in the tens place and one number has a 5 in the tens place.)

Is that digit greater or less than the other three? (5 is greater than 3; 5>3.)

Then where would we put the number 57.93 in the chart? Why? (Last. It is the greatest number and makes that skater the slowest.)

All of the other numbers have a 3 in the tens place; how do you know which of the three numbers is the largest? (You compare the one’s place next. The one with 7 in the ones place is the largest 7 > 5.)

Now let’s look at the remaining two numbers. How do you know which number is the largest? Why? (35.8; 35.8 is greater than 35.76; 35.8 > 35.76. We know this because .8 is greater than .7 .8 >. 7.)

To find the fastest time, how should we order the numbers? Explain your answer. (We should order the numbers least to greatest because the fastest skater has to have the smallest time.)

Tens Ones . Tenths Hundredths Thousandths


Which runner came in last? How do you know? (Evelyn came in last because she had the largest number.)

Which runner came in first? How do you know? (Angela came in first because she had the smallest number.)

Assessment:

1. Which of the following numbers is greater than .563 but less than .574? A. .561 B. .57 C. .585 D. .56

2. Which of the following shows 5.44 written in words?

F. five hundred forty‐four G. five and forty‐four thousandths H. five and forty‐four hundredths J. five and forty‐four tenths

3. Which year had the most rainfall amount?

YEAR INCHES

2000 26.6

2001 25.78

2002 26.72

2003 25.8

A. 2000 B. 2001 C. 2002 D. 2003

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Decimal Recording Sheet Reporting Category 1:TEKS 5.1(B)

Name ____________________________ Date ____________________________ Hundreds Tens Ones . Tenths Hundredths Thousandths


Guided Practice: Reporting Category 1: TEKS 5.1B Name: ____________________________ Date: __________________ Use the place value chart to order these decimals to find the fastest skater. You may use the work area below to solve the problem. The scores for the speed skating contest have been announced. Tamara’s time was 35.80 seconds while Angela’s time was 35.76 seconds. Evelyn had a time of 57.93 seconds, and Cynthia crossed the finish line with a time of 37.54 seconds. What was the fastest time?

Tens Ones . Tenths Hundredths Thousandths

**Delete answer choices and make a griddable**

1. Do all of the numbers have the same digit in the tens place?

________________________________________________________________________

2. Is that digit greater or less than the other three?

________________________________________________________________________

3. Then where would we put the number 57.93 in the chart? Why?

________________________________________________________________________

4. All of the other numbers have a 3 in the tens place; how do you know which of the three numbers is the largest?

________________________________________________________________________

5. Now let’s look at the remaining two numbers. How do you know which number is the largest? Why?

________________________________________________________________________


6. To find the fastest time, how should we order the numbers? Explain your answer.

________________________________________________________________________

7. Which runner came in last? How do you know?

________________________________________________________________________

8. Which runner came in first? How do you know?

________________________________________________________________________


Assessment: Reporting Category 1: TEKS 5.1(B) Name: ____________________________ Date: __________________ 1. Which of the following numbers is greater than .563 but less than .574?

A. .561 B. .57 C. .585 D. .56

2. Which of the following shows 5.44 written in words?

F. five hundred forty‐four G. five and forty‐four thousandths H. five and forty‐four hundredths J. five and forty‐four tenths

3. Which year had the most rainfall amount?

YEAR INCHES

2000 26.6

2001 25.78

2002 26.72

2003 25.8

A. 2000 B. 2001 C. 2002 D. 2003

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1 2 3


Decimal Grid #1 Reporting Category 1: TEKS 5.1 (B)

________ ________ ________

________ ________ ________ NUMBER SENTENCE: _____________________________ WORDS:_______________________________________________________



________ ______ ______

______ ______ ______ NUMBER SENTENCE: _____________________________ WORDS:_______________________________________________________


Decimal Grid #3 Reporting Category 1: TEKS 5.1 (B) _________ __________ __________ _________ __________ __________

NUMBER SENTENCE: _____________________________ WORDS:_______________________________________________________



______ ______ ______ _________ _________ __________

NUMBER SENTENCE: _____________________________ WORDS:_______________________________________________________



TEKS 5.2: The student uses fractions in problem‐solving situations.

Student Expectation: 5.2(A): The student is expected to generate a fraction equivalent to a given fraction such as 1/2 and 3/6 or 4/12 and 1/3.

Overview: This lesson uses an area model to generate equivalent fractions.

Materials:

Centimeter strips prepared with rectangles marked as “one whole” and fractional parts shaded (one per student) Centimeter Strips for Fractions (Introduction to TEKS 5.2(A)) Centimeter Strips for Equivalent Fractions (TEKS 5.2(A)) Pencils (one per student)

Vocabulary: Fraction, numerator, denominator, equivalent fractions, identity property of multiplication, identity property of division

Lesson: Parts 1 and 2 of this lesson:

(a) Review the definition of fraction, numerator, and denominator, and

(b) review the fact that when the numerator and the denominator are the same number (n

n),

the fraction is always equal to 1. 1. Today we will be working with fractions. What are fractions?

(Guide students into realizing that a fraction is a number that names part of a whole. The denominator tells the number of equal parts into which the whole has been divided. The numerator tells how many of the equal parts are selected, shaded, unshaded, etc. Emphasize that the parts must be equal.) Distribute centimeter strips for fractions handout [Introduction to TEKS 5.2 (A)].

Let’s look at the centimeter strip on number one of your student sheet. Notice that the strip is divided into eight equal parts. Will this 8 be the numerator or the denominator? (denominator) Why? (It tells how many equal parts the whole has been divided into.)

Of these eight equal parts, how many are shaded? (3)


Will this 3 be the numerator or the denominator? (numerator) Why? (It tells how many of the equal parts are shaded.)

So we would say that 3 out of the 8 equal parts are shaded. We could write this as the

fraction 3

8 and say that

3

8 of the strip is shaded. The 8 is called the denominator of the

fraction and tells us how many equal parts into which the whole has been divided. The 3 is called the numerator of the fraction and tells us how many of the equal parts are shaded.

We can also describe the fraction of the strip that is not shaded. How many equal parts is the strip divided into? (8)

How many of these equal parts are not shaded? (5)

What is the numerator of this fraction? (5)

What is the denominator? (8)

What fraction of the strip is not shaded? (5

8)

2. Consider centimeter strip “A” on number two of the student sheet below as “one whole

unit.”

How many equal parts are in the “one whole unit?” (8)

Will this be the numerator or the denominator? (denominator)

Why? (It tells how many equal parts the whole is divided into.)

How many are shaded? (8)

Will this be the numerator or the denominator? (numerator)

Why? (It tells how many equal parts are shaded.)

What do you notice about this fraction or model? (The numerator and the denominator are the same number, and the whole model is shaded.)

Since we have 8

8equal parts shaded, we have one “whole” unit.

So we know that 8

8 = 1.

If we had 3 out of 3 equal pieces shaded as in the strip “B”, we would have 3

3 of the

strip, or 1 whole unit.

A.

B.


In other words, anytime the numerator and the denominator of a fraction are the same number, the fraction is equal to “one whole unit.”

Look at these examples:

51

5

6

16

10

110

Stress to students that the fractional pieces of the “one whole” must be equal. However, each “one whole” may be a different size. An example would be a whole small pizza and a whole large pizza are not the same size, but they are each a whole unit.

Parts three‐eight of this activity involve generating equivalent fractions. (TEKS 5.2(A)) Distribute prepared centimeter strips to students:

(See Centimeter Strips for Equivalent Fractions, TEKS 5.2(A)) 3. Discuss with students that the top row of rectangles is “one whole unit,” and the

rectangles are all the same size. The bottom row of squares is also considered “one whole unit,” and the small squares are all the same size. Emphasize that both of the “one whole units” are equal.

Ask students to compare the shaded areas of the two whole units above:

How many equal rectangles are in the top “one whole unit?” (4)

Is this the numerator or the denominator? (denominator) Why? (It tells how many equal pieces the whole is divided into.)

How many equal rectangles are shaded? (1)

Is this the numerator or the denominator? (numerator) Why? (It tells how many of the equal parts are shaded.)

What fraction of the top “one whole unit” is shaded? (1

4)

How many squares are in the bottom “one whole unit?” (8)

Is this the numerator or the denominator? (denominator) Why? (It tells how many equal pieces the whole is divided into.)

How many equal squares are shaded? (2)


Is this the numerator or the denominator? (numerator) Why? (It tells how many of the equal parts are shaded.)

What fraction of the bottom “one whole unit” is shaded? (2

8)

If you fold your paper so that the two rectangles are on top of each other, does it

appear that 1

4=

2

8? (yes)

Since 1

4 =

2

8, we call these “equivalent fractions” because they name the same part of

a whole.

Talk to the students about the word “equivalent” and how it has part of the word “equal” in it. The two shaded sections cover equal areas.

4. Let’s look at this another way:

We know that 1

4 of the top rectangle is shaded since 1 out of 4 equal parts is shaded. We

also know that 2

8 of the bottom rectangle is shaded since 2 out of 8 equal parts is shaded.

We also decided that 1

4 =

2

8.

Let’s review for a while; what is 1 times 1? (1)

How about 2 times 1? (2)

And 3 times 1? (3)

Four times 1? (4)

Anything times 1? (anything)

This is called the identity property of multiplication, also called the multiplication property of one. This property says that a number does not change when that number is multiplied by 1. Therefore, anytime I multiply anything times 1, I do NOT change that number.

This also applies to fractions. Who can remind us what a 1 looks like in fractional form? (When the numerator and denominator of a fraction are the same number.)

Can someone give us an example of 1 in fractional form? (8/8, 4/4, 9/9, etc.)

What does 3

3 equal? (1)

Let’s get back to the ¼ = 2/8. Let’s look mathematically at how these two fractions are equivalent. In order for the fractional units to be equivalent, and not change in value, we must use the identity property of multiplication (anything times 1 = anything).


We could say that 1

4

2

2=

2

8. Since

2

2 = 1, we have not changed the value of the

fraction, only the way it looks. Why do you think that I chose to multiply by 2

2?

(Lead students into “discovering” the fact that 2 of the eighths are equal to 1 of the fourths.)

5. Let’s look at another example:

How many equal rectangles are in the top “one whole unit?” (3)

Will this be the numerator or the denominator? (denominator). Why? (It tells how many equal pieces the whole is divided into.)

How many equal rectangles are shaded? (2)

Will this be the numerator or denominator? (numerator). Why? (It tells how many of the equal parts are shaded.)


3)


Will this be the numerator or the denominator? (denominator) Why? (It tells how many equal pieces the whole is divided into.)


Will this be the numerator or the denominator? (numerator) Why? (It tells how many of the equal parts are shaded.)


9)

If you fold your paper so that the two rectangles are on top of each other, does it

appear that 2

3 =

6

9? (yes)

Since 2

3 =

6

9, we call these “equivalent fractions” because they name the same part of a

whole.

Using what we now know about the identity property of multiplication, we can say

2

3

3

3 =

6

9. Why do you think that I chose to multiply by

3

3?

(Lead students into “discovering” the fact that 3 of the ninths are equal to 1 of the thirds.)

We could also say that6 3 2

9 3 3

. Remember that

3

3 = 1 and dividing by 1 also gives us the

same number we had. This is called the Identity Property of Division.


For example, 6 1 = 6, 8 1 = 8. When we use this property with fractional units, we do not change the value of the original fraction, only the way it looks.

6. One more example with rectangles:

How many equal rectangles are in the top “one whole unit?” (5) Will this be the numerator or the denominator? (denominator) Why? (It tells how many equal pieces the whole is divided into.)

How many equal rectangles are shaded? (3) Will this be the numerator or the denominator? (numerator) Why? (It tells how many of the equal parts are shaded.)


5)


Will this be the numerator or the denominator? (denominator)

Why? (It tells how many equal pieces the whole is divided into.)


Will this be the numerator or denominator? (numerator)

Why? (It tells how many of the equal parts are shaded.)


10)

If you fold your paper so that the two rectangles are on top of each other, does it appear

that 3

5 =

6

10? (yes)

Since 3

5 =

6

10, we call these “equivalent fractions” because they name the same part of a

whole.

Using the Identity Property of Multiplication, we can say 3

5

2

2 =

6

10. Why do you think

that we chose to multiply by 2

2?

We could also say that 6 2 3

10 2 5

. Remember that

2

2 = 1 and dividing by 1 also gives us

the same number we had. For example, we know that 6 1 = 6 and 8 1 = 8. This is called the Identity Property of Division. When we use this property with our fractions, it does NOT change the value of the original fraction, only the way it looks.

7. Since we know that we can find equivalent fractions by using the Identity Property of

Multiplication or the Identity Property of Division (multiplying or dividing by a fraction that is equal to 1), let’s try some examples without the centimeter strips.


What fraction is equivalent to 4

5and has a 30 for the denominator?

We can multiply 4

5 by a fraction equal to 1 to get 30 in the denominator. What can we

multiply 5 by to get 30? (6)

What fraction do you think would work? (6

6) Why? (It is equal to 1). So,

4

5

6

6=

24

30,

4

5 and

24

30 are equivalent fractions.


Check for understanding with these questions:

What is a fraction? (A fraction names a part of the whole.)

What does the numerator represent? (how many of the equal parts are selected, shaded, unshaded, etc.)

What does the denominator represent? (the number of equal parts into which the whole has been divided)

What are equivalent fractions? (fractions that name the same amount of a whole) Stress that for fractions to be equivalent, they must represent part of equal “wholes.”

For example, 1

4 of a small pizza is not equivalent to

1

4of a large pizza.

How can we mathematically find a fraction that is equivalent to a given fraction? (by using the identity property of multiplication or the identity property of division)

What do those properties tell us? (That when we multiply or divide anything by 1, it stays “anything.”)

How do I know when I have a fraction equal to one whole? (when the numerator and the denominator are the same number)

How do I know what fractional “one whole” unit to use when using the Identity Property to find an equivalent fraction? (Look at what numerator or denominator you want your equivalent fraction to have, and decide what you can multiply or divide to your original numerator or denominator to get your new one.)


Guided Practice:

Distribute the guided practice worksheet.

1. Let’s practice finding equivalent fractions by completing the table below:

Original Fraction

Fraction Equal to One

Multiply or Divide Equivalent Fraction

4

6

2

2

4 2

6 2

8

8

12

4

5 7

7

4

5

4 7

5 7

35

28

35

25

30

5

5 25 5

30 5

6

5

6

2

9 7

7

2 7

9 7

14

63

8

14 2

2

8 2

14 2

4

7

6

7 8

8

6 8

7 8

56

48

56

2. John drank 3

5 of a cup of milk. Mary drank an equivalent amount of milk as John. What

fraction of milk did she drink if she used a cup divided into 15 equal parts? (9/15) 3. Mary ate 6/18 of a large pizza. Kathy ate 2/9 of a large pizza. Did Mary and Kathy eat an

equal amount of pizza? (no)


Assessment:

1. Which fraction is equivalent to5

9?

A. 10

27

B. 5

36

C. 20

36

D. 20

32

2. Martha and Chad made homemade pizzas using the same mold. Martha cut her pizza into 6

equal pieces. Chad cut his pizza into 12 equal pieces. If Martha ate 2 out of 6 pieces of her pizza, how many pieces would Chad have to eat of his to eat an equivalent amount?

A. 2 out of 12 B. 6 out of 18 C. 4 out of 12 D. 3 out of 12

3. What fraction does the shaded part represent?

A.

16

20

B.

2

3

C.

1

3

D.

8

16

*

*

*


1. Sandra made 8 out of 10 soccer goals. Which fraction is equivalent to 8

10?

F.

4

5

G.

8

9

H.

9

10

J.

2

3

*


Reporting Category 1: TEKS 5.2(A) Student Sheet: Page 1

Centimeter Strips for Fractions, Introduction to TEKS 5.2(A)

1.

2. A. B.

51

5

6

16

101

10


Reporting Category: TEKS 5.2(A) Student Sheet: Page 2 Centimeter Strips for Equivalent Fractions, TEKS 5.2(A)

3.

4. 5. 6.


Guided Practice: Reporting Category 1: TEKS 5.2(A) Name: ____________________________ Date: __________________ Let’s practice finding equivalent fractions by completing the table below:

1.

Original Fraction

Fraction Equal to One

Multiply or Divide

Equivalent Fraction

4

6

2

2 4 2

6 2

8

4

5 4

5

35

25

30 5

5 25 5

30 5

6

2

9 14

63 8

14 4

7

6

7 56



2. John drank 3

5 of a cup of milk. Mary drank an equivalent amount of milk as John. What

fraction of milk did she drink if she used a cup divided into 15 equal parts? 3. Mary ate 6/18 of a large pizza. Kathy ate 2/9 of a large pizza. Did Mary and Kathy eat an

equal amount of pizza?


Assessment: Reporting Category 1: TEKS 5.2(A) Name: ____________________________ Date: __________________

1. Which fraction is equivalent to 5

9?

A. 10

27

B. 5

36

C. 20

36

D. 20

32

2. Martha and Chad made homemade pizzas using the same mold. Martha cut her pizza into 6

equal pieces. Chad cut his pizza into 12 equal pieces. If Martha ate 2 out of 6 pieces of her pizza, how many pieces would Chad have to eat of his to eat an equivalent amount?

A. 2 out of 12 B. 6 out of 18 C. 4 out of 12 D. 3 out of 12



3. What fraction does the shaded part represent?

A. 16

20

B. 2

3

C. 1

3

D. 8

16

4. Sandra made 8 out of 10 soccer goals. Which fraction is equivalent to 8

10?

F. 4

5

G. 8

9

H. 9

10

J. 2

3




Student Expectation: 5.2(B) The student is expected to generate a mixed number equivalent to a given improper fraction or generate an improper fraction equivalent to a given mixed number.

Overview:

This lesson gives meaning to the terms numerator and denominator and provides hands‐on experiences with improper fractions and mixed numbers.

Materials: Fraction Spinner Sheet Fraction Game Rules Sheet Fraction Recording Sheet Paperclips for spinners Fraction Pieces (run on different colored cardstock) Pattern Blocks Fraction Exploration Sheet

Vocabulary: proper fraction, improper fraction, numerator, denominator, mixed number, whole number, integer, total, equal parts, whole, halves, thirds, fourths, sixths

Procedure: Activity 1: The Whole Thing

1. Today we are going to play a game called “The Whole Thing” using two spinners. You can play with a partner or play pair against pair. The object of the game is to get an improper fraction and mixed number with the highest value.

2. The teacher will need to model the game by using the spinners, the fraction pieces, the

Recording Sheet, and the Game Rules Sheet. Watch carefully as I play the game. I will spin the denominator spinner first to determine the size of the playing piece or how many parts will be needed to make one whole. Pick up one fraction piece that matches the spin and show it to the students. Notice where I write the number for the denominator on the Recording Sheet.

3. Now I will spin the numerator spinner to find the number of pieces I will get to build the

circles. Spin the numerator spinner. I already have one piece, so how many more pieces do I


need to pick up? (one less than the spin) Notice how I write the number of my spin above the fraction bar. Write the numerator on the recording sheet.

4. I will now place the playing pieces on the table and to try to make circles. How many circles

did I make? (See example on the bottom of the Game Rules) I will draw a picture of the circles on the recording sheet.

5. The last step is to write the fraction or whole number on the Recording Sheet represented

in the picture. Do I have a proper fraction, a whole number or mixed number represented by the circles in the column to the left? (see Scaffolding Questions)

6. It is time for your group to play the game. Remember that you and your partner get three

chances to create the largest mixed number to win the game. 7. As the students continue building fractions and collecting data, ask students the following

questions.

What does the numerator mean? (the number of equal size pieces in the fraction)

What does the denominator mean? (the size of the piece or the number of equal size pieces that make one whole)

When you look at a fraction, how do you know when the fraction will be greater than one whole? (if the numerator is larger than the denominator)

Activity 2: Fraction Exploration

After students have an opportunity to successfully play the game, pass out a set of pattern blocks to each pair of students and a Fraction Exploration sheet. Using the hexagon as 1 whole, how many trapezoids make up the whole? (2) What fraction of the whole is one trapezoid? (one half) Is this a proper fraction or improper fraction? (proper) How do you know? ( the numerator is less than the denominator)

Scaffolding/ Debriefing Questions: • What is a proper fraction? (a fraction in which the numerator is less than the denominator) • What is an improper fraction? (An improper fraction is a fraction in which the numerator is equal to or greater than the denominator; improper fractions are usually changed to whole or mixed numbers.)

• What is a mixed number, and why is it called “mixed?” (A number that is a combination of a whole number and a proper fraction.) • What is the relationship between the denominator and the size of the part? (The larger the denominator, the smaller the part is.) • When comparing the denominator to the numerator, how do you determine if the answer will be a proper fraction, mixed number, or whole number? (If the denominator is larger than the numerator, the answer will be a proper fraction. If the numerator is larger than the denominator and is a multiple of the denominator, the answer will be a whole number. If the numerator is larger than the denominator and is not a multiple of the denominator, the answer will be a mixed number).


Guided Practice: 1. Use trapezoids to represent one and a half hexagons. Draw a picture below.

• How many trapezoids were needed? ___ • If one hexagon equals one whole, what improper fraction would the trapezoids represent? ___

Students should be able to decide which pattern block represents half of a hexagon (trapezoid) and place three trapezoids on the hexagons to make one and a half. They should

recognize that 12

1 is a mixed number. They should also be able to explain that there are

three of the trapezoids used to make 12

1 , and when described this way, it would be read

three halves or 2

3 . Students should be able to explain the difference between the mixed

number representation and the improper fraction representation. 2. What pattern block represents one third of a hexagon? (rhombus)

Use blocks to build the fraction 3

7 . Sketch and shade 3

7 hexagons below.

• What does the denominator represent? (the number of equal size pieces in the fraction)

• What does the numerator represent? (the number of equal pieces you referenced e.g., shaded, unshaded, used, etc.)

• What is an improper fraction? (A fraction in which the numerator is equal to or greater than the denominator is an improper fraction. Improper fractions are usually changed to whole or mixed numbers.)

• What mixed number does the picture represent? (2) • Compare the mixed number to the improper fraction. How are they alike and how are they different? (Answers will vary.)

3. Build 2 6

1 hexagons using green triangles and draw a picture below.

• What does the 2 represent? (whole number) • How many sixths are there in all? (13)

• What improper fraction does the picture represent? 6

13

• Compare the improper number and mixed number. How are they alike, and how are they different? (Answers will vary.)


Assessment:

1. What part of the model is shaded?

A. 3

2 *C. 3/2

B. 4

1 D.

3

4

2. Which model below correctly shows 3

8 ?

A. B. C.

*D.


3. What fraction is represented by the shaded model below?

A. 212

1

*B. 24

3

C. 23

1

D. 28

1


Activity 1: The Whole Thing: Game Rules TEKS 5.2(B)

Game Rules: 1. Spin the denominator spinner.

2. Write the number below the fraction bar in the “Fraction” column on the Recording Sheet. Pick up one fraction piece that matches the spin. (E.g., spin 2, write a 2 in the fraction column, and pick up a “half” fraction piece.)

3. Spin the numerator spinner.

4. Write the number for the numerator in the Fraction column, and pick up that many fraction pieces minus the one selected in step 2. (E.g., spin 4, write four in the fraction column, and pick up three more half pieces.)

5. Use the pieces to build circles on the table.

6. Sketch the circle pieces in the Pictorial Representation column.

7. Look at your picture and write the number represented in your sketch in the last column. Identify the number as a proper fraction, a whole number, or a mixed number.

8. Repeat all steps two more times, and select your highest improper fraction.

Spins

Fraction

Pictorial Representation

Proper Fraction, Whole Number

Or Mixed Fraction

1

4 2

2 Whole number


The Whole Thing: Recording Sheet TEKS 5.2(B)

My largest improper fraction is _____________________________, which is equal to

________________________.

Spins

Fraction

Pictorial Representation

Proper Fraction, Whole Number

Or Mixed Fraction

1

2

3


The Whole Thing: Spinner TEKS 5.2(B)

1

2 3

4Step 1:

Denominator

Number of equal size parts in a

whole or a set

Step 2:

Numerator How many pieces

1

2 3

4

5


Activity 2: Fraction Exploration: TEKS 5.2B

Use the hexagon to represent one whole in each of the following tasks. Place the other blocks on top of the hexagon when building. 1. Using trapezoids cover the hexagon. Draw a picture below.

How many trapezoids did it take to make one whole? _____

Each trapezoid equals what fraction of a hexagon? ______ 2. Using trapezoids cover the hexagons. Draw a picture below.

How many trapezoids did it take to cover three hexagons? _____

Each trapezoid equals what fraction of a hexagon? ______

What improper fraction is represented by the trapezoids in the picture above? ____________

What whole number does this improper fraction represent? __________


Guided Practice: Page 1 TEKS 5.2B 1. Use trapezoids to represent one and a half hexagons? Draw a picture below.

How many trapezoids were needed? ___

If one hexagon equals one whole, what improper fraction would the trapezoids represent? ___

2. What pattern block represents one third of a hexagon? _______

Use blocks to build the fraction3

7 . Sketch and shade 3

7 hexagons below.

What does the denominator represent? __________________

What does the numerator represent? ___________________

What improper fraction does the picture represent? ___________________________

What mixed number does the picture represent? ____________

Compare the mixed number to the improper fraction. How are they alike, and how are they different? ______________________________________________________________________

______________________________________________________________________

______________________________________________________________________ ______________________________________________________________________


Guided Practice: Page 2 TEKS 5.2B

3. Build 2 6

1 hexagons using green triangles and draw a picture below.

What does the 2 represent? ___________________

How many sixths are there in all? ______________

What improper fraction does the picture represent? ________

Compare the improper fraction and mixed number. How are they alike and how are

they different?

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________


Fraction Pieces


Assessment: Reporting Category 1: TEKS 5.2 B


A. 3

2 C.

2

3

B. 4

1 D.

3

4

2. Which model below correctly shows 3

8?

A. B.

C.

*D.


3. What fraction is represented by the shaded model below?

A. 212

1

B. 24

3

C. 23

1

D. 28

1

Copyright©2011 ESC Region XIII 5.2C



Student Expectation: 5.2(C): The student is expected to compare two fractional quantities in problem‐solving situations using a variety of methods, including common denominators.

Overview:

This lesson uses an area model to compare two fractional quantities by finding common denominators.

Materials:

Centimeter strips prepared with rectangles marked as “one whole” and fractional parts shaded (one per student).

Centimeter Strips for Fractions (Introduction to TEKS 5.2(A)& (C))

Centimeter Strips for Comparing Fractions (TEKS 5.2(C))

Pencils (one per student)

Vocabulary: common denominators, equivalent fractions, proper fraction, improper fraction, identity property of multiplication, identity property of division, multiple

Lesson: Parts 1 and 2 of this lesson:

Review the definition of fraction, numerator, and denominator.

Review the fact that when the numerator and the denominator are the same number

(n

n), the fraction is always equal to 1.

Review equivalent fractions.

Review the Identity Property of Multiplication and the Identity Property of Division.

Today we are going to be comparing fractions. Who can remind us what is a fraction? (equal parts of a whole unit)

What is the top number of a fraction called and what does it represent? (Numerator: It represents how many parts of the whole are selected, shaded, unshaded, etc.)

What is the bottom number of a fraction called and what does it represent? (Denominator: It represents how many equal parts the whole was divided into.)

How do I make a fraction equivalent to one whole? Give an example of this. (Make the numerator and denominator have the same number. E.g., 3/3, 6/6, 7/7, etc.)


What does the Identity Property of Multiplication say? (When you multiply anything times one, you get “anything.”)

What does the Identity Property of Division say? (When you divide anything times one, you get “anything.”)

What are equivalent fractions? (fractions that name the same amount of a whole)

How can we find a fraction that is equivalent to a given fraction? (by using the Identity property of multiplication or the identity property of division–multiplying or dividing both the numerator and denominator by the same number)

Distribute prepared centimeter strips to students: (Centimeter Strips for Comparing Fractions, TEKS 5.2(C)) Now that we can find equivalent fractions, let’s practice comparing fractions.

1. If fractions have the same denominator, such as 4

7and

6

7, then we can compare the

numerators to decide which fraction is larger. Look at the centimeter strips below:

We can easily see that 6

7>

4

7.

2. If fractions do not have the same denominator, we can use our knowledge of

equivalent fractions to rewrite the fractions with the same denominator. Look at the sample below:

Which is greater, 2

3 or

3

5?

We want both fractions to have the same denominator. Since 15 is a multiple of 3 and 5, we can use 15 for the common denominator. Let’s change each fraction into an equivalent fraction by using the Identity property of multiplication (multiplying by 1).

2

3 =

15 ;

What fractional unit of one should we multiply 2

3 by to get a denominator

of 15? (5

5) Why? (because 3 x 5 = 15)

3

5 =

15;


What should we multiply 3

5 by to get a denominator of 15? (

3

3) Why?

(because 5 x 3 = 15) This gives us 2 5 10

3 5 15

;

and

3 3 9

5 3 15

Since we know that 10

15>

9

15, we can say that

2

3>

3

5.

Let’s try another example:

Which is greater, 7

9 or

6

7?

Again, let’s find a common denominator.

What number is a common multiple of 9 and 7? (63) Let’s change each fraction into an equivalent fraction by using the identity property of multiplication (multiplying by 1). 7 7

9 7

= 49

63

6 9

7 9

= 54

63 Since

54

63 >

49

63, we know that

6

7 >

7

9.

Debriefing Questions: Check for understanding with these questions:

What is a fraction? (A fraction names a part of the whole.)

What does the numerator represent? (how many of the equal parts are selected, shaded, unshaded, etc.)

What does the denominator represent? (the number of equal parts into which the whole has been divided)

What are equivalent fractions? (fractions that name the same amount of a whole) Stress that for fractions to be equivalent, they must represent part of equal “wholes.”

For example, 1

4 of a small pizza is not equivalent to

1

4of a large pizza.

How can we find a fraction that is equivalent to a given fraction? (multiplying or dividing both the numerator and denominator by the same number–using the identity property of multiplication or the identity property of division)

How can we tell if one fraction is larger than another fraction? (changing both to the same denominator by finding equivalent fractions for each, then comparing the numerators).


Guided Practice:

1. Let’s practice comparing fractions by completing the table below:

<, >, =

5/9 (>) 3/7

2/3 (<) 5/6

6/12 (=) 18/36

14/18 (>) 6/9

3/9 (=) 6/18

2. Which fraction is greater 5

6 or

3

4? (

5

6)

3. John drank 3

5 of a cup of milk. Mary drank

2

3of a cup of milk. Who drank the most milk?

(Mary)

4. If 4

7 of Mrs. Smith’s math class made an “A” on a test, and

3

8of Mrs. Smith’s math class

made a “B” on the same test, were there more “A’s” or more “B’s” on the test? (more A’s)


Assessment:

1. Bob needs a piece of string longer than 5

9of an inch. Which of the following could Bob use?

A. 10

27

B. 5

36

C. 20

36

D. 45

27

2. The students in Mary’s class have a total of 8 cats and 4 dogs. Which class below has a

larger fraction of cats than Mary?

F. Bob ‐ 10 cats and 8 dogs G. Elizabeth ‐ 4 cats and 8 dogs H. Adriana ‐ 10 cats and 10 dogs J. Charles ‐ 14 cats and 4 dogs

3. Jose rode his bike 16

10 of a mile on Monday. Jill rode her bike 20/40 of a mile on Monday.

Which of the following statements is correct?

A. Jill rode her bike farther than Jose. B. Jose rode his bike farther than Jill. C. Jill and Jose rode their bikes the same distance. D. Beth rode her bike farther than Jose.

4. Steve made 8 out of 10 soccer goals. Jaime made more goals than Steve. Which of the

following could NOT be how many goals Jaime scores?

F. 4

5

G. 8

9

H. 9

10

J. 12

10

*

*

*

*


Student Sheet: Reporting Category 1: TEKS 5.2(C) Centimeter Strips for Comparing Fractions, TEKS 5.2(C) 8A.

8B.


Guided Practice: Reporting Category 1:TEKS 5.2(C) Name: ____________________________ Date: __________________ Let’s practice comparing fractions by completing the table below: 1.

<, >, =

9

5 7

3

3

2 6

5

12

6 36

18

18

14 9

6

9

3 18

6

2. Which fraction is greater 5

6 or

3

4?


1. John drank 3

5 of a cup of milk. Mary drank

2

3of a cup of milk. Who drank the most milk?

2. If 4

7 of Mrs. Smith’s math class made an “A” on a test, and

3

8of Mrs. Smith’s math class

made a “B” on the same test, were there more “A” s or more “B”s on the test?


Assessment: Reporting Category 1: TEKS 5.2(C) Name: ____________________________ Date: __________________

1. Bob needs a piece of string longer than 5

9of an inch. Which of the following could Bob

use?

A. 10

27

B. 5

36

C. 20

36

D. 45

27

2. The students in Mary’s class have a total of 8 cats and 4 dogs. Which class below has a larger fraction of cats than Mary?

F. Bob ‐ 10 cats and 8 dogs

G. Elizabeth ‐ 4 cats and 8 dogs

H. Adriana ‐ 10 cats and 10 dogs

J. Charles ‐ 14 cats and 4 dogs

3. Jose rode his bike 16

10 of a mile on Monday. Jill rode her bike 20/40 of a mile on Monday.

Which of the following statements is correct?

A. Jill rode her bike farther than Jose.

B. Jose rode his bike farther than Jill.

C. Jill and Jose rode their bikes the same distance.

D. Beth rode her bike farther than Jose.


4. Steve made 8 out of 10 soccer goals. Jaime made more goals than Steve. Which of the following could NOT be how many goals Jaime scores?

F. 4

5

G. 8

9

H. 9

10

J. 12

10

Copyright©2011 ESC Region XIII 5.2D

STAAR Reporting Category 1: Numbers, Operations, and Quantitative Reasoning: The student demonstrates an understanding of number, operations, and quantitative reasoning.


Student Expectation: 5.2(D): The student is expected to use models to relate decimals to fractions that name tenths, hundredths, and thousandths.

Overview:

This lesson will give students the opportunity to create their own model. They will practice writing fractions and decimals from a model. The teacher will need models of tenths, hundredths, and thousandths. Students will create their own design and identify the fractions and decimals.

Materials: Sample Grids and Models Handouts Base Ten Blocks (tenths, hundredths, thousandths) Scissors (1 for every 2 students) Index Cards (2‐3 per student) Glue Highlighters

Vocabulary: decimals, fractions, tenths, hundredths, thousandths, shaded, grid ELL – shaded, part, endings such as “ths”

Lesson: 1. Review base ten blocks (tenths, hundredths, thousandths) and sample grids and fraction

models with students. Recall: ELL students struggle with endings such as “ths.” Practice pronunciation and listening skills for place values to the left versus the right of the decimal. On the board, write ten and tenths, and draw a model underneath each number.

2. Explain to students that they are going to be demonstrating how to use models to relate decimal and fractions.

3. Allow each student to select a grid or a model.

Which grid or model do you want to use? (E.g., stars) Make sure a variety of grids and models are being used by the students. 4. Ask each student to cut the grid or model out and paste it onto an index card. 5. Instruct each student to shade an amount on his or her grid or model.


Example: Joyce shaded eight out of the ten stars. What is the decimal and the fraction that represents her design? 6. After shading, have students record on the back of the index card the fraction and decimal

representing their shaded model or grid. A strategy for students with disabilities is to highlight each column a different color to make it easier to count.

Ask students:

What is the number on the bottom called? (denominator)

What number should go in the denominator? Why? (10 should go in the denominator because there are 10 total stars.)

What number should go in the numerator? Why? (8 should go in the numerator because there are 8 shaded stars.)

What is the fraction for the shaded amount? (E.g., 10

8 )

What is the decimal for the fraction? (0.8) 7. Students will then challenge a partner by showing only the front of the card of their shaded

model. Other students must correctly identify the decimal and fraction of the card. Once both students have correctly identified each other’s cards, they trade cards. Ask the students:

On the back of the card you just received beneath the fraction and decimal, write the words to describe the model.

Show your card to a new partner asking his or her to look at the model and give the fraction, decimal, and the words to describe the model.

(E.g., 10

8, 0.8, eight tenths, 8 out of 10 equal parts)

Exchange cards. Next to the model on the card you just received, draw another model that could represent this fraction or decimal?

Note: Students could draw a four shaded stars out of five. or a completely new model such as eight shaded sections out of 10 on a tens grids


Show the card to a new partner and ask him or her to describe and explain why in both models are the fractions, decimals, and word descriptions exactly the same? Why or why not? (It could depend on the model you have chosen. In the example of the tens grids, the model is different, but the fraction, decimal, and words described are basically the same. If the other representation of stars, four shaded stars out of five stars, is used, then the answer is no. The model is an equivalent representation; the fraction is an

equivalent representation because 10

8 or

10

8

2

2 =

5

4. However, the decimal is still

0.8. The word description is four fifths or four shaded stars out of five total stars). 8. Students continue to trade cards and challenge each other by asking if they can draw another

representation describing the relationships. (E.g., 80 shaded squares on a hundreds grid)


If you were to start over, would you choose the same model or another model to begin? (Answers may vary.)

What does equivalent mean? (naming the same number)

How do you write the decimal or fraction in words? (Write the number shown after the decimal followed by the name of the place the last digit is in. E.g., .89 = eighty nine hundredths–the 9 is in the hundredths place. Therefore it is followed by the word hundredths.)

How would you shade the hundredths grid to represent 0.8?

Since 0.8 is the fraction 10

8, then

10

8 x

10

10 =

100

80 or 0.80.

So shade 80 squares on the hundredths grid.


How would you write 0.80 in words? (eighty hundredths)

Since equivalent means naming the same number or

fraction, then 10

8,

100

80,

5

4, 0.8, 0.80, eight tenths,

eighty hundredths are all equivalent.

Once students have practiced from models to fractions and decimals, have students practice going from fractions and decimals to the models.

Example: What model will students use to represent the fraction 100

70?

What is the total? (100)

What is the amount shaded? (70)

Could another model be used to represent the fraction 100

70?

Since 100

70

10

10 =

10

7, use the tenths grid.


What is the amount shaded? (7)

Sample Answer:


Guided Practice:


Is this a tenths, hundredths, or thousandths grid? (hundredths)

What is the total? (hundred)

What part of the model is shaded? (50)

What is the fraction? 100

50

What is the decimal? (0.50)

Shade the tenths grid to show an equivalent representation of this model.

Draw another equivalent representation of this grid. (Answers may vary.)

2. Draw a picture to represent the decimal 0.3.

Write the fraction for the decimal 0.3. (10

3)

How do you write 0.3 in words? (three tenths)


3. How would you write a decimal for a model or fraction that did not have a 10 or 100 as the denominator? Show students the following example:

Example:


How many are shaded? (3)

What is the fraction? (3/5)

How can I find the decimal for this model? (Find the equivalent fraction that has a denominator of 10 or 100.) 3/5 x □/□ = □/10 3/5 x 2/2 = 6/10 or 0.6

How do I write 0.6 in words? (six tenths)

How would I shade the tenths grid to show an equivalent representation of this model?

How would I shade the hundredths grid to show an equivalent representation of this model?

What is the fraction? (60/100)

What is the decimal? (.60)

How do you write .60 in words? (sixty hundredths)


Assessment:

1. What fractional part of the model is shaded?

A. 5.8 *B. 0.58 C. 0.058 D. None of the above

2. Elisa made an art design. What decimal number represents the shaded part of her design?

*F. 0.5 G. 0.05 H. 0.005 J. 0.0005



*A. 0.30 B. 0.03 C. 0.003 D. 3.0


TEKS 5.2(D) Sample Grids and Models (Students could create their own models)


Guided Practice: Reporting Category 1:TEKS 5.2(D) Name: __________________________ Date: __________________ 1. What part of the model is shaded?

Is this a tenths, hundredths, or thousandths grid? ____________________

What is the total? ___________________

What part of the model is shaded? _____________

What is the fraction? __________

What is the decimal? __________

Shade the tenths grid to show an equivalent representation of his model.

Draw another equivalent representation.


2. Draw a picture to represent the decimal 0.3?

Write the fraction for the decimal 0.3. ___________

How do you write 0.3 in words? ___________________________ 3. Look at the following model.

What is the total? ___________________

What part of the model is shaded? ______________________

What is the fraction? _______________________

How can I find the decimal for this model if it is not a tenth or hundredth? (Answer in words.)

____________________________________________________________

What is the decimal? _____________________________

Write this in words. ______________________________


Shade the tenths grid to show an equivalent representation of this model.

Shade the hundredths grid to show an equivalent representation of this model.

What is the fraction? ______________________

What is the decimal? ______________________

How do I write this decimal in words? ___________________


Assessment: Reporting Category 1: TEKS 5.2(D) Name: __________________________ Date: __________________ 1. What part of the model is shaded?

A. 5.8 B. 0.58 C. 0.058 D. None of the above

2. Elisa shaded 2

1of her design. What decimal number represents the shaded part of her

design?

F. 0.5 G. 0.05 H. 0.005 .J 0.0005



A. 0.30 B. 0.03 C. 0.003 D. 3.0

Copyright©2011 ESC Region XIII 5.3A, 5.14A, 5.14B

STAAR Reporting Category 1:

Numbers, Operations, and Quantitative Reasoning: The student will demonstrate an

understanding of number, operations, and quantitative reasoning.

