Unit Writing GuideInstructional Unit Design Outline

Unit Title: Comparing 3-digit numbers.

Unit Designer(s): Clare Harrington

Grade Level(s): 2

Time Span: Focus lessons – 3 days, continuing practice throughout the year.

Math program used: Everyday Mathematics, CCSS edition

Content Area(s):

Career Prep Health and PE M & C Languages Social Studies

English Language Arts Mathematics Science and Technology Visual & Performing Arts

Common Core State Standard(s) focus: CCSS.Math.Content.2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Domain Progression:

Grade 1: Grade 2: Grade 4:CCSS.Math.Content.1.NBT.B.2  Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

CCSS.Math.Content.1.NBT.B.2a  10 can be thought of as a bundle of ten ones — called a “ten.”

CCSS.Math.Content.1.NBT.B.2b  The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

CCSS.Math.Content.1.NBT.B.2c  The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

CCSS.Math.Content.1.NBT.B.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

CCSS.Math.Content.2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

CCSS.Math.Content.2.NBT.A.1a 100 can be thought of as a bundle of ten tens — called a “hundred.”

CCSS.Math.Content.2.NBT.A.1b The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

Target Standard:CCSS.Math.Content.2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

CCSS.Math.Content.4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

(10 ones) = (1 ten)

= 2,000 is ten times greater than 200. 200 is ten times greater than 20. 20 is ten times greater than 2.

10 tens = 1 hundred

> <

>

53 > 32, look to the tens place first to determine which number has the greatest value

146 < 423, look to the hundreds place first to determine which number has the greatest value

3,132 > 2, 121, look to the digit farthest to the left place to determine which number has the greatest value

Grade 1 students use their base-ten work from Kindergarten to help them formally recognize the “ten” unit. Students understand a two-digit number represents an amount of tens and ones. This leads to knowing that the digit in the tens place is more important than the digit in the ones place for determining the size of a two-digit number. They use this understanding to compare two two-digit numbers, using the appropriate symbols ,<, = and >. Grade 2 students continue their understanding of the base ten system by learning about the unit “hundred”. This also begins the foundations of understanding that our base ten system works on repeated groupings of ten. Students use their understanding of three-digit numbers to form comparisons. They know that if a number has three digits that the number with the “hundred” is larger than any two digit number. They also know that, similar to the tens units, 2 hundreds in greater than 1 hundred. They compare numbers, using the <,=, and > symbols. They also know that in order to compare numbers they must look to the hundreds place first in order to compare the magnitude of the numbers. In Grade 3, the focus of the standards shift to multiplication, so students are applying their understanding of the base ten system without having formally instruction in the understanding of ones, tens and hundreds.Grade 4 students use their knowledge of the base ten system to extend to multi-digit numbers. With their understanding of multiplication from third grade, students use those methods to understand that each digit to the left is 10 times larger than its place value to the right. They can compare any multi-digit number, using the symbols <,=, and >, knowing that the digit farthest to the left has the greatest value.

Resources for content knowledge: http://www.maine.gov/doe/math/standards/ccssm/professional/module2/

index.html - Maine Department of Education site has resources to look at domains of progressions.

Everyday Mathematics Teacher’s Reference Manual . McGraw Hill Wright Group, 2007 Shumway, Jessica F. and West, Lucy, Number Sense Routines: Building Numerical

Literacy Every Day in Grades K-3. Stenhouse Publishers, 2011. Van de Walle, John A., Elementary and Middle School Mathematics: Teaching

Developmentally, Pearson Publishing, 2012. Wright, Robert J., Martland, James, Stafford, Ann K., Stanger, Garry, Teaching Number

in the Classroom with 4-8 year olds. Paul Chapman Publishing, 2006.

Key Pre-RequisitesDeclarative Knowledge Procedural Knowledge

Key Terms: Ones, Tens <, >, = Greater than, Less than Compare

Key Content Specificity: Students will understand tens and ones. Students can record the results of

comparing 2 digit numbers.

Skills: Compare 2 digit numbers Understand ones and tens and

know that 1 ten equals 10 ones.

Key Next ConceptsDeclarative Knowledge Procedural Knowledge

Key Terms: Ones, tens, hundreds, thousands,

ten thousands, hundred thousands Compare 10 times larger

Skills: Compare multi-digit numbers. Recognize that a digit in one place

represents ten times what is represents in the place to its right.

Read and write multi-digit whole numbers.

Summary of Unit: Description: Students will be able to compare three digit numbers and record the

results using appropriate math symbols, >, < and =. Real life experience: This concept is important for students to understand as it

creates the basis for understanding the base ten number system we use in our world. Understanding that a three digit whole number has more value than a two digit whole number helps students understand the magnitude of a number. In order for children to perform multidigit arithmetic successfully, they need to know the value

of any digit based on its place in the numeral. Prior Knowledge: Students should come to this unit with an understanding of ones

and tens and also how to compare 2 digit numbers using the appropriate math symbols. Students should also have had experience with base ten blocks in the earlier grades.

Student Learning Targets: o I know how to compare numbers that have 3 digits in them.o I understand the value of digits in the ones, tens, and hundreds places.o I can use base ten blocks or other manipulatives or visuals to model my

knowledge of place value. Rubric: CCSS.Math.Content.2.NBT.A.4 Compare two three-digit numbers based on meanings

of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

4.0 - In addition to a score of a 3.0 performance, in-depth applications that do beyond what was taught. Student is able to compare numbers beyond 3 digits and explain and/or defend his reasoning.

3.5 - In addition to a score of 3.0 performance, partial success at inferences and application that do beyond what was taught.

3.0- No major errors or omissions regarding any of the information and/or processes (simple or complex) that were explicitly taught. CCSS.Math.Content.2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

2.5 - No major errors or omissions regarding the simpler details and process and partial knowledge of the more complex ideas and processes.

2.0 - No major errors or omissions regarding the simpler details and process but major errors of omissions regarding the more complex ideas and processes. Student can compare three digit numbers, but makes major errors in reasoning.

1.5 - Partial knowledge of eh simpler details and process but with major errors or omissions regarding the more complex ideas and processes.

1.0 - With help, a partial understanding of some of the simpler details and processes and some of the more complex topics. With help, student can compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

0.5 - With help, a partial understanding of some of the simpler details and processes but not with the more complex topics.

0.0 - Even with help, no understanding or skill demonstrated. Student is unable to compare three digit numbers.

Declarative and Procedural knowledge that students will acquire:

New KnowledgeDeclarative Knowledge Procedural Knowledge (skills/reasoning)

Key Terms (for word wall): Hundreds 3-digit number Compare

Key content specificity: Students will understand 3 digit

numbers and the value of each place in a 3 digit number.

Students can record the results of comparing 3 digit numbers.

Skills: Compare 3-digit numbers. Solve comparison word problems Write or illustrate how to compare 3

digit numbers Apply understanding of comparing

3 digit numbers to larger numbers Identify the place value of each digit

in a 3 digit number.

*students have had an introduction and some practice with comparing 3 digit numbers in grade 1 but need to be proficient with it by the end of grade 2.

Key Pre-RequisitesDeclarative Knowledge Procedural Knowledge (skills/reasoning)

Key Terms (for word wall): Ones Tens Digit 2-digit number Greater than Less than Equal to <, >, = symbols

Skills: Compare 2-digit numbers. Solve comparison word problems Identify the place value of each digit

in a 2 digit number.

How will students provide evidence of their developing understandings?(formative assessment)

Teacher will informally check in with students as they are working to check who is successful with the daily tasks.

Circulate the classroom with check list to make notes on observations of student work.During the group lesson, teacher will ask questions and ask various students to

demonstrate examples. Students will engage in think-pair-share times to share their understandings with either

another student or the teacher. Exit slip questions will be required throughout the year to check in on understanding. Recording sheets from games will help guide the teacher as to student’s success on the

activities. Math boxes in student journals will provide quick written check-ins with students.*** refer to unit outline below to see where opportunities are provided throughout the year.

How students will demonstrate successful achievement of the standard: (Summative Assessment)

Summative Assessment is attached below.

Teaching and learning experiences used to help students understand:List all activities.

Activate prior knowledge (e.g. What do you think you know? Preview questions; Brief teacher summary; Skimming; Teacher-prepared notes, etc.)

o In previous lessons, students have learned about comparing 2 digit numbers, do some practice comparing 2-digit numbers on white boards.

o Have students give examples of when they use <,>, or = signs.o Elicit conversation about why it is important to be able to compare

numbers. Share real world examples of why this might be important.