TEKS 5.3:

The student adds, subtracts, multiplies, and divides to solve meaningful problems.

TEKS 5.14: The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

Student Expectations: 5.3(A) The student is expected to use addition and subtraction to solve problems involving whole numbers and decimals. (Readiness Standard) 5.14(A) The student is expected to identify the mathematics in everyday situations. 5.14(B) Solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. Overview:

This lesson will reinforce the operations of addition and subtraction. Students will discuss how to use addition or subtraction.

Materials: 0‐9 Spinner Paper to record problem solving

Vocabulary: Add, addition, total, sum, join, including tax, subtract, minus, subtraction, difference, increase, decrease, change

Lesson: The object of today’s game is to be the person closest to the target number set prior to each game. You will be spinning a spinner to generate two numbers. You will then decide if you should add or subtract your two numbers to get as close to the target number as possible. The person closest to the target number wins that round. You will be playing five rounds of this game.

1. Play with 2‐3 players. The teacher sets a specific number. (E.g., 42,635) 2. Students take turns spinning a spinner to generate a five digit number. (E.g., 15,256 ) Students will get five spins each. Record this number in your math journal. 3. Students take turns spinning the spinner a second time to generate a second number.

This number may be either four or five digits long. The student must decide what he or she needs and spin the spinner the appropriate number of times. (E.g., first spin 41,035 which means on the second spin the student tries to spin 1,600, so the student needs to spin four times.) Record the second number in your math journal.

4. Students decide whether they need to find the sum or difference of their two spins to get closest to the target number.


5. The player with the sum or difference closest to the specific number wins. 6. The winner generates the next target number. 7. The students play five rounds.

Variation: Use decimals (E.g., 4 6 . 2 6) tenths, hundredths, and/or thousandths in your target number.

Debriefing Questions: • How did you solve the problem? • What strategy did you use? • Can you solve the problem another way? • How can you break the numbers apart? • How did you decide which operation to use?

Guided Practice:

Mrs. Ramos went on a trip to Destin, Florida and drove 1,468 miles round trip. She now has 46,283 miles on the odometer in her car. She will need an oil change at 50,000 miles. How many more miles will Mrs. Ramos drive her car before she will need an oil change?

1. What do you know about Mrs. Ramos’ car? (The car has 46,283 miles on the odometer.)

2. What do you need to find? (how many miles can Mrs. Ramos drive before she needs

to get her oil changed) 3. Is there any extra information in this problem? Explain. (How many miles she

drove round trip to Destin, Florida. These miles are already a part of the 46,283 miles on her odometer.)

4. How will you solve the problem? (Sample answer: I could subtract 46,283 from

50,000) 5. Is there another way to solve this problem? (I could draw a picture–see sample

model below.)

Sample Model:

6. How many more miles will Mrs. Ramos drive her car before she will need an oil change? (3,717 miles)

46,283 47,000 50,000

3,000 717


Assessment:

1. Madaline spent $41.42 on art supplies. She bought a painting canvas for $16.65, a tube of bright pink paint for $7.26, a large tube of black paint for $11.89, and a fan brush. What was the total cost of the fan brush?

A. $77.22 B. $14.42

*C. $5.62 D. $6.42

2. Fantastic Pens manufacturing plant produced 1,250 red pens, 2,584 blue pens, 3,417 black

pens, and 2,142 mechanical pencils on Tuesday morning. How many total pens did Fantastic Pens produce on Tuesday morning?

F. 3,834 G. 6,941 *H. 7,251 J. 9,393

3. Mickey is saving his money to buy a bicycle that costs $169.95. His grandmother gave him

$50 for his birthday. He made $28.75 mowing his neighbors yards. Mickey made $15.23 at his family’s garage sale. How much more does Mickey need in order to buy the bicycle he wants?

A. $169.95 B. $93.98 C. $75.93

* D. Not here


Spinners for TEKS 5.3(A), 5.14(A), and 5.14(B)

1 2 3

4

5

67

8

9

0

1 2 3

4

5

67

8

9

0


Guided Practice: Reporting Category 1: TEKS 5.3(A), 5.14(A), and 5.14(B)

Name: ___________________ Date: __________________ Mrs. Ramos went on a trip to Destin, Florida and drove 1,468 miles round trip. She now has 46,283 miles on the odometer in her car. She will need an oil change at 50,000 miles. How many more miles will Mrs. Ramos drive her car before she will need an oil change?

1. What information will you use? 2. What do you know about Mrs. Ramos’ car?

3. What do you need to find?

4. Is there any extra information in this problem? Explain.

5. How will you solve the problem?

6. Is there another way to solve this problem?

7. How many more miles will Mrs. Ramos drive her car before she will need an oil change?


Assessment: Reporting Category 1: TEKS 5.3(A), 5.14(A), and 5.14(B)

Name: ______________________ Date: __________________ 1. Madaline spent $41.42 on art supplies. She bought a painting canvas for $16.65, a tube of

bright pink paint for $7.26, a large tube of black paint for $11.89, and a fan brush. What was the total cost of the fan brush?

A. $77.22 B. $14.42 C. $5.62 D. $6.42

2. Fantastic Pens manufacturing plant produced 1,250 red pens, 2,584 blue pens, 3,417 black pens, and 2,142 mechanical pencils on Tuesday morning. How many total pens did Fantastic Pens produce on Tuesday morning?

F. 3,834 G. 6,941 H. 7,251 J. 9,393

3. Mickey is saving his money to buy a bicycle that costs $169.95. His grandmother gave him $50 for his birthday. He made $28.75 mowing his neighbors yards. Mickey made $15.23 at his family’s garage sale. How much more does Mickey need in order to buy the bicycle he wants?

A. $169.95 B. $93.98 C. $75.93 D. Not here

Copyright©2011 ESC Region XIII 5.3E, 5.14B

STAAR Reporting Category 1: Numbers, Operations, and Quantitative Reasoning: The student will demonstrate an understanding of number, operations, and quantitative reasoning.

TEKS 5.3: The student adds, subtracts, multiplies, and divides to solve meaningful problems


Student Expectations: 5.3(E) The student is expected to model situations using addition and/or subtraction involving fractions with like denominators using concrete objects, pictures, words and numbers. 5.14(B) The student is expected to solve problems that incorporate understanding the problem, making plan, carrying out the plan, and evaluating the solution for reasonableness.

Overview

Students will use models to solve problems involving fractions with like denominators.

Materials Fraction Bars Circles or Rods Copy of Fraction Table

Vocabulary fraction, numerator, denominator, like denominators, lowest terms

Lesson: 1. Use fractions pieces (or a drawing), the fraction table (included), and a Part‐Part‐Whole

Box to model the following problem with the students. (This is problem #1 on the guided practice page.)

Jeff ate 5

1 of his chocolate chip cookies on. His sister Lisa ate

5

2 of the cookies. What

fraction of the cookies did they eat? What fraction of the cookies remain? Using a drawing:

How many total cookies did Jeff and Lisa start with? Explain. (Five because the denominator always tells the total number of equal pieces or parts you have.)


Let’s draw our five cookies that Jeff started with.

How many cookies did Jeff eat? Explain. (One because the numerator on 1/5 tells how many he ate out of the five on Tuesday.)

Let’s circle what Jeff ate.

Tuesday

How many did Lisa eat? Explain. (Two because the numerator on 2/5 tells how many he ate out of the five on Wednesday.)

Circle a representation of what Lisa ate.

Tuesday Wednesday Remaining

How many cookies did Jeff and Lisa eat? (3)

How many total cookies did they start with? (5)

What fraction of the cookies did they eat? (3/5)

How many cookies did they have remaining (did they not eat)? (2)

How many total cookies did they start with? (5)

What fraction of the cookies did they have remaining? (2/5)


Model using a Fraction Table.

1 whole

Jeff Lisa Remaining Cookies

2

1 2

1

3

1 3

1 3

1

4

1 4

1 4

1 4

1

5

1 5

1 5

1 5

1 5

1

6

1 6

1 6

1 6

1 6

1 6

1

7

1 7

1 7

1 7

1 7

1 7

1 7

1

8

1 8

1 8

1 8

1 8

1 8

1 8

1 8

1

9

1 9

1 9

1 9

1 9

1 9

1 9

1 9

1 9

1

10

1 10

1 10

1 10

1 10

1 10

1 10

1 10

1 10

1 10

1

11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1

12

1 12

1 12

1 12

1 12

1 12

1

12

1

12

1

12

1

12

1

12

1

12

1 Jeff Lisa Remaining Use a Part‐Part‐Whole Box to represent the information. See example below.

Whole (total number of pieces)

1 cookie

2 cookies

2 cookies (Remaining)

5 cookies (Total number started with)


Using a Part‐Part‐Whole Box can help organize the information in the problem and allow

students to see all of the fractions. You can see that 5

3of the cookies have been eaten because

(1 out of 5) + (2 out of 5) is (3 out of 5). Therefore, 5

2of the cookies must remain because

5 – 3 = 2. The parts must add up to the whole.

5

1 +

5

2 =

5

3 and

5

5 -

5

3 =

5

2

Always make sure that fraction answers are in lowest terms.


• Is there a “rule” for adding and subtracting fractions with the same denominators? (When adding or subtracting fractions with the same denominator, add or subtract the numerators and leave the denominator the same.)

• Why does the denominator not change when we add and subtract fractions with like denominators? (The total number of pieces that I start with NEVER changes. I started with five cookies the whole way through the problem. That never changed; therefore, my denominator did not change.)

• What could be the “whole” in each of the problems? (the total number of pieces you start with)

• How can a Part‐Part‐Whole Box be used with fractions? (The Part‐Part‐Whole Box organizes the information into the parts and the whole. The parts have to add up to the whole.)


Guided Practice:

Have students model the following problems with fraction pieces, the Fractions Table and Part‐ Part‐Whole Boxes. We want the students practicing all three strategies.

1. Jeff ate 5

1 of his chocolate chip cookies. His sister Lisa ate

5

2 of the cookies. What

fraction of the cookies did they eat? What fraction of the cookies remain?

(This question was demonstrated in the lesson.)

1. Josh wants to arrange his collection of 12 model cars on a shelf. Three of the cars are red, four are blue, 2/12 of the cars are yellow, and the rest are multi‐colored. He arranged the red cars and blue cars on a shelf. What fraction of the cars still needs to go on the shelf?

(12

5of the cars)

3. Carla is working on her reading project over the weekend. She completed 2/9 of it on

Friday evening, 5/9 of it on Saturday, and the rest on Sunday. How much more of her project did she complete on Saturday than on Friday and Sunday?

(1/9 more on Saturday than Friday and Sunday)

2. Katie plays basketball. Her team scored 10 baskets at their last game. She made 3 baskets in the first half of the game and 3 baskets in the second half of the game. What fraction of the baskets did Katie make for her team?

5

3of total baskets


Assessment:

1. The table below shows the number of toy cars in Jose’s collection.

What fraction of the cars are red or green?

A. 4

2

B. 12

6

*C. 8

3

D. 10

6

2. Jessica had 8 cups of sugar in her pantry. She used 3/8 of the sugar to make cookies, 2 cups of sugar to make the brownies, and 1 cup of sugar to make the lemonade. What fraction of sugar does Jessica have left?

F. 8

8

G. 2

1

H. 4

3

*J. 4

1

Color of Cars Number of Cars

Red 4

Blue 3

Green 2

Yellow 5

Orange 2


3. Thomas is working on a puzzle. He put together 5/8 of the puzzle pieces on Tuesday,

2/8 of the puzzle pieces on Wednesday, and the rest of the puzzle pieces on Thursday. How much more of the puzzle did Thomas do on Tuesday than on Wednesday and Thursday?

A. 8

1

B. 8

8

*C. 4

1

D. 8

3

4. Madison has a collection of 12 stuffed cat toys and 10 stuffed dog toys. Five of the cats

are white, and 3 of the cats are gray. What fraction of the cats is not white or gray?

*F. 3

1

G. 12

8

H. 3

2

J. 12

10


FRACTION TABLE

1 whole

2

1 2

1

3

1 3

1 3

1

4

1 4

1 4

1 4

1

5

1 5

1 5

1 5

1 5

1

6

1 6

1 6

1 6

1 6

1 6

1

7

1 7

1 7

1 7

1 7

1 7

1 7

1

8

1 8

1 8

1 8

1 8

1 8

1 8

1 8

1

9

1 9

1 9

1 9

1 9

1 9

1 9

1 9

1 9

1

10

1 10

1 10

1 10

1 10

1 10

1 10

1 10

1 10

1 10

1

11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1

12

1 12

1 12

1 12

1 12

1 12

1 12

1 12

1 12

1 12

1 12

1 12

1


Guided Practice: Reporting Category 1: TEKS 5.3(E) and 5.14(B) Name: ________________________ Date: __________________

1. Jeff ate 5

1 of his chocolate chip cookies on. His sister Lisa ate

5

2 of the cookie. What fraction

of the cookies did they eat? What fraction of the cookies remain? 2. Josh wants to arrange his collection of 12 model cars on a shelf. Three of the cars are red,

four are blue, 2/12 of the cars are yellow, and the rest are multi‐colored. He arranged the red cars and blue cars on a shelf. What fraction of the cars still need to go on the shelf?

3. Carla is working on her reading project over the weekend. She completed 2/9 of it on Friday

evening, 5/9 of it on Saturday, and the rest on Sunday. How much more of her project did she complete on Saturday than on Friday and Sunday?

4. Katie plays basketball. Her team scored 10 baskets at their last game. She made 3 baskets in

the first half of the game and 3 baskets in the second half of the game. What fraction of the baskets did Katie make for her team?


Assessment: Reporting Category 1: TEKS 5.3(E) and 5.14(B) Name: _________________________ Date: __________________

1. The table below shows the number of toy cars in Jose’s collection. What fraction of the cars are red or green?

A. 4

2

B. 12

6

C. 8

3

D. 10

6

2. Jessica had 8 cups of sugar in her pantry. She used 3/8 of the sugar to make cookies, 2

cups of sugar to make the brownies, and 1 cup of sugar to make the lemonade. What fraction of sugar does Jessica have left?

F. 8

8

G. 2

1

H. 4

3

J. 4

1

Color of Cars Number of Cars

Red 4

Blue 3

Green 2

Yellow 5

Orange 2


3. Thomas is working on a puzzle. He put together 5/8 of the puzzle pieces on Tuesday,

2/8 of the puzzle pieces on Wednesday, and the rest of the puzzle pieces on Thursday. How much more of the puzzle did Thomas do on Tuesday than on Wednesday and Thursday?

A. 8

1

B. 8

8

C. 4

1

D. 8

3

4. Madison has a collection of 12 stuffed cat toys and 10 stuffed dog toys. Five of the cats are white and 3 of the cats are gray. What fraction of the cats is not white or gray?

F. 3

1

G. 12

8

H. 3

2

J. 12

10


STAAR Reporting Category 5: Probability and Statistics: The student will demonstrate an understanding of probability and statistics.

TEKS 5.12: The student describes and predicts the results of a probability experiment.

Student Expectation: 5.12 (A): The student is expected to use fractions to describe the results of an experiment.

Overview:

This activity begins with a teacher demonstration of simple probability then continues with students describing the results of an experiment.

Materials: For whole group introduction by teacher:

A spinner with four equal sections with different colors Color tiles Brown paper bag (optional)

Vocabulary: Experiment: a situation involving chance in mathematical probability Outcome: the result of one trial of an experiment Probability: how likely an event is to happen; written as the ratio of the number of ways an

event can occur to the number of possible outcomes favorable outcome: the outcome you want to happen; the desirable outcome.

Lesson: Part one of this activity is an introduction to the vocabulary used in probability.

1. Place the 4‐color spinner under the document camera (or on the overhead) and say:

I have a spinner. Who can describe this spinner to me? Students should reply that the spinner is divided into 4 EQUAL parts, and each part is a different color. (The fact that the 4 parts are equal in area must be stressed to the students.)

What color do you think the needle will land on when I spin the needle? Allow several students to hypothesize the outcome to one spin. Spin the spinner and write the outcome on the board.

When I spin the spinner, that is called an experiment. An experiment in mathematics is a situation involving chance. In this example, the experiment is spinning the spinner.

What color did the needle land on? Allow students to respond.

The color that the needle actually landed on is called the outcome of the experiment. An outcome is the result of a single trial in an experiment. What


are all of the possible outcomes of our experiment? (red, yellow, blue, green; Record these on the board as the students answer.)

Can someone think of another example of a mathematical experiment? (Let several students respond, and write these examples on the board.)

What are some of the outcomes for each of these experiments? (Go through each experiment that you wrote on the board one by one, and write some of the different outcomes that could happen.)

Let’s run another experiment with our spinner and record our outcomes. Spin the spinner several times, recording the outcome each time.

2. Part two of this activity introduces writing probability in fraction form.

I really like the color red. When I spin the needle again, what do you think my chances are that the needle will land on red? Since I want the needle to land on red, red is called a “favorable outcome.” In other words, a “favorable outcome” is the outcome that you want to happen or the desired outcome.

Allow students to hypothesize the chances.

Who can remind us of how many possible outcomes I have when I spin the needle? (4)

What are these possible outcomes again? (red, yellow, blue, and green)

And of these four possible outcomes, how many chances do I have of spinning a red? (1) How do I know that I just have 1 chance? (Because only one section is red.)

What if I had a spinner that had 2 sections of red? How many chances would I have of spinning a red then? (2) Why? (Because I would have 2 sections that it could land on that are red.)

Since I have only 1 chance of red out of the 4 possible outcomes when I spin the needle one time, I have a one out of four chance of the needle to land on red. Who remembers where we have heard the phrase one out of four and what that represents mathematically? (Fractions: It means to write it as a fraction. The first number is the numerator and the second is the denominator.)

That’s right. Well, we say that the probability of spinning a red is 1

4. In mathematics,

probability is written P = 1

4.

Can you tell me what the numerator of the ratio represents? (the number of red sections on the spinner or the number of favorable outcomes)

Can you tell me what the denominator of the ratio represents? (the total number of possible outcomes)

Have students determine the probability of each color on the spinner. Record the probabilities on the board.


Parts three and four of this activity involve using tables to find the probability of an outcome.

3. Let’s find the probability of choosing colors of tiles. I have some color tiles here. I have 3 red tiles, 4 blue tiles, 2 yellow tiles, and 1 green tile. Place the color tiles under the document camera (on the overhead).

Let’s organize this into a table. Draw table on the board.

Tile Color Number of Tiles

Red 3

Blue 4

Yellow 2

Green 1

How many tiles do I have in all? (10)

If I chose one tile without looking, how likely am I to choose a red tile? Allow students to hypothesize.

Lets find the probability of choosing a red tile. How many red tiles are here? (3)

How many total tiles are here? (10)

So, we know that the number of red tiles is 3, and the total number of possible outcomes is 10. So the probability of drawing a red tile is 3 out of 10.

Remember how to write this? P = 3

10?

Record on board as students respond. If students do not respond, state the probability as you record it on the board. Continue finding the probability of the blue, yellow, and green tiles. Record these on the board in the proper format.

4. Let’s find the probability of choosing tiles in a different bag. Now I have 6 red tiles, 8

blue tiles, 4 yellow tiles, and 2 green tiles. Place the color tiles under the document camera (on the overhead).

Let’s organize this into a table. Draw table on the board.

Tile Color Number of Tiles

Red 6

Blue 8

Yellow 4

Green 2

How many tiles do I have in all? (20)

If I chose one tile without looking, how likely am I to choose a red tile? Allow students to hypothesize.


Lets find the probability of choosing a red tile. How many red tiles are here? (6)

How many total tiles are here? (20)

So, we know that the number of red tiles is 6 and the total number of possible outcomes is 20. So the probability of drawing a red tile is 6 out of 20. Remember how to write this?

(P = 6

20and simplify to

3

10.)

Record on board as students respond. If students do not respond, state the probability as you record it in the board. Continue finding the probability of the blue, yellow, and green tiles. Record these on the board in the proper format.

5. Now it is your turn to do a few mathematical experiments, determine outcomes, and

find probabilities. Hand out Guided Practice Handout, one to each student. Give each pair of students 25 different colored tiles and 1 standard number cube. One student will record the results of pulling one colored tile from a paper bag (be sure the student returns the color tile after he or she records each result). The other student will record the results from rolling one standard number cube. Each student will complete each task 10 times. They need to then combine their results and answer the questions found on the handout. The results need to be recorded using tally marks.

1. What was the total number of pulls from the color tile bag?

______________________

2. What fraction of pulls from the bag were: (Don’t forget lowest terms.)

Red _____________________ Blue _____________________ Green ___________________ Yellow ___________________

Color of Tile Frequency

Red

Blue

Yellow

Green

Number of Pips Frequency

1

2

3

4

5

6


3. What was the total number of rolls you made? _________________

4. What fraction of rolls were: (Don’t forget lowest terms.) 1 = ______________________________ 2 = ______________________________ 3 = ______________________________ 4 = ______________________________ 5 = ______________________________ 6 = ______________________________

Debriefing Questions: Check for understanding with these questions:

1. What is the definition of “probability?” (how likely an event is to happen) 2. What is the definition of “outcomes”, “favorable outcomes?” (the result of one trial of

an experiment), (the outcome that you want to happen or the desired outcome)

3. How do we write the probability of an event? (in fraction form ‐ desired outcomes

total outcomes )

4. What does it mean if an event has a probability of 2

3? (2 out of the 3 possible

outcomes are desired)

5. Give me an example of an event that has a probability of 2

3. (Students should give

their own examples such as: I have three coins, 2 nickels, and 1 dime. The probability of

drawing a nickel from my pocket is 2 out of 3 or 2

3.)

Guided Practice: Distribute the guided practice handout two.

Let’s practice our probability skills. 1. Suppose we had a bag of marbles with 4 red marbles, 7 green marbles, and 5 blue

marbles. What is the probability of choosing a green marble from the bag? A favorable outcome in this experiment is to take a (green)________________marble from the bag. (color)

How many of the favorable colors are in the bag? __(7)___

How many marbles are in the bag all together? __(4)____ + __(7)____ + ___(5)____ = __(16)______


This total number means there are __(16)__ possible outcomes.

The probability of choosing a green marble is (7

16).

2. For a school project, Mark and Jill were recording the color of cars that drove by the

school during one afternoon. The table shows the results of their survey.

Color Frequency Blue 10

White 5

Black 8

Red 15

Green 18

Yellow 4

Based on their notes, what is the probability that a white car will drive by next?

A favorable outcome is a __ (white)__________car. (color)

How many cars of the favorable color drove by the school?_(5)___

How many cars drove by all together? _(10)_ + _(5)_ + _(8)_ + _(15)_ + _(18)_ + _(4)_ = _(60)_ This total number means there are __(60)__ possible outcomes.


Kelsey and Steven were drawing pattern blocks out of a bag without looking. Every time a pattern block was drawn from the bag, they recorded the type of pattern block that was selected. The table shows the results.

Type of Block Frequency

Triangle 15

Square 23

Rhombus 17

Hexagon 25

Trapezoid 20

3. What is the probability of choosing a trapezoid from the bag?

A favorable outcome is to take a _(trapezoid)_block from the bag. (type)

The number of favorable outcomes is __(20)____.

The probability of choosing a trapezoid is:

Number of favorable outcomes = (20

100)

Number of possible outcomes

When simplified, the probability of choosing a trapezoid is (1

5).

5. What is the probability of NOT choosing a hexagon or square from the bag?

A favorable outcome is to NOT take a _____(hexagon)__ or __(square)___ block from the bag.

The total number of favorable outcomes is ____(52)____.

The total number of blocks is _____(100)_______.

The probability of NOT choosing a hexagon or square is ___(52/100)____.

When simplified, the probability of NOT choosing a trapezoid is ___(13/25)________.


Assessment: 1. Mark was recording the type of sandwich that students ate for lunch at school during

one week. The table shows the results of his survey.

Type of Sandwich Frequency

Ham 16

Peanut butter and jelly 5

Turkey 8

Chicken 15

Cheese 12

Bacon 4

What fraction of the students ate a chicken sandwich for lunch?

A.

8

15

B.

1

10

C.

3

10

*D. 1

4

2. Sandy’s mother has a box of fruit containing 12 apples, 30 pears, and 28 oranges. If

Sandy reaches into the box without looking and takes out one item, what is the probability that she will select an orange?

F.

1

42

G.

1

28

*H.

2

5

J. 2

3


3. Monica’s math teacher keeps a box of markers on her desk for students to use when

they are making graphs. The table shows how many of each color of markers are in the box.

Color Frequency

Red 15

Blue 10

Green 10

Purple 15

Black 25

Brown 25

Based on the table, if Monica reaches into the box without looking and takes out one marker, what is the probability that she will select a purple marker?

A.

1

15

*B.

3

20

C.

3

17

D.

2

3

4. Melanie has 2 quarters, 3 nickels, 4 dimes, and 1 penny in her coin purse. If she takes one coin from her purse without looking, what is the probability that she will NOT get a dime?

F. 5

2

G. 11

7

H. 9

5

* J. 5

3


Guided Practice: Handout 1 Reporting Category 5: TEKS 5.12(A) Name: ______________________________ Date: __________________________ Color Tile Experiment: Role a Cube Experiment:

1. What was the total number of pulls from the color tile bag? ______________________ 2. What fraction of pulls from the bag were: (Don’t forget lowest terms.) Red _____________________ Blue _____________________ Green ___________________ Yellow ___________________ 3. What was the total number of rolls you made? _________________ 4. What fraction of rolls were: (Don’t forget lowest terms.) 1 = ______________________________ 2 = ______________________________ 3 = ______________________________ 4 = ______________________________ 5 = ______________________________ 6 = ______________________________

Color Tiles Frequency

Red

Green

Blue

Yellow

Number of Pips Frequency

1

2

3

4

5

6


Guided Practice: Handout 1 Reporting Category 5: TEKS 5.12(A) Name: ________________________ Date: __________________

1. Suppose we had a bag of marbles with 4 red marbles, 7 green marbles, and 5 blue marbles. What is the probability of choosing a green marble from the bag?

A favorable outcome in this experiment is to take a ________________ marble from the bag. (color)

How many of the favorable colors are in the bag? ___________

How many marbles are in the bag all together?

_________ + _________ + __________ = ____________

This total number means there are __________ possible outcomes.

The probability of choosing a green marble is .

2. For a school project, Mark and Jill were recording the color of cars that drove by the

school during one afternoon. The table shows the results of their survey.

Color Frequency

Blue 10

White 5

Black 8

Red 15

Green 18

Yellow 4

Based on their notes, what is the probability that a white car will drive by next?

A favorable outcome is a __________________car. (color)

How many cars of the favorable color drove by the school?___________

How many cars drove by all together? ______ + ______ +______ + _____ + _____ + _____ = ___________

This total number means there are __________ possible outcomes.


Kelsey and Steven were drawing pattern blocks out of a bag without looking. Every time a pattern block was drawn from the bag, they recorded the type of pattern block that was selected. The table shows the results.


Triangle 15

Square 23

Rhombus 17

Hexagon 25

Trapezoid 20

3. What is the probability of choosing a trapezoid from the bag?

A favorable outcome is to take a _______________________block from the bag. (type)

The number of favorable outcomes is ___________.

The probability of choosing a trapezoid is:

Number of favorable outcomes

Number of possible outcomes =

When simplified, the probability of choosing a trapezoid is .

4. What is the probability of NOT choosing a hexagon or square from the bag?

A favorable outcome is to NOT take a ______________________ or _______________ block from the bag.

The total number of favorable outcomes is___________________________.

The total number of blocks is _____________________________________.

The probability of NOT choosing a hexagon or square is ________________.

When simplified, the probability of NOT choosing a trapezoid is ___________.


Assessment: Reporting Category 5: TEKS 5.12(A) Name: ___________________ Date: __________________

1. Mark was recording of the type of sandwich that students ate for lunch at school during one week. The table shows the results of his survey.

Type of Sandwich Frequency

Ham 16

Peanut butter and jelly 5

Turkey 8

Chicken 15

Cheese 12

Bacon 4

What fraction of the students ate a chicken sandwich for lunch?

A. 8

15

B. 1

10

C. 3

10

D. 1

4

2. Sandy’s mother has a box of fruit containing 12 apples, 30 pears, and 28 oranges. If

Sandy reaches into the box without looking and takes out one item, what is the probability that she will select an orange?

F. 1

42

G. 1

28

H. 2

5

J. 2

3


3. Monica’s math teacher keeps a box of markers on her desk for students to use when they are making graphs. The table shows how many of each color of markers are in the box.

Color Frequency

Red 15

Blue 10

Green 10

Purple 15

Black 25

Brown 25

Based on the table, if Monica reaches into the box without looking and takes out one marker, what is the probability that she will select a purple marker?

A. 1

15

B. 3

20

C. 3

17

D. 2

3

4. Melanie has 2 quarters, 3 nickels, 4 dimes, and 1 penny in her coin purse. If she takes

one coin from her purse without looking, what is the probability that she will NOT get a dime?

F. 5

2

G. 11

7

H. 9

5

J. 5

3

Copyright©2011 ESC Region XIII 5.3B, 5.14C


TEKS 5.3: The student adds, subtracts, multiplies, and divides to solve meaningful problems.


Student Expectations:

5.3(B) The student is expected to use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology). 5.14(C) The student is expected to select or develop an appropriate problem‐solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

Overview:

Students will use a problem solving plan to organize and solve a problem.

Materials: Chart paper

Vocabulary: Reasonable, product, factors, composing numbers, decomposing numbers

Lesson: Looking at multiplication conceptually: 1. Review vocabulary with the class.

What is multiplication? (when I put things into groups)

What is the answer to a multiplication problem called? (the product)

What are the two numbers that I multiply together called? (factors) 2. Give each student a bag of 25 counters or square tiles. Have each student use the

manipulatives to model the following problem: 6 x 4

What does the 6 represent in this problem? (either the number of groups, how many are in each group, or a factor)

What does the 4 represent in this problem? (whichever one you did not use above–either the number of groups, how many are in each group, or a factor).

Note: If students have a difficult time with this task, they do not understand the concept of multiplication (that it is about putting things into groups). You may need to go back to this concept during small groups for some of your students.


3. Write the following problem on the board: 167 X 43

What does the 167 represent? (the number of objects in the group)

What does the 43 represent? (the number of groups)

I could also think of this problem as 40 groups of 167 and 3 more groups of 167. 167 167

X 40 AND X 3

What is it called when I break numbers into its different parts (for example 43 = 40 + 3)? (decomposing numbers)

167 167 X 40 AND x 3 6,680 + 501 = 7,181 Show the steps using the “traditional method” (using this same problem). Make the connection with the students that you are doing the same thing (decomposing the number) when you follow these steps; you are just doing it vertically instead of horizontally. 4. Let’s see if we can do a few multiplication problems using mental math and decomposing

numbers.

12 x 14 = ? We don’t know this fact, be we DO know some facts that can help us figure this problem out. What are some ways we can decompose this problem to help us solve it mentally?

Decompose 14 into 10 and 4. You would have 12 x 10=120 and 12 x 4= 48 and 120 + 48 = 168.

Decompose 14 into 12 and 2. You would have 12 x 12=144 and 12 x 2 = 24 and 144 + 24 =168.

Decompose 12 into 10 + 1 + 1. You would have 10 x 14 = 140 + 14 = 154 + 14 = 168.

5. Your turn. Write the following problem in your math journal: 15 x 13 = ? I would like for

you to take a few minute, and think of 3 or 4 different ways you could decompose this problem to help you solve it mentally.

Give students a few minutes to write down a few different ways they can decompose this problem. Have students share their strategies. Some examples are:

15 x 10 = 150 and 15 x 2 = 30 and 15 x 1 = 15. 30 + 15=45 and 150 + 45 = 195

13 x 10 = 130 and 10 x 5 = 50 130 + 50 = 180 and 5 x 3 = 15 and 180 + 15 = 195


6. Try one more. Write the following problem in your math journal: 16 x 14 = ?

I would like for you to take a few minutes and think of 3 or 4 different ways you could decompose this problem to help you solve it mentally. Give students a few minutes to write down a few different ways they can decompose this problem. Have students share their strategies. Some examples are:

10 x 14 = 140 and 14 x 3 = 42 and 14 x 3 = 42. 42 doubled is 84 and 84 + 140 = 224

16 x 10 = 160 and 16 doubled is 32 and 32 doubled is 64 and 160 + 64 = 224 Looking at multiplication within problem solving situations:

7. Write the following problem on the board.

Carolyn wants to make a doll dress for her Barbie. The pattern calls for 3 pink buttons. Carolyn can buy a package of 10 buttons for $1.05 or buy them individually for 34 cents each. Which is the better buy?

8. Students read the problem twice and answer the following questions.

What are we looking for? (which is a better buy)

What is the first way she can buy buttons? (10 buttons for $1.05)

About how much would each button cost if she bought them this way? (about 10 cents each.)

What is the second way she can buy buttons? (34 cents each)

How much would it cost if she bought 10 of them? ($3.40)

Which is a better buy? (10 buttons for $1.05) Why? (Answers will vary.)

What strategies could we have used to figure this out? (drawn a picture or made a table)

9. Terry bought 25 T‐shirts for $6 each, including tax. She sold them all for $9 each. What is

the difference between the amount of money Terry made and the amount of money she spent on these 25 T‐shirts?

Have the students read the problem twice. Give them some time to work the problem in their math journals. (Remind them that they can use several strategies: draw a picture, make a table, solve a simpler problem, etc.) Then ask the following questions:

What are we looking for? (the difference between how much she made and how much she spent)

What did she buy? (25 T‐shirts)

How much did she buy each shirt for? ($6)

How much did she pay for all 25 t‐shirts? ($150)

What did she sell? (25 T‐shirts)

How much did she sell each shirt for? ($9)

How much did she make for selling all 25 t‐shirts? ($225)

What is the difference between $225 and $150? ($75)


Guided Practice:

Carlos needs to buy pencils to give to his classmates for birthday favors. There are 2 dozen students in his class. The pencils cost 10¢ each or 3 for a quarter. How much will Carlos save by buying the pencils in groups of 3?

What do you know about the problem?

How many students are in his class? (conversion of 2 dozen to 24 students)

How much would Carlos spend if each pencil costs 10¢?

(24 $0.10=$2.40) How much would Carlos spend if he spends 25¢ for 3 pencils?

(24 ÷ 3=8) (8 x $0.25=$2.00)

How much will Carlos save by buying the pencils 3 for 25¢? ($2.40 ‐ $2.00=$0.40)

How do you know your answer is correct? Explain in 1‐2 sentences. (Answers will vary.)


Assessment:

1. Suzanne purchased a package of erasers for $0.63. She received $0.37 in change. What is the fewest number of coins she could have received?

A. 3 *B. 4 C. 5 D. 6

2. Mrs. Parker is buying candy bars for her 5 dozen fifth grade students at Govalle

Elementary School. The candy bars are in packages of 9 to a bag. How many packages will she need to buy to give each fifth grade student a candy bar?

F. 5 *G. 6 H. 7 J. 8

3. Ted has 4 old stamps: A, B, C, and D. Stamp A is worth $3.00. Stamp D is worth half the

value of Stamp B. Stamp B is worth 4 times the value of Stamp A. The 4 stamps are worth $30 altogether. What is the value of Stamp C?

A. $14 B. $18 *C. $9 D. $19 The table below shows the price (including tax) of different sizes of bags of chips.

Chips

If Mrs. Brown spent exactly $8.00 on chips, which of the following could NOT be a combination of chips that she purchased?

F. Two 14‐ounce bags and one 10‐ounce bag *G. Two 10‐ounce bags and one 14‐ounce bag H. Two 10‐ounce bags and one 20‐ounce bag J. Four 10‐ounce bags

Bag Size Price

10 ounces $2.00

14 ounces $3.00

20 ounces $4.00


Guided Practice: Reporting Category 1: TEKS 5.3(B) and 5.14(C)

Name: _________________________ Date: __________________ Carlos needs to buy pencils to give to his classmates for birthday favors. There are 2 dozen students in his class. The pencils cost 10¢ each or 3 for a quarter. How much will Carlos save by buying the pencils in groups of 3?

1. What do you know about the problem?

2. How many students are in his class?

3. How much would Carlos spend if each pencil cost 10¢?

4. How much would Carlos spend if he spends 25¢ for 3 pencils?

5. How much will Carlos save by buying the pencils 3 for 25¢?

6. How do you know your answer is correct? Explain in 1‐2 sentences.


Assessment: Reporting Category 1: TEKS 5.3(B) and 5.14(C)

Name: _________________________ Date: __________________

1. Suzanne purchased a package of erasers for $0.63. She received $0.37 in change. What is the fewest number of coins she could have received?

A. 3 B. 4 C. 5 D. 6

2. Mrs. Parker is buying candy bars for her 5 dozen fifth grade students at Govalle Elementary School. The candy bars are in packages of 9 to a bag. How many packages will she need to buy to give each fifth grade student a candy bar?

F. 5 G. 6 H. 7 J. 8

3. Ted has 4 old stamps: A, B, C, and D. Stamp A is worth $3. Stamp D is worth half the

value of Stamp B. Stamp B is worth 4 times the value of Stamp A. The 4 stamps are worth $30 altogether. What is the value of Stamp C?

A. $14 B. $18 C. $9 D. $19


4. The table below shows the price (including tax) of different sizes of bags of chips.

Chips

If Mrs. Brown spent exactly $8.00 on chips, which of the following could NOT be a combination of chips that she purchased?

F. Two 14‐ounce bags and one 10‐ounce bag G. Two 10‐ounce bags and one 14‐ounce bag H. Two 10‐ounce bags and one 20‐ounce bag J. Four 10‐ounce bags

Bag Size Price

10 ounces $2.00

14 ounces $3.00

20 ounces $4.00

Copyright©2011 ESC Region XIII 5.3C, 5.15B



TEKS 5.15: The student communicates about Grade 5 mathematics using informal language.

Student Expectations: 5.3(C) The student is expected to use division to solve problems involving whole numbers (no more than two‐digit divisors and three‐digit dividends without technology), including interpreting the remainder within a given context. 5.15(B) The student is expected to relate informal language to mathematical language and symbols. TEKS 5.3(C) has been divided into two separate lessons. Lesson one of two: Two Types of Division Problems

Overview: Division is a difficult skill for students to master. To help them become proficient and comfortable solving division problems, they need to be given many opportunities to solve a variety of division problems. Allow them to work together in pairs or small groups so that they will be able to explain their thinking and reasoning. Keep in mind that students may use different methods for division. In this lesson, students will explore the two types of division problems which are the “sharing problems” and the “grouping problems.”

Materials: Two pieces of chart paper (one labeled sharing problem, one grouping problem) Notecards (two for each group) Colored dots (at least 15 of two different colors) Tape Student Sheet (One per student) Light Colored Construction Paper (One per student)

Vocabulary: divisor, dividend, quotient, remainder, reasonable, Sharing Problem, Grouping Problem


Lesson: Prior to the lesson, make two different charts like the ones shown below: Place a different colored dot sticker in the corner of each chart. Also take enough notecards for each pair of students. On half of the notecards, place the same color dot as you did on the “Sharing Problem” chart. On the other half, place the same color dot as you did on the “Grouping Problem” chart. ). Write two labels (objects) you want the students to use in their word problem. Make sure the two objects have something to do with each other. Example:

1. What is division? (when something is broken into equal groups). Write the following problem on the board:

114 ÷ 16 = 7 r. 2

Which is the divisor in this problem? (16)

Which is the dividend in this problem? (114)

What do we call the answer in a division problem? (quotient)

What does the remainder in a division problem represent? (how much of the dividend is left over)

2. Take a couple of minutes and in your journal write a word problem that could

represent this equation. Give students a few minutes to try to write their own word problem for the equation above. Have some students share out and discuss if they are truly a division problem.

Sharing Problem I know how many groups I have. I need to find out how many will be in each.

Grouping ProblemI know how many items I have in each group. I need to find out how many groups I will have.

RabbitsCages


3. There are two different ways division word problems can be presented.

Let’s take a look at them:

Bob has 114 antique toy cars that he has collected over the years. He wants to build glass shelving units that will hold 16 cars each. How many shelving units will Bob need to hold all of his toy cars?

Do we know how many total objects we are working with? (yes: 114 antique toy cars.)

Do we know how many groups we are putting the cars into? (No: that is what we are looking for.)

Do we know how many objects go in each group? (yes: 16 cars go in each group–or each case.)

In this problem, we know the total number of objects we are working with and how many of those objects we want in each group; however, we have to find the number of groups we will have in the end. This is called a Grouping Problem. I know how many items I have in each group. I need to find out how many groups I will have. How about this one: Sylvia and James are planning a party to wrap‐up their summer break. They have invited 120 of their closest friends to attend. If they have rented 15 tables for the party, how many friends will they need to put at each table?

Do we know how many total objects we are working with? (yes: 120 of our closest friends.)

Do we know how many groups we are putting the friends into? (yes: 15 groups because there are 15 tables)

Do we know how many friends go in each group? (no: that is what we are looking for.)

In this problem, we know the total number of objects we are working with and how many groups we are making; however, we have to find the number of friends (or objects) that go into each group. This is called a Sharing Problem. I know how many groups I have. I need to find out how many will be in each group.

What do both problems have in common? (They both told us the total number of objects we were working with.)

How are they different? (One problem gave us the number of groups, and we had to find how many went into each group, the other problem gave us how many went into each group, and we had to find how many groups.)


4. Students will be working with a partner for this activity.

Hang up the two charts stating Sharing Problem and Grouping Problem. Tell students that they will be working with their partner to write either a Sharing Problem or a Grouping Problem. Pass out one of the notecards you made prior to the lesson to each group. Also give each group five number cubes. (If you do not have enough for each group to get five, you can give each group one and have the students roll it five times getting five different digits.) Have the group roll their number cubes grouping three to make up one number and two to make up another number. Students will assign the three‐digit number to one of the labels on their notecard and the two‐digit number to the other label on their notecard. Students will find which dot matches theirs and write that type of a division problem using their numbers and labels. (E.g., 156 rabbits, 16 cages, gray dot represents a Sharing Problem.) Have students write their finished product on a clean notecard. Pick these notecards up.

5. Shuffle the notecards and pass one out to each group (making sure a group does not get

their own notecard). Students will read the problem that was given to them and will go post on the chart paper (Grouping Problem/Sharing Problem).

6. Once they are all posted, tell students how many cards are right.

There are ___________ number of cards correct on the charts.

Have students scan the notecards and see if they can find one that is on the wrong chart. Have them come up and change it. Continue doing this until you are able to say that all of the cards are correct on the charts.


Guided Practice: Give each student a copy of the student sheet. Have students cut out each division problem card. Students will fold a piece of construction paper in half (landscape). Write Sharing Problem on one side and Grouping Problem on the other side. Students will sort their problem cards and glue them in the right section. Then, they will complete the questions on the guided practice.

The baseball team had 127 raffle tickets to hand out to its 29 players. Each player got the same number of tickets. How many raffle tickets did

each player get?

(sharing)

A farmer was planting a vegetable garden. He had 225 seeds to plant. He planted 34 seeds in each row. How many rows of vegetables did he

plant in his garden?

(grouping)

The pet shop was setting up aquariums for display. They had 127 guppies. They used 13 guppies in each aquarium. How many aquariums could

they set up?

(grouping)

Henry had 224 sports trading cards that included athletes from 8 different types of

sports. If each type of sport had the same number of

cards, how many cards did he have for each sport?

(sharing)

A store clerk was arranging a display of winter caps. He had 97 caps to display. He

wanted each row to have the same number of caps. The display had 15 rows. How

many winter caps should be in each row?

(sharing)

The fifth grade at Cowan Elementary needed to be

divided equally into teams for a relay race. There were 224 fifth‐graders. Each relay team needed 13 students. How

many relay teams could there be?

(grouping)

A candy machine at the movie theater had 12 dispensers. The supplier had 135 rolls of

candy. He filled the dispensers in the machine equally. How many rolls of candy did the supplier put in

each dispenser?

(sharing)

Carol made some handmade stationery to sell at a craft fair. She completed 118

sheets. She wanted to put 39 sheets in a set. How many sets of stationery could she

make?

(grouping)

Sylvia is working as a manager at a local restaurant. Her

income is $26,000 dollars per year. How much money does

Sylvia make weekly?

(Hint: Think about how many weeks are in a year.)

(sharing)


1. Which word problems are considered grouping problems? (2,3,6, 8) 2. Which word problems are considered sharing problems? (1,4,5,7,9) 3. What is a sharing problem? (It is a problem where I know how many groups I have, but I

need to find out how many will be in each group.) 4. What is a grouping problem? (It is a problem where I know how many items I have in each

group, but I need to find out how many groups I will have.) Questions 5–7 come from problem card #1. 5. What does the 127 represent? (the total number of raffle tickets that were handed out) 6. What does the 29 represent? (the number of baseball players that received raffle tickets –

the number of groups) 7. What am I looking for? (the number of raffle tickets each player got–how many are in each

group) 8. Write the equation showing the answer to this problem. (127 ÷ 29 = 4 tickets with 11 tickets left over)


Assessment:

1. At the school store, Phillip can purchase 4 pencils for $1. He likes to have the same number of pencils for each of his 8 classes. If Phillip spent $6 on pencils, which is a correct way of finding the number of pencils Phillip has for each class?

A. Add 4 and 6, and then divide the sum by 8. B. Add 4 and 6, and then multiply the sum by 8. *C. Multiply 4 by 6, and then divide the product by 8. D. Multiply 4 by 6, and then multiply the product by 8.

2. At a lighting store, there were 180 light bulbs on the shelves. There were 6 different wattages of light bulbs, and there were an equal number of light bulbs of each watt. What is a way of determining the number of light bulbs of each watt on the shelves?

A. Subtract 6 from 180 B. Add 6 and 180 C. Multiply 180 by 6 *D. Divide 180 by 6

3. An auditorium has a total of 25 rows of seats, and each row contains 15 seats. During a

drama presentation, half of the seats were filled. What is one way of finding the number of seats that were empty during the drama?

*A. Multiply 25 by 15 and then divide the product by 2 B. Add 25 and 15 and then divide the sum by 2 C. Multiply 25 by 15 and then multiply the product by 2 D. Add 25 and 15 and then multiply the sum by 2

4. Caroline’s choir put on a concert. There were 152 people in the audience. Each ticket to

the concert cost $6. The audience was seated in 4 sections. If each section had the same number of people in it, how many people were in each section? (38 people)


Student Sheet: Reporting Category 1: TEKS 5.3(C) and 5.15(B)

1.

The baseball team had 127 raffle tickets to hand out to its 29 players. Each player got the same number of tickets. How many raffle tickets did

each player get?

2.

A farmer was planting a vegetable garden. He had 225 seeds to plant. He planted 34 seeds in each row. How many rows of vegetables did he

plant in his garden?

3.

The pet shop was setting up aquariums for display. They had 127 guppies. They used 13 guppies in each aquarium. How many aquariums could

they set up?

4.

Henry had 224 sports trading cards that included athletes from 8 different types of

sports. If each type of sport had the same number of

cards, how many cards did he have for each sport?

5.

A store clerk was arranging a display of winter caps. He had 97 caps to display. He

wanted each row to have the same number of caps. The display had 15 rows. How

many winter caps should be in each row?

6.

The fifth grade at Cowan Elementary needed to be

divided equally into teams for a relay race. There were 224 fifth graders. Each relay team needed 13 students. How

many relay teams could there be?

7.

A candy machine at the movie theater had 12 dispensers. The supplier had 135 rolls of

candy. He filled the dispensers in the machine equally. How many rolls of candy did the supplier put in

each dispenser?

8.

Carol made some handmade stationery to sell at a craft fair. She completed 118

sheets. She wanted to put 39 sheets in a set. How many sets of stationery could she

make?

9.

Sylvia is working as a manager at a local restaurant. Her

income is $26,000 dollars per year. How much money does

Sylvia make weekly?

(Hint: Think about how many weeks are in a year.)


Guided Practice: Reporting Category 1: TEKS 5.3(C) and 5.15(B)

Name___________________________________ Date______________________ 1. Which word problems are considered grouping problems? __________________________________________________________________________ 2. Which word problems are considered sharing problems?

___________________________________________________________________________ 3. What is a sharing problem? ____________________________________________________

___________________________________________________________________________ 4. What is a grouping problem? __________________________________________________

___________________________________________________________________________ Questions 5–7 come from problem card #1. 5. What does the 127 represent? _________________________________________________

___________________________________________________________________________ 6. What does the 29 represent? __________________________________________________

__________________________________________________________________________ 7. What am I looking for? _______________________________________________________

___________________________________________________________________________ 8. Write the equation showing the answer to this problem. ____________________________


Assessment: Reporting Category 1: TEKS 5.3(C) and 5.15(B)

Name_______________________________________ Date_______________________ 1. At the school store, Phillip can purchase 4 pencils for $1. He likes to have the same number

of pencils for each of his 8 classes. If Phillip spent $6 on pencils, which is a correct way of finding the number of pencils Phillip has for each class?

A. Add 4 and 6, and then divide the sum by 8. B. Add 4 and 6, and then multiply the sum by 8. C. Multiply 4 by 6, and then divide the product by 8. D. Multiply 4 by 6, and then multiply the product by 8.

2. At a lighting store, there were 180 light bulbs on the shelves. There were 6 different

wattages of light bulbs, and there were an equal number of light bulbs of each watt. What is a way of determining the number of light bulbs of each watt on the shelves?

A. Subtract 6 from 180. B. Add 6 and 180. C. Multiply 180 by 6. D. Divide 180 by 6.


3. An auditorium has a total of 25 rows of seats, and each row contains 15 seats. During a drama presentation, half of the seats were filled. What is one way of finding the number of seats that were empty during the drama?

A. Multiply 25 by 15, and then divide the product by 2. B. Add 25 and 15, and then divide the sum by 2. C. Multiply 25 by 15, and then multiply the product by 2. D. Add 25 and 15, and then multiply the sum by 2.

4. Caroline’s choir put on a concert. There were 152 people in the audience. Each ticket to the

concert cost $6.00. The audience was seated in 4 sections. If each section had the same number of people in it, how many people were in each section? Make this one a griddable.





Student Expectations: 5.3(C) The student is expected to use division to solve problems involving whole numbers (no more than two‐digit divisors and three‐digit dividends without technology), including interpreting the remainder within a given context. 5.14(B) The student is expected to solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. TEKS 5.3(C) has been divided into two separate lessons. Lesson two of two: Interpreting remainders

Overview: In this lesson, students will explore division situations that require them to interpret remainders. To help them interpret the meaning of the remainder, it is important that they answer the question by labeling the answer. Here are a couple of examples.

If 11 CDs were going to be given to 2 people, how many would each person receive? The answer would be 5 CDs not 5 ½ CDs.

If 11 inches of ribbon was cut into 2 equal pieces, how long would each piece be? The answer here would be 5 ½ inches, not 5 inches.

NOTE: Most students will need to work with manipulatives in the beginning to understand conceptually why a remainder is dropped completely or why a quotient is rounded up.

Materials: Paper for students to work the problems Chart paper with each of the 3 types of division problems written on it Student Sheet (1 per student) Post‐Its (3 per group) Note cards (1 per group) Chart paper (for guided practice) Markers

Vocabulary: divisor, dividend, quotient, remainder, reasonable, divisible


Lesson 1. What is division? (when something is broken into equal groups)

What does divisible mean? (when something is able to be divided into equal groups without having anything left over)

What do you do know about remainders? (It depends on the problem. Sometimes the remainder is written as a fraction, dropped and the quotient is rounded up, or dropped and the quotient remains the same)

NOTE: Interpreting remainders is a difficult concept for students. They need opportunities to work these different kinds of problems and discuss the answers. Today we are going to take a good look at some division problems.

Someone give me a number less than 20 and greater than 10. Record this number.

Now someone give me a number greater than 1 and less than 10. Record this number.

What happens when we divide the first number by the second?

Is there a remainder? What if we had (first number) pencils and were giving (second number) pencils to students. How many students would get pencils?

What happens to the remainder? (The remainder is dropped and the quotient remains the same.)

What if we had (first number) inches of ribbon and were going to cut it into (second number) of pieces. How long would each piece be?

What happens to the remainder? (We would write it as a fraction.) Why would we not drop it like we did in the problem above? (Because you can have a fraction of a piece of ribbon, but you can’t have a fraction of a piece of a student.)

2. A big part of solving division problems is deciding what needs to happen when there

is a remainder. There are three options to decide from when a quotient has a remainder. Let’s look at the three options in detail.

Hang up three pieces of chart paper. Each one needs to be labeled as one of the following:

1. “Sometimes the remainder is written as a fraction.” 2. “Sometimes the remainder is dropped, and the quotient is rounded up.” 3. “Sometimes the remainder is dropped, and the quotient remains the same.”

Let’s go back to our original problem (first number) divided by (second number). When we found our quotient it had a remainder.

How would this answer look if we wrote it to fit chart #1 (remainder written as fraction)? (Write this on board UNDER the chart, not on the chart).

How would this answer look if we wrote it to fit chart #2 (remainder dropped quotient rounded up)? (Write this on board UNDER the chart.)


How would this answer look if we wrote it to fit chart #3 (remainder dropped quotient remains same)? (Write this on board UNDER the chart.)

If we wrote a word problem for each one of these situations, it would look completely different expect for the two numbers.

3. Give each student a Student Sheet. Give them a few minutes to read through and work

each problem. They are to decide which of the three categories each problem would fall under. Have them “pair/share” with their partner before asking the class questions.

Problem #1: Clearview Elementary pulled 150 books in their library that they wanted to replace. They were going to give an equal number of books to the first 12 students that asked for them. How many books would each of the 12 students receive? Model how to solve the division problem up on the board.

What does my quotient represent in this problem? (how many books each student gets)

Which category did this problem fall under? (Drop the remainder, and the quotient remains the same.)

Why will I not write the remainder as a fraction? (No one wants a fraction of a book because you want to read the whole thing.)

Why will I not drop the remainder and round the quotient up? (You don’t have enough books to give everyone one more instead of cutting it in half. You just need to leave off the ½.)

NOTE: Review with your students the IMPORTANCE of labeling their answers. This will help them in determining what needs to happen to the remainder. (The answer to this problem is 12 books not 12 ½ books.) So how many books will each student get? (12 books)

Problem #2: Clearview Elementary pulled 150 books in their library to send over to the library at Charleston Elementary. The librarian can fit 12 books into each box. How many boxes will she need? Model how to solve the division problem up on the board.

What does my quotient represent in this problem? (how many boxes I need in order to pack ALL 150 books)

Which category did this problem fall under? (Drop the remainder and round the quotient up.)


Why will I not write the remainder as a fraction? (No one wants a fraction of a box because everything would fall out of it.)

Why will I not drop the remainder and my quotient remain the same? (You would have 6 books that did not make it in a box to send over to the other school. You need one more box to be able to ship all 150 books over.)

So, how many boxes will she need? (13 boxes)

Problem #3: Ms. Smith made cookies for the 12 students made a 100 on their math test last week. She made 150 cookies for the students to share equally. How many cookies will each student get? Model how to solve the division problem up on the board.

What does my quotient represent in this problem? (how many cookies each student will get)

Which category did this problem fall under? (turn my remainder into a fraction.)

Can I have a fraction of a cookie? (Yes: I can cut it into equal pieces and it will still function as a cookie.)

Why will I not drop the remainder and round my quotient up? (You do not have enough cookies to give everyone an extra one.)

Why will I not drop the remainder and my quotient remain the same? (You would waste 6 cookies that can be cut in ½ and given to each student.)

So, how many cookies will each student get? (12 ½ cookies) 1. Discuss the three kinds of problems that were solved. In the first problem, the remainder

was dropped and the quotient was the answer. In the second problem, the remainder was dropped and the quotient was rounded up. In the third problem, the remainder was written as a fraction.

2. Students will be working in groups of two or three. Have each group count off one to three. Groups that said “1” will be writing a division word problem that would fit under chart #1. Groups that said “2” will be writing a division word problem that would fit under chart #2. Groups that said “3” will be writing a division word problem that would fit under chart #3. Remind students that division problems reflect putting objects into equal groups. Write the following “helpful hints” on the board for them.

Choose two numbers: one greater than 200 and one between 10 and 30.

Decide on labels for these two numbers. The large number tells how many objects you are splitting into groups. The small number tells how many groups you are splitting it into.

Make sure you think about things you can either have a fraction of, things that you would be able to round up, or things you can have leftovers of whichever your problem will reflect.

Make sure it makes sense! You need to walk around the room monitoring the writing of the problems to ensure they reflect the type of problem they are supposed to be writing. Writing word problems can be quite difficult for students.


3. When students are finished, have them write their final draft on a note card and post it somewhere around the room. Along with their problem, have them post three post‐its underneath. One saying “remainder as fraction”, one saying “quotient stays same”, and one saying “quotient rounds up.” Students will stay with their group and will complete a gallery walk marking (with a tally mark) which problem they think it is. Have groups read their problem when finished and tell what chart they were to reflect. Post problems on the charts from the beginning of lesson where they belong. These will remain up on the wall for several weeks to serve as a reminder of the choices one must make when solving division problems.


How do you know what to do with the remainder? (It depended on the problem. Sometimes the remainder was dropped and the quotient stayed the same or was rounded up. Sometimes the remainder was written as a fraction.)

What can you do to make sure your answer is reasonable? (Labeling your answer should help determine if the answer is reasonable.)

How can you check the answer using the inverse operation? (Multiplication)

Guided Practice: Give each pair of students a piece of chart paper, markers, and one problem to solve. To solve the problem, students should write the division sentence, show how they solved the problem, and explain how they interpreted the remainder. After solving their problem, they will share their answer with the group. The teacher should guide the discussion to ensure that the students understand the different ways to interpret remainders.

1. The student council is having a bake sale. Eighteen of the student council members

are baking cookies. If they want to sell 200 cookies, how many cookies should each

member bring? (The division sentence is 200 divided by 18. When the problem is

solved the answer is 11 r 2. Each member should bring 12 cookies. We dropped the

remainder and rounded the quotient up so that we would have enough cookies. The

explanation for reasonableness will vary. Answers could include that 200 divided by 20

is 10. Another explanation could be using the inverse property of multiplication. 18 X

12 = 216. There will be 16 cookies left over for the student council members to eat.)

2. The student council made $94 at their bake sale. They want to give an equal amount to four different charities. How much will each charity receive? (The division sentence

is 94 divided by 4. The answer is 23 r 2. Each charity will receive 23 2

1 dollars or $23.50.

We wrote the remainder as a fraction or decimal because you can have 2

1 dollar or fifty

cents. The explanation for reasonableness will vary. One possible explanation could be using the inverse property of multiplication. Another possible explanation could include

repeated addition. 232

1+ 23

2

1 + 23

2

1 + 23

2

1 = 94 or 23.50 + 23.50 + 23.50 + 23.50 =

94.)


3. The student council also collected stuffed animals to give to 20 foster children. They collected 170 stuffed animals. How many stuffed animals will each child receive? (The division sentence is 170 divided by 20. The answer is 8 r 10. Each child will receive 8 stuffed animals. We dropped the remainder and the quotient remained the same. You cannot have a part of a stuffed animal. If we had rounded the quotient up, we would not have had enough stuffed animals to give each child the same number of animals. The explanation for reasonableness will vary. One possible explanation could be using the inverse property of multiplication. 20 X 8 = 160 with 10 stuffed animals left over.)


Assessment: 1. Mary’s mom bought a large bag of mixed candy for Mary’s birthday party. The bag had

163 pieces in it. Mary’s mom wanted to make sure each of the 13 girls would receive the same number of pieces of candy while at the party. How many pieces would each girl get?

A. 11 pieces B. 12 pieces C. 12 ½ pieces D. 13 pieces

2. Johnson Elementary School is having a science fair with 134 entries. In setting up for the fair, six entries will be put on each table. How many tables will be needed for the science fair?

F. 20 tables G. 21 tables H. 22 tables J. 23 tables

3. The science teachers are making sixteen award ribbons to be given to the science fair winners. They have 100 inches of ribbon. How long will each ribbon be?

A. 5 inches B. 6 inches

* C. 6 4

1 inches

D. 6 2

1 inches

*

*


Student Sheet: Reporting Category 1: Interpreting the Remainder

Problem #1: Clearview Elementary wanted to replace 150 library books. They were going to give an equal number of books to the first 12 students that asked for them. How many books would each of the 12 students receive? Problem #2: Clearview ELementary wanted to send 150 library books to Charleston Elementary. The librarian can fit 12 books into each box. How many boxes will she need? Problem #3: Ms. Smith made cookies for the 12 students who made a 100 on their math test last week. She made 150 cookies for the students to share equally. How many cookies will each student get?


Guided Practice: Reporting Category 1: TEKS 5.3(C) and 5.14(B)

Name: ________________________ Date: __________________

Your teacher will assign you a problem to solve. Remember to write the division sentence. Show how you solved the problem. Explain how you interpreted the remainder. 1. The student council is having a bake sale. Eighteen of the student council members are

baking cookies. If they want to sell 200 cookies, how many cookies should each member bring?

Division sentence: How we worked the problem: Each member should bring _____________ cookies. This is what happened to the remainder: This answer is reasonable or makes sense to us because ____________________________________________________________________________.


2. The student council made $94.00 at their bake sale. They want to give an equal amount to four different charities. How much will each charity receive?

Division sentence: How we worked the problem: Each charity will receive ____________________. This is what happened to the remainder: This answer is reasonable or makes sense to us because __________________ _________________________________________________________________.


3. The student council also collected stuffed animals to give to 20 foster children. They collected 170 stuffed animals. How many stuffed animals will each child receive? Division sentence: How we worked the problem: Each child will receive _________________ stuffed animals. This is what happened to the remainder: This answer is reasonable or makes sense to us because __________________ _________________________________________________________________.


Assessment: Reporting Category 1: TEKS 5.3(C) and 5.14(B)

Name: __________________________ Date: __________________

1. Mary’s mom bought a large bag of mixed candy for Mary’s birthday party. The bag had 163 pieces in it. Mary’s mom wanted to make sure each of the 13 girls would receive the same number of pieces of candy while at the party. How many pieces would each girl get?

A. 11 pieces

B. 12 pieces

C. 12 ½ pieces

D. 13 pieces

2. Johnson Elementary School is having a science fair with 134 entries. In setting up for the

fair, six entries will be put on each table. How many tables will be needed for the science fair?

F. 20 tables

G. 21 tables

H. 22 tables

J. 23 tables

3. The science teachers are making 16 award ribbons to be given to the science fair

winners. They have 100 inches of ribbon. How long will each ribbon be?

A. 5 inches B. 6 inches

C. 6 4

1 inches

D. 6 2

1 inches




Student Expectations: 5.3(D) The student is expected to identify common factors of a set of whole numbers.

Overview: This lesson will look at how to identify common factors of a set of numbers. Understanding this skill helps lay the foundation for finding equivalent fractions and reducing fractions to lowest terms.

Materials: For each pair of students:

A pair of dice of two different colors Paper Multiplication flash cards (optional for students with disabilities)

Vocabulary:

factors, factor pairs, common factors, prime factors, prime factorization, product

Lesson: 1. In groups of three or four, give students three to five minutes to jot down everything

they know about factors. Have each group read what they came up with to the class. Write down some of their responses on a class chart.

2. Who can tell me what it means to find the factors of a number? (a number that will

divide into another number evenly with no remainder)

3. Find something that two people have in common in the class. Call these two students to the front and ask the class: What do these two students have in common? (Have students respond until they say what you had in mind.) If you have something in common with someone, what does this mean? (You share something with someone or you and someone else have something alike.) So what do you think it means to find common factors of a set of numbers? (Common factors are factors that a set of numbers share, or numbers that will evenly divide into each number in a set of numbers.)

4. What are the factors of 24? (You may want to use a set of flashcards and explain that 2

X 12, 3 X 8, 4 X 6 are factor pairs of 24.) Are there other factors of 24? (1 X 24)

Let’s list the factors of 24 in order from smallest to largest: (1, 2, 3, 4, 6, 8, 12, 24)


What are the prime factors of 24? (2 and 3)

How can we write 24 as the product of only prime factors? We call this the prime factorization of a number. Let’s Start with two factors of 24. Suppose we start with 4 X 6:

24 4 6 2 2 2 3

All of these factors are prime, so the prime factorization of 24 is 2X2X2X3. How do we know we have all of the prime factors of 24? (All of the factors are prime. Their product equals 24.) What if we started with 3 X 8 instead of 4 X 6? ? Construct another factor tree beginning with 3 X 8 so that they will see that the prime factorization is the same.

5. What are the factors of 32? Can you tell me what flashcards will show factors of 32?

(4X8) Are these all of the factors of 32? What other factors of 32 can you find? (1 X 32, 2 X 16)

Let’s list all of the factors of 32 in order from least to greatest. (1, 2, 4, 8, 16, 32)

What are the prime factors of 32? (There is only one: 2)

How can we write the prime factorization of 32? Let’s Start with 4 X 8.

TREE TOWER 32 4 8 or 2 2 2 4 2 2 2 2 2

So the prime factorization of 32 is 2 X 2 X 2 X 2 X 2.

Factors of 24 1 2 3 4 6 8 12 24

Factors of 32 1 2 4 8 16 32

32 16 8 4 2 1

2 2 2 2 2 2


6. Let’s look back at the factors of 24 and 32 that we listed earlier. Let’s put these in a chart. (Have students draw the chart.) If both numbers have the same factor, place these factors in the same column.

7. Using the chart, tell me what factors 24 and 32 have in common? (1, 2, 4, 8)

8. What is the greatest common factor of 24 and 32? (8)


How do you determine a factor of a number? (It has to divide the number evenly with no remainder.)

When you have found one factor of a number, how does this help you find another factor of that number? (factor pairs)

How do you know if you have listed all of the factors of a number? (No other numbers will divide it.)

What factor do all numbers have in common? (one)

Guided Practice: You and a partner will be given a pair of dice of different colors. You will each roll a die to determine four numbers. You and your partner need to decide which die will give you the digit for the ten’s place and which one will give you the digit for the one’s place. You will each roll at least four times to get four different numbers. Write the factors for each number and then determine the common factors. Determine the prime factors for each and the prime factorization of each number.


Assessment:

1. Which of the following shows the prime factorization of 54?

A. 6 X 9 B. 3 X 3 X 6 C. 2 X 3 X 9 D. 2 X 3 X 3 X 3

2. Two numbers have a common factor of 15. Select the pair of numbers that have a

common factor of 15.

F. 15 and 25 G. 35 and 75 H. 60 and 100 J. 45 and 75

3. Joyce listed the factors of 48 and 90. She then found the common factors of 48 and 90.

How many common factors did Joyce find?

A. 2 B. 3 C. 4 D. 5

4. What is the greatest common factor of 48 and 90?

F. 1 G. 2 H. 6 J. 8

*

*

*

*


Guided Practice: Reporting Category 1: TEKS 5.3(D)

Name: ____________________________ Date: __________________ You and a partner will be given a pair of dice of different colors. You will each roll a die to determine four numbers. You and your partner need to decide which die will give you the digit for the ten’s place and which one will give you the digit for the one’s place. You will each roll at least four times to get four different numbers. First number: Factors of this number: Prime factors of this number: Prime factorization of this number: Second number: Factors of this number: Prime factors of this number: Prime factorization of this number:

Factors of

Factors of

Common factors of these two numbers: Greatest Common Factor:


Third number: Factors of this number: Prime factors of this number: Prime factorization of this number:

Fourth number: Factors of this number: Prime factors of this number: Prime factorization of this number:

Factors of

Factors of

Common factors of these two numbers: Greatest Common Factor:


Assessment: Reporting Category 1: TEKS 5.3(D)

1. Which of the following shows the prime factorization of 54?

A. 6 X 9 B. 3 X 3 X 6 C. 2 X 3 X 9 D. 2 X 3 X 3 X 3

2. Two numbers have a common factor of 15. Select the pair of numbers that have a

common factor of 15.

F. 15 and 25 G. 35 and 75 H. 60 and 100 J. 45 and 75

3. Joyce listed the factors of 48 and 90. She then found the common factors of 48 and 90.

How many common factors did Joyce find?

A. 2 B. 3 C. 4 D. 5

4. What is the greatest common factor of 48 and 90?

F. 1 G. 2 H. 6 J. 8



TEKS 5.4: The student estimates to determine reasonable results. Student Expectations: 5.4(A) The student is expected to use strategies, including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems. 5.4 TEKS has been divided into 2 separate lessons. Lesson one of two uses rounding as a type of estimation. Lesson two of two uses compatible numbers as a type of estimation.

Overview: This lesson will give students the opportunity to round whole numbers and decimals. Students will hunt through newspaper ads and catalogs as they compete in a rounding challenge.

Materials: Newspaper ads or catalogs Scissors Glue Chart paper Markers

Vocabulary: round, whole numbers, decimals, digits, tenths, hundredths, reasonable, compatible

Lesson: Teacher note: Students are expected to use different strategies to estimate. The suggested types of estimation strategies from TEA include rounding and compatible numbers. Prior to this lesson, have students bring in newspaper ads from Sunday’s paper and old magazines. 1. Today we are going to practice rounding whole numbers and decimals. What does it mean

to round a number? (Answers will vary but may include finding the closest multiple of ten, or hundred, or other place value to your number.)

Why do we round numbers in math sometimes? (Answers will vary but may include to make a number that is easier to work with.) Rounding allows you to create numbers you can work with mentally. Often times when you are out in the real world you do not have pen and paper to work a problem. You have to do it mentally. What are some examples of when we use mental math in the real world? (Answers will vary. Make a list of what students say on the board.)


2. There are several different strategies to use when rounding. Let’s review a couple of them. Review the “traditional rounding” strategy. Example: Round 168 to the tens place.

The student underlines the 6: 168. Since the digit to the right of the underlined digit is greater than 5, the 6 would be increased to the next highest value, 7, and everything after it would be replaced with zeros. So 168 would become 170 when it is rounded to the tens place.

Rounding rules:

Have students underline the place value in which they have been instructed to round.

Then instruct students to look only at the digit to the right of the underlined digit. If the digit to the right is a 0, 1, 2, 3, or 4, do not change the underlined digit, and the remaining digits to the right of the underlined digit become zeros.

If the digit to the right of the underlined number is a 5, 6, 7, 8, or 9, increase the underlined number to the next highest value, and change all digits to the right of the underlined digit to zeros.

If the underlined digit is a 9 and the digit to the right is greater than 5, then the 9 becomes a 0, and the next digit to the left of the 0 is increased to the next highest value.

Review the “rounding using a number line” strategy. Example: Round 168 to the tens place. The student visualizes or makes a number line. Since we are rounding to the nearest ten, we focus on what multiples of ten 168 would fall between on the number line. It would be 160 and 170. Then students decide which multiple of ten 168 is closest to when put on the number line: 160 or 170. 168 is closest to 170; therefore, 168 rounds to 170. Allow students to choose which strategy makes sense to them. Practice rounding a few whole numbers and decimals to make sure everyone has it.

3. Now that we have reviewed rounding, you are all ready for the rounding challenge.

Rounding Challenge: You may have students work independently or with a partner. Each person will get newspaper ads or a magazine to look through. They are to find 10 items (no more, no less) that when rounded to the tenths place gets them as close as possible to $100.00 without going over. Have them cut out each item (including the price), glue on chart paper, and write the rounded amount beside it. They may keep a running total record on scratch paper if they would like. Once it is glued on the chart paper, they must keep that item. Have students post their chart paper around the room and have a gallery walk so students can see what other’s purchased.



If you have $0 .45, what is the nearest tenth? ($0.50)

If you have $0.99, what is the nearest tenth? ($1.00)

If you have $6.49, what is the nearest dollar? ($6.00)


What words will I see in word problems that let me know that I am not looking for an exact answer? (about, estimate, closest, approximately)

Guided Practice: The table below shows items that are sold at the school store.

Item Cost

Candy $0.29

3‐Ring Notebook $1.49

Markers $2.99

Spiral Notebook $1.13

Neon Pens $0.69

If John bought three neon pens, one spiral notebook, five pencils, and a soda, about how much money will he spend? A. $3.10 B. $5.60 * C. $6.50 D. $6.70 1. What items is John buying? ____(neon pens, spiral, pencils, soda)___ 2. What word in my question tells me that I am not looking for an exact answer?

_____(about)_______ 3. Round the price of each of these items to the nearest tenth. Pens ‐ $0.70 Spiral ‐ $1.10 Pencils ‐ $0.50 Soda ‐ $0.80 4. About how much will three pens cost? ___($2.10)________ 5. About how much will five pencils cost? _______($2.50)______ 6. What operation do I need to do to figure out how much money he will spend at the school

store? ____(addition)______ 7. Solve the problem in the space below. 2.10 1.10 2.50 + 0.80 6.50


Assessment:

1. The baseball team participated in 2 tournaments last week and drove a total of 611 miles. They drove 118.4 miles to the first tournament and 206.8 miles to the second tournament. What is the best estimate of how many miles they drove to get back home?

A. 936 B. 325 *C. 286 D. 314 2. Candy went to the store to buy some grocery items. She bought the items listed below. If

Candy paid with a $10 bill, about how much money did she have left?

Milk: $2.79 Bag of chips: $0.89 Bananas: $1.33 Cookies: $2.13

F. $7.00

*G. $4.00 H. $5.00 J. $2.00

3. Carrianne went shopping with her mother. She got a dress for $52, a dress jacket for $38,

and a pair of shoes for $45. Which is the best estimate of the total amount of money Carrianne paid for this outfit, not including tax?

A. less than $100 B. Between $100 and $130 *C. Between $130 and $160 D. More than $160 4. Fairview Elementary school has 529 third, fourth, and fifth grade students. There are 179

third‐graders and 164 fourth‐graders. About how many students are in fifth grade at Fairview Elementary school?

* F. 190 students G. 180 students H. 510 students J. 220 students



Name: _________________________ Date: __________________ The table below shows items that are sold at the school store. If John bought three neon pens, one spiral notebook, five pencils, and a soda, about how much money will he spend?

A. $3.10 B. $5.60 C. $6.50 D. $6.70 1. What items is John buying? ______________________________________________ 2. What word in my question tells me that I am NOT looking for an exact answer? ________________________________________ 3. Round the price of each of his items to the nearest tenth. 4. About how much will three pens cost? _________________________ 5. About how much will five pencils cost? ________________________ 6. What operation do I use in this problem to figure out how much money he will spend at the school store? ____________________________________________ 7. Solve the problem in the space below.

Item Cost

Candy $0.29


Markers $2.99


Neon Pens $0.69

Soda $0.84

Pencils $0.49



Name: ________________________ Date: __________________ 1. The baseball team participated in two tournaments last week and drove a total of 611 miles.

They drove 118.4 miles to the first tournament and 206.8 miles to the second tournament. What is the best estimate of how many miles they drove to get back home?

A. 936 B. 325 C. 286 D. 314 2. Candy went to the store to buy some grocery items. She bought the items listed below.

Milk $2.79 Bag of chips $0.89 Bananas $1.33 Cookies $2.13

If Candy paid with a $10 bill, about how much money did she have left?

F. $7.00 G. $4.00 H. $5.00 J. $2.00



A. less than $100 B. Between $100 and $130 C. Between $130 and $160 D. More than $160

4. Fairview Elementary school has 529 third, fourth, and fifth grade students. There are 179

third‐graders and 164 fourth‐graders. About how many students are in fifth grade at Fairview Elementary school?

F. 190 students G. 180 students H. 510 students J. 220 students



TEKS 5.4: The student estimates to determine reasonable results. Student Expectations: 5.4(A) The student is expected to use strategies, including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems. 5.4 TEKS has been divided into two separate lessons. Lesson one of two uses rounding as a type of estimation. Lesson two of two uses compatible numbers as a type of estimation.

Overview: This lesson will give students the opportunity to practice using compatible numbers while racing to make 100.

Materials: Student Sheet #1 Student Sheet #2 Markers or colored pencils

Vocabulary: estimate, reasonable, round, compatible numbers, compose, decompose

Lesson:

Teacher note: Using compatible numbers is a type of estimation. There are no specific conforming rules for this type of estimation. Compatible numbers can be referred to as “friendly numbers.” For example 13 may not be considered to be a “friendly number.” Students may choose to use 10 or 15. Usually a student will consider a number ending in a 5 or 0 to be “friendly.” Stress to students they are to choose their numbers. Students should have numerous experiences comparing their estimates to the actual answer in order for students to develop reasonableness. Compatible numbers and rounding could be used simultaneously to determine if their answers are reasonable estimates.


1. Today I am going to be using compatible numbers to estimate. Sometimes compatible numbers are referred to as “friendly numbers,” because they are easy to work with. I am going to use the problem 13 + 12 as an example. Let’s pretend that I do not like to work with 13 and do not think it is very friendly. I might want to change the number 13 to the number 12. That would make the problem 12 + 12, which would be easier to add. Let’s look at other ways to change the problem 13 + 12. The teacher will put the other examples of the problem on the board or overhead. Can you think of other ways to change the problem? (Answers will vary.)

E.g., 13 + 12 (10+3) + (10+2) (10+10) + (3+2) 20 + 5 25 E.g., 13 + 12 10 + 10 20 E.g., 13 + 12 (13+2) + (12‐2) 15 + 10

2. Now it’s your turn to use compatible numbers. Work with your partner on the problem 17 + 19. Let’s see how many different ways you can use compatible numbers to solve the problem. Be ready to share your compatible numbers with the class. After the students have presented their solutions, the teacher may want to share some of the examples below.

E.g., 17 + 19 15 + 20 35 E.g., 17 + 19 17 + 20 37 E.g., 17 + 19 20 + 20

40

Note: Using decomposition numbers can

sometimes give you an exact answer.

Note: Should a student use 10 + 10, you get 20. This is not an exact answer, but an

estimated answer.

Note: Should a student use 15 + 20, the answer is close to the exact answer.

Note: Should a student use 17 + 20, the

answer is closer to the exact answer.

Note: Should a student use 20 + 20, the answer is not as close to the exact answer. This is an example where compatible number is more exact than

rounding.

Note: This is the ultimate of compose and decompose strategy. This will help students with their basic fact memorization.


E.g., 17 + 19 (10+5+2) + (10+5+4)

(10+10) + (5+5) + (2+4) 20 + 10 + 6 36 E.g., 17 + 19 (17‐1) + (19+1) 16 + 20 E.g., 17 + 19 (17+3) + (19‐3)

20 + 16 36

3. How would you use compatible numbers to solve the problem 27‐14? Work with your partner again to solve the problem in several different ways. After the students share their solutions, show the sample below.

Sample solutions: E.g., 27 – 14

(24+3) – (14) (24‐14) + 3 10 + 3 13

E.g., 27 – 14 30 – 10 20 E.g., 27 – 14

30 – 10 20

Note: Should a student use

decomposition, the answer is exact.



Note: This is not a close estimate to actual answer. This is why students should be comparing estimate to actual.


4. Talk with students about “making sets of 10” when adding. This is another way to use compatible numbers. When adding a long list of numbers, it is sometimes useful to look for two or three numbers that can be grouped to make sums of 10 or 100. Often the numbers in the list can be adjusted slightly to produce these groups of 10 or 100 to make finding an estimate easier. E.g., 23 + 17 = 40

5. You may have students work individually or with a partner. Distribute Student Sheet #1 to each student/group face down. Students MAY NOT use pencils or scratch paper in this activity. They may only use the marker to write their answer (no other marks can be made on the sheet). Set the timer for 1‐2 minutes (depending on the ability level within your class). Have students turn over their paper and complete as many as they can using compatible numbers in the time given. The total of each line goes in the box on the right and the total of all of the sums goes in the very bottom box. All markers must be put down when the timer goes off. Discuss the compatible numbers within each row as a class.

6. Now that you have this compatible number or “friendly numbers” thing down, let’s have

a race. I am going to give you a 6 by 6 grid that has numbers in it. I want you to find as many sets of 100 as you can. A set can be two or more numbers that are beside each other horizontally or vertically. They may NOT be diagonal. When you find a set, circle it. You may use a number in more than one set. You MUST find these sets using compatible numbers. You may not use scratch paper or the sides of this paper to do any computations. EVERYTHING IS MENTAL! Are there any questions?

Pass out Student Sheet #2 face down to each student. Have students use markers or colored pencils to circle their sets. Walk around making sure everyone is computing mentally and not on paper or the desk. Give class as much time as you feel appropriate for them to find as many combinations as they can. When finished, have a class discussion on the different strategies that students used to find the compatible numbers as quickly as they could.


What are compatible numbers? (friendly numbers–numbers that work well together.)

What does it mean to compose numbers? (put numbers together)

What does it mean to decompose numbers? (take numbers apart)

3 + 7 = 10 so…

20 + 10 + 10 = 40


Guided Practice: Wraps and Ribbons had all of their seasonal ribbon on sale for the same price. The chart below shows how much they sold each day.

Day of Week # of yards sold

Monday 58

Tuesday 37

Wednesday 42

Thursday 30

Friday 83

If they made a total of $315 during these five days, what is the best estimate of the sale price for each yard of ribbon?

*A. $2 B. $3 C. $4 D. $5

1. What is the total amount of ribbon they sold during these five day? ___________(150 yards)____________ 2. How did you get this information? ____(I added the numbers in the chart together.)_ 3. What compatible numbers could you use in the chart to make it easier? ___(58+42=100 and 37+83=120 and 120+30=150)____ 4. How much money did they make during their sale last week? ____($315)____ 5. How did you get this information? _____(It was given in the problem.)________ 6. What operation should be done to find out the price of each yard?

_____(divide)________________ 7. Using compatible numbers, what will that equation look like? ___(300 ÷ 150= 2)______ 8. Explain in words why you chose those two compatible numbers to make this problem

easier? _____(Answers will vary.)______


Assessment: 1. Ms. Adams ordered pencils and pens for the teachers. Each package contained 36 pens.

Each pack contained 18 pencils. Ms. Adams ordered 3 packages of pens and 5 packs of pencils. Which is the best estimate of the total number of pens and pencils Ms. Adams ordered?

A. 140 B. 175 *C. 220 D. 260

2. Jackie went to the store. She bought some chocolate milk for $1.49, a pack of gum for $0.99,

and a candy bar for $0.59. To the nearest dollar, what is the best estimate of how much Jackie spent?

*F. $3.00 G. $4.00 H. $5.00 J. $6.00

3. Johnny bought a cordless phone on sale for $15.99. The regular price of the phone was

$20.26. He also bought an alarm clock on sale for $7.89. The regular price of the clock was $12.68. What is the best estimate of the total amount of money Johnny saved by buying the phone and clock on sale?