Interacting with new knowledge activities:o Introduce the “hundred” base ten block with students. Show how ten tens

when put together equal a hundred “flat.”o Display word wall terms on the board and have student give examples of

what each term might mean.o Introduce place value mats with hundreds included. Have students place

numbers on the individual places and build the number with manipulatives.

Practicing-knowledge and deepening-knowledge activities: o Play the Digit Gameo Complete Math box problems with comparison problems throughout the

year o Design your own place value mato With teacher guidance, continue to discuss place value when learning new

topics (addition algorithm, etc). Applying the new knowledge (Generating and testing hypotheses)

o Use word problems, requiring written answers, to allow students to share their thinking about how to compare numbers.

o Use understanding of place value to create the highest and lowest possible 3 digit numbers with a given set of digits.

Provisions for extending learning: Explain how these learning activities exceed the expectations.

Students will be introduced to 4 and 5 digit numbers. Students will have opportunities in their math journals and on other tasks to

read, write, record and compare 4 and 5 digit numbers. Students can make their own place value mat to include 4 or more digits.

How will technology be used to increase student achievement? http://www.ixl.com/math/grade-2 - provides opportunities for students to

practice comparing numbers, using both the words and symbols for 2 and 3 digit numbers.

http://www.toonuniversity.com/flash.asp?err=509&engine=9 – online activity to practice comparing 3 digit numbers.

http://www.hbschool.com/activity/elab2004/gr3/2.html - teaching site where

students can see a number line with two numbers on it. Students write a comparison sentence on their white boards or on the recording sheet provided.

www.Thatquiz.com – create online assessments for the students to practice their understanding of comparing three-digit numbers.

www.math-aids.com – dynamically created worksheets. Enables teachers to create practice worksheets based on student needs.

http://exchange.smarttech.com – resource for smartboard activities for the EDM program.

http://www.aaamath.com/g22_cox1.htm#section2 – online practice comparing 3 digit numbers using the symbols and words to compare numbers.

Instructional resources Everyday Mathematics, CCSS edition (teacher manuals, student reference

books, student journals, teacher reference book) Base ten blocks, digi-blocks, place value mats, number cards Technology resources – see above Everyday Math games- Digit Game, High Number toss

Interventions Struggling students:

o In a small group, work on 2 digit place valueo Practice trading game with tens and oneso Modify activities to use 2 not 3 digit numberso Provide base ten blocks or other manipulatives to allow students to

make each number before comparing themo Modify games to simplify for struggling students

Advanced students:o Introduce larger multi-digit numberso Have students create a game or activity that would teach place value to

other students. o Provide opportunities to have students take their place value

understanding to as many digits as possible, including decimals.o Modify games to increase numbers for students.

Grade 2, Everyday Mathematics, CCSS edition, 2012 Outline for CCSS.Math.Content.2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. This outline is intended to show the progression of teaching and assessment opportunities throughout the year for this standard.

Formative and Summative Assessment opportunities within the program, including their student journals.Red – indicates formal assessment opportunities.Green – indicate informal written assessment opportunities.1) 3.1 (2-day lesson)– Use base ten blocks to model 2 and 3 digit numbers. Show how students can

draw models to represent the numbers. Use place value mats to match 2 and 3 digit written numbers to a display of the same number using base ten blocks. a) This can be modified to either decrease or increase the number of digits in the number. Have

access to a place value mat that has thousands on it.b) The Digit Game can be modified to increase or decrease the number of digits used when

creating and comparing the numbers.c) Enrichment opportunity – p.189d) Assessment: Math Journal 1, p. 53, #1 and 3. (#2, 4 and 5 are extension opportunities.)

2) 3.2 - Review coin values and exchanges between pennies, dimes and dollar bills. Play Penny-Nickel-Dollar exchange. Connect the real life application of money to place value.a) Exit slip question - Is $0.35 greater than $0.53? Why? Why is it important to know which

amount is greater?3) 3.7 – Practice 2 and 3 digit numbers by playing the Digit Game.

a) Exit slip questions – What is the largest number you can make using the digits 5 and 7. What is the largest number you can make using the digits 8, 2, 9? What is the smallest number you can make using the digits 7, 1, 4?

4) 4.1 – math journal 1, p. 84. Quick assessment on who can compare 4 digit numbers. 5) 4.3 - math journal 1, p. 886) 4.9 - While introducing the partial sums addition algorithm, much time is spent on making two-digit

numbers with base ten blocks then adding tens and ones together. Check in to make sure students are correctly building the 2 digit numbers using the correct number of tens and ones. Good place to review place value and how we add tens with tens and ones with ones. a) Math journal, p. 107

7) 4.10 – In the open response part of the summative assessment, students must create two 2-digit numbers that when added together will make the greatest sum.