A $5 *B $9 C $13 D $16

4. Ms. Harper drove 76 miles every day Monday through Friday. About how many miles did

Ms. Harper drive altogether? (Use compatible numbers below to solve.)


Student Sheet: #1 Reporting Category 1: TEKS 5.4(A)


Student Sheet: #2 Reporting Category 1: TEKS 5.4(A)

Making 100

18 23 59 55 45 74

15 46 50 13 87 36

46 46 49 28 23 15

39 8 66 29 25 45

38 43 57 28 17 5

62 81 19 72 83 35



Wraps and Ribbons had all of their seasonal ribbon on sale for the same price. The chart below shows how much they sold each day.


Monday 58

Tuesday 37

Wednesday 42

Thursday 30

Friday 83


A. $2 B. $3 C. $4 D. $5

1. What is the total amount of ribbon they sold during these five days? 2. How did you get this information? 3. What compatible numbers could you use in the chart to make it easier? 4. How much money did they make during their sale last week? 5. How did you get this information? 6. What operation should be done to find out the price of each yard? 7. Using compatible numbers, what will that equation look like? 8. Explain in words why you chose those two compatible numbers to make this problem

easier?



1. Ms. Adams ordered pencils and pens for the teachers. Each package contained 36 pens.

Each pack contained 18 pencils. Ms. Adams ordered 3 packages of pens and 5 packs of pencils. Which is the best estimate of the total number of pens and pencils Ms. Adams ordered?

A. 140 B. 175 C. 220 D. 260



F. $3.00 G. $4.00 H. $5.00 J. $6.00



A. $5 B. $9 C. $13 D. $16


Ms. Harper drive altogether? (Use compatible numbers below to solve.)


STAAR Reporting Category 2: Patterns, Relationships, and Algebraic Reasoning: The student will demonstrate an understanding of patterns, relationships, and algebraic reasoning.

TEKS 5.5: The student makes generalizations based on observed patterns and relationships. Student Expectations: 5.5(B) The student is expected to identify prime and composite numbers using concrete objects, pictorial models and patterns in factor pairs.

Overview:

This lesson will help students with the conceptual understanding of prime and composite numbers.

Materials: Colored Tiles (each pair should have 12 tiles) Journal or paper to record on Sample space visual for room Student sheet (1 per group) Chart paper Scissors Markers Glue

Vocabulary: Prime, composite, factor pair, factor, prime factors

Lesson: 1. Review the terms in the vocabulary section. 2. Students will be working in partners for today’s lesson. Give each group a set of 12 colored

tiles.

Today we are going to be making arrays with different amounts of square tiles. What is an array? (a number of items arranged in rows and columns) What operation do we use to represent an array? (multiplication)

I want you to take out two colored tiles. Make an array using only these two tiles. OR (2 x 1) (1 x 2) Sketch a model in your journal as well as write the expression that represents each model.


3. Explain to students that this represents the same number, so we only need to create one of

them.

What property of multiplication does this follow when I can change the order of my factors and still have the same answer? (commutative property of multiplication)

4. Have students repeat making arrays with colored tiles and sketching in their journals using the numbers 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

5. Reinforce the term factor pair.

What do you think is a factor pair? Did you notice that some numbers only had one array? (yes)

What number is always present in these factor pairs? (1) When a number has only two factors, the number one and itself, it is known as a prime number. An example would be the number three. You could use three colored tiles in one row of three or three rows of one.

What about four? You could have one row of four or two rows of two. How many array possibilities did you find? (2)

Identify the prime and composite numbers starting with two and ending with twelve. 6. Ask: What do you think will be the next prime number? Why? What about the number one? (One is neither prime nor composite.)

Which of these numbers is a prime number? 16, 21, 17, 42

List the factors of each number. A prime number has only two factors, one and itself. A

composite number has more three or more factors. FACTOR PAIRS FACTORS

16 = 4 4, 8 2, 1 x 16 1, 2, 4, 8, 16

21 = 3 7, 21 1 1, 3, 7, 21

17 = 17 1 1,17

42 = 6 7, 21 2, 3 14, 42 1 1, 2, 3, 6, 7, 14, 21, 42

Look at the factors of 21. Which factors are a prime number factor of the composite number 21. (3 and 7)

7. Give each group of students a Student Sheet. Have them cut out the cards and sort them

into “prime numbers” and “composite numbers.” Give each a piece of chart paper and have them create some type of graphic organizer (their choice) to display their sort. Once they are finished, have them hang up their finished products around the room and have a gallery walk with the class.



What do you notice about the factor pairs?

Which numbers have more than one factor pair?

Which numbers are composite? Why?

Which numbers are prime? Why?

Guided Practice: Look at the numbers below. 18, 11, 9, 23 1. Find the factors of 18. ____( 1,2,3,6,9,18)_____________ 2. Find the factors of 11. ______(1,11)_________________ 3. Find the factors of 9. ______(1,3,9)_________________ 4. Find the factors of 23 ______(1,23)__________________ 5. What does prime mean? A number with only two factors, one and itself. 6. What does composite mean? A number that has three or more factors. 7. Using the given numbers, the prime numbers are_{11and 23}, and the composite numbers

are {9 and 18}.

Assessment:

1. Veronica used square tiles in math class and made the following four designs.

Design 1 Design 2 Design 3 Design 4 Which design is composed of a prime number of tiles?

A. Design 1 B. Design 2 C. Design 3 * D. Design 4


2. The list below contains the factors of which number? 15, 3, 5, 9, 45, 1

F. 15 G. 27 *H. 45 J. 54

3. Which number pair is a factor pair of 64?

A. 6, 11 B. 3, 21 C. 4, 14 *D. 2, 32


Guided Practice: Reporting Category 2: TEKS 5.5(B)

Name: ______________________ Date: __________________ Look at the numbers below.

18, 11, 9, 23 1. Find the factors of 18. _________________________________________________________ 2. Find the factors of 11. _________________________________________________________ 3. Find the factors of 9. __________________________________________________________ 4. Find the factors of 23. _________________________________________________________ 5. What does prime mean? ______________________________________________________________________________ ______________________________________________________________________________ 6. What does composite mean? ______________________________________________________________________________ ______________________________________________________________________________ 7. Using the given numbers, the prime numbers are _____________ and the composite

numbers are _____________.


Assessment: Reporting Category 2: TEKS 5.5(B)

Name: _________________________ Date: __________________

1. Veronica used square tiles in math class and made the following four designs.

Design 1 Design 2 Design 3 Design 4 Which design is composed of a prime number of tiles?

A. Design 1 B. Design 2 C. Design 3 D. Design 4

2. The list below contains the factors of which number? 15, 3, 5, 9, 45, 1

F. 15 G. 27 H. 45 J. 54

3. Which number pair is a factor pair of 64?

A. 6, 11 B. 3, 21 C. 4, 14 D. 2, 32


Student Sheet: Reporting Category 2: TEKS 5.5(B)

43 31 27

46 72 93

85 61 15

53 39 64

Copyright©2011 ESC Region XIII 5.5A, 5.10C, 5.14A, 5.14B, 5.14C

STAAR Reporting Category 4: Measurement: The student will demonstrate an understanding of the concepts and uses of measurement. TEKS 5.5: The student makes generalizations based on observed patterns and relationships.

TEKS 5.10: The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems.

TEKS 5.14 The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

Student Expectations: 5.5(A) The student is expected to describe the relationship between sets of data in graphic organizers such as lists, tables, charts, and diagrams. 5.10(C) The student is expected to select and use appropriate units and formulas to measure length, perimeter, area, and volume. 5.14(A) The student is expected to identify the mathematics in everyday situations. 5.14(B) Solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. 5.14(C) Select or develop an appropriate problem‐solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

Overview: Finding patterns and making generalizations help form the foundation for algebraic reasoning. This can be done in any mathematical area and will be shown using measurement in this lesson. We will find patterns and make generalizations to help us solve problems involving perimeter, area, and volume.

Materials: Paper Color Tiles (optional)

Vocabulary: Perimeter, area, length, width, relationship, equation

Lesson:

Put the following problem on the board: Johnny and Marybeth were putting stone pavers around their rectangular swing set area like the one shown below.

4 feet

8 feet


Each stone paver was 2 feet square. Use a graphic organizer (chart, table, etc.) to show how many stone pavers Johnny and Marybeth would need to go around their swing set. Ask the students to open up their math journals and decide how best they will solve this problem using some type of a graphic organizer. NOTE: If students need a manipulative to help them conceptually understand, colored tiles would be a great one for them to use. Some students need to be able to visually see things in math first before they are able to understand the math behind it. The only way this can be done is through manipulatives. Students should always be allowed to use them when solving new types of problems.

What is this problem asking us for? (how many stone pavers they need to go around the swing set)

What does it mean mathematically if we “go around” something? (that we are finding the perimeter of something).

How do I find the perimeter? (accept any of the formulas for perimeter.)

What is the perimeter of Johnny and Marybeth’s swing set area? (24 feet)

I now know that I have to go 24 feet to get all of the way around the rectangular swing set area. Is that going to be my final answer? Why or why not? (No: it is not the final answer because you are looking for how many stone pavers they will need, not what the perimeter is.)

Now let’s see if we can use a graphic organizer, like a table, to help us figure out how many pavers we will need. Make the following chart on the board.

I know a graphic organizer, like a table or chart, is just a way of organizing what I know. I know there is a mathematical relationship between the two things I place in the chart. In this case, there is a mathematical relationship between my stone pavers and how many feet long they are.

Who thinks they can tell me what my relationship is between these two things? (1 stone paver is 2 feet long.)

Where did you get this information? (from the sentence in the problem that says “Each

stone paver was 2 feet square.” The word ‘each’ represents 1 and a square means that

each side is congruent; therefore, the length and width both are 2 feet.)

How can I represent that in my graphic organizer? Call on a student to come and put

that into your table.

Stone Pavers Feet Long


What if I put down 2 stone pavers? How many feet long will that be? (4 feet long)

What about 3 stone pavers? (6 feet long)

What am I solving for again? (how many stone pavers they need to go around their rectangular swing set area)

How do I know when I have gotten there on my chart? (when you have gone around the whole perimeter, which is 24 feet)

Have students go back into their journal and copy the chart down and complete it to get their final answer. Answer: (12 stone pavers)

Stone Pavers Feet Long

1 2

Stone Pavers

Feet Long

1 2

2 4

3 6

4 8

5 10

6 12

7 14

8 16

9 18

10 20

11 22

12 24



Do you see any patterns in this table? (You were multiplying the stone pavers by 2 to get the feet long.) If students say it is counting by 1’s under stone pavers and by 2’s under feet long, get them to understand that a relationship happens between the two sides, not down one side and then down the other.

I want you to go into your journals and write an equation to go along with this table using the pattern we just figured out. (feet long = stone pavers x 2)

Why was I able to use a table to help me solve this problem? (There was a relationship in this problem that would never change and that was 1 stone paver = 2 feet long). If students do not automatically come up with this answer, lead them to this conclusion with scaffolding questions.

Did I have to use this type of a graphic organizer or would others have worked? If so, what kinds? (Others would have worked. You could used a T‐chart, draw a pictorial representation with stones, made a list of 2’s to represent each stone paver)

Guided Practice:

The Collins family has decided to remodel their family room down in the basement. They will be using the 3 foot square, sticky carpet tiles to create a multi‐colored pattern. If there family room is a 6 foot wide square, how many square carpet tiles will the Collins family need to carpet their entire floor?

# of carpet tiles

Feet Covered

What are you trying to find? (The number of carpet tiles they will need.)

What do you have to find first? (The area of the family room.)

What is the relationship shown in the table? (1 carpet tile covers 3 square feet.)

When do you know when to stop in the table? (When you have covered 36 square feet.)

The answer is… (12 carpet tiles)


Assessment:

1. Kevin was decorating a project board like the one below for his Civil War project.

He decided to glue trees around the outside of his board. If each tree was placed ten inches apart, how many trees would Kevin need for his board?

# of trees Inches Used

2. Jesse is laying grass in his backyard. He can buy the grass in 10 square foot pallets. Sods ‘R’ Us only sells grass pallets in sets of 10 for $1,000 or individually for $139 each. If Jesse needs enough grass to cover his rectangular backyard that measures 8 feet wide by 15 feet long, what is the least amount of money he will spend?

A. $695 B. $1,278 C. $1,668 D. $12,000

14 in.

26 in.

*


3. Melanie wants to put a border up around the top of her bedroom. She found one she likes at Home Depot. Each roll is 15 feet long and costs $22.98. If Melanie’s bedroom is 13 feet long and 11 feet wide, how many rolls of border will she need to buy to have enough to go around the top of her entire bedroom? A. 3 rolls B. 4 rolls C. 9 rolls D. 10 rolls

*


Guided Practice: Reporting Category 4: TEKS 5.5(A), 5.10(C), and 5.14(A)(B)(C) Name: ____________________________ Date: __________________

The Collins family has decided to remodel their family room down in the basement. They will be using the 3 foot square, sticky carpet tiles to create a multi‐colored pattern. If there family room is a 6 foot wide square, how many square carpet tiles will the Collins family need to carpet their entire floor?

# of carpet tiles

Feet Covered

What are you trying to find? ______________________________________________________________________________ ______________________________________________________________________________ What do you have to find first? ______________________________________________________________________________ ______________________________________________________________________________ What is the relationship shown in the table? ______________________________________________________________________________ ______________________________________________________________________________ When do you know when to stop in the table? ______________________________________________________________________________ ______________________________________________________________________________ The answer is: ______________________________________________________________________________ ______________________________________________________________________________


Assessment: Reporting Category 4: TEKS 5.5(A), 5.10(C), and 5.14(A)(B)(C)

Name: ___________________________________ Date: _________________________ Kevin was decorating a project board like the one below for his Civil War project. He decided to glue trees around the outside of his board. If each tree was placed ten inches apart, how many trees would Kevin need for his board?

# of trees Inches Used

14 in.

26 in.


2. Jesse is laying grass in his backyard. He can buy the grass in 10 square foot pallets. Sods ‘R’ Us only sells grass pallets in sets of 10 for $1,000 or individually for $139 each. If Jesse needs enough grass to cover his rectangular backyard that measures 8 feet wide by 15 feet long, what is the least amount of money he will spend?

A. $695 B. $1,278 C. $1,668 D. $12,000

3. Melanie wants to put a border up around the top of her bedroom. She found one she likes at

Home Depot. Each roll is 15 feet long and costs $22.98. If Melanie’s bedroom is 13 feet long and 11 feet wide, how many rolls of border will she need to buy to have enough to go around the top of her entire bedroom?

A. 3 rolls B. 4 rolls C. 9 rolls D. 10 rolls

*

*

Copyright©2011 ESC Region XIII 5.10B, 5.10C, 5.14A

STAAR Reporting Category 4: Measurement: The student will demonstrate an understanding of the concepts and uses of measurement. TEKS 5.10: The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems.


Student Expectations: 5.10(B) The student is expected to connect models for perimeter, area, and volume with their respective formulas. 5.10(C) The student is expected to select and use appropriate units and formulas to measure length, perimeter, area, and volume. 5.14(A) The student is expected to identify the mathematics in everyday situations.

5.10(B) and (C) TEKS have been divided into two separate lessons. Lesson one of two: The Area Stays the Same

Overview:

The Area Stays the Same Find area and perimeter. The two are being contrasted as a possible method of alleviating the confusion for students.

Materials: 24 color tiles or area tiles Ruler Pencil, square grid paper Overhead color tiles

Vocabulary: perimeter, area, square, similar, length, width, key, dimensions

Lesson: 1. Allow students time to become familiar with squares by asking questions such as "What

shape are these color tiles? What do we know about all squares?" Students record their thinking in their journals. The students should know and recall that all sides of the squares are the same length. If the students do not know the definition of a square, introduce that word to them during this exploration. Have students trace one of the square tiles in their journals and use their ruler to measure each side. This will be further proof that all sides of a square are equal.

2. If I ask you to find the perimeter of our classroom, what am I asking you to find? Take a minute to answer this question in your journal. I would also like for you to make an illustration to accompany your answer. Lead students in a discussion of perimeter.


Have students share with the class. Direct students back to the drawing they made in their journal of the square tile. Have students determine its perimeter in their journal. Illustrate on the board that one square has a perimeter of four units (each side has a length of one). Now I want you to put two square tiles side by side and trace these in your journal. Take a minute in your journal to determine the perimeter of this figure. Give students a few moments to find the perimeter in their journal.

What is the perimeter of this figure? (6) You will be creating different shapes using all 24 of your tiles. Each tile must share at least one full edge with another tile and must form an array. Who can remind us what an array is? (a set of objects placed in organized rows and columns.)

Correct Incorrect

You need to sketch the shape of each array you discover with your 24 tiles on your grid paper. Once you have found all of your arrays, cut each out, glue into your journal, and find and record the perimeter for each array. Give students a little bit of time to get this task accomplished. Then, have students share their shapes with their neighbor and discuss the different arrays they found. What did we have to do to find the perimeter of each of our arrays? (Count each tile around the edge of our figure.) What if we were to find the perimeter of something that wasn’t made out of tiles. What if it was blank, like our math journal? (You would use your ruler to measure all of the way around it.) Let’s do that. Let’s get our ruler and measure each side of our figure and write above each side what that side measures. Give students a moment to do this. If you are using inch grid paper have them measure in inches. If they are using cm grid paper, have them measure with their cm ruler.

3. Ask students to try and make a square using all 24 tiles.

Is this possible? (no)

Using all 24 tiles, what shapes can you make? (rectangles)

How many different rectangles can you make? Inform the students that a 4 x 6 and a 6 x 4 form the same rectangle. (4, they are: 1x24, 2x12, 3x8, 4x6)

4. If I ask you to find the area of our classroom, what am I asking you to find? Take a minute to answer this question in your journal. I would also like for you to make an illustration to accompany your answer. Have a class discussion about area. Have students go back into their journal and find the tracings of the 1 square tile and 2 square tiles.

What do you think the area is for the one tile? (1)

Why do you think that? (because it is made up of only 1 tile)

What do you think the area is for the second drawing we made? (2)

Why do you think that? (because it is made up of two tiles) Discuss with the class that one color tile is the unit of measure for area. A = l x w – Area is 2 lengths that are multiplied together making a square unit of measure. Therefore, when we find the area of something in feet, we say: “That is _______ square feet.” If we find the area of something in yards we say: “That is ______square yards.” We are using squares of whatever that unit is to measure the inside of the space.


5. Ask students to go back to the grid figures they glued into their journal and record the

area of each shape they created. Remind students that the area is how many tiles are

placed INSIDE of their figure.

6. Now, let’s look at the dimensions we wrote in our journal above each side of our figures. Can anyone tell us how we can use these dimensions to find the area? Is there a formula to use? Can anyone tell us how to use these dimensions to find the perimeter? Is there a formula to use? NOTE: Encourage students to record all dimensions of a square shape. This will help to correct the mistake frequently made by students when the problem is asking them to find the perimeter, but they find the area.

6 ft 4 ft 4 ft 6 ft 7. Repeat the same activity using each rectangle.


1. What did you notice about the area of each of the shapes? (The area stays the same because all shapes are made of the same number of squares.)

2. What did you notice about the perimeter? (The perimeter changed each time.) 3. How do you find the perimeter of a figure?

E.g., 4 + 4 + 6 + 6 = 20 ft 2w + 2L E.g., 4 + 6 + 4 + 6 = 20 ft 2(L + w) E.g., 4 + 6 + 4 + 6 = 20 ft w + L + w + L

4. How did you find the area?

4 x 6 L x w = 24


Guided Practice: The owners of a new home have asked for a bid on the cost of putting grass in and a fence around their backyard. They need to decide on the shape and size of their lawn. You are the landscape company. I am going to give each group a rectangle dimension and a package of color tiles. (Give one of the following and a package of 20 color tiles to each pair: 1 x 20; 2 x 10; 5 x 4) In order to determine the cost, you will need to know the area of the space for the grass and the perimeter of the backyard space for the fence. Assign each group of 2 – 4 students a rectangle dimension. Give each group chart paper. For this plan you will use the color tile as your unit of measure.

One length of fence is equal to the length of one color tile. One length of fence costs $4.

One plot of grass is equal to the area of one color tile. One plot of grass costs $3.

You will need to find:

The number of lengths of fence needed to go around the backyard.

The cost for this number of length of fence for the backyard.

The number of plots of grass needed to fill the backyard completely.

The cost for this number of plots of grass for the backyard.

The total cost of both fence and grass for the backyard. 1. How many lengths of fence do you need to go around the backyard? (Answers will vary

according to the dimensions you have given the student. Let students decide whether they label the lengths as feet or yards.)

2. What would be the cost for this number of length of fence? (The answers will be the number of lengths x $4.)

3. How many plots of grass are needed to fill the backyard completely? (For all students, the answer will be 12 plots or 12 sq yds. Let the students decide whether they label the plots as feet or yards.)

4. What is the cost for this number of plots of grass for the backyard? (12 x 4 = $48) 5. What is the total cost of both fence and grass for the backyard? (The answers will vary

due to the different perimeters.) Adapted from Rethinking Elementary Mathematics, Part 2


Assessment: 1. How many feet of chain link fence will it take to enclose this garden plot? 13 ft. 10 ft.

A. 130 ft *B. 46 ft C. 23 ft D. 56 ft

2. Shannon is wrapping a present for her brother. She had enough paper to cover everything

but the top of the box. How much more paper does Shannon need to cover the top of her brother’s present?

12ft. 9ft.

*F. 108 sq ft G. 21 sq ft H. 42 sq ft J. 20 sq ft


3. How many inches of lace will Yuri need to decorate the outer edge of the scrapbook page? 8 in 11 in

A. 100 in B. 88 in

*C. 38 in D. 19 in

4. Daren wants to put a wooden trim around his bathroom mirror. He drew a sketch to take

with him to his woodshop. He buys the trim in 6 feet strips. Use your ruler to determine how many pieces of trim Daren needs to buy to have enough to go around his bathroom mirror.

Daren’s Bathroom Mirror Key 1 inch = 2 feet


Guided Practice: Reporting Category 4: TEKS 5.10(B), 5.10(C), and 5.14(A)

Name: __________________________ Date: __________________ Write your dimensions from your tile figure on the blanks provided with the rectangle diagram. ___________ ___________ ___________ ____________

One section of fence is equal to the length of one color tile. One length of fence costs $4.00.

One plot of grass is equal to the area of one color tile. One plot of grass costs $3.00.

You will need to find:

The number of section of fence needed to go around the backyard.

The cost for this number of section of fence for the backyard.

The number of plots of grass needed to fill the backyard completely.

The cost for this number of plots of grass for the backyard.

The total cost of both fence and grass for the backyard.

1. How many section of fence do you need to go around the backyard?

2. What would be the cost for this number of section of fence?

3. How many plots of grass are needed to fill the backyard completely?

4. What is the cost for this number of plots of grass for the backyard?

5. What is the total cost of both fence and grass for the backyard?


Assessment: Reporting Category 4: TEK 5.10(B), 5.10(C), and 5.14(A)

Name: ____________________________ Date: __________________________

1. How many feet of chain link fence will it take to enclose this garden plot? 13 ft 10 ft A. 130 ft B. 46 ft

C. 23 ft D. 56 ft

2. Shannon is wrapping a present for her brother. She had enough paper to cover

everything but the top of the box. How much more paper does Shannon need to

cover the top of her brother’s present?

12 ft

9ft F. 108 sq ft

G. 21 sq ft

H. 42 sq ft J. 20 sq ft


3. How many inches of lace will Yuri need to trim the scrapbook page?

A. 100 in 8 in

B. 88 in 11 in C. 38 in D. 19 in

4. Daren wants to put a wooden trim around his bathroom mirror. He drew a sketch to take

with him to his woodshop. He buys the trim in 6 feet strips. Use your ruler to determine how many pieces of trim Daren needs to buy to have enough to go around his bathroom mirror.

Daren’s Bathroom Mirror

Key 1 inch = 2 feet

Copyright©2011 ESC Region XIII 5.10B, 5.10C, 5.14A, 5.14D

Reporting Category 4: Measurement: The student will demonstrate an understanding of the concepts and uses of measurement. TEKS 5.10: The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems.


Student Expectations: 5.10(B) The student is expected to connect models for perimeter, area, and volume with their respective formulas. 5.10(C) The student is expected to select and use appropriate units and formulas to measure length, perimeter, area, and volume. 5.14(A) The student is expected to identify the mathematics in everyday situations. 5.14(D) Use tools such as real objects, manipulatives, and technology to solve problems.

5.10(B) and 5.10(C) TEKS have been divided into two separate lessons. Lesson two of two: Volume

Overview:

This lesson will give students practice visualizing the dimensions of rectangular prisms and enumerating the number of cubic units needed to fill the space occupied by a rectangular prism. Begin the lesson with a whole group introduction and discussion about rectangular prisms and volume. Briefly move through the introductory discussion about rectangular prisms if the students are already familiar with geometric attributes and properties of prisms. Follow up the whole group lesson with a practice session in which the students are working with partners building cubic towers and then estimating how many cubic units make up their towers.

Materials: Snap cubes or connecting centimeter cubes (if you have neither of these, base 10 units will also work. You just cannot pick the figure up once it is made.) Three boxes of different sizes and dimensions made from tag board that is measured to scale with snap cubes

(one that is a 3 4 5, another that is a 2 2 4, and another that is a 4 6 7) Chart paper

Vocabulary: Volume, fill, dimension, length, width, depth, height, layer, cube, rectangular prism, square, congruent, unit, inch, centimeter, foot


Lesson: Introduction (What is a Prism?) 1. Show the students a rectangular prism constructed out of snap cubes. Make its dimension

3 4 5 cubic units. Move the rectangular prism around so that the students can see each of its faces and edges.

I made this structure by putting together snap cubes.

How would you describe the shape of this structure? Anticipate a variety of informal descriptions that may or may not provide a complete definition of a rectangular prism. Some students may point out that the prism has straight edges with rectangular faces. Other students may actually count the number of faces. Some students may also just say that it is a rectangle. If this is the case, lead them to understand that a rectangle is a 2‐D figure and this is a 3‐D figure because you can measure three things: length, width, AND height.

2. After gathering a few descriptions from the students, conclude the discussion by summarizing the formal definition of a rectangular prism.

When I put together these snap cubes, they form a box‐like shape, which mathematicians call a rectangular prism. A rectangular prism has six rectangular faces, some of which may be squares. (Count the faces with the students. Keep track of the count by placing dot stickers on each face as you point.)

It also has 12 straight edges and 8 vertices. (Point to each edge and vertex.) 3. Remove one snap cube from the prism. Ask the students to compare the individual snap

cube to the prism.

How are the snap cube and prism alike and different?

Which one fits inside the other? How do you know?

Which is smaller? Which is larger?

Does the snap cube have faces and edges like the prism? Describe the faces on the cube. (If the students fail to mention, point out that the faces on the snap cube are squares that are all the same size and shape, which mathematicians call congruent.)

4. Wrap up this brief discussion by leading the students to understand that the cube is the smallest part of the whole prism.

This box like structure that we call a rectangular prism is made up of individual units that are the same size and shape. These units are the snap cubes. Each edge on a snap cube is the same length.

Introduction:

Volume: What Does It Mean to Take Up Space? 1. Show the student three boxes, each a different size and dimension—e.g., one box that is

too big, one that is not big enough, and one that is just the exact size to contain the 3 4 5 unit prism you made with snap cubes. Consider making these boxes with tag board so that they can be measured in cubic units equal to the dimension of the snap cubes. Label each

box “A,” “B,” and “C.” Ask the students to determine which box will hold the 3 4 5 unit prism.

This snap cube prism I made takes up just enough space to fit perfectly inside one of these boxes.

What does it mean to ‘take up’ space? (Answers will vary. ‘Take up’ space means how much space it will fill.)


Can you visualize what the space looks like inside each of these boxes? (Answers will vary. Examples are a cube, a small rectangular prism, a large rectangular prism, etc.)

If I were going to fill one of these boxes with cubes (not the rectangular prism that has already been made), how would I place the cubes so that I can fit the most cubes inside the box? (in straight rows and columns.)

2. Call on a volunteer to show how he/ she would arrange the cubes. As the student is

arranging the cubes, encourage him/ her to explain his/ her process. Use this demonstration as an opportunity to point out how stacking cubes in layers of straight rows and columns is the best way to fit the most amount of cubes into the box and still close its lid. Compare how the cubes look when they are simply poured haphazardly into the box versus stacked on top of each other in straight rows and columns.

Go back to the rectangular prism you have already built and the box that it fits into. Just by looking at this box, can you accurately tell how many snap cubes it will take to fill it? Why or why not? (no, I would need more information to determine how many would fit inside.)

What would you need to accurately determine how many cubes would fit inside? (Answers will vary.) Provide scaffolding questions if students say to fill the box with snap cubes and count as you put them inside. Lead students to see that if we knew how many snap cubes fit the box’s width and length, we could determine the area of the box. From there we could decide how many layers of that area we would need to fill box and do the math for an accurate answer.

Let’s look at another rectangular prism that I made earlier. (Have a 2 x 3 x 3 prism made with snap cubes to show the class. If you have a document camera, place the prism underneath for the students to be able to get a better look at the area of the top layer). How many cubes would I need to give each of you in order to recreate this prism without having any left over?

Provide some scaffolding questions for students who insist on taking the prism apart and counting all of the cubes:

Would you have to count each cube, or is there an easier way to predict the number of cubes that fill the prism?

Are there cubes you should count that you cannot see? If so, how should you count them?

3. Allow the students to share their answers. Encourage each student to explain how he or

she came to his or her results. Accept all strategies, even those that are inaccurate and inefficient. The goal of this lesson is to help the students reflect on their thinking. By listening to others justify their thinking, the students are empowered to make sense of these errors. Consequently, the end result of this sharing session is to help the students construct an understanding and appreciation for more efficient strategies for estimating cubic volume. Here is a list of some common errors:

Some students try to count each cube one‐by‐one while trying to visualize the entire prism without paying any attention to the way the prism is organized in congruent layers of cubic arrays. In doing so, they often loose track of their count.


Some students only count the outside cubes on the face of the prism. They count the faces of the individual cubes on the top, front, and right and left side faces of the prism. Consequently, the cubes on the outer edges are often counted twice.

4. Give each student the number of cubes he or she answered that he or she would need to recreate the prism. Allow 2‐5 minutes for the students to use their cubes to recreate your prism. Have students check their neighbor’s prism to see if it matches the one being displayed. Discuss who had enough cubes, who had too many, and who had too few. Have students go into their math journal and write a brief explanation on how they constructed their tower to match the one being shown.

Activity Part 1: Whole Group: Visualizing a Cubic Tower

1. On the document camera or overhead, display a copy of Student Sheet 1, which shows a 3‐D pictorial representation of a 3 × 2 × 1 rectangular prism made from snap cubes.

2. Distribute a copy of Student Sheet 1 for each student to look at while you go over the transparency on the overhead. Each student will also need a set of snap cubes to recreate the rectangular prisms pictured on the sheet.

3. Point out the prism’s top, front, and right side views highlighted on the sheet. Ask the students to discuss how looking at each of these different orientations could help them figure out how many cubes are in the prism.

4. Instruct the students to make the 2 × 4 × 2 rectangular prism pictured at the bottom of the sheet.

5. Instruct the students to record the number of cubes used. 6. As the students are making the 2 × 4 × 2 prism, walk around to check to see how they

are making the prism and if their models match the representation shown on the sheet.

Activity Part 2; Individual Practice: Building a Cubic Tower 1. Instruct students that they are going to make their own cube tower. Display Student

Sheet 2, which shows a set of 3 spinners that the students will use to determine how many cubes they will need to make the dimensions of their cube tower—e.g., the number of cubes in a row (length), the number of rows (width), and the number of floors (layers or height).

Front view

Right side view

Top view

Front view

Right side view

Top view

Student Sheet 1

Student Sheet 1


Now, you are going to make your own tower using the snap cubes. You must spin each of the 3 spinners on Student Sheet 2. First, spin Spinner A. Spinner A tells you how many cubes to snap together to make one row (length). Then, you will spin Spinner B to determine how many rows you will have on your base (array) (width). Finally, you will spin Spinner C to determine how many floors your tower will have. Think of the floors as layers (height). Each floor must be congruent to the base so that the entire tower is shaped like a rectangular prism.

2. Call on a volunteer to demonstrate how to use the spinners to make a tower. Instruct the student volunteer to make a tower that matches the dimensions indicated on the spinners.

3. When the students have made their cube tower, instruct them to record how many cubes there are in their tower altogether in the space provided on Student Sheet 2.

4. Encourage the students to visualize how their tower would look if they drew a 3‐D representation of the tower on paper. To help the students visualize how prisms can be measured by cubic units constructed as 3‐D arrays stacked in layers, demonstrate how to shade in the top, front, and right side views of their towers in the corresponding 10 by 10 grids at the bottom of Student Sheet 2.

Spinners

This is a sample cube tower that has 3 cubes in a row, 4 rows, and 2 layers.

Bottom portion of Student Sheet 2

Student Sheet 2

2

4

3


Debriefing Questions: 1. Debrief the students about their work with Student Sheet 1. On a piece of chart paper,

write down the dimensions of each student’s cube tower. Display the chart where all of the students can see it.

2. Ask each student to share how he or she determined how many cubes there are altogether in his or her tower.

How did you determine how many cubes there are altogether in your tower? (Accept any responses and explanations.)

Why is it difficult to count each cube in the tower? (You cannot see some of the cubes that are inside.)

How could you use the numbers you spun on the three spinners to help you figure out the total number of cubes in your tower? (I could multiply the number of cubes there are in one of my rows by the number of rows on my base floor. This will give me the area of each floor or layer. Then, I could multiply the number of cubes on the base by the number of floors (layers) there are in my tower.) If the student fails to provide a sample response like the one highlighted in parenthesis, scaffold the student’s thinking by asking more specific questions:

Remove the base floor from your tower. Notice how it looks like an array. Now, break apart the array into individual rows. How many rows are in your array? (The student should say the correct amount.)

How many cubes are in each row? (The student should say the correct amount.)

Does each row have the same number of cubes? (yes)

How do you know? (Each row is the same length and is made up of the same sized cubes.)

Which operation could you use to figure out the total number of cubes in the base? (multiplication or repeated addition) If the student says repeated addition, lead him or her to see its relationship to multiplication. Lead students to see that you are finding the area of the base of your prism when you multiply the length and width.

Now, put all of the rows on your bottom floor back together. How many floors are there in your tower (The student should say the correct amount.)

How many cubes did you say were in the bottom floor? (The student should say the correct amount.)

Does each floor have the same number of cubes? (yes)

How do you know? (Each floor is the same size and same shape, so each one must have the same number of cubes.)

Which operation could you use to figure out how many cubes there are altogether in the tower? (multiplication) Lead students to the formula for finding volume (V = L x W x H). Write the formula for volume on the board and demonstrate using the tower how L x W gives you the area of one layer, and multiplying H to the area is how you factor in how many layers the model is made up of. Therefore, that is why the formula V= L x W x H works. This is an important step in making sure the students have a conceptual understanding of the formula for volume.

Note: This is a good opportunity to discuss the notation for recording cubic volume. Lead the students to see the relationship between the three numbers they used on their spinners to figure out the total number of cubes in their tower to the notation that is


used to signify a number that is cubed—e.g., 12 in³ indicates the total number of cubic units (inches) in a 3 × 2 × 2 rectangular prism.

Guided Practice: Distribute Guided Practice Activity Sheet 5.10(A). Abby is constructing a bunker for her World War II project by gluing centimeter cubes together. She would like for her final product to look like the one below. If Abby bought a package of 150 centimeter cubes, would she have enough? Why or why not? (No, Abby would not have enough. She needs 168 centimeter cubes to complete this model.)

How big is the cubic unit used to measure this prism? (one centimeter)

How can you tell? (The problem says Abby is using centimeter cubes.)

How many layers are in the prism? (four)

How many cubes are in one layer? (forty‐two)

How could you determine how many cubes there are in one layer without counting each cube individually? (The layer is like an array of cubes. I know that there are 6 rows and that each row has 7 cubes. 7 + 7 =14 and there are 3 groups of 14, so 14 + 14 =28 and 14 more makes 42.)

Write a number sentence that represents this array. (6 × 7 = 42)

Write a number sentence that shows how many cubes there are altogether? (Accept any response that shows numerical reasoning—e.g., 42 × 4 = 168; or 40 × 4 = 160 + (2 × 4) =160 + 8 = 168.)

What does the symbol ³ stand for at the end of each abbreviation for the unit centimeters? (You can multiply 3 dimensions of the prism; its length by its width by its height (number of layers.))


Which of the following rectangular prisms does NOT have a volume of 24 cubic units? A. *C B. D.


Student Sheet 1: Reporting Category 4: TEKS 5.10(B)(C) and 5.14(A)(D)

Name: ____________________________________ Date: ___________________ This building can be viewed from 3 different angles: the top, front, and right side views. This is what the building would look like if you could only see its top. This is what the building would look like if you could only see its front. This is what the building would look like if you could only see it from its right. Make this building using snap cubes. How many cubes did you use?

Sketch the following views of the building in the space provided.

Top View

Front View Right View

Top View

Front View

Right Side View

Top View

Right Side View

Front View

Top View:

Front View:

Side View:


Student Sheet 2: Reporting Category 4: TEKS 5.10(B) and 5.10(C)

Name: _________________________________________ Date: _____________

Directions: Make a cube tower. First, spin Spinner A to determine how many cubes to put in a row. Then, spin Spinner B to determine how many rows are in the bottom floor. Finally, spin Spinner C to determine how many floors there are in your tower. Draw a picture of your snap cube tower in the space provided below.

Spinner A Number of Cubes in a Row

Spinner B Number of Rows

Spinner C Number of Floors (Layers)


How many cubes are there altogether? _____________ Explain how you figured out how many cubes there are altogether. _______________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show what your tower looks like from the top view, front view, and ride side view.

Top View

Front View Right side View


Student Sheet 3: Reporting Category 4: TEKS 5.10(B)(C) and 5.14(A)(D)

Name: __________________________ Date: ________________________ Abby is constructing a bunker for her World War II project by gluing centimeter cubes together. She would like for her final product to look like the one below. If Abby bought a package of 150 centimeter cubes, would she have enough? Why or why not? How big is the cubic unit used to measure this prism? ______________ How can you tell? __________________________________________ How many layers are in the prism? ________________________________ How many cubes are in one layer? _________________________________ How could you determine how many cubes there are in one layer without counting each cube individually? ______________________________________________________________________________ Write a number sentence that represents this array? _______________ Write a number sentence that shows how many cubes there are altogether? ____________________________________________________________ What does the symbol ³ stand for at the end of each abbreviation for the unit centimeters? ___________________________________________________


3. Which of the following rectangular prisms does NOT have a volume of 24 cubic units?

A. C.

B. D.

Copyright©2011 ESC Region XIII 5.5A, 5.16A

STAAR Reporting Category 2: Patterns, Relationships, and Algebraic Reasoning: The student will demonstrate an understanding of patterns, relationships, and algebraic reasoning

TEKS 5.5: The student makes generalizations based on observed patterns and relationships.

TEKS 5.16: The student uses logical reasoning. Student Expectations: 5.5(A) The student is expected to describe the relationship between sets of data in graphic organizers such as lists, tables, charts, and diagrams. 5.16(A) The student is expected to make generalizations from patterns or sets of examples and non‐examples.

Lesson 1: Generalizations from Patterns

Overview: TEKS 5.16(A) outlines two specific skills, both of which require the student to use logical reasoning to make generalizations. The first skill mentioned refers to making generalizations from patterns in order to predict what comes next, or to determine the rule that makes the pattern continue in a predictable way. The second skill alludes to being able to make generalizations by analyzing two sets: one set containing attributes that fit a rule, and another set containing attributes that do not fit the rule. In order to address both skills, the procedure, debriefing, and guided practice sections are divided into two activities. Lesson one, “The King’s Castles,” allows the student to make generalizations from patterns by looking at the relationship that exists from one term to the next.

Materials: Pattern blocks Transparent pattern blocks (Optional) or pattern block cutouts Overhead projector or document camera/overhead Chart paper

Vocabulary: Pattern, relationship, difference, add, subtract, multiply, continue, attribute, divide, operation

Procedure: Lesson One: “The King’s Castles”

1. Secure a set of transparent pattern blocks.


2. Use the set of transparent pattern blocks to make the following growing pattern on the overhead: If you do not have a set of transparent pattern blocks, replicate the pattern with pattern block cut‐outs or draw the pattern on grid paper and display it in the room where every student can see it.

3. Tell the students a story about the pattern block buildings featured in the problem:

A king decided to add more to his castle each year. The first castle pictured to the far left is what the king’s castle looked like the first year. The castle following the first one is what the king’s castle looked like the second year. Likewise, the castle following the second one is what his castle looked like the third year and so on.

How many years has the king been building his castle? (four years)

How do you know? (There are four castles lined up next to each other, each one representing a year.)

4. When the students have established the sequence of terms in the growing castle pattern, label each castle to show its corresponding year:

5. Ask the students to predict what the next castle will look like for the fifth year. Encourage them to briefly share their predictions with their partners.

6. Distribute sets of pattern blocks to pairs of students. Instruct each pair to build the fifth castle using only the square and triangle pattern blocks.

7. Tell the students to fill out Student Sheet 1 when they have finished building the fifth castle. This sheet allows the students to think about the numerical patterns and relationships that exist from one term to the next. See the table featured on Student Sheet 1 illustrated below:

Castle Number of Squares

Number of Triangles

Total Number of Pattern Blocks

Castle, Year 1 1 1 2





Year 1 Year 3 Year 4

Labeled Castles

Year 5

?


Debriefing Questions: Make sure the students have completed Student Sheet 1 before proceeding to the following questions for the debriefing portion of this lesson:

How many squares did you use to make the fifth castle? (fifteen)

How many triangles did you use? (five)

How many pattern blocks did you use altogether? (twenty)

What is happening to the number of each type of pattern block from each year to the next? Do you notice a pattern? (The number of squares, triangles, and total number of squares and triangles is growing.)

How did you figure out how many squares you would need to make the fifth castle? (The difference between the number of squares from year to year always increases by one. The difference from year one to year two is 2 (3 – 1 = 2.) The difference from year 2 to year 3 is 3 {6 – 3 = 3}. The difference between year three to year four is 4 (10 – 6 =4.) If this pattern continues, then the difference between year four to year five should be 5. So, I just added 5 to the number of squares used in the castle for year 4. (e.g., (10+5=15)).

How did you figure out how many triangles there would be in the fifth castle? (The number of triangles is growing by one. Since there are 4 triangles in the fourth castle, I just added 1 to 4 to get 5 triangles for the fifth year.) Or (The number of triangles is always the same as the number of years.)

How did you figure out how many squares and triangles there are altogether in the fifth castle? (Since I already figured out the number of squares and the number of triangles in the fifth castle, I just added the number of squares to the number of triangles.)

Is the total number of squares and triangles growing in a predictable way from year to year? If so, how? (It is just like the squares. The difference between the total number of squares and triangles is growing by one from year to year.)


Guided Practice: Look at the pattern in the sequence of numbers below:

7, 14, 12, 24, 22, 44, 42, 84, 82

Find the difference between each number in the sequence illustrated above. Continue this process between each number in the sequence, starting with the first number, 14. For example, the difference between 14 and 12 is 2.

1. What do you notice? (The difference between 14 and 12 is 2. Then, the difference between 12 and 24 is 12. It keeps on going like this: You double the number, then you have a difference of two.)

What do you have to do to a number in order to double it? (You multiply it by two.) 2. Do you see any patterns? Describe the patterns you see in your own words. (Accept

any reasonable response. Lead the student to see the relationship between his or her explanation and the formal description offered in the correct answer choice (e.g., multiply by 2, then subtract 2.) If the student is still struggling to see the relationship between each number in the sequence, proceed with the following questions:

3. How are the numbers changing from one number to the next? (First subtract 2, then they go up by doubling the number. For instance, to get from 14 to 12, you take 2 away from 14. Then double the 12 to get 24.)

4. Is the difference increasing or decreasing? (First, the number increases, then it decreases by 2.)

Which operation could you use to increase a whole number? (addition or multiplication)

Do you see the word “multiply” or “add” in any of the answer choices? (Two answer choices show the word “multiply” and the other two show the word “add.”)

Try out each rule listed in the answer choices. Do any of them work for EVERY

number in the sequence? (Answer choice ‘A’ works for the first three numbers, but

then if you add 7 to 12, you get 19, not 24. Answer choice ‘B’ works out with all of

the numbers.)

5. Which rule describes this pattern best?

* A. Subtract 2, multiply by 2

B. Multiply by 2, subtract 2

C. Add 14, subtract 7

D. Multiply by 2, subtract 7

14, 12, 24, 22, 44, 42, 84, 82

2 12 2 22 2 42 2


Student Sheet 1: Reporting Category 2 TEKS 5.5(A) and 5.16(A)

Name: ___________________________________ Date: ___________________ Fill out the table below that tells how many squares, triangles, and total number of pattern blocks there are in the king’s castle each consecutive year.

Castle Number of Squares

Number of Triangles

Total Number of Pattern Blocks


Castle, Year 2

Castle, Year 3

Castle, Year 4

Castle, Year 5

In the space provided below, draw a picture of how the king’s castle looks at year five.

How many squares, triangles, and total number of pattern blocks would the king need to build on to his castle for the ninth year? _______________________________________ Use numbers, pictures, and words to explain how you figured out how many pattern blocks the king would need for the ninth year.


Guided Practice 1: Reporting Category 2 TEKS 5.5(A) and 5.16(A)

Name: __________________________ Date: __________________ Look at the pattern in the sequence of numbers below: 14, 12, 24, 22, 44, 42, 84, 82 Find the difference between each number in the sequence illustrated above. Continue this process between each number in the sequence, starting with the first number, 14. For example, the difference between 14 and 12 is 2. Show your work in the space provided below. 1. What do you notice? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 2. Do you see any patterns? Describe the patterns you see in your own words. _________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 3. How are the numbers changing from one number to the next? _________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 4. Is the difference increasing or decreasing? Explain your thinking. _________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ______________________________________________________________________________________________________________________________________________________ 5. Which rule describes this pattern best? A. Subtract 2, multiply by 2


C. Add 14, subtract 7

D. Multiply by 2, subtract 7



TEKS 5.5: The student makes generalizations based on observed patterns and relationships.

TEKS 5.16: The student uses logical reasoning. Student Expectations: 5.5(A) The student is expected to describe the relationship between sets of data in graphic organizers such as lists, tables, charts, and diagrams. 5.16(A) The student is expected to make generalizations from patterns or sets of examples and non‐examples. 5.16(B) Justify why an answer is reasonable and explain the solution process.

Lesson two: Sorting Numbers and Geometric Figures

Overview: Lesson two provides the student with analysis skills to help him/ her sort numbers and geometric figures by common attributes (examples and non‐examples.)

Materials: Pattern Blocks Post‐It Notes Chart Paper Overhead projector (optional) Student Sheet 2

Vocabulary: non‐examples, examples, pattern, attribute, multiples, factors, prime numbers, composite numbers, odd numbers, even numbers

Procedure: Lesson Two: Staircase Castles and Non Staircase Castles

1. Extend the castle pattern activity to include the development of logic and analysis skills that will help the students to make generalizations from sets of examples and non‐examples.


2. Tell the students the following story: One day, a builder was admiring the shape of the king’s castle. The builder told the king that he wanted to build several castles just like the king’s castle for other kingdoms in faraway lands. The king thought that this would be a good way to make money, so before he sold the master floor plan to the builder, he came up with a market name that would describe the shape of his castle. From that day on, the king decided to call his castle design the “Staircase Castle.” The builder loved this idea and told the king that some kings would want smaller “Staircase Castles,” while other kings with large families would need bigger “Staircase Castles.” So, the king decided that he would make larger and smaller versions of the same castle to sell to the builder. Each of the castles, however, had to follow the pattern specifications.

3. Distribute sets of pattern blocks to pairs of students. 4. Instruct each student pair to use the pattern blocks to show of what a “Staircase

Castle” would NOT look like. Emphasize that the castles they make for this activity are “non‐examples” of the King’s Staircase Castle. To make this activity more challenging, tell the students that they can only use the square and triangle pattern blocks. Below are a few examples of what a “Staircase Castle” would NOT look like:

5. When the student pairs have completed their “Non Staircase Castles,” allow them to

share their design with the rest of the class. As each pair is sharing, encourage them to explain why their design is NOT a staircase castle.

6. Encourage the students to create a nonsensical word to describe their castle—e.g., a “Jozly Castle.”

7. After each student pair has shared, distribute number attribute cards (Student Sheet 2 cut apart) to groups of students. Each card contains a definition of a number attribute. Included are definitions for prime numbers, composite numbers, even numbers, odd numbers, factors, and multiples.

8. Tell the students that their job is to work together with their group members listing examples and non‐examples of the number attributes defined on their card. Instruct each group to record their numbers on chart paper, but not to include the definition or the name of the attribute.

Non Staircase Castles (Non‐examples)

If the students have difficulty understanding what a non‐example may look like, show them one of the castles featured here.


9. When each group has finished listing the examples and non‐examples of their respective “mystery” number attribute, instruct them to post their list somewhere around the room. Be sure to check to make sure that the examples and non‐examples do in fact correctly match the attribute described on each group’s card.

10. Distribute Student Sheet 2 to each student, which lists all of the number attributes

and their respective definitions.

11. Conduct a gallery walk around the room to allow the students to analyze each group’s chart. Distribute post‐it notes to the students and instruct them to use the notes to label each group’s chart with the corresponding number attribute listed on Student Sheet 2.

12. Walk around the room as the students are posting the labels on their classmates’ charts. Observe and eavesdrop on the students as they discuss which attribute best describes the examples of numbers on the chart.

Distribute Student Sheet 2 for the students to look at as they conduct a gallery walk to guess the “Mystery Number Attribute” for each group’s chart.

The “Mystery” attribute for this groups’ set of examples and nonexamples is “Factors of 1,000”

These numbers are _________. 5 100 25 200 50 10 These numbers are not ______. 30 400 569 700 10,000 6


Debriefing Questions: As you are walking around the room, ask the following questions to guide students who are having difficulty analyzing and categorizing all of the data on the charts:

Can you find a definition on Student Sheet 2 that describes each number on this chart listed as an example? (The student should try out one of the definitions to see if it matches all of the numbers.) If the student fails to do so, tell him or her to choose one definition on Student Sheet 2 and try it out on all of the examples listed on one chart.

Does this number match the definition? What about this number? (Student should respond yes or no depending on the definition.)

What should you do if all but one number that this group listed as examples matched the attribute you are trying out? (It means that this definition does not fit all of the numbers. So, I have to try out another definition until I find one that describes all of the examples on this chart.)

(Point to the non‐examples.) What do you notice about these numbers? (None of them fit the description for a ___________. (e.g., composite number)

Do you think this group includes all the possible examples of ___________ (e.g., composite numbers)? If not, tell me another number that would be an example. (The student should provide a correct number—e.g., 44.)

How do you know this number (44) is—e.g, a composite number?

(It has more than one factor than one and itself, like 2, 4, 11, and 22.)

Is it ever possible for a set of numbers to fit more than one attribute? (Yes, a set of numbers can be even and composite.)

Then, how could you figure out which of the two attributes match the numbers on a chart? (I could look at the set of non‐examples to see if any of them are composite or even. If so, the mystery attribute has to be one or the other. E.g., 4, 6, 8, 12, and 24 are all even and composite numbers. But, when I looked at the set of non‐examples, I saw a 2, which is an even number, NOT a composite number. Therefore, the “Mystery Number Attribute” for this set of numbers—e.g., 4, 6, 8, 12, and 24—has to be “Composite.”)


Guided Practice: Look at the numbers highlighted on this 100s chart:

1. Which expression describes the numbers highlighted on the 100s Chart?

F. Odd numbers

G. Composite numbers

*H. Prime numbers

J. Multiples of 11

Are all of the numbers that are highlighted on the 100s Chart odd, as suggested in Answer Choice E? (no) How do you know? (The number 2 is highlighted on the chart, and 2 is not an odd number.)

Is there any Answer Choice that you could tell instantly was not the correct answer? Accept any appropriate response, as each student will have a different level of familiarity with either of the attributes listed in the answer choices. What is important here is the student’s analysis and elimination skills. Here is one possible response: (Yes, any number that is less than 11 cannot be a multiple of 11. So, 1, 2, 3, 5, and 7 are all less than 11, and all of those numbers were the first ones I saw.)

How do you know that all of the numbers highlighted on the 100s chart are prime? (Each of these numbers only has one and itself as its factors.)

Is there another answer choice that almost describes each of the numbers highlighted on the 100s Chart? (All but one of the numbers, the number 2, is odd. The 2 gave it away.)

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100


2. Are there any numbers that are not highlighted on the chart that are also prime? (yes) Which other numbers are prime? (53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.)

Assessment: 1. Look for the pattern in the sequence of numbers below.

144, 72, 80, 40, 48, 24 Which rule describes this pattern best?

*A. Divide by 2, add 8


C. Divide by 2, subtract 8

D. Multiply by 2, add 8 2. Which statement about this group of numbers is true?

42, 6, 24, 78, 18

F. They are all prime.

* G. They are all multiples of 6.

H. They are all divisible by 4. J. They are all factors of 6


3. The figures below are all Hollits.

Which of the figures on the right are a Hollits? A. B.

C. D.


Student Sheet 2: Reporting Category 2: TEKS 5.16(A)

Attributes that Describe Numbers

Multiples of 3 The product of 3 and another number

Factors of 1,000 A whole number that divides evenly into 1,000

Prime A number that has only 1 and itself as factors

Composite A number that has 1, itself, and at least one other number as its factors

Odd A whole number that is not divisible by 2

Even A whole number that is divisible by 2


Guided Practice: Reporting Category 2: TEKS 5.16(A)(B)

Name: __________________________ Date: __________________ Look at the numbers highlighted on this 100s chart:

1. Which expression describes the numbers highlighted on the 100s Chart?

F Odd numbers G Composite numbers

H Prime numbers

J Multiples of 11

2. After you select the correct answer choice, check to see if there are any more numbers that have not been highlighted on the 100s Chart that are examples of the expression that you chose. If there are other numbers, mark them on the chart and explain how you know they are examples of the selected expression. ________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

_________

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100



Name: _________________________ Date: __________________ 1. Look for the pattern in the sequence of numbers below.

144, 72, 80, 40, 48, 24

Which rule describes this pattern best? A. Divide by 2, add 8 B. Multiply by 2, subtract 8 C. Divide by 2, subtract 8 D. Multiply by 2, add 8

2. Which statement about this group of numbers is true?

42, 6, 24, 78, 18

F. They are all prime.

G. They are all multiples of 6.

H. They are all divisible by 4.

J. They are all factors of 6


3. The figures below are all Hollits.

Which of the following figures is a Hollits?

A. B. C. D.

Copyright©2011 ESC Region XIII 5.12B, 5.16A



TEKS 5.16: The student uses logical reasoning. Student Expectations: 5.12(B): The student is expected to use experimental results to make predictions. 5.16(A) The student is expected to make generalizations from patterns or sets of examples and non‐examples.

Overview: This activity begins with a quick review of simple probability and then continues with students predicting results.

Materials: Spinner from Student Sheet Chart paper (three pieces) Three post‐it notes for each student

Vocabulary: Experiment: a situation involving chance in mathematical probability Outcome: the result of one trial of an experiment Probability: how likely an event is to happen; written as the ratio of the number of ways an

event can occur to the number of possible outcomes Prediction: a guess about something in the future

Review: Part one of this activity is a review of probability. TEKS 5.12(A) 1. Place the spinner from Student the Student sheet under the document

camera/overhead for all students to see. I have a spinner. Who can describe this spinner to me?

Students should reply that the spinner is divided into 6 equal parts with 2 parts containing a star, 1 part containing a heart, and 3 parts containing a smiley face. The fact that the 6 parts are equal in area must be stressed to the students.

What picture do you think the needle will land on when I spin the needle? Why? (a smiley face because there are more of them than the other 2)

Who remembers what it is called when I spin the spinner? (an experiment.)


An experiment in mathematics is a situation involving chance. In this example, the experiment is spinning the spinner.

Who remembers what the picture that the needle actually lands on is called? (the outcome of the experiment) An outcome is the result of a single trial in an experiment.

What are all of the possible outcomes of our experiment? (heart, star, or smiley face)

Who remembers what it is called when you really want a certain outcome in an experiment? (a favorable outcome) A “favorable outcome” is the outcome that you want to happen or the desired outcome.

Who remembers how I set up a probability answer? (like a fraction or a ratio)

Can you tell me what the numerator of the fraction (or ratio) represents? (the number of sections on the spinner that represent the favorable outcome, what you want to happen or are asked about happening)

Can you tell me what the denominator of the fraction (or ratio) represents? (the total number of possible outcomes)

Have students determine the probability of each picture on the spinner. Record the probabilities on the board.

2. Give each student a Student Sheet and a paperclip. Post three pieces of chart paper in

the front of the room. One that has a black heart at the top, one with a black star at the top, and one with a smiley face at the top.

You will spin the paperclip five times, recording your results each time in the table on your paper (using tally marks). When you are finished, I want you to write the probability of each picture on each post‐it (one for each post‐it) and go post it on the chart paper that has that picture. (E.g., If a student’s results were heart = 1/5, star=2/5, smiley face= 2/5, he or she would put each of these on a post‐it, and go post the 1/5 on the chart paper with the heart at the top, 2/5 on the chart paper with the star at the top, and so on.) Discuss results as a class. Look to see if there was a common answer for each of the pictures. Did it come out the way you would have thought?


Lesson: Part 2 of this activity incorporates using the experimental results to make predictions. TEKS 5.12(B) 3. Now we are going to use these results to help us make predictions. Who knows what

a prediction is? (Answers will vary but may include a guess about something that is going to happen in the future.) Instead of performing the experiment and giving experimental results, sometimes we are asked to make a prediction on what we think will happen next and base that prediction on results that we already have.

For example, what if we wanted to predict how many times the spinner would land on the heart if we spun it 25 more times. We already know how many times it landed on the heart when we spun it 5 times. Let’s use the fraction (or ratio) that occurred the most on our chart. Find a post‐it that has the fraction that occurred the most. Put it under the document camera or overhead so that the students can see it clearly. This is how many times we know for a FACT that it landed on the heart in five spins.

How will we write the fraction or ratio that represents how many times it lands on the heart in 25 spins? (# of times it lands on heart/25)

What will our numerator be? (the number of times it lands on the heart).

What will our denominator be? (25)

Why will it be 25 now instead of 5 like it was here (point to the five in the old probability fraction)? (because we are going to spin it 25 times now, NOT five like before).

Write the following on the board: __(The fraction from the post‐it) = ?/25 (For this part of the lesson, I will be using 1/5 to represent the fraction from the post‐it.)

Does this look like something we have done before? (Yes, it is finding equivalent fractions.)

We are just going to find the fraction (or ratio) that is equivalent to our original fraction (or ratio) that has a denominator of 25 because that is how many spins I am predicting for. Show students on board how to find equivalent fractions using the problem you already have written on the board. My example: 1/5 = ?/25 Using the identity property for multiplication, I must multiply my original fraction by a fraction equivalent to one that will give me 25 as a denominator. That fraction is 5/5. So… 1/5 x 5/5 = 5/25


Therefore, the number of times I predict my spinner will land on the heart is __(five)___ times out of the 25 times I spin it.

I want you to go into your journal and now use your results from before and predict a reasonable number of times your spinner will land on the smiley face when we spin it 25 times. Walk around the room making sure students are correctly predicting. In your journal, use your results to predict a reasonable number of times your spinner will land on the star when we spin it 65 times. Continue walking around the room making sure students are still predicting correctly.


Check for understanding with these questions:

How do we write the probability of an event? (the fraction or ratio of desired outcomes

total outcomes )

What are we looking for mathematically if we are predicting what will happen in the future based on results we already have? (We are looking for an equivalent fraction or ratio.)

Guided Practice:

Distribute the guided practice sheet. Kelsey and Steven were drawing pattern blocks out of a bag without looking. Every time a pattern block was drawn from the bag, they recorded the type of pattern block that was selected. The table shows the results.


Triangle 15

Square 23

Rhombus 17

Hexagon 25

Trapezoid 20

Based on this information, what is the most reasonable prediction for the number of times Kelsey will pull out a trapezoid in her next 200 pulls? How about in her next 250 pulls? 1. Looking at the results in the table, how many times did Kelsey pull out a trapezoid?

___(20)____.


2. How many total times did Kelsey draw from the bag to get the results shown in the table? _____(100)_____.

3. What is the probability that Kelsey will pull out a trapezoid? ___(20/100)______. 4. How many spins will it be out of when I make my prediction? _(200)_ 5. Based on the results above, how many times will Kelsey pull out a trapezoid in her next

200 pulls?_____(40)_______. 6. Based on the results above, how many times will Kelsey pull out a trapezoid in her next

250 pulls? ______(50)_________. (Hint: Try putting your results from the table above in simplest form first.)

Assessment: 1. Sandy’s mother has a box of fruit containing 12 apples, 33 pears, and 27 plums. Sandy’s

father comes in from working and adds 18 apples to the box of fruit. Sandy reaches into the box without looking and gets a pear out of three times. Based on these results, what is the most reasonable amount of pears Sandy will pull out of the box in 24 attempts?

A. 8 pears *B. 16 pears C. 11 pears D. 33 pears



they are making graphs. The table shows how many times a color is pulled without looking from the box.

Color Frequency

Red 15

Blue 10

Green 10

Purple 20

Black 25

Brown 20

Based on these results, if everyone in the next class of 25 students came through and got a marker without looking, which is the most reasonable prediction of the number of students that would have purple?

F. 2 people G. 3 people H. 4 people *J. 5 people

3. Michael is the leading scorer for his basketball team. So far this season, he has made 35

out of 45 shots attempted. Based on this information, which is the most reasonable prediction for the number of shots Michael will make out of 72 shots attempted?

*A. 56 B. 37 C. 10 D. 27


4. Mario, Simon, and Felix are on the same soccer team in a city league. They keep a record

of how many times each boy attempts a goal and how many they make. The chart shows how each one has done so far this season.

Soccer Goal Records

Name Number of Attempts

Number of Goals

Mario 21 12

Simon 31 15

Felix 21 7

Based on the results, which is the most reasonable prediction for the number of goal Mario will make in his next 35 attempts?

F. 26 goals

*G. 20 goals H. 33 goals J. 19 goals


Student Sheet: Reporting Category 5: TEKS 5.12(B) and 5.16(A)


Guided Practice: Reporting Category 5: TEKS 5.12(B) and 5.16(A)

Name: ________________________ Date: __________________ Kelsey and Steven were drawing pattern blocks out of a bag without looking. Every time a pattern block was drawn from the bag, they recorded the type of pattern block that was selected. The table shows the results.


Triangle 15

Square 23

Rhombus 17

Hexagon 25

Trapezoid 20

Based on this information, what is the most reasonable prediction for the number of times Kelsey will pull out a trapezoid in her next 200 pulls? How about in her next 250 pulls? 1. Looking at the results in the table, how many times did Kelsey pull out a trapezoid? ___________________________ 2. How many total times did Kelsey draw from the bag to get the results shown in the table? __________________________ 3. What is the probability that Kelsey will pull out a trapezoid? __________________ 4. How many spins will it be out of when I make my prediction? __________________ 5. Based on the results above, how many times will Kelsey pull out a trapezoid in her next 200 pulls? ______________________________________ 6. Based on the results above, how many times will Kelsey pull out a trapezoid in her next 250 pulls? _______________________________________ (Hint: Try putting your results from the table above in simplest form first.)


Assessment: Reporting Category 5: TEKS 5.12(B) & 5.16(A)

Name: ___________________ Date: __________________ 1. Sandy’s mother has a box of fruit containing 12 apples, 33 pears, and 27 plums. Sandy’s

father comes in from working and adds 18 apples to the box of fruit. Sandy reaches into the box without looking and gets a pear out of three times. Based on these results, what is the most reasonable amount of pears Sandy will pull out of the box in 24 attempts?

A. 8 pears B. 16 pears C. 11 pears D. 33 pears


they are making graphs. The table shows how many times a color is pulled without looking from the box.

Color Frequency

Red 15

Blue 10

Green 10

Purple 20

Black 25

Brown 20

Based on these results, if everyone in the next class of 25 students came through and got a marker without looking, which is the most reasonable prediction of the number of students that would have purple?

F. 2 people G. 3 people H. 4 people J. 5 people


3. Michael is the leading scorer for his basketball team. So far this season, he has made 35 out of 45 shots attempted. Based on this information, which is the most reasonable prediction for the number of shots Michael will make out of 72 shots attempted?

A 56 B 37 C 10 D 27

4. Mario, Simon, and Felix are on the same soccer team in a city league. They keep a record of how many times each boy attempts a goal and how many they make. The chart shows how each one has done so far this season. Soccer Goal Records

Name Number of Attempts

Number of Goals

Mario 21 12

Simon 31 15

Felix 21 7

Based on the results, which is the most reasonable prediction for the number of goals Mario will make in his next 35 attempts?

F. 26 goals G. 20 goals H. 33 goals J. 19 goals




Student Expectations: 5.12(C) The student is expected to list all the possible outcomes of a probability experiment such as tossing a coin.

Overview:

Using concrete objects or pictures to determine all possible combinations is helpful to students who have difficulty in finding combinations. Modeling all possible combinations using manipulatives and then putting these manipulatives in a tree diagram provides them with a graphic organizer to better organize their generalizations.

Materials: Food picture cards Color tiles: red, blue, green (10 of each color per student) Overhead color tiles Construction paper circles: orange and purple (4 of each color per student) Paper

Vocabulary: list, tree diagram, combinations

Procedure: 1. Today we are going to find all the possible combinations of an experiment. I need six

volunteers to come to the front of the room. Give each child a picture card (chicken, steak, orange, banana, grapes, or apple) and have students stand in a straight line in the front of the room.

The cafeteria is thinking of offering a lunch special that consists of two items: a meat and a fruit. The meat offerings are chicken and steak. The fruit offerings are oranges, bananas, grapes, or apples. How many different entrees will students have to choose from for lunch? Have students model the following possible combinations. I would like chicken and apple students to step forward. This represents one of the possible entrees for lunch. In your math journal, decide how you are going to record your answer. Now have chicken and apple students step back in the straight line. Now challenge the students to find all possible lunch entrees that could be offered. When the students feel they have found all the possible combinations, ask students with a partner to create a tree diagram to justify their findings.


Tree: Chicken/Orange Steak/Orange Chicken/Banana Steak/Banana Chicken/Grapes Steak/Grapes Chicken/Apple Steak/Apple So there are 8 different combinations.

What would happen if you had just a choice of two fruits out of the four fruits above? Apple/Banana Banana/Grapes Orange/Grapes Apple/Grapes Banana/Orange Apple/Orange

So there are six different combinations.

What would happen if we added two vegetables (carrots and peas) and only two choices were allowed. Choices must be one meat and either one fruit or one vegetable.

Chicken/Orange Chicken/Peas Steak/Orange Steak/Peas Chicken/Banana Chicken/Carrots Steak/Banana Steak/Carrots Chicken/Grapes Steak/Grapes Chicken/Apple Steak/Apple

So there are 12 different combinations.

What would happen if we added two vegetables (carrots and peas) and three choices were allowed? Choices must be one meat, one fruit, and one vegetable. Have students model this and create a tree diagram in their math journals.

I want you to look back at each of these examples we just worked in our journal and see if you can see a consistent pattern that occurs. Have students do “Think/Pair/Share” once you have given them ample time to look for a pattern. Lead students to discover that when you multiply the number of choices you have for each part of the combination, you come up with your answer. Discuss why this works mathematically.

Meat (two choices) x Fruit (four choices) x Vegetables (two choices) So, 2 x 4 x 2 = 16 different combinations.

Chicken Steak

Orange OrangeGrapes Banana GrapesBananaApple Apple


2. Now I am going to give you two paper circles, one will be orange and one will be purple

and three colors, red, blue, and green. Let’s see if we can find all of the different combinations of one color tile and one circle. Remember we need to model each combination and record what we find.

Orange Plate

Purple Plate

Shaunda rolled 3 six‐sided dice. The following numbers represent her roll.

How many three‐digit numbers can be made with the above digits if each number is used only once? Record all possible solutions.

Six different numbers: 346, 436, 463, 643, 634, 364


How did you know that you had found all of the combinations? (modeled using a tree diagram and a list)

Were you able to organize the combinations into a pattern? (Yes, first I found all of the combinations that began with the red tile. Then I did the same for the blue and green tiles.)

Can you find a strategy that will help you find all of the combinations? (tree diagram, lists, pictures–see visual for room)

Red Tile

GreenTile

BlueTile

BlueTile

Red Tile

GreenTile

3 4 6


Guided Practice: At snack time, you have a choice of a package of cookies and one drink. The choices of cookies are chocolate chip, peanut butter, or chocolate mint. The drink choices are milk or juice.

How many different combinations are possible?

Write down all of the possible combinations.

If it helps, you can use color tiles for the cookie choices and the circles for the drink choices.

(chocolate chip/milk chocolate chip/juice peanut butter/milk peanut butter/juice chocolate mint/milk chocolate mint/juice)

Assessment: 1. At the school cafeteria, Wednesday is Pizza Day. You have a choice of one meat topping,

either pepperoni, sausage, or hamburger, and a choice of thick or thin crust. Draw a model to represent the different combinations possible. How many possible combinations are there?

Six combinations 2. For her birthday, Kathryn received four new tops and three pairs of pants. How many

different combinations of one top and one pair of pants are there?

F. 7 combinations G. 10 combinations

* H. 12 combinations J. 16 combinations

3. At Math‐O‐World Theme park there are three rides and two arcade games. The park is

about to close. There is enough time to choose one ride and one arcade game. How many different combinations are possible?

Six possible combinations

Thick Thin

Pepperoni Sausage Hamburger Pepperoni Sausage Hamburger


4. Lori’s name was drawn to win a prize from the public library. Her prize was any two of the following books.

How many different combinations of two books are possible if the order in which Lori chooses the books does not matter?

Six different choices Fiction, History Fiction, Biography Fiction, Non‐Fiction History, Biography History, Non‐Fiction Biography, Non‐Fiction

Fict

ion

His

tory

Bio

grap

hy

Non

-Fic

tion


5.12C Food Cards for Lesson D

Apple Banana

Orange Grapes

Steak Chicken

Carrots Peas


Guided Practice: Reporting Category 5: TEKS 5.12(C)

Name: ____________________________ Date: __________________

At snack time, you have a choice of a package of cookies and one drink. The choices of cookies are chocolate chip, peanut butter, chocolate mint. The drink choices are milk or juice. How many different combinations are possible? Write down all of the possible combinations.

If it helps, you can use color tiles for the cookie choices and the circles for the drink choices.


Assessment: Reporting Category 5: TEKS 5.12(C)

Name: ____________________________ Date: __________________

1. At the school cafeteria, Wednesday is Pizza Day. You have a choice of one meat topping, either pepperoni, sausage, or hamburger, and a choice of thick or thin crust. Draw a

model to represent the different combinations possible. How many possible combinations are there?

2. For her birthday, Kathryn received four new tops and three pairs of pants. How many different combinations of one top and one pair of pants are there?

F. 7 combinations G. 10 combinations H. 12 combinations J. 16 combinations

3. At Math‐O‐World Theme park there are three rides and two arcade games. The park is about to close. There is enough time to choose one ride and one arcade game. How many different combinations are possible? 4. Lori’s name was drawn to win a prize from the public library. Her prize was any two of the following books.

How many different combinations of two books are possible if the order in which Lori chooses the books does not matter?

Fict

ion

His

tory

Bio

grap

hy

Non

-Fic

tion


5.12(C) Sample Space Visual for Room

Sample SpacesSet of all

possible outcomes

Ex: Find all the possible outcomesof the 2 spinners

List Table Diagram

Move forward

Move backward

1

Space

3

Spaces

2

Spaces

Move forward

Move backward

1 space

2 spaces

3 spaces

1 space

2 spaces

3 spaces

Move forward, 1 space

Move forward, 2 spaces

Move forward, 3 spaces

Move backward, 1 space

Move backward, 2 spaces

Move backward, 3 spaces3 spaces3 spaces

2 spaces2 spaces

1 space1 space

Move backward

Move forward



TEKS 5.13 The student solves problems by collecting, organizing, displaying, and interpreting sets of data.

Student Expectations: 5.13(A): The student is expected to use tables of related number pairs to make line graphs.

Overview:

This lesson will give students the opportunity to use tables of number pairs to make line graphs. Students will become fluent in plotting points.

Materials: Grid paper Markers

Vocabulary: Grid, x‐axis, y‐axis, coordinate pair, origin, point

Lesson: Have students play Tic‐Tac‐Toe on a coordinate grid to help them become flexible with reading and plotting points. 1. Students play with a partner to see who can get four of their points in a line first. 2. Each student must record a coordinate pair on paper before plotting the point on the

coordinate grid. For example, Student A writes down the coordinate point (2,2) and then plots the point on the grid. Student B writes down the coordinate point (2,3) and then plots the point.

3. Students check each other’s work to make sure that the point on the grid matches the

coordinate pair recorded on paper. 4. Students must record their coordinate pairs in a table.

Debriefing Questions: Look at the coordinate pair (3,5).

Which number identifies the x‐axis? (3)

Which number identifies the y‐axis? (5)

Which line is the x‐axis? (horizontal)

Which line is the y‐axis? (vertical)


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Guided Practice: The table below shows the coordinates of four points.

Point x y

Q 2 3

R 3 6

S 4 7

T 5 8

Write each point as a coordinate pair. Q (2,3) R(3,6) S(4,7) T(5,8)

In the ordered pair (x,y), which coordinate do you graph first? (x‐coordinate)

Which graph contains the above four points?

A.

*B. D.

Q

Q Q

Q

R R

S S

T

R S

T

RS

T

C.

T


Assessment: 1. The graph shows a figure with four points labeled.

Which table shows the coordinates of these 4 points?

A.

B.

C.

*D.

Point x y

A 4 2

B 2 3

C 4 4

D 5 2

Point x y

A 4 1

B 3 2

C 4 4

D 2 5

Point x y

A 1 4

B 2 3

C 4 4

D 2 5

Point x y

A 1 4

B 3 2

C 4 4

D 5 2

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A

B

C

D


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Assessment:

2. The graph shows a figure with 4 points labeled.

Which table shows the coordinates of these four points?

Point x y

L 5 1

M 2 3

N 2 5

P 0 6

Point x y

L 1 5

M 3 2

N 5 2

P 6 0

Point x y

L 1 5

M 2 3

N 2 5

P 6 0

Point x y

L 5 1

M 3 2

N 2 5

P 0 6

F.

*G.

H.

J.

L

Point x y A 1 4 B 3 2 C 4 4 D 5 2

M N

P


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3. The table below shows the coordinates of four points.

Point x y

E 3 4

F 5 6

G 6 8

H 8 9

Which graph contains these four points?

F

E

B.

G H

E F

G

HA. C.

*D.

E E

FF

GG

H H


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Name: _________________________ Date: __________________ The table below shows the coordinates of four points.

Point x y

Q 2 3

R 3 6

S 4 7

T 5 8

Write each point as a coordinate pair. _________________________________ ________________________________________________________________ 2. In the ordered pair (x,y), which coordinate do you graph first? _____________ 3. Which graph contains the above four points?

Q Q

Q Q

R S

T

RS

T

R S

T

RS

T

A.

B.

C.

D.



Name: _________________________ Date: __________________ The graph shows a figure with four points labeled. Which table shows the coordinates of these four points? A. B. C. D.

Point x y

A 4 2

B 2 3

C 4 4

D 5 2

Point x y

A 4 1

B 3 2

C 4 4

D 2 5

Point x y

A 1 4

B 2 3

C 4 4

D 2 5

Point x y

A 1 4

B 3 2

C 4 4

D 5 2

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A

B

C

D


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2. The graph shows a figure with four points labeled. Which table shows the coordinates of these four points?

Point x y

L 5 1

M 2 3

N 2 5

P 0 6

Point x y

L 1 5

M 3 2

N 5 2

P 6 0

Point x y

L 1 5

M 2 3

N 2 5

P 6 0

Point x y

L 5 1

M 3 2

N 2 5

P 0 6

F.

G.

H.

J.

L

M N

P


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A C.

B. D.

3. The table below shows the coordinates of four points.

Point x y

E 3 4

F 5 6

G 6 8

H 8 9

Which graph contains these four points?

E

F G

H

G

G

G

E

E E

F

F F

H

H H



TEKS 5.13: The student solves problems by collecting, organizing, displaying, and interpreting sets of data.

TEKS 5.14: The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school. Student Expectations: 5.13(B) The student is expected to describe characteristics of data presented in tables and graphs including median, mode, and range. 5.14(A) The student is expected to identify the mathematics in everyday situations.

Overview:

This lesson will give students the opportunity to collect their data and create a graph or table in order to determine the mode, median, and range. This will help students to interpret sets of data.

Materials: Chart paper (grid paper if available) Markers Rulers Scissors Note cards Colored dot stickers

Vocabulary: Graph, table, median, middle number, mode, range, numerical data, categorical data, survey

Lesson: Teachers need to introduce data collecting ideas the day before this lesson. Have students select a topic and gather information (through surveys) throughout the following day. Students might ask classmates about their favorite football team or how many hours they watch T.V. in one week.

How will you collect the data? (tally marks, chart, table) 1. Discuss the gathered information and the results of the student surveys.

What are some ways to show your information? Is it easier to compare the data in a graph, table, list, or picture? Have the students share their opinions with the group.

2. Have students create a table or bar graph with the information collected. Table:

What does each column represent?

What does each row represent?


Bar Graphs:

What will go on the x‐axis?

What will go on the y‐axis?

What is the scale that you will use for your x and y axis? 3. Discuss with students the word NOT when interpreting conclusions.

Sometimes the question can be asked, “Which statement is NOT true? (Students should think of this as a false statement.)

4. Have students write statements based on the information collected. For example, the football team with the most votes was the Dallas Cowboys. The range of the data for watching T.V. in one week was 12.

5. On a note card, have students write three true statements and one false statement (in no particular order). Students need to include information about range, median, and mode.

6. Have students post their graph and note card around the room. Once all are posted, have a gallery walk where students walk around with colored dot stickers and stick a dot by the statement they believe is false.

7. Have students share graphs and the correct answers when the gallery walk is complete. Have a class discussion on the graphs where the false statement was not apparent to the whole class (this can be seen by having dots posted on more than one answer).


What is range? (Range is the difference between the largest number and the smallest number in the data, and subtract to find the difference.)

What is the median? (The median is the middle value when all the data is listed in numerical order. If the data does not have a single middle number, find the two numbers in the middle. Add up the two middle numbers and divide by two.)

What is mode? (The number that appears most frequently in a set of numbers is the mode. There may be one, more than one, or no mode.)

Have students compare one group to another. Other example type of data analysis questions could be:

If five more people had voted for the Washington Redskins, how many more students would have voted for the Dallas Cowboys than the Washington Redskins?

If 75 people were surveyed and the remaining votes had been for the Miami Dolphins, how many people’s favorite team would have been the Dolphins?


Guided Practice: The table below shows the number of points that the girls’ basketball team scored in the last six games. Girls’ Basketball Team

Game Score

1 47

2 40

3 52

4 40

5 55

6 44

1. Which statement about the data shown in the table is NOT true?

*A. The range of the data is 6 B. The median number is 45 C. The girls combined scores in games 1 and 3 were the same as in games 5 and 6 D. The mode is 40.

2. List the scores in order from lowest to highest. (40, 40, 44, 46, 52, 55) 3. Explain how to find the range. (You subtract 40 from 55. The answer is 15.) 4. Explain how to find the median. (You find the middle data. The answer is 45.) 5. Write an equation showing how many combined points were scored in games 1 and 3.

(47 + 52 = 99) 6. Write an equation showing how many combined points were scored in games 5 and 6.

(55 + 44 = 99) 7. What is the mode? (40 is the most frequent answer.)


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Assessment: 1. The bar graph below shows the number of DVD’s purchased at a store in one week.

Which number represents the range?

*A. 45 B. 50 C. 40 D. 35

2. The table below shows the salaries for 8 teachers at a school. Teacher 1 2 3 4 5 6 7 8

Salary $26,200 $36,000 $38,500 $40,050 $32,000 $28,990 $39,750 $29,000

Which statement about the data shown in the table is NOT true?

*F. The median number is 36,000 G. The range is 13,850 H. The median is greater than the range J. The total for the 8 teachers is $270,490


3. Bikes ‘R’ Us sold a total of 295 bikes from January through July. The graph below shows

the number of bikes sold for the first five months.

If they sold 35 bikes in July, which of the seven months would represent the median?

A. March B. July *C. June D. January

Number of Bikes Sold

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10

20

30

40

50

60

70

January February March April May


Guided Practice: Reporting Category 5: TEKS 5.13(B) and 5.14(A)

Name: _________________________ Date: __________________ The table below shows the number of points that the girls’ basketball team scored in the last six games.

Girls’ Basketball Team

Game Score

1 47

2 40

3 52

4 40

5 55

6 44

1. Which statement about the data shown in the table is NOT true?

A. The range of the data is 6 B. The median number is 45 C. The girls combined scores in games 1 and 3 were the same as in games 5 and 6 D. The mode is 40.

2. List the scores in order from lowest to highest. ___________________________________________________________________ 3. Explain how to find the range.

________________________________________________________________________ ________________________________________________________________________

4. Explain how to find the median.

________________________________________________________________________ ________________________________________________________________________

5. Write an equation showing how many combined points were scored in games 1 and 3.

___________________________________________ 6. Write an equation showing how many combined points were scored in games 5 and 6. ___________________________________________ 7. What is the mode? _________________________________________________


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Assessment: Reporting Category 5: TEKS 5.13(B) and 5.14(A)

Name: _________________________ Date: __________________ The bar graph below shows the number of DVD’s purchased at a store in one week.

Which number represents the range?

A. 45 B. 50 C. 40 D. 35

2. The table below shows the salaries for 8 teachers at a school.

Teacher 1 2 3 4 5 6 7 8

Salary $26,200

$36,000

$38,500

$40,050

$32,000

$28,990

$39,750

$29,000

Which statement about the data shown in the table is NOT true?

F. The median number is 36,000. G. The range is 13,850. H. The median is greater than the range. J. The total for the 8 teachers is $270,490.


3. Bikes ‘R’ Us sold a total of 295 bikes from January through July. The graph below shows the number of bikes sold for the first five months.

If they sold 35 bikes in July, which of the seven months would represent the median?

A. March B. July C. June D. January

Number of Bikes Sold

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TEKS 5.13: The student solves problems by collecting, organizing, displaying, and interpreting sets of data.

Student Expectations: 5.13(C) The student is expected to graph a given set of data using an appropriate graphical representation, such as a picture or line graph.

Overview: Graphical displays provide ways to organize and display data. Students need to understand the process and steps that are required to graph a set of data. Creating a graph requires students to determine the graph to use, label the graph and axes, and determine an appropriate interval and scale for the given data. Bar graphs, pictographs, and circle graphs are commonly used to compare data.

A bar graph uses solid bars, vertical or horizontal, to compare quantities.

A pictograph uses pictures or symbols to compare data. A pictograph has a key that explains what each picture or symbol represents.

A circle graph relates the parts to the whole.

A line graph is commonly used to show the change of data over time. To create a graph, a title should be chosen for the graph. Each axis needs to be drawn and labeled. The next step is to determine an appropriate scale. The scales are the numbers that are on each axis. The difference between the numbers is called an interval.

Materials: Big chart or graph paper Markers Rulers

Vocabulary: Bar graphs, line graphs, pictographs, data, key, axis, horizontal axis, vertical axis, scale, interval

Lesson: 1. Today we are going to study some different ways to organize and display data or

information. What are some ways that you have seen data or a group of numbers organized? (Possible answers include tables, charts, graphs, least to greatest, greatest to least)

2. What kind of graphs have you seen? (bar graphs, pictographs, line graphs, circle graphs)


As you discuss the different kinds of graphs, show the examples given on the Student Sheet.

Can you think of some examples when we use bar graphs? (Student responses will vary but could include compare something like favorite candy.) Lead them to “compare two or more things.”

Can you think of some examples when we use pictographs? (Student responses will vary but could include compare information just like in a bar graph but want to create a “jazzier” graph.) Lead them to “compare two or more things.”

Can you think of some examples when we use circle graphs? (Student responses will vary but could include comparing parts to a whole. For example, a circle graph might be used to compare the favorite sport of a group of fifth grade students.) Lead them to “compare parts to a whole.”

Can you think of some examples when we use line graphs? (Student responses will vary. You may need to help them understand that line graphs are generally used to show a change in data over time. An example might be the change in population of a city.)

3. Now let’s look at some data. Give the students a set of data such as average high

temperatures in Fahrenheit for Austin for the first six months of the year.

Month Average High Temperature

January 60

February 64

March 72

April 79

May 85

(Source: U. S. National Climatic Data Center, Asheville, N.C.)

4. What kind of graph do you think we should use to create a graph for this data? Is it

comparing data or is it showing a change over time? (Change over time) Since it is showing a change in temperature over time, what kind of graph should we create? (line graph) What are some things we need to think about to create this line graph? (title of the graph, labeling the axes, the scale, and the interval)


This example has a scale of 20.

The next example has a scale of 10.

5. The fifth grade students in one school were asked to tell what their favorite television

show is. Here are the results of that survey.

Favorite Type of TV Show Number of Students

Sports 55

Reality 60

Comedy 35

Wildlife 20

Mystery 5

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20

40

60

80

100


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6. What kind of graph do you think we should use to create a graph for this data? Is it comparing data or is it showing a change over time? (comparing data) Since it is comparing data, what kind of graph should we create? (bar graph or pictograph) Guide them to consider using a pictograph. What are some things we need to think about to create a pictograph? (title of the graph, the key). I want you to go into your journal and create a pictograph for this data. (An appropriate key for this information would be each picture represents five students. Allow students to figure this out on their own. If you see a student drawing one picture for each student, lead them to understand when using larger numbers, you allow each picture to represent more than one.)


How do you decide which graphical representation will best represent the data? (It depends on the kind of data.)

When would you use a bar graph? (to compare data)

When would you use a line graph? (to show change over time)

When would you use a pictograph? (to compare small unit data or data that can be easily represented using a key of increments)

When analyzing a graph, what are the key components of the graph? (the title of the graph, what the graph is about, the intervals)


Guided Practice: Create a graph using this data. Please put your graph on a big sheet of graph paper and use a ruler when drawing straight lines. When you have completed your graph, display it in the room. Mrs. Russell’s math students surveyed fifth grade students to determine their favorite food. Here are the results of their survey.

Favorite Food Number of students

Pizza 95

Hamburgers 52

Corn Dogs 14

Spaghetti 8

Tacos 31

Use this information to create a bar graph, a line graph, or pictograph. Explain why you chose that graph. 1. What kind of graph are you going to create? (bar graph) 2. What is the title of your graph? (Favorite Food of 5th Grade Students) 3. What are you going to label the horizontal axis? (number of students) 4. What are you going to label the vertical axis? (Favorite Food) 5. What interval are you going to use? (could be by 2,5,10, etc.) 6. Now create your graph. (sample graphs) Favorite Food of 5th Grade Students

0 20 40 60 80 100

pizza

hamburger

corn dog

spaghetti

tacos

Number of Students

Food


After students have displayed their graphs, discuss the different ways the data was organized.

Assessment: 1. The table below shows the number of games four NBA basketball players played in

during the 2003‐2004 regular season.

Player Number of Games

Tim Duncan 69

Yao Ming 82

Tony Parker 75

Shaquille O’Neal 67

(www.nba.com) Which bar graph matches the data in the table? A.

Favorite Food of 5th Grade Students

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pizza hamburger corn dog spaghetti tacos

Favorite Food

Number of

Students

Number of Games Played

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TimDuncan

Yao Ming TonyParker

ShaquilleO'Neal

Name of Player

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d


*B. C. D.

Data extracted from (www.nba.com)


0102030405060708090

TimDuncan

Yao Ming TonyParker

ShaquilleO'Neal

Name of Player

Nu

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of

Ga

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0102030405060708090

Tim Duncan Yao Ming TonyParker

ShaquilleO'Neal

Name of Player

Nu

mb

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f G

ames

Pla

yed


0102030405060708090


ShaquilleO'Neal

Name of Player

Nu

mb

er o

f G

ames

Pla

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2. The chart below shows the number of movies rented from Movies ‘R’ Us Store for the past five days:

Day Number of

Movies Rented

Wednesday 20

Thursday 25

Friday 50

Saturday 75

Sunday 15

Which of these graphs best represents the same data?

*F. G. H.

Movie Rentals

0 10 20 30 40 50 60 70 80

Wednesday

Thursday

Friday

Saturday

Sunday

Day

of

the

Wee

k

Number of Movies Rented

Movie Rentals

Wednesday

Thursday

Friday

Saturday

Sunday

Movie Rentals

0

10

20

30

40

50

60

70

80

Wednesday Thursday Friday Saturday Sunday

Day of the Week

Nu

mb

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ente

d


J. 3. The newspaper has published a chart showing the population of Williamson County for

the past ten years. You are going to create a graph to show this information. What would be the most appropriate graph to display this data?

A. Bar graph B. Circle graph *C. Line graph D. Pictograph

Movie Rentals

0

20

40

60

80

100


Day of the Week

Nu

mb

er o

f M

ovi

es

Ren

ted


Student Sheet: Reporting Category 5: TEKS 5.13(C)

Circle Graph Line Graph

Bar Graph Pictograph


Guided Practice: Reporting Category 5: TEKS 5.13(C)

Name: ____________________________ Date: __________________

Mrs. Russell’s math students surveyed fifth grade students to determine their favorite food. Here are the results of their survey:

Favorite Food Number of students

Pizza 95

Hamburgers 52

Corn Dogs 14

Spaghetti 8

Tacos 31

Use this information to create a bar graph, a line graph, or pictograph. Explain why you chose that graph.

1. What kind of graph are you going to create?

2. What are you going to title your graph?

3. What are you going to label the horizontal axis?

4. What are you going to label the vertical axis?

5. What interval are you going to use?

6. Create a graph to display the data.


Assessment: Reporting Category 5: TEKS 5.13(C)

1. The table below shows the number of games four NBA basketball players played in during the 2003‐2004 regular season.

Player Number of Games

Tim Duncan 69

Yao Ming 82

Tony Parker 75

Shaquille O’Neal 67

(www.nba.com) Which bar graph matches the data in the table?

A.

B.


0102030405060708090

TimDuncan

Yao Ming TonyParker

ShaquilleO'Neal

Name of Player

Nu

mb

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of

Ga

me

s

Pla

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d


0102030405060708090

TimDuncan

Yao Ming TonyParker

ShaquilleO'Neal

Name of Player

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C.

D. Data extracted from (www.nba.com) 2. The chart below shows the number of movies rented from Movies ‘R’ Us Store for the past

five days.

Day Number of Movies

Rented

Wednesday 20

Thursday 25

Friday 50

Saturday 75

Sunday 15


0102030405060708090


ShaquilleO'Neal

Name of Player

Nu

mb

er o

f G

ames

Pla

yed


0102030405060708090


ShaquilleO'Neal

Name of Player

Nu

mb

er o

f G

ames

Pla

yed


Which of these graphs best represents the same data? F. G. H.

Movie Rentals

0 10 20 30 40 50 60 70 80

Wednesday

Thursday

Friday

Saturday

Sunday

Day

of

the

Wee

k

Number of Movies Rented

Movie Rentals

Wednesday

Thursday

Friday

Saturday

Sunday

Movie Rentals

0

10

20

30

40

50

60

70

80


Day of the Week

Nu

mb

er o

f M

ovi

es R

ente

d


J. 3. The newspaper has published a chart showing the population of Williamson County for the

past ten years. You are going to create a graph to show this information. What would be the most appropriate graph to display this data?

A. Bar graph B. Circle graph C. Line graph D. Pictograph

Movie Rentals

0

20

40

60

80

100


Day of the Week

Nu

mb

er o

f M

ovi

es

Ren

ted

Copyright©2011 ESC Region XIII 5.4A, 5.14B, 5.14C


TEKS 5.4: The student estimates to determine reasonable results. Student Expectations: 5.4(A) The student is expected to use strategies, including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems. 5.14(B) Solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. 5.14(C) Select or develop an appropriate problem‐solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

5.4 TEKS has been divided into two separate lessons. Lesson one of two uses rounding as a type

of estimation. Lesson two of two uses compatible numbers as a type of estimation.

Overview: This lesson will give students the opportunity to round whole numbers and decimals. Students will hunt through newspaper ads and magazines as they compete in a rounding challenge.

Materials: Newspaper ads or catalogs Scissors Glue Chart paper Markers

Vocabulary: round, whole numbers, decimals, digits, tenths, hundredths, reasonable, compatible

Lesson: Teacher note: Students are expected to use different strategies to estimate. The suggested types of estimation strategies from TEA include rounding and compatible numbers. Prior to this lesson, have students bring in newspaper ads (from Sunday’s paper) and old magazines. 1. Today we are going to practice rounding whole numbers and decimals. What does it mean

to round a number? (Answers will vary but may include finding the closest multiple of ten, hundred, or other place value to your number.)

Why do we round numbers in math sometimes? (Answers will vary but may include to make a number that is easier to work with.)


Rounding allows you to create numbers you can work with mentally. Often times when you are out in the real world you do not have pen and paper to work a problem. You have to do it mentally. What are some examples of when we use mental math in the real world? (Answers will vary. Make a list of what students say on the board.)

2. There are several different strategies to use when rounding. Let’s review a couple of them. Review the “traditional rounding” strategy.

Example: Round 168 to the tens place. The student underlines the 6: 168. Since the digit to the right of the underlined digit is greater than 5, the 6 would be increased to the next highest value, 7, and everything after it would be replaced with zeros. So 168 would become 170 when it is rounded to the tens place.

Rounding rules:

Have students underline the place value, which they have been instructed to round.

Then instruct students to look only at the digit to the right of the underlined digit. If the digit to the right is a 0, 1, 2, 3, or 4, do not change the underlined digit, and the remaining digits to the right of the underlined digit become zeros.

If the digit to the right of the underlined number is a 5, 6, 7, 8, or 9, increase the underlined number to the next highest value, and change all digits to the right of the underlined digit to zeros.

If the underlined digit is a 9 and the digit to the right is greater than 5, then the 9 becomes a 0, and the next digit to the left of the 0 is increased to the next highest value.

Review the “rounding using a number line” strategy. Example: Round 168 to the tens place.

The student visualizes or makes a number line. Since we are rounding to the nearest ten, we focus on what multiples of ten 168 would fall between on the number line. It would be 160 and 170. Then students decide which multiple of ten 168 is closest to when put on the number line: 160 or 170. 168 is closest to 170; therefore, 168 rounds to 170.

Allow students to choose which strategy makes sense to them. Practice rounding a few whole numbers and decimals to make sure everyone has it.

3. Now that we have reviewed rounding, you are all ready for the rounding challenge.

Rounding Challenge: You may have students work independently or with a partner. Each person will get newspaper ads or a magazine to look through. They are to find 10 items (no more, no less) that when rounded to the tenths place gets them as close to $100 without going over as possible. Have them cut out each item (including the price), glue on chart paper, and write the rounded amount beside it. They may keep a running total record on scratch paper if they would like. Once it is glued on the chart paper, they must keep that item. Have students post their chart paper around the room and have a gallery walk, so students can see what other’s purchased.



If you have $0 .45, what is the nearest tenth? ($0.50)

If you have $0.99, what is the nearest tenth? ($1.00)



What words will I see in word problems that let me know that I am not looking for an exact answer? (about, estimate, closest, approximately)

Guided Practice:

The table below shows items that are sold at the school store.

Item Cost

Candy $0.29


Markers $2.99


Neon Pens $0.69

Soda $0.84

Pencils $0.49

If John bought three neon pens, one spiral notebook, five pencils, and a soda, about how much money will he spend?

A. $3.10 B. $5.60 * C. $6.50 D. $6.70

1. What items is John buying? ____(neon pens, spiral, pencils, soda)___ 2. What word in my question tells me that I am not looking for an exact answer? _____(about)_______ 3. Round the price of each of these items to the nearest tenth. Pens: $0.70 Spiral: $1.10 Pencils: $0.50 Soda: $0.80 4. About how much will three pens cost? ___($2.10)________ 5. About how much will five pencils cost? _______($2.50)______ 6. What operation do I need to do to figure out how much money he will spend at the school

store? ____(addition)______ 7. Solve the problem in the space below. 2.10 1.10 2.50 + 0.80 6.50


Assessment: 1. The baseball team participated in two tournaments last week and drove a total of 611 miles.


A. 936 B. 325 *C. 286 D. 314

2. Candy went to the store to buy some grocery items. She bought the items listed below. If

Candy paid with a $10 bill, about how much money did she have left?

Milk: $2.79 Bag of chips: $0.89 Bananas: $1.33 Cookies: $2.13 F. $7.00 *G. $4.00 H. $5.00 J. $2.00



A. less than $100 B. between $100 and $130 *C. between $130 and $160 D. more than $160


third graders and 164 fourth graders. About how many students are in fifth grade at Fairview Elementary school?

* F. 190 students G. 180 students H. 510 students J. 220 students


Guided Practice: Reporting Category 1: TEKS 5.4(A) and 5.14(B)(C)

Name: _________________________ Date: __________________ The table below shows items that are sold at the school store. If John bought three neon pens, one spiral notebook, five pencils, and a soda, about how much money will he spend?

A. $3.10 B. $5.60 C. $6.50 D. $6.70

1. What items is John buying? ______________________________________________

2. What word in my question tells me that I am NOT looking for an exact answer? ________________________________________

3. Round the price of each of his items to the nearest tenth. 4. About how much will three pens cost? _________________________

5. About how much will five pencils cost? ________________________

6. What operation do I use in this problem to figure out how much money he will spend at the school store? ____________________________________________

7. Solve the problem in the space below.

Item Cost

Candy $0.29


Markers $2.99


Neon Pens $0.69

Soda $0.84

Pencils $0.49



Name: ________________________ Date: __________________ 1. The baseball team participated in two tournaments last week and drove a total of 611 miles.


A. 936 mi. B. 325 mi. C. 286 mi. D. 314 mi.

2. Candy went to the store to buy some grocery items. She bought the items listed below.

Milk: $2.79 Bag of chips: $0.89 Bananas: $1.33 Cookies: $2.13

If Candy paid with a $10 bill, about how much money did she have left?

F. $7.00 G. $4.00 H. $5.00 J. $2.00




A. less than $100 B. between $100 and $130 C. between $130 and $160 D. more than $160


third graders and 164 fourth graders. About how many students are in fifth grade at Fairview Elementary school?

F. 190 students G. 180 students H. 510 students J. 220 students

Copyright©2011 ESC Region XIII 5.4A, 5.14C


TEKS 5.4: The student estimates to determine reasonable results. Student Expectations: 5.4(A) The student is expected to use strategies, including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems. 5.14(C) Select or develop an appropriate problem‐solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

5.4 TEKS has been divided into two separate lessons. Lesson one of two uses rounding as a type

of estimation. Lesson two of two uses compatible numbers as a type of estimation.

Overview: This lesson will give students the opportunity to practice using compatible numbers while racing to make 100.

Materials: Student Sheet #1 Student Sheet #2 Markers or colored pencils

Vocabulary: estimate, reasonable, round, compatible numbers, compose, decompose

Lesson: Teacher note: Using compatible numbers is a type of estimation. There are no specific conforming rules for this type of estimation. Compatible numbers can be referred to as “friendly numbers.” For example 13 may not be considered to be a “friendly number.” Students may choose to use 10 or 15. Usually a student will consider a number ending in a 5 or 0 to be “friendly.” Stress to students they are to choose their numbers. Students should have numerous experiences comparing their estimates to the actual answer in order for students to develop reasonableness. Compatible numbers and rounding could be used simultaneously to determine if their answers are reasonable estimates.


1. Today I am going to be using compatible numbers to estimate. Sometimes compatible numbers are referred to as “friendly numbers” because they are easy to work with. I am going to use the problem 13 + 12 as an example. Let’s pretend that I do not like to work with 13 and do not think it is very friendly. I might want to change the number 13 to the number 12. That would make the problem 12 + 12, which would be easier to add. Let’s look at other ways to change the problem 13 + 12. The teacher will put the other examples of the problem on the board or overhead. Can you think of other ways to change the problem? (Answers will vary.)

E.g., 13 + 12 (10+3) + (10+2) (10+10) + (3+2) 20 + 5 25

E.g., 13 + 12 10 + 10 20

E.g., 13 + 12 (13+2) + (12‐2) 15 + 10

2. Now it’s your turn to use compatible numbers. Work with your partner on the problem 17 + 19. Let’s see how many different ways you can use compatible numbers to solve the problem. Be ready to share your compatible numbers with the class. After the students have presented their solutions, the teacher may want to share some of the examples below.

E.g., 17 + 19

15 + 20 35

E.g., 17 + 19

17 + 20 37

E.g., 17 + 19 20 + 20 40

Note: Using decomposition numbers can sometimes give you an exact answer.

Note: Should a student use 10 + 10, you get 20. This is not an exact answer, but an estimated answer.

Note: Should a student use 15 + 20, the answer is close to the exact answer.

Note: Should a student use 17 + 20, the answer is closer to the exact answer.

Note: Should a student use 20 + 20, the answer is not as close to the exact answer. This is an example where compatible number is more exact than rounding.



E.g., 17 + 19 (10+5+2) + (10+5+4) (10+10) + (5+5) + (2+4) 20 + 10 + 6 36

E.g., 17 + 19 (17‐1) + (19+1)

16 + 20

E.g., 17 + 19 (17+3) + (19‐3) 20 + 16 36

3. How would you use compatible numbers to solve the problem 27‐14? Work with your

partner again to solve the problem in several different ways. After the students share their solutions, show the sample below.

Sample solutions: E.g., 27 – 14

(24+3) – (14) (24‐14) + 3 10 + 3 13

E.g., 27 – 14

30 – 10 20

E.g., 27 – 14

30 – 10 20

4. Talk with students about “making sets of 10” when adding. This is another way to use

compatible numbers. When adding a long list of numbers, it is sometimes useful to look for two or three numbers that can be grouped to make sums of 10 or 100. Often the numbers in the list can be adjusted slightly to produce these groups of 10 or 100 to make finding an estimate easier. E.g., 23 + 17 = 40

Note: Should a student use decomposition, the answer is exact.



Note: This is not a close estimate to actual answer. This is why students should be comparing estimate to actual.

3 + 7 = 10 so…

20 + 10 + 10 = 40


5. You may have students work individually or with a partner. Distribute Student Sheet #1 to each student/group face down. Students MAY NOT use pencils or scratch paper in this activity. They may only use the marker to write their answer (no other marks can be made on the sheet). Set the timer for 1‐2 minutes (depending on the ability level within your class). Have students turn over their paper and complete as many as they can using compatible numbers in the time given. The total of each line goes in the box on the right and the total of all of the sums goes in the very bottom box. All markers must be put down when the timer goes off. Discuss the compatible numbers within each row as a class.

6. Now that you have this compatible number or “friendly numbers” thing down, let’s

have a race. I am going to give you a six by six grid that has numbers in it. I want you to find as many sets of 100 as you can. A set can be two or more numbers that are beside each other horizontally or vertically. They may NOT be diagonal. When you find a set, circle it. You may use a number in more than one set. You MUST find these sets using compatible numbers. You may not use scratch paper or the sides of this paper to do any computations. EVERYTHING IS MENTAL! Are there any questions?

Pass out Student Sheet #2 face down to each student. Have students use markers or colored pencils to circle their sets. Walk around making sure everyone is computing mentally and not on paper or the desk. Give class as much time as you feel appropriate for them to find as many combinations as they can. When finished, have a class discussion on the different strategies that students used to find the compatible numbers as quickly as they could.


What are compatible numbers? (friendly numbers – numbers that work well together.)

What does it mean to compose numbers? (put numbers together)

What does it mean to decompose numbers? (take numbers apart)


Guided Practice: Wraps and Ribbons had all of their seasonal ribbon on sale for the same price. The chart below shows how much they sold each day.


Monday 58

Tuesday 37

Wednesday 42

Thursday 30

Friday 83


*A. $2 B. $3 C. $4 D. $5

1. What is the total amount of ribbon they sold during these five day? ___________(150 yards)____________ 2. How did you get this information?

____(I added the numbers in the chart together.)__________ 3. What compatible numbers could you use in the chart to make it easier? ___(58+42=100 and 37+83=120 and 120+30=150)____ 4. How much money did they make during their sale last week? _____($315)________________ 5. How did you get this information? _____(It was given in the problem.)________ 6. What operation should be done to find out the price of each yard? ____________

(division)________________ 7. Using compatible numbers, what will that equation look like? (300 ÷ 150 = 2)_______ 8. Explain in words why you chose those two compatible numbers to make this problem

easier? _____(Answers will vary.)______


Assessment: 1. Ms. Adams ordered pencils and pens for the teachers. Each package contained 36 pens.

Each pack contained 18 pencils. Ms. Adams ordered three packages of pens and five packs of pencils. Which is the best estimate of the total number of pens and pencils Ms. Adams ordered?

A. 140 B. 175 *C. 220 D. 260



*F. $3.00 G. $4.00 H. $5.00 J. $6.00



A. $5 *B. $9 C. $13 D. $16

4. Ms. Harper drove 76 miles every day Monday through Friday. About how many miles did Ms.

Harper drive altogether? (Use compatible numbers below to solve.)


Student Sheet #1 Reporting Category 1: TEKS 5.4(A) and 5.14(C)


Student Sheet 2: Reporting Category 1: TEKS 5.4(A) and 5.14(C)

Making 100

18 23 59 55 45 74

15 46 50 13 87 36

46 46 49 28 23 15

39 8 66 29 25 45

38 43 57 28 17 5

62 81 19 72 83 35


Guided Practice: Reporting Category 1: TEKS 5.4(A) and 5.14(C)

Name: ______________________ Date: __________________ 1. Wraps and Ribbons had all of their seasonal ribbon on sale for the same price. The chart

below shows how much they sold each day.


A. $2 B. $3 C. $4 D. $5

1. What is the total amount of ribbon they sold during these five days?

____________________________________________________________________ 2. How did you get this information? ________________________________________

____________________________________________________________________ 3. What compatible numbers could you use in the chart to make it easier? ____________________________________________________________________ 4. How much money did they make during their sale last week? __________________ 5. How did you get this information? ________________________________________ 6. What operation should be done to find out the price of each yard? ______________ 7. Using compatible numbers, what will that equation look like? __________________ ____________________________________________________________________ 8. Explain in words why you chose those two compatible numbers to make this problem

easier? ________________________________________________________________

_______________________________________________________________________


Monday 58

Tuesday 37

Wednesday 42

Thursday 30

Friday 83


Assessment: Reporting Category 1: TEKS 5.4(A) and 5.14(C)

Name: ____________________________ Date: __________________ 1. Ms. Adams ordered pencils and pens for the teachers. Each package contained 36 pens. Each pack contained 18 pencils. Ms. Adams ordered three packages of pens and five packs of pencils. Which is the best estimate of the total number of pens and pencils Ms. Adams ordered?

A. 140 B. 175 C. 220 D. 260

2. Jackie went to the store. She bought some chocolate milk for $1.49, a pack of gum for $0.99, and a candy bar for $0.59. What is the best estimate of how much Jackie spent?

F. $3.00 G. $4.00 H. $5.00 J. $6.00

3. Johnny bought a cordless phone on sale for $15.99. The regular price of the phone was $20. He also bought an alarm clock on sale for $7.89. The regular price of the clock was $13. What is the best estimate of the total amount of money Johnny saved by buying the phone and clock on sale?

A. $5 B. $9 C. $13 D. $16


Ms. Harper drive altogether? (Use compatible numbers below to solve)


STAAR Reporting Category 3: Geometry and Spatial Reasoning: The student will demonstrate an understanding of geometry and spatial reasoning.

TEKS 5.7: The student generates geometric definitions using critical attributes.

Student Expectations: 5.7(A) The student is expected to identify essential attributes including parallel, perpendicular, and congruent parts of two‐ and three‐dimensional geometric figures. 5.16(A) Make generalizations from patterns or sets of examples and nonexamples.

TEKS 5.7(A) has been divided into three separate lessons. Lesson 1 of 3: Identify critical attributes of two‐dimensional geometric shapes. *The Assessment for 5.7 follows lesson #3.

Overview: The students will make vocabulary cards (two dimensional figures) to demonstrate the meaning of words using pictures and definitions modeled by the teacher. Students will also give their own examples of what the attribute means to them. Students will then play a matching activity to assess their understanding.

Materials: One copy of geometric definitions using critical attributes for teacher Pattern blocks (one of each block per student) Rulers 4 x 6 ruled index cards (20 per student) Note: You can have students bring spiraled note cards or tape cards on a piece of card stock paper and make a flip chart. Guided Practice requires: one copy of two‐Dimensional Figure Cards per student Straws/pipe cleaners

Vocabulary: parallel, perpendicular, two‐dimensional, polygon (regular and irregular), triangle, quadrilateral, pentagon, hexagon, octagon, quadrilateral, parallelogram, rectangle, rhombus, square, trapezoid, right angle, acute angle, obtuse angle, congruent, vertex Note: An attribute is a characteristic that helps define a figure Example: A parallelogram has four sides with opposite sides parallel and opposite sides

congruent.


Lesson: 1. Distribute 4 x 6 index cards to the students. Draw a model of your 4 x 6 index card on the

board.

Now on your 4 X 6 index card I want each of you to divide the card into four parts.

Write the word, parallel in the first box starting on the upper left hand side. Ask students: Could someone draw parallel lines on the board?

Make sure student draws the parallel lines in the upper right hand corner of his or her card. Once an appropriate drawing of parallel lines is drawn on the board, instruct students to copy this onto their note card.

Now, move down to the bottom left box to write the definition of parallel lines. Allow students to derive as much about the definition as they can from their drawing or examples of parallel lines in the room.

In the bottom right hand box, I would like for you to draw a Picture that reminds you of what parallel lines look like in the real world. Ask students after a minute or two of reflecting, What did you draw? It is very important that children come up with a meaning that makes sense to them. The idea of a ladder might be their example. The ideal situation would be to find something from the classroom or examples from the real world. This is a great tool to use with ELL learners to connect vocabulary to visuals.

2. Continue this style of inquiry with the students until all terms have been defined and

modeled. Pattern blocks are a great tool to use as a visual. Make sure students use some real world connection or example that they can relate to on their vocabulary cards. It is imperative that the definitions, pictures, and personal associations be mathematically correct.

3. Some students might be able to immediately make their cards without any instruction. You

could allow students to review the vocabulary words with a partner and try to complete as many vocabulary cards as possible. Then you could discuss orally the cards made. Remember, each card may be a little different. It is especially important that the students use objects or pictures to visualize their figure and analyze the critical attributes of the vocabulary words. Personal meanings of the terms will help students to recall figures and their attributes.

4. Once the cards are complete, have the students review each of their note cards before

attempting the guided practice matching activity.

parallel

Lines that do not intersect and would not ever cross if they were extended.

Ladder


Debriefing Questions: Here are some sample guiding questions that could be used either as students are making vocabulary cards or after the completion of their cards.

For perpendicular lines: If I move the two lines and have them cross or intersect like the letter T, what kind of lines are these? (perpendicular lines). Help me think of other examples that could represent perpendicular lines.

Polygons are 2‐dimensional made of line segments. Name some polygons. (triangle, square, rectangle, etc). Closed figures that are not made of line segments are not polygons. Which shape could not be a polygon? (circle)

If I use four straws and lay each one perpendicular to another (like a square or rectangle), what kind of figure have I made? (This would be a polygon: a closed figure made by joining line segments. Polygons are defined by number of sides and angles.)

Using pattern blocks, ask the students to name the geometric figure? How would you describe this figure? (hold one up) Are any of the sides parallel? Are any of the sides congruent? Are any of the angles congruent? A figure with all of the sides congruent and all of the angles congruent is called a regular figure. Are any of these shapes regular? Why or why not?

Do you remember how to define a parallelogram? Are rectangles and squares also parallelograms?

Guided Practice:

This activity is to be done without the note cards. It could be done the next day or immediately following the students reviewing of cards. 1. Distribute one copy of the two‐dimensional cards to each student. 2. Students should separate the picture card from the definition/attribute card by cutting along the solid lines. 3. Shuffle and put the attribute cards in one pile face down on the desk. 4. Place the picture cards face up scattered on the desk. 5. Students draw an attribute card from the pile and try to match it with the picture card. 6. Once students have matched all cards, they should check their work with their note cards.


Assessment: Assessment follows lesson #2.


5.7 Geometric Definitions Using Critical Attributes Acute angle – an angle with a measure less than 90 Circle – the set of all points that lie in the same distance from the center and lie in one plane. *Cone – three‐dimensional figure having one circular base, and one‐curved surface Congruent – same size, same shape *Cube – (square prism) three‐dimensional figure having six square sides faces, 12 edges, and

eight vertices (corner points) *Cylinder – three‐dimensional figure having two congruent circular bases that are parallel and

one‐curved surface

*Edge – a line segment where two faces meet on a solid

*Face – the flat surface of a three‐dimensional figure

Hexagon – a polygon with six sides, six angles, and six vertices *Hexagonal Prism ‐ three‐dimensional figure, two hexagonal faces, six rectangular faces, 18

edges and 12 vertices Obtuse angle – an angle whose measure is greater than 90 but less than 180º Octagon – a polygon with eight sides, eight angles, and eight vertices Parallel lines ‐ two lines in the same plane which never intersect and are the same distance

apart at all points Parallelogram – four‐sided (quadrilateral) with opposite sides parallel and opposite sides

congruent Perpendicular lines – lines that intersect at right angles (90 º) to each other * indicates Lesson two of two (three‐dimensional representation)


Pentagon – a polygon with five sides, five angles, and five vertices *Pentagonal Prism ‐ three‐dimensional figure with two pentagonal faces, five rectangular faces,

15 edges and 10 vertices *Pentagonal Pyramid‐ three‐dimensional figure, one pentagonal face, five triangular faces, 10

edges and six vertices Polygon – a closed figure made by joining line segments, where each line segment intersects

exactly two others only at the endpoints. *Polyhedron – three dimensional figure where all the faces are polygons *Prism – three‐dimensional figure with two congruent, parallel faces (bases) with sides that are

faces Quadrilateral – any four‐sided polygon Rectangle – four‐sided (quadrilateral) with four right (90º) angles, adjacent sides perpendicular,

opposite sides congruent, and opposite sides parallel *Rectangular prism – three‐dimensional figure with bases that are rectangular, six rectangular

faces, 12 edges, and eight vertices Right angle – the figure made by two rays that share an endpoint that is the same shape as the

corner of a square, 90 Rhombus – four‐sided quadrilateral having all four sides congruent and opposite sides parallel *Sphere – three‐dimensional figure having all of its points the same distance from its center Square – four‐sided (quadrilateral) with all sides congruent, opposite sides parallel, four right

(90 ) angles, and adjacent sides perpendicular *Square pyramid – three‐dimensional figure with one square face, four triangular‐shaped

faces, eight edges, and five vertices. *Three‐dimensional or space figure – a solid figure that has measurements including length,

depth (width), and height Trapezoid – four–sided (quadrilateral) with exactly one pair of parallel sides * indicates Lesson two of two (three‐dimensional representation)


Triangle – a three‐sided polygon with three sides, three angles, and three vertices *Triangular prism – three‐dimensional figure with two triangular faces, three rectangular faces,

nine edges, six vertices Two dimensional – a figure that has the two basic units of measurement *Vertex – the point (corner) where three or more edges at their endpoints meet in a three‐

dimensional figure Vertex – the point (corner) where two line segments meet on their endpoints in a two dimensional figure.

* indicates Lesson two of two (three‐dimensional representation)


Two‐Dimensional Attribute Cards TEKS 5.7(A) and 5.16(A) Parallel lines

two lines in the same plane which never intersect, and are the same

distance apart at all points

Perpendicular lines

lines that intersect at right angles (90 degrees) to each other

Two‐dimensional figure

a figure that has two basic units of measurements

Polygon Regular Irregular

a closed figure made by joining line segments, where each line segment intersects exactly two others at endpoints

Quadrilateral Parallelogram

any four‐sided polygon four‐sided (quadrilateral) with

opposite sides parallel

opposite sides congruent


Rectangle

four‐sided (quadrilateral) with

four right (90 ) angles

adjacent sides perpendicular

opposite sides congruent


Square


all sides congruent

opposite sides are parallel

four right (90 ) angles

adjacent sides perpendicular

Rhombus


all sides congruent


Trapezoid four–sided (quadrilateral) with

exactly one pair of parallel sides

Triangle

a polygon with

three sides

three angles

three vertices


Pentagon

a polygon with

five sides

five angles

five vertices

Hexagon

a polygon with

six sides

six angles

six vertices

Octagon

a polygon with

eight sides

eight angles

eight vertices

Right angle

the figure made by two rays that share an endpoint that is the same shape as the corner of a square, 90

Acute angle

an angle with a measure less than 90


Obtuse angle an angle whose measure is greater

than 90 but less than 180

Congruent

same size, same shape

Circle

the set of all points that are the same distance from its center and lie in the same plane.



TEKS 5.7: The student generates geometric definitions using critical attributes. Student Expectations: 5.7(A) The student is expected to identify essential attributes including parallel, perpendicular, and congruent parts of two‐ and three‐dimensional geometric figures. 5.16(A) Make generalizations from patterns or sets of examples and nonexamples

TEKS 5.7(A) has been divided into three separate lessons. Lesson two of three: Identify critical attributes of three‐dimensional geometric shapes *The Assessment for 5.7(A) follows lesson #3.

Overview: The students will make vocabulary cards (three‐dimensional figures) to demonstrate the meaning of words using pictures and definitions modeled by the teacher. Students will also give their own examples of what the attribute means to them. Students will then play a matching activity to assess their understanding.

Materials: Note cards (This lesson requires 16 more note cards.) Geometric solids and a collection of boxes resembling geometric solids Pattern Blocks For Guided Practice: one copy three‐dimensional cards per student

Vocabulary: three‐dimensional, face, vertex (vertices), edge, prism, triangular prism, rectangular prism, cube (square prism), pentagonal prism, hexagonal prism, square pyramid, hexagonal pyramid, cylinder, cone, sphere, polyhedron An attribute is a characteristic that helps define a figure. E.g., A triangular prism has two triangular faces (bases), three rectangular faces, nine edges, and six vertices.


Lesson: 1. Distribute 4 x 6 index cards to the students. Draw a model of your 4 x 6 index card on

the board.

Now on your 4 x 6 index card, I want each of you to divide the card into four parts.

Write the word: “cube” in the first box starting on the upper left hand side.

Ask students: Could someone draw a cube on the board or pick the cube out of these geometric solid visuals? When it comes to drawing the cube on the note card, you might have to help students with this drawing. You could have some pictures (see three‐dimensional cards) for them to cut out and paste if necessary.

Make sure students draw a cube in the upper right hand corner of their card. Once an appropriate drawing of a cube is drawn on the board, instruct students to copy this onto their note card.

Now, move down to the bottom left box to write the definition of a cube. Allow students to derive as much about the definition they can from their drawing or geometric solid visuals.

In the bottom right hand box, I would like for you to draw a picture of something that reminds you of a cube. Ask students after a minute or two of reflecting, what did you draw? It is very important that children come up with a meaning that makes sense to them. The ideas of an alphabet block or square box might be their drawing. The ideal situation would be to find something from the classroom or examples from the real world. This is a great tool to use with ELL learners to connect vocabulary to visuals.

2. Continue this style of inquiry with the students until all terms have been defined and modeled. Pattern blocks are a great tool to use as a visual. Make sure students use some real world connection or example that they can relate to on their vocabulary cards. It is imperative that the definitions, pictures, and personal associations be mathematically correct.

3. Some students might be able to immediately make their cards without any instruction.

You could allow students to review the vocabulary words with a partner and try to complete as many vocabulary cards as possible. Then you could discuss orally the cards made. Remember, each card may be a little different. It is especially important that the students use objects or pictures to visualize their figure and analyze the critical

cube

Square prism with 6 square faces, 12 edges, and 8 vertices.

A BC


attributes of the vocabulary words. Personal meanings of the terms will help students to recall figures and their attributes.

4. Once the cards are complete, have the students review each of their note cards before

attempting the guided practice matching activity.

Debriefing Questions: Here are some sample guiding questions that could be used either as students are making vocabulary cards or after the completion of their cards.

Three Dimensional: How does this flat square differ from a cube? There is another dimension. All of these figures take up space which is why we call them three‐dimensional shapes or geometric solids.

What do we call the flat surface of each of these figures? (faces) Notice that the faces of each figure are polygons.

Help the children to identify the edges and vertices of the solids.

Can you name these geometric solids? The discussion will identify the students who can name the solids.

Place the prisms on the table. These are all called prisms. Can you tell me why these are called prisms? The flat sides of a geometric solid are called faces. Prisms are three‐dimensional figures with two congruent, parallel faces (or bases) with sides called faces.

Looking at prisms: Which of these faces are the bases (the faces that are parallel and congruent to each other) of this prism? The shape of the base will name the prism. What would be the name of this prism? Hold up a geometric model of a rectangular prism. Continue with the triangular prism.

Repeat the prism questions with the pyramid. These are called pyramids. Like prisms, the shape of its base names a pyramid. A pyramid only has one face that is a base. The side faces of a pyramid are triangles. What is the name of this pyramid?

Guided Practice:

This activity is to be done without the note cards. It could be done the next day or immediately following the students reviewing of cards. 1. Distribute one copy of the two‐dimensional cards to each student. 2. Students should separate the picture card from the definition/attribute card by cutting along the solid lines. 3. Shuffle and put the attribute cards in one pile face down on the desk. 4. Place the picture cards face up scattered on the desk. 5. Students draw an attribute card from the pile and try to match it with the picture card. 6. Once students have matched all cards, they should check their work with their note cards. Note: Before students take assessment in 5.7 have students mix both the two‐dimensional cards and three‐dimensional cards together and play the matching game. This could be a partner review.

Assessment: The Assessment for 5.7(A) follows lesson #3.


Three‐Dimensional Cards (to be used with Guided Practice) Three‐dimensional or geometric solids

a solid figure measurements including

length

depth (width)

height

Cylinder

three‐dimensional figure

two congruent circular bases that are parallel

1 curved surface

Sphere


all of its points the same distance from its center

one curved surface

Cone


one circular base

one curved surface

Square pyramid


one square face

four triangular faces

eight edges

five vertices

Polyhedrons Prism


two congruent, parallel faces

sides are polygon faces


Triangular prism


two triangular faces

three rectangular faces

nine edges

six vertices

Rectangular prism


six rectangular faces

12 edges

eight vertices

Cube (Square prism)


six square faces

12 edges

eight vertices

Face

the flat surface of a three‐ dimensional figure

Edge

line segment where two faces meet on a solid

Vertex

a point (corner) where three or more edges meet on a three‐dimensional figure


Pentagonal Prism


two pentagonal faces

five rectangular faces

15 edges

10 vertices

Hexagonal Prism


two hexagonal faces

six rectangular faces

18 edges

12 vertices

Triangular Pyramid


four triangular faces

six edges

four vertices



TEKS 5.7: The student generates geometric definitions using critical attributes.

Student Expectations: 5.7(A) The student is expected to identify essential attributes including parallel, perpendicular, and congruent parts of two‐ and three‐dimensional geometric figures.

TEKS 5.7(A) has been divided into three separate lessons. Lesson three of three: Identify critical attributes of three‐dimensional geometric shapes *The Assessment for 5.7(A) follows this lesson.

Overview: This lesson has three different games. 1st Game: Students play “Who Am I” Part l; 2nd Game: “What Am I” part 2; 3rd Game: “The Big Picture”. In each game, students must use critical attributes to define geometric shapes or solids.

Materials: Geometric solids and a collection of boxes resembling geometric solids Pattern Blocks Geometric Definitions Using Critical Attributes Two‐dimensional and three‐dimensional Cards

Vocabulary: An attribute is a characteristic that helps define a figure (e.g., A triangular prism has nine edges.) Parallel, perpendicular, two‐dimensional, triangle, quadrilateral, pentagon, hexagon, octagon, quadrilateral, parallelogram, rectangle, rhombus, square, trapezoid, three‐dimensional, face, vertex (vertices), edge, triangular prism, rectangular prism, cube, square pyramid, cylinder, cone, sphere, right angle, acute angle, obtuse angle, congruent.


Lesson: Game 1: Today we are going to play a game called “Who Am ?” Students play “Who Am I” as a practice evaluation. Let a student select a picture card (See two‐dimensional and three‐dimensional cards.) Model to class how to be the “Who Am I?” in this activity first and then allow students to play this role.

1. Teacher draws one picture card from the stack of cards. She then allows the students to begin the attribute questioning.

2. Students in the classroom may ask attribute questions like: Is your shape two‐

dimensional or three‐dimensional? Does your polygon have right angles? Is your shape four sided?

3. Students may only ask up to 20 questions. Students in the room continue to question

(up to 20) and eliminate figures until they think they know the figure. Note: Students may not begin questioning with, “Is it a rectangle?” before asking the clarifying attributes.)

4. Once students identify the figure, have students define the figure by the

attributes they used. These definitions should match the definitions on the cards. If not all attributes are discussed, ask the students what do you know about……the sides, angles, number vertices, etc

5. Once this is modeled by the teacher, allow a selected student to choose a picture card

and continue “Who Am I?” Part 1 Game 2: “What Am I?” Part 2 (each student needs a set of picture cards) Have student spread the picture cards face up on top of the desk. Teacher uses the below clues and ask the students to hold up the picture card that is being described. Some of the clues may have more than one answer. Encourage students to find all possible answers.

1. I am a four‐sided polygon. I have one pair of parallel sides.

2. I am a two‐dimensional shape. I have exactly three sides and three angles.

3. I am a polygon. I have four sides. All four sides are equal length. None of the angles are right angles.

4. I am a polygon. I have five sides. I have five angles.

5. I am a polygon. I have four sides. I have two pairs of parallel sides that are equal.

6. I am a polygon. I have six sides. I have six angles.

7. I am a solid figure, which means I am three‐dimensional. I have six faces, eight vertices,

and twelve edges. All of the faces are square.


8. I am a three‐dimensional figure. My base is circular. I have a single vertex.

9. I am solid figure. I have five faces. I have six vertices and nine edges. Two of my faces

are triangular and three are rectangular.

10. I am a three‐dimensional figure. I have six faces, eight vertices, and 12 edges. I have rectangles and squares for faces.

11. I am a polygon. I look like a stop sign. I have eight sides and eight angles.

12. I am a three‐dimensional figure. I have two congruent circular bases. These two bases

are parallel.

13. I am a solid figure. I have a square base. I have four other faces. These faces are triangular‐shaped.

14. I am a three‐dimensional figure. All of my points are the same distance from my center.

15. I am a three‐dimensional figure. I have two congruent, parallel bases. The bases are

polygons. The sides are parallelograms. Game 3: “The Big Picture” using two‐dimensional cards and three‐dimensional cards This activity can be done as a whole group with teacher questioning students about the placement of the cards.

Students use the pictures and attribute cards to make a tree diagram showing how the figures are interrelated.

See attached sample of a tree diagram. Place the picture and attribute cards where the title of the figure is located.


What strategy did you use to guess the correct shape?

Did your strategy work?

Why or why not?

Which figure is a special rectangle and a special rhombus? (square)


Guided Practice: 1. Draw this on the board. Look at these two lines. What do we call these lines? (parallel lines) Which of the following statements is true about these lines? A. Parallel lines never intersect. B. Parallel lines are not the same distance apart. C. Parallel lines will intersect at a point. D. Parallel lines are always perpendicular.

Look at your definition of parallel lines.

Will these lines ever intersect? (no)

But before we choose that answer, let’s analyze the other three answers. Are these lines the same distance apart? (yes)

Is answer choice b true then? (no)

Did you tell me they would never intersect? (yes)

What does that tell us about answer choice c? (not true)

Are these lines always perpendicular? (no)

Is answer choice D true or false? (false)

This means that answer A is the correct answer.


Assessment: 1. Identify this figure.

A. Pentagon B. Triangle C. Polygon D. Parallelogram

2. Look at the figure below. Which statement is not true about this figure?

F. The figure has exactly 12 edges. G. The figure has exactly eight vertices. H. The figure has exactly six faces. J. The figure has no parallel lines.

3. Which figure below has six vertices?

A. Figure Y B. Figure U *C. Figure R D. Figure T

Y

U

R

T

*

*



Name: _________________________ Date: __________________ 1. Identify this figure:

A. Polyhedron B. Triangle C. Polygon D. Parallelogram

2. Look at the figure below:

Which statement is NOT true about this figure?

F. The figure has exactly 12 edges. G. The figure has exactly eight vertices. H. The figure has exactly six faces. J. The figure has no parallel lines.

3. Which figure below has six vertices?

A. Figure Y B. Figure U C. Figure R D. Figure T

Y

U

R

T


Tree Diagram of Polygons

Polygon

Triangle Quadrilateral Pentagon Hexagon Octagon

Parallelogram Trapezoid

Rectangle Rhombus

Square


Tree of Three Dimensional Figures

3‐D Figures

Prisms

Triangular Prism

Rectangular

Prism

CUBE

Pentagonal

Prism

Hexagonal Prism

Pyramids

Triangular Pyramid

Square Pyramid

Pentagonal Pyramid

Circle Based Figures

Cylinder Cone

Sphere

Copyright©2011 ESC Region XIII 5.8A, 5.14D, 5.15A


TEKS 5.8: The student models transformations. TEKS 5.15 The student communicates about Grade 5 mathematics using informal language. Student Expectations: 5.8(A) The student is expected to sketch the results of translations, rotations, and reflections on a Quadrant I coordinate grid. 5.14(D) Use tools such as real objects, manipulatives, and technology to solve problems. 5.15(A) The student is expected to explain and record observations using objects, words, pictures, numbers, and technology.

Overview: This lesson is designed to help the student visualize the changes geometric shapes undergo when they are translated, rotated, and reflected on a grid. The student will be guided through a series of procedures to sketch the results of translations, rotations, and reflections as well as identify the respective transformations.

Materials: Overhead projector Blank transparency sheets Pentomino cutouts & grid paper (several sheets per student) Transparent pentomino cutouts for the overhead projector Patty paper or wax paper Colored pencils Construction paper Scissors Glue

Vocabulary: Transformation, translation, reflection, rotation, vertical, horizontal, diagonal, edge, exterior, interior, grid, congruent

Lesson: 1. Activate any prior knowledge the students have with the term, transformation:

What do you think of when I say the word, transformation or transform? 2. Record the students’ responses on chart paper. Regardless of how undeveloped their

understanding about transformations may be, the point of this introductory activity is to bridge the students’ informal knowledge of this concept to its formal, mathematical definition, “ways of moving a figure in a plane.”

3. To help them see the connection between their interpretations and the formal definition, ask the students to generalize what all of their descriptions have in common.


If they are unable to extrapolate any generalizations, lead the students to see that the underlying relationship is best summarized by the word, “change.” Help the students create a more visual and concrete connection to the formal definition by breaking the word into its subparts—i.e., its prefix, root word, and suffix. Make a chart with three columns and three rows as illustrated in the diagram on the following page:

4. Distribute pentomino cutouts and grid paper to the students. 5. Have students cut out the pentomino of their choice. Instruct the students to orient

their selected pentomino so that its edges fit perfectly inside the squares on the grid paper.

6. Ask the students to discuss how they think they could transform (change the look of) the pentomino on the grid paper without changing the figure’s size or shape. After the students have shared their conjectures, point out that if the pentomino maintains its size and shape, the only way it could look differently on the grid is by moving it.

7. Collect suggestions from the students on how they could move their selected pentomino so that its orientation will change on the grid. Dictate the students’ responses on chart paper. If the students do not mention the targeted movements, model the transformations on the overhead projector. As you model each transformation, lead the students to describe the movements: What am I doing to change this pentomino’s orientation? Write down each of these movements—(turn, flip, slide).

8. Inform the students that each of these movements (turning, sliding, and flipping) is called by a special term used in geometry to describe transformations of congruent figures. Tell the students that a slide is called a “translation,” a turn is called a “rotation,” and a flip is called a “reflection.”

9. Explain to the students how transformations are used in real life situations. Use the example of an engineer:

An engineer has to know how to sketch transformations so that he/she can predict how an object,r a piece of machinery, or points in space will move from one point to another. To be successful at making these predictions, the engineer has to have precise measurements. For example, a translation is measured by the number of units it moves up or down and to the right or to the left.

Demonstrate this type of transformation on the overhead, counting the number of square units you move a transparent pentomino up or down and to the right or left.

10. Provide some time for the students to practice sliding one of their pentomino cutouts in different directions—i.e., up, down, to the left, and to the right. After they have had some opportunity for free exploration, instruct the students to shade in a pentomino on a sheet of grid paper. Then, tell the students to place a sheet of wax paper (slick side face down) on top of the shaded figure and trace around its outline. Allow the students to give each other directions on how to slide the pentomino image they traced on the


wax paper to a new position on the grid. The students should be able to describe the translation using words such as: five units to the right, three units down.

11. After illustrating a translation, compare and contrast it to a rotation:

When I take this same pentomino and turn it, I can make it look different than I can when I just slide it up, down, to the right or to the left.

12. As you turn the pentomino, encourage the students to discuss how the pentomino changes:

How does it look different? How can you be sure it is still the same shape? 13. Remind the students that just like a translation, a rotation must adhere to a set of

precise and rigid rules:

When I rotate this pentomino, I have to be sure that each side of its outline will eventually fit perfectly inside the squares in the grid. To do this, I could turn the pentomino around a point on the edge of the pentomino or around a point on the grid. This type of precision ensures that all points on the pentomino’s exterior are always the same distance from its point of rotation regardless of how much the figure is turned. Notice how when I rotate the pentomino clockwise ¼ of a turn, each of the sides of its outline fit perfectly inside the grid. Why do you think I called this turn ¼ of a rotation? If the students have difficulty visualizing why this is ¼ of a rotation, take a separate transparency, place it on the grid, and trace around the original pentomino. Then, draw a line on the transparency that connects the point of rotation to its corresponding point on the pentomino. Place a sharpened pencil on top of the point of rotation and turn the traced figure. As you are turning the figure, emphasize the distance traveled by the line connecting the pentomino to its point of rotation. Highlight this distance by drawing an arc that is ¼ of a circle, which makes a complete 90° angle. Shade in the interior of the angle that shows the 90° turn so that the students can see that it is ¼ of a circle. Repeat the same steps listed above to illustrate a ½ turn (180°), a ¾ turn (270°), and one complete turn (360°). See illustration below:

Note: Be aware that 5th graders are not required to know how to measure angles in degrees. The measurement of angles is a TEKS that is introduced in 6th grade.

14. Allocate some time for the students to practice sketching the different types of rotations you demonstrated.


15. At this point in the lesson, the students should have an in depth understanding of how to create different types of rotations on and off of a figure turned clockwise and counter clockwise. Now you can begin to guide the students in understanding how to reflect a figure on a grid:

There is still one last transformation you need to be able to visualize and sketch. A reflection is another type of transformation in which a figure has been reflected across a diagonal, horizontal, or a vertical line. To reflect the entire image, the line of reflection has to be either on the edge of the original figure or off of it completely. Notice how all of the points on the reflected image are the same distance away from the line of reflection as the corresponding points on the original figure.

16. To illustrate how both images are equidistant from the line of reflection, outline each edge of the pentomino’s exterior a different color. Then, call on volunteers to come up to the overhead and mark the edges on the reflected image with colors that match the ones on the corresponding edges of the original pentomino. Count the number of square units each corresponding edge on both images is from the line of reflection.

17. Allocate some time for the students to practice making reflections. First, direct them to shade in a pentomino figure on a sheet of grid paper. Second, distribute sheets of wax paper to the students. Instruct the students to take the wax paper, fold it in half, and then place it on top of the pentomino they shaded in on the grid paper. Then, instruct the students to trace around the outline of the pentomino on the wax paper. Next, tell the students to open the wax paper and make a dotted line along the fold. Inform the students that the fold is the line of reflection. Draw the students’ attention to the movement they make as they open the fold.

Notice that when you open the wax paper, the image you made from tracing around the original pentomino flips across the grid.

18. Students will make a model to hang in the classroom as a reference to use throughout

this unit. a. Take a page of the grid paper provided in this lesson and have students cut it

into four equal parts (each part will be a 7 x 7 array). They will only be using three of the parts for this activity.

b. Students will trace their pentomino onto three of the grids. They need to trace their figure on the left side of the grid so that they have room to sketch a

All of the vertical edges of the pentomino are marked by different patterned lines to show where their corresponding edges are located on the reflected pentomino.


transformation on the right side. They also need to position their pentomino the same way on each of the four grids. Have students shade in their pentominos once they have been traced. (They may use colored pencils to add some color if they would like.)

c. Have student place their pentomino on the corner of their desk. They will no longer be allowed to use them. Students will choose a transformation and sketch the results of that transformation onto the first grid. They will then choose a different transformation and sketch those results on the second grid, and sketch the third transformation on the third grid. Remind students that transformations involve congruent figures (figures that are the same size and shape). They need to make sure their figures are congruent by counting squares. NOTE: The students should be completing this step WITHOUT using their pentomino. This is part of spatial reasoning that students need to be practicing. Again, have students shade in their pentominoes once they are done.

d. Give each student a piece of construction paper. Have students fold their paper into fourths giving them four equal parts. In the top left quadrant students will glue their original pentomino. In the remaining three quadrants they will glue each of their grids.

e. Label each section with the transformation and describe that transformation using the words “slide, turn, flip.”

Guided Practice:

Distribute the Guided Practice Activity sheet. This activity allows the students to locate and identify specific examples of each type of transformation. Go over this sheet orally with the students so as to prepare them for how to approach sample items assessing this knowledge and skill. For each answer choice, ask the student to justify how he or she knew he or she is correct.

Which of these figures shows a translation? (Figure B, the present.)

Why do you think Figure B is a translation? (Accept any reasonable response.)

Which of these figures shows a rotation? (Figure D, the bus.)

Why do you think Figure D is a rotation? (Accept any reasonable response.)

Which of these figures is a reflection? (Figure A, the arc.)

Why do you think that Figure A is a reflection? (Accept any reasonable response.)

Which of these figures does NOT show any transformation? (Figure C, the star.)

Why do you think that Figure C is NOT a transformation? (Its’ size has changed. In order for a figure to undergo any transformation, it must always be congruent.)


Assessment: 1. On the grid below, sketch the results of a translation of the figure shown:

2. On the grid below, sketch the results of a rotation of the figure shown: 3. On the grid below, sketch the results of a reflection of the figure shown:


Pentomino Cutouts and Grid Blackline: TEKS 5.8(A), 5.14(D), and 5.15(A)


Guided Practice: Reporting Category 3: TEKS 5.8(A), 5.14(D), and 5.15(A)

Name: _________________________ Date: _________________ Directions: Look carefully at Figures A, B, C, and D. Each of the figures, except for one, shows a specific type of transformation. Which of these figures shows a translation? Which one shows a rotation? Which one shows a reflection? Which of the figures does NOT show a transformation? Justify your answer in the space designated below each figure. Figure A Figure B

Explain why you think Figure A is… Explain why you think Figure B is…

Figure C Figure D

Explain why you think Figure C is… Explain why you think Figure D is…


Assessment: Reporting Category 3: TEKS 5.8(A), 5.14(D), and 5.15(A)

Name: _________________________ Date: __________________ 1. On the grid below, sketch the results of a translation of the figure shown:

2. On the grid below, sketch the results of a rotation of the figure shown: 3. On the grid below, sketch the results of a reflection of the figure shown:

Copyright©2011 ESC Region XIII 5.8B, 5.16B,


TEKS 5.8: The student models transformations. Student Expectations:. 5.8(B) The student is expected to identify the transformation that generates one figure from the other when given two congruent figures on a Quadrant I coordinate grid. 5.16(B) Justify why an answer is reasonable and explain the solution process.

Overview: This lesson is designed to help the student describe the changes geometric shapes undergo when they are translated, rotated, and reflected on a grid. The student will proceed through a series of activities using informal language—slide, turn, and flip—to describe motions that transform figures. Through teacher guidance, the student will link informal language to the formal vocabulary used in mathematics to describe these transformations—i.e., translation, rotation, and reflection.

Materials: Overhead projector Teacher set of transformation vocabulary cards Transformation sorting cards (one set per pair) Transformation Recording Sheet (Guided Practice) Chart paper Markers Glue Scissors

Vocabulary: Transformation, translation, reflection, rotation, congruent, orientation, three‐dimensional

Lesson: 1. Make transparencies of the transformation vocabulary cards. Discuss how the informal

vocabulary that the students use to describe the pictures shown on the transformation vocabulary cards are used in geometry:

Mathematicians use specific words to describe how a geometric figure moves. 2. Show the vocabulary card that illustrates a translation. Lead the students to visualize a

slide as a “translation.”

Listen for the ‘sl’ sound as I say, “translation.” Which movement did we discuss that starts with the ‘sl’ sound? In mathematics, a slide is a translation.

3. Next, show the vocabulary card illustrating a rotation. Emphasize the ‘t’ sound in “rotation.”


When I say the word, “rotation,” listen for the ‘t’ sound in “turn.” In mathematics, we say “rotation” to describe turns.

4. Finally, display the vocabulary card showing a reflection. Emphasize the ‘fl’ sound in reflection so that the students associate it with the word, flip.

When I say the word reflection, listen for the ‘fl’ sound as in flip. When a figure has been flipped, a mathematician calls this transformation a “reflection.”

5. As an extension to the vocabulary cards, make further visual connections to transformations by leading the students to think of other situations in which an object slides (such as sliding into home base), turns (such as a second hand turning around the clock face), or flips (such as cooking pancakes). Record the student suggestions on the respective vocabulary card.

6. Distribute Student Sheet #1 to each student. Do the first problem together as a whole group:

Look closely at the first set of pentominoes. Two pentominoes within this set are congruent.

What does it mean if something is congruent? (same shape and same size) Which two in Set 1 are congruent? (Figure G and Figure I).

Talk with your partner about why you think the two figures you selected are congruent. (Answers will vary but may include: They are the same size and shape; they cover the same area; they have the same number of squares.)

Which type of transformation made Figure I look different from Figure G? (rotation) Why? (because figure I is turned ¼ turn to the left)

7. After the students have discussed their thinking with their partners, chart the responses

on the board.


8. Direct the students to complete Set 2 on Student Sheet 1 independently:

Debriefing Questions: When the students have finished Set 2 on Student Sheet 1, allow them to share their justifications with the rest of the class. Guide this discussion by asking questions that will lead the students to understand how the figures are the same size and shape but have different orientations:

Figures J, L, and R are congruent.

How can you be sure they are the same? (They have the same number of squares, and they are all the same size.)

How would you describe the transformation that made Figure L look different than Figure J? (Figure J was rotated clockwise ¼ of a complete rotation to look just like Figure J.)

How would you describe the transformation undergone by Figure R? (Figure R is a reflection of Figure J across a horizontal line.)

How can you prove that these three pentominoes are the same size? (I could take Figure R and rotate it to show that it is congruent to Figure L. Then, I could take Figure J and reflect it across a horizontal line to show that it is congruent to Figure J.)

Guided Practice: 1. Inform the students about how the knowledge and skills they just learned for describing

transformations will be presented in test question format. You will see an image of two congruent figures that have undergone one of the transformations we have just learned about. Among the answer choices, you will have to select one of the vocabulary words such as translation, rotation, or reflection that best describes the transformation illustrated in the picture. As a test taking strategy to help you remember these words, try to visualize the pictures and words. Show the students the vocabulary cards, emphasizing the pictures that illustrate slides, turns, and flips.

2. Distribute sets of the Transformation Sorting Cards to pairs or small groups of students. Make sure the cards are mixed in the pile. Instruct the students to categorize the cards by transformations: Look closely at these cards. Your job is to work with a partner sorting these cards into four groups—i.e., “translations,” “rotations,” “reflections,” and “None of the above.”

3. When the students finish sorting the cards into the four categories, have them create some type of graphic organizer on their chart paper using the cards to show how they sorted them. Make sure they label their organizer to show what they labeled each


group. They will be presenting their organizer to the class when every group has finished.

4. Direct the students to record how they sorted the cards on the Guided Practice Sheet for TEKS 5.8(B).

Which of the sorting cards show translations? (cards C, E, G, K, and I.)

How do you know they are translations? (Accept any appropriate response.)

Which of the sorting cards show rotations? (cards F, J, L, and P.)

How do you know they are rotations? (Accept any appropriate response.)

Which of the sorting cards show reflections? (cards A, D, H, N, and R.)

How do you know they are reflections? (Accept any appropriate response.)

Which of the sorting cards do NOT show any transformation? (cards B, M, O, and Q.)

How do you know they are NOT transformations? (Accept any appropriate response.)


Assessment: 1. Which transformation is represented in the diagram?

A. Reflection

B. Translation

*C. Rotation

D. Not Here

2. The figures below are congruent. Which transformation is shown?

F. Translation *G. Reflection H. Rotation J. Not Here


3. Which transformation is represented by the shaded figures in the diagram below?

A. Rotation

B. Reflection

C. Translation

*D. Not Here


Student Sheet 1 Reporting Category 3: TEKS 5.8(B) and 5.16(B)

Name: __________________________________ Date: ___________________

Mathematicians use the word congruent to describe two figures that are the same size and same shape. Closely observe the pentominoes shown in Set #1. Only two of these figures are congruent. Identify which two figures are the same size and same shape. Explain in the space provided below.

Figure ___ and Figure ___ are congruent because…

Closely observe the pentominoes shown in Set #2. Three of these figures are congruent. Identify which three are the same size and same shape. Explain your thinking in the space provided below.

Figure ___, Figure___, and Figure ___ are congruent because…

Set#1

Set#2


Transformation Sorting Cards TEKS 5.8(B) and 5.16(B)

Card A Card J

Card B Card K

Card C Card L

Card D Card M

Card E Card N

Card F Card O


Card G Card P

Card H Card Q

Card I Card R


Guided Practice: Reporting Category 3: TEKS 5.8(B) and 5.16(B)

Name: __________________________ Date: __________________

These transformation cards are all examples of translations because…

List the corresponding translation cards here:

These transformation cards are all examples of rotations because…

List the corresponding rotation cards here:

These transformation cards are all examples of reflections because…

List the corresponding reflection cards here:

These cards are NOT transformations because…

List the corresponding cards that are NOT transformations here:


Assessment: Reporting Category 3: TEKS 5.8(B) and 5.16(B)

Name: __________________________ Date: __________________

1. Which transformation is represented in the diagram?

A. Reflection B. Translation C. Rotation

D. Not Here

2. The figures below are congruent.

Which transformation is shown?

F. Translation G. Reflection H. Rotation J. Not Here


3. Which transformation is represented by the shaded figures in the diagram below?

A. Rotation

B. Reflection C. Translation D. Not Here


STAAR Reporting Category 4: Measurement: The student will demonstrate an understanding of the concepts and uses of measurement.

TEKS 5.10: The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems. Student Expectations:. 5.10(A): The student is expected to perform simple conversions within the same measurement system (SI (metric) or customary). TEKS 5.10(A) has been divided into three separate lessons. Lesson 1 of 3: Capacity *The Assessment for 5.10(A) follows lesson #3.

Overview: How much does it hold? Students will divide a large quantity of liquid into smaller quantities.

Materials: Gallon and liter container of colored water or juice Measuring cup (both customary and metric) Pint Quart container Mathematics Reference Chart Chart paper Markers Gallon Graphic Organizer

Vocabulary: capacity, gallon, quart, pint, cup, liter, milliliter, customary, metric

Procedure: NOTE: It is important with measurement conversions that students understand conceptually why we multiply and divide by certain numbers. This lesson as well as other hands‐on lessons, need to be done BEFORE teaching them the “steps” of measurement conversion, which occurs in lesson #3.

1. Give each group of students a set of measurement containers (four quarts, two pints, two cups, eight oz.). If you do not have enough to do it in groups, do this as a demonstration lesson calling students up to perform the different parts of the activity.

2. Ask: What does capacity mean? (the maximum amount that can be contained) I want you to determine the capacity of the containers I have gathered here for you. We will begin with customary measure. Distribute gallon container of liquid to students. Ask them to select the next smallest containers and divide the liquid among that size. (They will choose the quarts and distribute the liquid equally among the four quart containers.)


3. Students will continue to divide liquid going to smaller containers each time. (The students will first put the liquid into four quarts, then empty one of the quarts into two pints, then empty one of the pints into two one‐cup measures.) Have the students record the following as they are doing the dividing of the liquid: (Four quarts equal one gallon; two pints equal one quart; two cups equal one pint). Students must use the Mathematics Reference Chart as they record in their journals. Have the students sketch a picture to accompany their recordings to use as a reference later on. (E.g., draw one large container = four smaller containers to show one gallon = four quarts.)

4. Break students into groups and have them make a graphic representation (one that

makes sense to them) of the breakdown from one gallon to 128 ounces on chart paper. Have groups share their work with the class. Post around the room and leave up as a reference for the rest of the measurement unit. At the end of the presentations, refer to the Gallon Graphic Organizer. Give each student a copy to paste into his or her math journal as a reference tool.

5. Repeat the activity in metric measure using the liter bottle filled with the liquid and pour

into a measuring cup that is metric measurement probably 250 milliliters (mL). Empty into another container such as a mixing bowl and continue to pour the contents of the liter bottle into the metric measuring cup until the liter bottle is empty. The students should record how many milliliters the liter bottle contains. Discuss with the students how many times they filled the 250 milliliter cup with the liquid. (250 x 4 = 1000 ml or 1

liter. Therefore 250 ml is 41 of a liter.) Have students sketch a picture to accompany

their recordings to use as a reference later on in their journals. (E.g., draw 1 liter bottle = four 250 mL bottles, then show the math 1 liter = 250 mL + 250 mL + 250 mL+250 mL so 1 liter = 1,000 mL)


Which holds more two quarts or one gallon? Why? (one gallon because it takes four quarts to equal one gallon)

Which holds less 32 ounces or four cups? Why? (neither, they hold the same because one cup equals eight ounces so four cups equals 32 ounces)

Which holds more 4 L or 4,500 mL? Why? (4,500 mL because four L is equal to 4,000 mL)


Guided Practice: 1. Which holds more: six pints or two quarts? Explain your answer. ____(6 pints because two quarts is four pints)_ 2. Which holds less: eight cups or five pints? Explain your answer. _____(eight cups because five pints is 10 cups)_____________________ 3. Which holds less: 12 quarts or three gallons? Explain your answer. ______(they are equal because three gallons = 12 quarts)__ 4. Which holds more: 48 fluid ounces or nine cups? Explain your answer. _____(nine cups because it is 72 ounces)_________ 5. Which holds less: 16 fluid ounces or five cups? Explain your answer. ______(16 fl oz because five cups is 40 fl. oz)__________ 6. Which holds more: 15 quarts or three gallons? Explain your answer. ______(15 quarts because three gallons is 12 quarts)______________ 7. Which holds more: 1,300 milliliters or two liters? Explain your answer. ____(two liters because it is 2,000milliliters)__ 8. Which holds less: six pints or three quarts? Explain your answer. ______(they are equal because three quarts is 6 pints)_____________

Assessment: Assessment for TEKS 5.10(A) will follow lesson #3.


Guided Practice: Capacity Reporting Category 4: TEKS 5.10(A)

Name: ____________________________ Date: __________________ 1. Which holds more six pints or two quarts? Explain your answer. __________________________________________________________________ 2. Which holds less eight cups or five pints? Explain your answer. __________________________________________________________________ 3. Which holds less 12 quarts or three gallons? Explain your answer. __________________________________________________________________ 4. Which holds more 48 fluid ounces or nine cups? Explain your answer. ___________________________________________________________________ 5. Which holds less 16 fluid ounces or five cups? Explain your answer. ___________________________________________________________________ 6. Which holds more 15 quarts or three gallons? Explain your answer. ___________________________________________________________________ 7. Which holds more 1,300 milliliters or two liters? Explain your answer. ___________________________________________________________________ 8. Which holds less six pints or three quarts? Explain your answer. __________________________________________________________________


Gallon Graphic TEKS 5.10(A) Lesson 1 of 3 Printed by permission from Aurora Freire/Niki Konecki. This sheet should be introduced AFTER the students have had lots of hands‐on instruction with capacity.



TEKS 5.10: The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems. Student Expectations:. 5.10(A): The student is expected to perform simple conversions within the same measurement system (SI (metric) or customary). TEKS 5.10(A) has been divided into three separate lessons. Lesson 2 of 3: Weight *The Assessment for 5.10(A) follows lesson #3.

Overview: How much does the bag of popcorn weigh? Students will work with weight (in both customary and metric) using bags of popcorn.

Materials: Spring scale Big bag of popcorn Pan balance (including a 1 Kg and 1 gram weight) One large ziplock bag and 16 snack‐size ziplocks (for each each) Mathematics Reference Chart

Vocabulary: weight, mass, pound, ounce, gram, kilogram

Procedure: Note: It is important with measurement conversions that students understand conceptually why we multiply and divide by certain numbers. This lesson as well as other hands‐on lessons, need to be done BEFORE teaching them the “steps” of measurement conversion.

1. Prior to the lesson, take out 1 pound of popcorn and put into a large ziplock bag. Make a 1 pound bag for each group you will have working in this lesson.

Customary Measurement:

2. Ask: What does weight mean? (how heavy something is) What is mass? (amount of matter in an object) What is the difference between the two? (The mass of something remains the same no matter where it is. The weight of something has to do with the pull of gravity on that object.)


Since we have the pull of gravity here with us today and will not be measuring things in a non‐gravity chamber, we are going to be working with weight. I want you to estimate the weight of this bag of popcorn. Distribute a 1 pound bag of popcorn to each group. Allow students to estimate the weight of the bag by how heavy it feels. Once everyone in the group has estimated the weight of the bag, have them use the spring scale to find the actual weight in pounds.

3. Have the group divide out the popcorn evenly among 16 small snack‐size ziplocks. Have

the group use the spring scale to measure the weight of 1 small snack‐size ziplock. They should see that it is 1 oz.

4. Have students refer to the Mathematics Reference Chart to see that 1 pound = 16

ounces. Have students draw a representation of this equation in their journal along with what the reference chart says. (E.g., draw one large bag of popcorn = 16 small bags of popcorn to represent 1 pound = 16 ounces.

5. In front of the whole group, show students the large bag of popcorn you brought in. Ask

students to estimate the weight of the bag in pounds. Have the groups discuss what their estimation is. Record each group’s estimation on the board. Use the scale to find the actual weight (round to the nearest pound for this activity). Have groups work together to determine how many one‐ounce bags I could fill up with popcorn using the large bag.

6. Ask the students to carefully put their 16 ounces of popcorn back into their large ziplock

to make their 1 pound again to use in the next activity.

Metric Measurement: 7. Now we are going to switch over to metric conversions. Who remembers units we use

in the metric system to measure weight? (grams, kilograms, and milligrams. If students do not know these, remind them that they have their Mathematics Reference Chart that they could look at to help them.) I want you to talk with your group and make a prediction as to how you think a kilogram compares to the weight of a pound. (examples include: a little heavier, a lot heavier, a little lighter, a lot lighter, about the same) Allow students to discuss this for a few minutes in their group. Have each group give their prediction as you write them on the board.

8. Groups will take their 1 pound bag of popcorn and use a pan balance to compare it to

the 1 Kg weight. Have students determine by how much of a tilt there is if a Kg is a little heavier or a lot heavier. Discuss the results as a class. Have students draw a picture of the pan balance with the popcorn and the 1 Kg weight and write a sentence or two describing the comparison in their math journal.

9. Have each group measure back out 1 ounce of popcorn. Complete steps #6 and #7 from

above this time comparing ounces and grams.

10. Have students look at the Mathematics Reference Chart and get the equation showing Kg and g. Discuss with the class that it takes 1,000 grams of anything to make up a Kg.



Which weighs more: 24 ounces or 2 pounds? Why? (2 pounds because it is equal to 32 ounces.)

Which weighs less 3 pounds or 48 ounces? Why? (neither, they weigh the same because 1 pound equals 16 ounces so 3 pounds equals 48 ounces)

Which is more 6 Kg or 8,000 grams? Why? (8,000 grams because 1 Kg = 1,000 grams so 6 kg = 6,000 grams)

Guided Practice:

1. Which weighs more 6 pounds or 64 ounces? Explain your answer. ____(6 pounds because 6 pounds is 96 ounces)____________________ 2. Which weighs less 4,800 grams or 7 kilograms? Explain your answer. _____(4,800 grams because 7 kg is 7,000 grams)__________________ 3. Which weighs less 8,000 grams or 8 kilograms? Explain your answer. ______(they are equal because 8 kg = 8,000 grams)__________ 4. Which weighs more 48 ounces or 4 pounds? Explain your answer. _____(4 pounds because it is 64 ounces)___________________ 5. Which weighs less 16 ounces or ½ pound? Explain your answer. __(1/2 pound because 1 pound is 16 ounces so ½ pound is 8 oz)_____ 6. Which weighs more 1,500 grams or 1 ½ kg? Explain your answer. (they weigh the same because 1 kg is 1,000 grams and ½ kg is 500 grams so 1 ½ kg is 1,500 grams) 7. Which weighs more 1,300 grams or 2 kilograms? Explain your answer. ______(2 kilograms because 2 kg is 2,000 grams)___________ 8. Which weighs less 4 pounds or 60 ounces? Explain your answer. ______(60 ounce because 4 pounds is 64 ounces)_____________

Assessment: Assessment for TEKS 5.10(A) will follow lesson #3.


Guided Practice: Weight Reporting Category 4: TEKS 5.10(A)

Name: ____________________________ Date: __________________ 1. Which weighs more: 6 pounds or 64 ounces? Explain your answer. ______________________________________________________________________ 2. Which weighs less: 4,800 grams or 7 kilograms? Explain your answer. ______________________________________________________________________ 3. Which weighs less: 8,000 grams or 8 kilograms? Explain your answer. ______________________________________________________________________ 4. Which weighs more: 48 ounces or 4 pounds? Explain your answer. _______________________________________________________________________ 5. Which weighs less: 16 ounces or ½ pound? Explain your answer. _______________________________________________________________________ 6. Which weighs more: 1,500 grams or 1 ½ kilograms? Explain your answer. _______________________________________________________________________ 7. Which weighs more: 1,300 grams or 2 kilograms? Explain your answer ________________________________________________________________________ 8. Which weighs less: 4 pounds or 60 ounces? Explain your answer. ________________________________________________________________________



TEKS 5.10: The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems.

TEKS 5.14 The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school. Student Expectations:. 5.10(A): The student is expected to perform simple conversions within the same measurement system (SI (metric) or customary). 5.14(C) The student is expected to select or develop an appropriate problem‐solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem . TEKS 5.10(A) has been divided into three separate lessons. Lesson 3 of 3: Measurement Conversion *The Assessment for 5.10(A) follows lesson #3.

Overview:

Students will use a table and the relationships found on the Mathematics Reference Chart to solve simple conversion problems.

Materials: Mathematics Reference Chart (one per student) Student Sheet (cut into 15 problem cards) Chart paper Markers

Vocabulary: Relationship, conversion, equivalent, units

Procedure: In the last two lessons, we have compared the different customary and metric units used when measuring capacity and weight. In this lesson we are going to look at how to convert between different units.

What does the word “convert” mean? (changing from one unit to another without changing the value of how much it weighs or holds)

I want you to talk to your neighbor and come up with at least one example of when this would be a valuable skill out in the real world.


Give students a few minutes to come up with a few examples. Go around the room and have students give their examples. Create a list on chart paper.

What information do you think I need to know in order to convert from one unit to another? (Answers will vary. You want to lead the students to answer the relationship between the two units involved. For example, the relationship between gallons and quarts.)

Anytime I convert between two different units, I must know the relationship that they share. Today we will be using our Mathematics Reference Chart to help give us those relationships. Let’s look at the following problem: (Write the following problem on the board.) Martha is baking cookies for the school bake sale. The recipe she is using calls for 2 cups of butter. Martha needs to quadruple the recipe in order to have enough cookies. The containers of butter are measured in ounces. How many ounces of butter will Martha need to make all of her cookies?

What unit does the recipe use? (cups)

What unit does the store use? (ounces)

So I know I will be converting or changing cups to ounces in this problem.

What’s the relationship between cups and ounces? (Remind students that they may use their Mathematics Reference Chart to help them with the relationship.) (The relationship is 1 cup is equal to 8 ounces.)

What does the word ‘quadruple’ mean? (She will need 4 times what the recipe calls for)

How many cups of butter is Martha going to need to be able to make all of her cookies? (8 cups of butter)

How do you know this? (because the recipe calls for 2 cups but she needs 4 times that which is 8 cups)

We know that 1 cup is equal to 8 ounces, so how many ounces would 2 cups equal? (16 ounces)

3 cups? (24 ounces)

How can we start organizing all of this information? (in a table or chart)

Let’s go ahead and make our chart. What will our two columns be labeled? (cups and ounces)

Cups Ounces

1 8

2 16

3 24


When do we know when we can stop in our chart? (when we get to how many ounces are in 8 cups)

Go into your journal and complete the chart I have begun for you.

How many ounces are in 8 cups? (64 ounces) Let’s try another problem. Charlie and his father are cleaning out the garage. They found a bag of soda cans that weighed 64 ounces. Charlie brought the cans to the recycling center and got 25 cents a pound. How much money did Charlie make recycling the cans?

What unit do we know from the problem? (ounces)

What unit do we need it to be in? (pounds)

What is the relationship between the two units? (1 pound is 16 ounces) Go into your journal and create a table using this relationship.

We know that the 64 ounces of cans is equivalent to 4 pounds.

Is that going to be the answer to our problem? (no)

Why? (The question is how much money will he make selling the cans.)

How much money does he get for each pound he sells? (25 cents)

So how much will he make if he sells all 4 pounds? ($1.00)

What did you do to get the answer? (multiply 25 and 4)

Take the Student Sheet and cut out each problem card. Give each group of two to three students a problem card and a piece of chart paper. Have each group solve their problem using a table or chart on their chart paper. When everyone is finished, have each group present their problem and solution to the class.

Pounds Ounces

1 16

2 32

3 48

4 64



How many quarts are there in a gallon? (four)

How many ounces are in 3 pounds? (48)

How many ounces are there in a pint? (16 ounces equal one pint)

A cup is equal to how many ounces? (8 ounces)

Which is larger, a gallon or a quart? (gallon)

Then when I want to convert from a gallon to a quart, do I multiply or divide? (We multiply when we convert from a larger capacity to a smaller capacity.)

When you are using metric measurement for capacity, how many milliliters equal one liter? (one thousand; milli‐ means 1000)

Guided Practice:

Karen is on the soccer team at her school. Part of her training includes running 5 miles over a one week period of time. She runs 1,200 yards every day after school and on Saturday. How many yards does Karen need to run on Sunday in order to finish her training? 1. How far does she need to run in one week? ____(5 miles)_______ 2. How far does she run Monday through Saturday? ___(7,200 yards)__ 3. What unit will your answer be in? ____(yards)_________ 4. What relationship do I need to solve this problem? ____(1 mile = 1,760 yards)__________ 5. Organize your information in the chart below. 6. How many yards does Karen need to run on Sunday in order to finish her training?_______(1,600 yards)_____________ 7. Write an equation showing how you came up with the answer to question #6. ______(8,800 – 7,200 = 1,600)____________

Miles Yards

1 1,760

2 3,520

3 5,280

4 7,040

5 8,800


Assessment: 1. Mary drinks 64 ounces of water every day. How many cups of water does she drink?

A. 128 cups *B. 8 cups C. 7 cups D. 2 cups

2. A candy bar weighs 2 ounces. What fractional part of a pound does this represent?

A. 2

1 pound

*B. 8

1 pound

C. 3

1 pound

D. 9

1 pound

3. The table below shows the liquid capacity of 4 household objects:

4. Which of these objects has a capacity of exactly 9 cups?

A. cereal bowl B. mixing bowl *C. small trash can D. water canteen

5. Samuel’s sister weighed 7 pounds 3 ounces when she was born. How many ounces did his sister weigh when she was born?

A. 84 ounces B. 160 ounces C. 112 ounces *D. 115 ounces

Object Capacity

Cereal bowl 24 fl. oz.

Mixing bowl 56 fl. oz.

Small trash can 72 fl. oz.

Water canteen 20 fl. oz.


Student Sheet: Measurement Conversion Reporting Category 4: TEKS 5.10(A) and 5.14(C)

Mary is having an ice cream party at her house. She would like to serve each of her 35 guests one cup of ice cream with toppings. How many

quarts of ice cream does Mary need to buy?

Calvin was performing an experiment in Science class. He needed to find out how many kilograms a particular object weighed. He only had gram weights and discovered it weighed 4,500 grams. How many kilograms was it?

Judith and Sam were helping their father build 6 flower boxes for their back patio. Each box required 14 inches of plywood. How many feet of plywood will

they need to buy?

Megan’s mother is making punch for her birthday party. She combined 4 quarts of pineapple juice, 2 pints of

orange juice and a ½ gallon of sprite. How many cups of punch did Megan’s mother

make?

Garrett works at the docks at Lake Travis. He uses 17 inches of rope to tie each boat to the

dock. If he has 8 ½ feet of rope in the office, how many boats can he tie up?

Tabitha and Marcie went to the store to buy soup. If they

bought a quart of soup to share, how many cups of soup will

each girl get?

Phillip has a pet skunk named Vinnie that weighs 128 ounces. Phillip researched the average weight of a skunk, and it is 12

pounds. Has Vinnie reached this weight? Why or why not?

Darnell was on the track team at his Jr. High with 7 other boys. Each boy ran 1,980 feet on

Tuesday. If the coach put all of their distances together, how

many miles would it be?

Deja was buying fabric for her Halloween costume. She needs 72 inches to make her Supergirl cape. The fabric is on sale for

$2.45 a yard. How much money will Deja spend on fabric for her

cape?

Eli has a 5 ½ gallon fish tank in his bedroom. His mother asked that he clean it out on Sunday. If he uses a quart container to empty the tank, how many times will he have to fill it before the tank is empty?

Maria bought 3 pounds of candy for her birthday party. If she gives her 8 friends an equal amount of candy, how many

ounces of candy will each friend get?

Felix is helping his teacher fill 4 ounce cups with punch for his class. If they have 24 students in the class, how many cups of punch did the class drink?

Samantha uses her mother’s spring scale to measure the

weight of her math book. The scale shows 56 ounces. How many pounds is Samantha’s

math book?

Marion recorded how much liquid she drank in one week. If she drank 640 fl. oz., how many gallons did Marion drink in a

week?

Derrick measured the perimeter of his square shaped bedroom. It measured 120 inches. How many feet is the length of one

wall in his bedroom?


Guided Practice: Measurement Conversion Reporting Category 4: TEKS 5.10(A) and 5.14(C)

Name: ____________________________ Date: __________________ Karen is on the soccer team at her school. Part of her training includes running 5 miles over a one week period of time. She runs 1,200 yards every day after school and on Saturday. How many yards does Karen need to run on Sunday in order to finish her training? 1. How far does she need to run in one week? _________________________________ 2. How far does she run Monday through Saturday? _____________________________ 3. What unit will your answer be in? _______________________________________ 4. What relationship do I need to solve this problem? ___________________________ ________________________________________________________________________ 5. Organize your information in the chart below. 6. How many yards does Karen need to run on


Sunday in order to finish her training? _____________________________________________________________ 7. Write an equation showing how you came up with the answer to question #6. _______________________________________________________________________


Assessment: Measurement Conversion Reporting Category 4: TEKS 5.10(A) and 5.14 (C)

1. Mary drinks 64 ounces of water every day. How many cups of water is that?

A. 128 cups B. 8 cups C. 7 cups D. 2 cups

2. A candy bar weighs 2 ounces. What fractional part of a pound does this represent?

A. 2

1 pound

B. 8

1 pound

C. 3

1 pound

D. 9

1 pound

3. The table below shows the liquid capacity of 4 household objects.

Which of these objects has a capacity of exactly 9 cups? A. cereal bowl B. mixing bowl C. small trash can D. water canteen

4. Samuel’s sister weighed 7 pounds 3 ounces when she was born. How many ounces did

his sister weigh when she was born? A. 84 ounces B. 160 ounces C. 112 ounces D. 115 ounces

Object Capacity

Cereal bowl 24 fl. oz.

Mixing bowl 56 fl. oz.

Small trash can 72 fl. oz.

Water canteen 20 fl. oz.



TEKS 5.11: The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius). Student Expectations:. 5.11(A) The student is expected to solve problems involving changes in temperature

Overview: Students will learn to use thermometers and collect temperature readings from newspapers. They will use a variety of scales (counting by 1, 2, 3, 4, etc.) to construct thermometers.

Materials: Newspaper weather data Thermometers Glass of ice water

Vocabulary: thermometer, temperature, degrees, Fahrenheit, Celsius, scale, interval

Lesson: 1. Examine two thermometers, one at room temperature and one that has been placed in

a glass of ice water. Point out the scale used on the thermometer. What interval does the thermometer show?

2. Work with students to construct number lines counting by 1, 2, 3, 4, etc. on paper. 3. Have newspaper pages giving weather data available for children to use to collect

temperature readings. 4. Let each student select a temperature reading and decide on a scale to show that

temperature on a thermometer. 5. After each student has completed a thermometer, have students exchange papers, and

allow each student to read the thermometer traded to the group.

6. Students must also identify the scale being used.


What is temperature? (a numerical number telling how hot or cold an object is in degrees.)

How do we measure temperature? (by degrees on a thermometer)

What do we mean by the scale being used on the thermometer? (the interval being the marks on the thermometer, which may be counting by 1, 2, or 4, etc).

What is the interval on most thermometers? (Usually the interval is in 2 degrees.)


Guided Practice: 1. The high temperature for the day is 77 degrees Fahrenheit. The low temperature is 45

degrees Fahrenheit. What is the difference between the high and low temperature?

What interval is being used on these thermometers? (4 degrees)

How would you find the difference in the temperature? (Subtract to find the difference.)

I found the difference by: (Answers may vary.)

Let’s practice reading a Celsius thermometer. (See: Practice Reading Thermometer is Celsius student handout.)

2. Ask the students to compare and contrast the two thermometers.

What is the reading of the first thermometer? (29º C)

What is the reading of the second thermometer? (37º C)

Write a complete sentence describing the temperature change. Be sure to include the words increased or decreased. (The temperature on the second thermometer increased by 8º C.)

3. Ask the students to compare and contrast the two thermometers.

What is the reading of the first thermometer? (27º C)

What is the reading of the second thermometer? (15º C)

Write a complete sentence describing the temperature change. Be sure to include the words increased or decreased. (The temperature on the second thermometer decreased by (12º C.)

4. Practice thermometers in Celsius. See handout.

80°

76°

72°

68°

64°

60°

56°

52°

48°

44°

40°

80°

76°

72°

68°

64°

60°

56°

52°

48°

44°

40°


Assessment: 1. Look at the thermometer pictured below and read it correctly.

A. 75 *B. 72 C. 71 D. 70

2. Jimmy went outside to play ball at 3:30 p.m. The temperature was 78 degrees. While he

was playing, a cold front blew in. By 5:30 p.m. the temperature was 52 degrees. How much did the temperature drop in two hours?

F. 12 degrees G. 20 degrees *H. 26 degrees J. 100 degrees

3. At noon, the temperature was 23 degrees warmer than it was at 7:00 a.m. The

temperature at 7:00 a.m. was 38 degrees. What was the temperature at noon?

A. 71 degrees B. 15 degrees *C. 61 degrees D. 62 degrees

80°

76°

72°

68°

64°

60°

56°

52°

48°

44° F


Guided Practice: Temperature Reporting Category 4: TEKS 5.11(A)

Name: ____________________________ Date: __________________ 1. The high temperature for the day is 77 degrees Fahrenheit. The low temperature is 45 degrees Fahrenheit. What is the difference between the high and low temperature?

What interval is being used on these thermometers? ________________________________________________________________________ ________________________________________________________________________

How would you find the difference between the high and low temperatures? ________________________________________________________________________ ________________________________________________________________________

I found the difference by: ________________________________________________________________________ ________________________________________________________________________

80°

76°

72°

68°

64°

60°

56°

52°

48°

44°

40°

80°

76°

72°

68°

64°

60°

56°

52°

48°

44°

40°


Guided Practice: Reporting Category 4: TEKS 5.11(A) Temperature

42°

40°

38°

36°

34°

32°

30°

28°

26°

24°

22°Cº

42°

40°

38°

36°

34°

32°

30°

28°

26°

24°

22° Cº

What is the reading of the first thermometer? ______________________________

What is the reading of the second thermometer? ______________________________

Write a complete sentence describing the temperature change. Be sure to include the words increased or decreased. _____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

2.

1st 2nd


Guided Practice: Temperature Reporting Category 4: TEKS 5.11(A)

60°

54°

48°

42°

36°

30°

24°

18°

12°

6°

0° Cº

60°

54°

48°

42°

36°

30°

24°

18°

12°

6°

0°Cº

3.

What is the reading of the first thermometer? ______________________________

What is the reading of the second thermometer? ____________________________

Write a complete sentence describing the temperature change. Be sure to include the words increased or decreased. _____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

1st 2nd


Assessment: Temperature Reporting Category 4: TEKS 5.11(A)

Name: ____________________________ Date: __________________

1. Look at the thermometer pictured below and read it correctly.

A. 75 B. 72 C. 71 D. 70

2. Jimmy went outside to play ball at 3:30 p.m. The temperature was 78 degrees. While he was playing a cold front blew in. By 5:30 p.m. the temperature was 52 degrees. How much did the temperature drop in two hours?

F. 12 degrees G. 20 degrees H. 26 degrees J. 100 degrees

3. At noon, the temperature was 23 degrees warmer than it was at 7:00 a.m. The temperature at 7:00 a.m. was 38 degrees. What was the temperature at noon?

A. 71 degrees B. 15 degrees C. 61 degrees D. 62 degrees

80°

76°

72°

68°

64°

60°

56°

52°

48°

44° F



TEKS 5.6: The student describes relationships mathematically.


Student Expectations:. 5.6(A): The student is expected to select from and use diagrams and equations such as y = 5 + 3 to represent meaningful problem situations. 5.14(A): The student is expected to identify the mathematics in everyday situations. TEKS 5.6(A) has been divided into two separate lessons. Lesson 1: Use diagrams to represent real‐life situations. Assessment will follow Lesson #2

Overview Students will read number sentences with labels to determine if the story makes sense and matches the story given.

Materials Blank paper

Vocabulary number sentence (or equation), number expression, real‐life situation

Lesson 1. Write the problem below on the board or overhead.

Tomisha wanted to plant 30 plants in five rows in the front of her house and 18 plants in 3 rows on the side of her house. By noon, Tomisha had planted one row in the front and one row on the side. Which expression models the total number of plants Tomisha had planted by noon?

A. (30 ‐ 5) x (18 ‐ 3) B. (30 + 18) x (5 + 3) C. (30 x 5) + (18 x 3) D. (30 ÷ 5) + (18 ÷ 3)

2. Ask students to read each sentence in the problem and draw a representation of it in

their journal. Pay close attention to what the problem is saying. It is important for students to process the information in the problem before looking at the answer choices.


3. Study the labels that go with each number in the problem to help draw the representation (E.g., 30 plants – the label tells me what it is I am to draw. In this example I would draw 30 “plants.”)

4. Instruct students to choose which expression with labels makes the most sense for the given problem. It is important to explain that there can be more than one way to express a real‐life situation mathematically.

Ask:

What does “30” represent? (30 = number of plants in front of the house)

What does “5” represent? (5 = number of rows in the front of the house)

What does “18” represent? (18 = number of plants on the side of the house)

What does “3” represent? (3 = number of rows on the side of the house)

What is being asked in this problem? (Determine which expressions represent the information in the problem.)

Look at answer A. Does it make sense when you put the labels with the numbers?

(30 plants minus 5 rows) times (18 plants minus 3 rows) will tell us the total number of plants that Tomisha had planted in one row in the front and one row on the side (does not make sense.)

Look at answer B. Does it make sense when you put the labels with the numbers? (30 plants plus 18 plants) times (5 rows plus 3 rows) will tell us the total number of plants that Tomisha had planted in one row in the front and one row on the side (does not make sense.)

Look at answer C. Does it make sense when you put the labels with the numbers? (30 plants times 5 rows) plus (18 plants times 3 rows) will tell us the total number of plants that Tomisha had planted in one row in the front and one row on the side (does not make sense.)

Look at answer D. Does it make sense when you put the labels with the numbers? (30 plants divided by 5 rows) plus (18 plants divided by 3 rows) will tell us the total number of plants that Tomisha had planted in one row in the front and one row on the side (yes this answer makes sense.)

Which one makes sense? The expression needs to tell the same story as the

problem. How many plants are there in each row?



How do we know what the numbers represent in a math problem?

(The sentence will tell students what the number stands for in the problem. We call this the “label.” For example, “five rows of flowers” means there are five rows. The “5” describes the number of rows.)

What is the difference between a “number sentence” and an “expression”? (Number expressions describe real‐life situations using numbers and operations but do NOT have an equal sign. Number sentences describe real‐life situations using numbers, operation signs, and DOES include an equal sign. The number sentence or expression tells the same story as the story in the problem.)

What can you do to help you figure out what the problem is saying? (You can draw a representation of the problem.)

Guided Practice:

Caroline and her four brothers are buying hot dog buns for a party she is throwing at the park. She needs at least 96 buns. Each package of hot dog buns contains eight buns. A package of buns costs $2.00 at the store. Which expression models how much she will pay for enough bun packages to meet her needs?

A. (96 + 4) ÷ (8 x 2) B. (96 – 4) ÷ (8 x 2) C. (96 ÷ 2) x 8 D. (96 ÷8) x 2

What does “4” represent? (4 = number of brothers Caroline has)

What does “96” represent? (96 = number of hot dog buns she needs)

What does “8” represent? (8 = number of buns in 1 package)

What does “2” represent? (2 = how much 1 package of buns cost)

What is being asked in this problem? (Determine which expressions shows how much money the buns will cost in all.)

Look at answer A. Does it make sense when you put the labels with the numbers?

(96 _______ + 4___________)÷(8_____________ x 2___________) will tell us how much money the buns will cost.

Does this make sense? Why or why not? __________________________________________________________________


Look at answer B. Does it make sense when you put the labels with the numbers?

(96 __________ – 4_____________) ÷ (8 _____________x 2_________________) will tell us how much money the buns will cost.


Look at answer C. Does it make sense when you put the labels with the numbers?

(96 _________________÷ 2__________________) x _________________________ will tell us how much money the buns will cost.


Look at answer D. Does it make sense when you put the labels with the numbers?

(96 ___________________÷8___________________) x _______________________ will tell us how much money the buns will cost.


The expression needs to tell the same story as the problem. How much money will the buns cost in all?

Assessment: Assessment will follow Lesson #2.


Guided Practice: Reporting Category 2: TEKS 5.6(A) and 5.14(A)

Name_________________________________________ Date________________________ Caroline and her 4 brothers are buying hot dog buns for a party she is throwing at the park. She needs at least 96 buns. Each package of hot dog buns contains 8 buns. A package of buns costs $2.00 at the store. Which expression models how much she will pay for enough bun packages to meet her needs?

A. (96 + 4) ÷ (8 x 2) B. (96 – 4) ÷ (8 x 2) C. (96 ÷ 2) x 8 D. (96 ÷8) x 2

1. What does “4” represent? __________________________________________________________

2. What does “96” represent? _________________________________________________________ 3. What does “8” represent? __________________________________________________________ 4. What does “2” represent? __________________________________________________________

5. What is being asked in this problem? __________________________________________ _________________________________________________________________________ 6. Look at answer A. Does it make sense when you put the labels with the numbers? (96 _______ + 4___________)÷(8_____________ x 2___________) will tell us how much money the buns will cost. Does this make sense? Why or why not? _______________________________________ _________________________________________________________________________ 7. Look at answer B. Does it make sense when you put the labels with the numbers?

(96 ____________ – 4_______________) ÷ (8 _____________x 2___________________) will tell us how much money the buns will cost. Does this make sense? Why or why not? ______________________________________


_________________________________________________________________________ 8. Look at answer C. Does it make sense when you put the labels with the numbers?

(96 _____________________÷ 2______________________) x 8_____________________

will tell us how much money the buns will cost.

Does this make sense? Why or why not? _________________________________________

___________________________________________________________________________ 9. Look at answer D. Does it make sense when you put the labels with the numbers?

(96 ______________________÷8______________________) x 2_____________________ will tell us how much money the buns will cost. Does this make sense? Why or why not? ________________________________________

10. The expression needs to tell the same story as the problem. How much money will the buns cost in all? ___________________________________________________________



TEKS 5.6: The student describes relationships mathematically.


Student Expectations:. 5.6(A) The student is expected to select from and use diagrams and equations such as y = 5 + 3 to represent meaningful problem situations. 5.14(A) The student is expected to identify the mathematics in everyday situations. TEKS 5.6(A) has been divided into two separate lessons. Lesson 2: Select equations to represent real‐life situations. Assessment follows Lesson #2

Overview: Students will match cards of real‐life situations and number sentences.

Materials: Set of Matching cards

Vocabulary: equation, expression, real‐life situation

Lesson: 1. Copy the cards on the following page onto card stock paper. Cut out, mix up, and place

in a bag.

2. Instruct students to match the real‐life situation to its equation or expression.

3. Variation: Give students three situation cards with all five equations.

DebriefingQuestions:

What is the difference between a “number sentence” or “equation” and an “expression?” (Number expressions describe real‐life situations using numbers and operations but do NOT have an equal sign. Number sentences (or equations) describe real‐life situations using numbers, operation signs, and DOES include an equal sign. The number sentence or expression tells the same story as the story in the problem.)


Guided Practice:

Read each problem first. Read each sentence.

Stop and draw a representation of what is written.

Read another sentence.

Stop and draw a representation of what it says.

Continue to do this until the whole problem has been read.

Read each answer choice with the labels in the problem and ask yourself if it makes sense. (For example, in the first problem, the equation 12 x 8 = p means 12 pages x 8 pictures on each page equals p, the total number of pictures.)

1. Elisa put pictures in a scrapbook. She finished 12 pages in the book with 8 pictures on each page. Which equation cannot be used to find p, the total number of pictures in the scrapbook?

A. 12 x 8 = p *B. 8 + p = 12 C. p ÷ 8 = 12 D. p ÷12 = 8

2. David packaged cookies for a school bake sale. He had 36 medium‐sized chocolate chip

cookies and 24 large peanut butter cookies. He made bags of 3 chocolate chip cookies and bags of 2 peanut butter cookies. Which equation shows how many bags of cookies David has for the bake sale?

F. 36 + 24 + 5 = 65 G. (36 x 3) + (24 x 2) = 156

* H. (36 ÷ 3) + (24 ÷ 2) = 24 J. (36 – 24) x (3 + 2) = 60


Assessment: 1. Billy needs to place new tile on his kitchen floor. Each tile is one square foot. If the room

is 12 ft. long and 11 ft. wide, which equation will show how many tiles, t, Billy needs to buy.

A. 12 + 11 = t *B. 11 x 12 = t C. t x 11 = 12 D. 12 ÷ t = 11

2. Over the summer Tanya earned $21 dollars babysitting, $14 doing extra chores, and $16

for taking care of the neighbor’s dogs. She wants to buy a shirt for $12, a pair of pants for $18, and a pair of shoes for $15. Which shows what Tanya needs to do in order to find out if she has enough money to buy the new clothes?

*F. m= (21 + 14 + 16) ‐ (12 + 18 + 15) G. m= (21 + 14 + 16) + (12 + 18 + 15) H. m= (12 + 18 + 15) ‐ (21 + 14 + 16) J. m= (21 + 14 + 16 ) x (12 + 18 + 15)

3. John is driving out of state to visit his mother. John is planning on driving between 450 and 550 miles each day. He figures it will take him 4 days to get to his mother’s house. Which equation shows about how far John lives from his mother?

A. 450 + 550 = d B. d= (450 + 550) x 4 *C. 500 x 4 = d D. d=(550 – 450) x 4


Matching Cards TEKS 5.6(A) and 514(A) Lesson 2

Danny bought 5 pencils for $0.45 each. He bought 2 packs of paper for $1.25 each. Which equation can be used to find out how much change Danny would get back if he paid for the supplies with a $10.00 bill?

10.00 – (5 x 0.45) – (2 x 1.25) = c

Juan bought 2 erasers for $0.45 each and 5 gel pens for $1.25 each. Which equation can be used to find out how much change Juan would get back if he paid for the supplies with a $10.00 bill?

c= 10.00 – (2 x 0.45) – (5 x 1.25)

Jessica went to a baseball game and bought 2 lunches for $10.00, 5 pieces of gum for $0.45, and a piece of pie for $1.25. Which equation shows how much Jessica spent on food at the baseball game?

10.00 + 0.45 + 1.25 = $11.70

Alexi bought 5 bracelets for $1.25 each, 2 rings for $0.45 each, and purse for $10.00. Which equation shows how much money, Alexi spent at the store?

10.00 +(5 x 1.25) + (2 x 0.45) = $17.15

Jimmy bought 5 candy bars for $0.45 each and 2 comic books for $1.25 each. He paid for everything with a $10.00 bill. Which equation shows how much more Jimmy spent on the comic books than on the candy bars?

(2 x 1.25) – (5 x 0.45) = c


Guided Practice: Reporting Category 2: TEKS 5.6(A) and 5.14(A)

Name: ____________________________ Date: __________________

1. Elisa put pictures in a scrapbook. She finished 12 pages in the book with 8 pictures on each page. Which equation cannot be used to find p, the total number of pictures in the scrapbook?

A. 12 x 8 = p B. 8 + p = 12 C. p ÷ 8 = 12 D. p ÷12 = 8

2. David packaged cookies for a school bake sale. He had 36 medium‐sized chocolate chip cookies and 24 large peanut butter cookies. He made bags of 3 chocolate chip cookies and bags of 2 peanut butter cookies. Which equation shows how many bags of cookies David has for the bake sale?

F. 36 + 24 + 5 = 65 G. (36 x 3) + (24 x 2) = 156 H. (36 ÷ 3) + (24 ÷ 2) = 24 J. (36 – 24) x (3 + 2) = 60


Assessment: Reporting Category 2: TEKS 5.6(A) and 5.14(A)

Name: ____________________________ Date: __________________ 1. Billy needs to place new tile inside of his kitchen. Each tile is one square foot. If the room is 12 ft. long and 11 ft. wide, which equation will show how many tiles, t, Billy needs to buy.

A. 12 + 11 = t B. 11 x 12 = t C. t x 11 = 12 D. 12 ÷ t = 11

2. Over the summer Tanya earned $21.00 dollars babysitting, $14.00 doing extra chores, and $16.00 for taking care of the neighbor’s dogs. She wants to buy a shirt for $12.00, a pair of pants for $18.00, and a pair of shoes for $15.00. Which equation shows what Tanya needs to do in order to find out if she has enough money to buy the new clothes?

F. m=(21 + 14 + 16) ‐ (12 + 18 + 15) G. m=(21 + 14 + 16) + (12 + 18 + 15) H. (12 + 18 + 15) ‐ (21 + 14 + 16) = m J. (21 + 14 + 16) x (12 + 18 + 15) = m

3. John is driving out of state to visit his mother. John is planning on driving between 450 and 550 miles each day. He figures it will take him four days to get to his mother’s house. Which equation shows about how far John lives from his mother?

A. 450 + 550 = d B. d= (450 + 550) x 4 C. 500 x 4 = d D. d= (550 – 450) x 4



TEKS 5.9: The student recognizes the connection between ordered pairs of numbers and locations of points on a plane.

Student Expectations: 5.9(A) The student is expected to locate and name points on a coordinate grid using ordered pairs of whole numbers.

Overview:

This activity will allow students to practice locating points on a coordinate grid. This activity is intended for groups of four to six students.

Materials: Masking tape in two colors E.g., 3X5 index cards with an ordered pair of street names and houses written large enough to be seen from a distance (see sample page; one per student) Pencils

Vocabulary: horizontal line, vertical line, plane, coordinate plane, ordered pair, origin, coordinates, number line

Lesson: 1. Prior to the introduction above, mark a coordinate grid on the floor with masking tape.

Use one color of tape for the “x”‐axis and a different color of tape for the “y”‐axis. Label the “x”‐axis with several names of local streets or the street names given in the sample list. Label the “y”‐axis with numbers from 0 to about 15. Scale the axis with numbers approximately twelve inches apart. The origin (0,0) should be clearly labeled. A partial sample is below:

6

5

4

3

2

1

2 4 6 8(0, 0) Travis Seguin

Streets


2. Does the mailman ever deliver mail to your house? Allow students to respond briefly. When the mailman delivers a letter to your house, how does he know which house is yours? Lead a brief discussion about the street name and the house number.

Does the mailman find your street first or your house number first? (street first, then house number)

Why? (If he tried to find your house number first, he would be looking on every street.) The street name and your house number are used to locate your house. We could write your address as an ordered pair to help us find your house. For example, I live at 720 Main Street. I could write this as the ordered pair of (Main Street, 720) since the mailman finds Main Street first, then my house number. This is called an ordered pair because we have two bits of information, street and house number, and the order makes a difference. The mailman always finds the street first and the house second. How would we write your address as an ordered pair? On a sheet of paper, have students write their name and addresses as ordered pairs. Discuss these with the students as needed.

Today we are going to use ordered pairs of numbers to locate, or find, locations on a coordinate grid.

3. Distribute an ordered pair of street name and house number to each student, keeping

one for yourself for demonstration purposes.

4. Have students gather around the floor grid. Say:

We are going to use addresses to locate houses on this grid. I have a grid marked on the floor. The horizontal axis is usually called the “x”‐axis and represents the streets in this situation. Can you point to the horizontal axis? (Allow all students to point to the x‐axis)

The vertical axis is usually called the “y”‐axis and represents the house numbers in this situation. Can you point to the vertical axis? (Allow all students to point to the y‐axis.)

5. Tell the students:

I have the ordered pair (Seguin, 6). This ordered pair gives us enough information to locate point on this particular grid. Can you tell me why this is called an ordered pair? (because there are two bits of information and the order is important)

What is the first bit of information in my ordered pair? (Seguin)

This means I should walk along the “x”‐axis to the line that is labeled “Seguin.” Where should I start walking? It is important that the students understand to start at the origin (0, 0).

How big a step should I take? It is also important that students understand that you are to take one step for each street on the grid.


With the students coaching you, walk the appropriate number of steps along the x‐axis to the line representing Seguin Street. Still standing on the x‐axis, ask the students, I am now ready to use the second bit of information in the ordered pair, the house number of 6. Since the vertical axis represents the house number, I should walk six steps parallel to the vertical axis. Demonstrate walking the six steps. Place the index card on the location of the ordered pair. Lead a brief discussion reviewing how you found the location of your house. Stress to the students that you started walking the six steps from where you were on the x‐axis. You did not go back to the origin as some students erroneously try to do.

6. Allow each student to repeat the process of walking to the location of the ordered pair

assigned to him or her. If needed, other students can coach the current participant. Each student should place his or her index card on the correct location. Check that the students are placing the cards at the intersection of the lines rather than in the squares between the lines.


Stress to the students that when plotting ordered pairs on a coordinate grid, the first number always indicates how far to move to the right, and the second number indicates how far to move vertically. A saying that seems to help students remember this is, “you have to walk to the elevator before you can go up.” Check for understanding with these questions:

Give me an example of an ordered pair. (E.g., (4, 6))

Why is this called an ordered pair? (because the order makes a difference)

Which direction does the first number in the pair go? (to the right or horizontally)

Which direction does the first number in the pair go? (up or vertically)

Show me on the graph where the ordered pair (3, 2) would be located. (Watch as student places the point at (3, 2)).


Guided Practice: Distribute the guided practice worksheet. Say: Let’s practice our skills.

1. Look at the coordinate grid:

What are the coordinates of Point E?

A. Beginning at 0, Point E is _(4)_____ units to the right. B. Going up from the x‐axis, Point E is _(4)____units up. C. The coordinates of Point E are ( __4_____, ___4____).


What are the coordinates of Point A, Point B, and Point C, Point D, and Point E? A. The coordinates of Point A are (__0__, __ 5___). B. The coordinates of Point B are (__1___, __3__). C. The coordinates of Point C are (__3___, __1___). D. The coordinates of Point D are (__5___, __0__). E. The coordinates of Point E are (__4__, __4___).

6

5

4

3

2

1

2 4 6 8

E

D

C

B

A

0

6

5

4

3

2

1

2 4 6 8

E

D

C

B

A

0


Assessment: 1. Which ordered pair names the location of Point M?

A. (3, 3) *B. (2, 5) C. (6, 3) D. (5, 5)

2. Which point is located at (5, 0)?

F. Point M G. Point A H. Point T *J. Point H

6

5

4

3

2

1

2 4 6 8

HT

AM

(0, 0)

6

5

4

3

2

1

2 4 6 8

G

0H

T AM


3. The graph shows some areas of a zoo.

Which area of the zoo is best represented by the ordered pair (1, 3)?

A. Bears B. Giraffes C. Monkeys

*D. Elephants

6

5

4

3

2

1

2 4 6 8

Bears

Elephants

Giraffs

Lions

Monkeys

0


Reporting Category 3: TEKS 5.9(A)

Sample Ordered Pairs of Streets and House Numbers

1. (Main, 7)

2. (Elm, 5)

3. (Pecan, 10)

4. (River, 2)

5. (King, 0)

6. (Bowie, 8)

7. (Travis, 1)

8. (Seguin, 6)

9. (Court, 4)

10. (Congress, 3)



Name: __________________________ Date: _________________


What are the coordinates of Point E?

A. Beginning at 0, Point E is _________ units to the right.

B. Going up from the x‐axis, Point E is ________units up.

C. The coordinates of Point E are ( ________, ________).

6

5

4

3

2

1

2 4 6 8

E

D

C

B

A

0



What are the coordinates of Point A, Point B, Point C, Point D, and Point E?

A. The coordinates of Point A are (_____, _____).

B. The coordinates of Point B are (_____, _____).

C. The coordinates of Point C are (_____, _____).

D. The coordinates of Point D are (_____, _____).

E. The coordinates of Point E are (_____, _____).

1 3 5 7 9

6

5

4

3

2

1

2 4 6 8

E

D

C

B

A

0



Name: ___________________________ Date: __________________

1. Which ordered pair names the location of Point M?

A. (3, 3) B. (2, 5) C. (6, 3) D. (5, 5)

1 3 5 7 9

6

5

4

3

2

1

2 4 6 8

HT

AM

(0, 0)


2. Which point is located at (5, 0)?

F. Point M G. Point A H. Point T J. Point H

6

5

4

3

2

1

2 4 6 8

G

0H

T AM


3. The graph shows some areas of a zoo.

Which area of the zoo is best represented by the ordered pair (1, 3)?

A. Bears B. Giraffes C. Monkeys D. Elephants

6

5

4

3

2

1

2 4 6 8

Bears

Elephants

Giraffs

Lions

Monkeys

0



TEKS 5.11: The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius).

Student Expectations: 5.11(B) The student is expected to solve problems involving elapsed time.

Overview: Students will practice telling time, reading an analog clock, and working with elapsed time.

Materials: Paper plate clock with hour hand attached with brad – one per student Judy Clock (or other clock manipulative) – one per student Number lines Ruler Yardstick Hour Arrow Minute Arrow Index Cards with a time written on each – one per student

Vocabulary: elapsed time, analog clock, digital clock, hour hand, minute hand, start time, stop time

Procedure: Before this lesson begins, cut out the hour and minute hand arrows. Tape the hour arrow to a ruler (12 in.), and tape the minute arrow to the end of a meter or yard stick. These will be visuals to help students better identify the hands of a clock. Note: This lesson is broken into two parts: (1) Telling Time Review and (2) Elapsed Time. It is important that students are comfortable reading times on an analog clock BEFORE learning elapsed time.

Part 1: Telling Time Review 1. Ask students what the term time means to them.

2. Each student should have a paper plate clock with ONLY the hour hand present. It is

important to review with students the placement of the hour hand on an analog clock as the hour progresses. The closer the time is to the next hour, the closer the hour hand is to the next number. Students show hour hand on their clocks as they answer the following questions.

Suppose class begins at 8:00 a.m. How would the hour hand look on the clock? (The hour hand would be right on the 8).


Show me on your clock. Suppose class ends at 3:30 p.m. How would the hour hand look on the clock? (halfway between 3 o’clock and 4 o’clock)

Show me on your clock. Suppose school got out at 2:50 p.m. How would the hour hand look on the clock? (almost to the 3 o’clock)

Show me on your clock. Discuss with students the movement of the hour hand. The hour hand moves 60 times between each hour. With each minute that passes, the hour hand moves closer to the next hour. Because the movement is 1/60 of the space between the numbers, it is too small for us to see it move, but it does.

Give students a few more times to show where the hour hand would be on their plate clock to practice this skill before moving on.

3. Discuss counting by minute intervals. What else would we need to put on the clock to

show the minute intervals? (minute hand)

Use the one‐handed clocks each set to a different hour. Place them in a large circle forming a clock face. Take the meter stick (known as the minute hand) and the ruler (known as the hour hand), and place them in the middle of the clock face to show 12:00 p.m. Have students sit on the floor around the human size clock so that they can see the times being shown.

We are going to practice showing and telling time on our human size analog clock. What time is the clock showing? (12:00 p.m.)

This will be our starting point for each time. When it is your turn, you will need to put the clock hands at 12:00 to start your turn. I’m going to start. I am going to show you a time on the human size clock. I want you to write the time you think I am showing on your dry erase board. Please do NOT shout out the time or tell your neighbor. Show the time 1:50 p.m. on the clock. Allow students time to write the time on their dry erase boards, and then ask them to hold it up so that you can check.

How did you know it wasn’t 2:50 p.m.? (because the hour hand wasn’t on the 2 yet)

How did you know the minute was 50 and not 10? (Because when dealing with minutes, each number on the clock face represents a multiple of 5 so when it is pointing to the ten that represents 50.)

Give each student an index card with a time written on it. They may NOT show anyone their card. This will be the time they are to represent on the human size clock when it is their turn. Each student will be given a turn to go to the human size clock, create the time on their index card, and the other students will write down the time they believe is being shown. Remind the students that the hour hand is ONLY on one of the clock face numbers when it is “o’clock.” Students will show their dry erase boards to the student and he or she will say yes or no.


Part 2: Elapsed Time 1. Pass out the Judy Clocks (or other clock manipulatives) for the students to work with

during this part of the lesson. Present the following problem on the board:

Suppose on early dismissal day school begins at 8:10 a.m. Class is dismissed at 1:30 p.m. How many hours and minutes is class on that day?

Let’s use our Judy Clocks to help us answer this problem.

What time does school begin? (8:10 a.m.)

Let’s make our clock represent that time. What does the question ask us to find? (How many hours and minutes we are in school.)

Write __________ hours and _____________ minutes on the board. They are asking us for two different things–hours AND minutes. We are going to work with them one at a time. Let’s start with hours first.

If our clock is showing 8:10 and we sit in class for one hour, what time will our clock show? (9:10) Show this with your clock.

What if we sit in class for another hour? (10:10) Show this with your clock.

Another hour? (11:10)



Can I add another hour to my clock? (No, we cannot because school lets out at 1:30 and if we add another hour, it would be 2:10 and that is past the time we want.)

So how many hours was that? (5 hours) Write a 5 in the hours blank on the board. Now we are going to work on the second part, which is the minutes. Our clocks should be at 1:10 p.m.

What should our counting interval be when counting our minutes? (five minute intervals)

What time will our clock show if I add 1 five minutes interval? (1:15 p.m.)

Can I add another 5 minute interval? (yes)

What time will it be? (1:20 p.m.)





Can I add another 5 minute interval? (no) Why not? (because we have reached our end time of 1:30 p.m.)

How many 5 minute intervals did we add to 1:10 p.m. to get to 1:30 p.m.? (four 5‐minute intervals)

So how many minutes total is that? (20 minutes because 4 x 5 = 20) Write that in the minutes blank on the board.


Practice this quite a few times together. Give the class a start and stop time, and have them use their Judy Clocks to determine how many hours and minutes it is between the two times.

2. Once students have become familiar with counting the hours and minutes using a clock

manipulative, teach students how to organize their information either by using a number line or a chart. Examples of both using the first example are shown below.

Using a number line:

Hours Minutes 8:10 9:10 10:10 11:10 12:10 1:10 1:15 1:20 1:25 1:30

Start 5 hr 5 5 5 5 End This could be called the bar and loop method. Have students count the sections marked by the bars as hours and the loops as the minutes.

Using a chart:

Hours Minutes

8:10 1:10

9:10 1:15

10:10 1:20

11:10 1:25

12:10 1:30

1:10

Answer: 5 hours and 20 minutes

3. Show students how to use both methods when they are:

given the start and stop times, and they are to find the elapsed time.

given the start time and elapsed time, and they are to find the stop time.

given the stop time and elapsed time and they are to find the start time.

Guided Practice: On Saturday, Daniel went to bed at 9:05 p.m. He watched television for 2 hours and 20 minutes? What time did he begin watching TV?

What time did Daniel go to bed? (Let’s begin with 9:05 p.m.) This can also be thought of as 5 minutes past 9:00).

Put that time on your clock.

How long did he watch TV? (2 hours and 20 minutes)

1 hour

1 hour

1 hour

1 hour

1 hour

5 min

5 min

5 min

5 min


If you wanted to show that time on your clock, which way do you move the clock hands? (Counterclockwise) You may find it necessary to discuss the terms clockwise and counterclockwise. Allow students to observe a large wall clock and the movement of the second hand.

Which hand do you have to move on the clock? (hour hand)

By how much do you move the clock hands? (Move your clock hand back one hour. What time is it now? (8:05 p.m.)

Do you need to move the clock hands back another hour? (yes, one more hour) . What time is it now? (7:05 p.m.)

Do you need to move the clock hand back another hour? (no)

Which hand do you have to move now? (minute hand) By how much? (20 minutes)

What time did Daniel begin watching TV? (6:45 p.m.)

Can you model this on a number line and in the chart to check your answer? 6:45 7:05 8:05 9:05

End Start 5 5 5 5 Minutes Hours

OR

Hours Minutes

9:05 7:05

8:05 7:00

7:05 6:55

6:50

6:45

Answer: 6:45 p.m.

1 hour

1 hour

5 min

5 min

5 min

5 min


Assessment: 1. Look at the clocks.

The football game began at 3:15 p.m. and ended at 5:45 p.m. How long did the game last?

A. 3 hours B. 30 minutes *C. 2 hours 30 minutes D. 2 hours 45 minutes

2. Susie began reading at 8:30 a.m. She read for 2 hours and 45 minutes. What time did

Susie finish reading?

F. 4:15 a.m. *G. 11:15 a.m. H. 10:15 a.m. J. 11:45 a.m..

3. Juan and his family left home at 7:16 a.m. and returned at 9:45 p.m. as shown on the

clock faces below?

How many hours and minutes was the family gone from home?

A. 2 hours 29 minutes B. 15 hours 29 minutes C. 14 hours 31 minutes *D. 14 hours 29 minutes

4. John went canoeing down the Guadalupe River for 95 minutes. If he began his canoeing

adventure at 11:00 a.m., what time did he finish? F. 35 minutes past one G. one thirty‐five H. eleven thirty‐five J. 35 minutes past noon *


Guided Practice: Reporting Category 4: TEKS 5.11(B)

Name: ____________________________ Date: __________________ On Saturday, Daniel went to bed at 9:05 p.m. He watched television for 2 hours and 20 minutes? What time did he begin watching TV? 1. What time did Daniel go to bed? ____________________________________________ 2. Put that time on your clock. 3. How long did he watch TV? _______________________________________________ 4. If you wanted to show that time on your clock, which way do you move the clock hands? _______________________________________________________________________ 5. Which hand do you have to move on the clock? ______________________________ 6. By how much do you move the clock hands? __________________________________ What time is it now? ___________ 7. Do you need to move the clock hands back another hour? _______________________ What time is it now? ___________ 8. Do you need to move the clock hand back another hour? ________________________ 9. Which hand do you have to move now? _______________________________________ By how much? __________________________________________________________ 10. What time did Daniel begin watching TV? ____________________________________


11. Can you model this on a number line and in the chart to check your answer?

Hours Minutes


Assessment: Reporting Category 4: TEKS 5.11(B)

Name: ____________________________ Date: __________________

1. Look at the clocks.

The football game began at 3:15 p.m. and ended at 5:45 p.m. How long did the game last?

A. 3 hours B. 30 minutes C. 2 hours 30 minutes D. 2 hours 45 minutes

2. Susie began reading at 8:30 a.m. She read for 2 hours and 45 minutes. What time did

Susie finish reading?

F. 4:15 a.m. G. 11:15 a.m. H. 10:15 a.m.. J. 11:45 a.m.

3. Juan and his family left home at 7:16 a.m. and returned at 9:45 p.m. as shown on the

clock faces below?

How many hours and minutes was the family gone from home? A. 2 hours 29 minutes B. 15 hours 29 minutes C. 14 hours 31 minutes D. 14 hours 29 minutes

Start Finish


4. John went canoeing down the Guadalupe River for 95 minutes. If he began his canoeing adventure at 11:00 a.m., what time did he finish?

F. 35 minutes past one G. one thirty‐five H. eleven thirty‐five J. 35 minutes past noon


Analog Clock Transparency

5th sense math book

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