8) 5.1/5.3 – Math journal, p. 112 and 119, #3. Student writes the value of the number represented by base ten blocks.

9) 5.4 – math journal p. 121. Student writes 5 numbers that are larger than a given number.10) 5.9 – Unit assessment, # 3. Student must order numbers from least to greatest. 11) 6. 1 – Math journal, p. 133, #5. Order numbers from least to greatest.12) 6. 4 – math journal, p. 143, #3. Student must solve and then compare answers using <,>, or =13) 6.5 – lessons on subtracting utilizes making 2 digits numbers using base tens blocks. 14) 6.7 – math journal, p. 149 and p. 153, #1 – write the equivalent number to the given base ten blocks.

15) 6.10 – math journal, p. 157, #1 – using a series of digits, write the largest and smallest possible number.

16) 6.11 – unit assessment, #4 – using symbols to compare 2 and three digit numbers.17) 9.1/9.3 – math journal 2, p. 211 and p. 215, #2 – practice adding 3 addends and then compare using

<,>, or =. Activity presents an example of when you might compare numbers in real life.18) Unit 10 – throughout this unit on money, relate comparing whole numbers to comparing decimal

numbers. It is a real life example of the value of knowing how to compare numbers. This is highlighted in lesson 10. 8 Students will compare money using the base ten blocks. The place value mats have been modified here to show how the base then blocks can represent dollars, dime and pennies. a) Math masters, p. 322 provides an opportunity to check for understanding for both 3 and four

digit numbers. b) 10.9 – students make their own place value book to practice comparing numbers and knowing

the value of each digit based on its place in the numeral.19) 10.10 – extension work for 4 and 5 digit numbers. 20) Math journal 2, p. 258 – assessment opportunity for both place value and ordering numbers.21) Math masters, p. 339 – extension work for 4 and 5 digit numbers.

SUMMATIVE ASSESSMENT

Name: Date:Comparing 3-digit numbers1. Compare using <, >, or =

36 ____ 53 74 ____ 47

2. Circle the larger number.465 546 239 293 590 509

83 38 50 60 12 21

3. Compare using <, >, or =134 ____ 143 218 ____ 812

706 ____ 607 401 ____ 401

4. Jane picked 147 apples. Susan picked 174 apples. Jane and Susan both think they picked the most apples. Who is right? Explain your answer using words or pictures.

5. Is this statement true: 536 > 436?

Circle one: Yes No

Explain why you chose your answer.

6. Compare using <, >, or =36 ____ 53

5,216 _____ 6,216

8,360 _____ 8,036

7.Rob has $5,350 and Joe has $5,530. Who has more money?

Circle one: Rob Joe

Explain why you chose your answer.

High Number TossMaterials: One six-sided die (or number cards 1-6)

Object: To make the largest number possible.

Directions:1. Each player draws four blank lines on a sheet of paper to

record the numbers that come up on the role of the die.

2. Player 1 rolls the die and writes the number on any one of his/her four blanks.

3. Player 2 then rolls the die and writes the number on one of his/her blanks.

4. Take turns rolling the die and recording the numbers three more times each.

5. Each player then uses the four numbers on his or her blanks to build a number.

The numbers on the first three blanks are the first three digits of the number the player builds.

The number on the fourth blank tells the number of zeros that come after the first three digits.

6. Each player reads his or her number. The player with the larger number wins the round. Players MUST read aloud their number correctly. The first player to win four rounds wins.

* To play with decimals, draw four blank lines and place a decimal point to the right of the first blank. ** You can change this to any number of spaces desired (and disregard the last space to zeros). For K and 1, you may want to have 2 spaces. Grades 2 and 3 may want 3 – 5 spaces, etc.***Assessment opportunity – after every two rounds, have student rewrite and compare the numbers using appropriate symbols.The Digit GameMaterials: Set of number cards 0-9, 4 cards for each number.

Number of Players: 2

Directions:1.Shuffle the deck and place it facedown

between the partners.

2.Each player draws 2 cards from the deck and uses the cards to make the largest number possible.

3.The player who makes the largest number takes all of the cards.

4.Play continues until all of the cards have been used. The player with the most cards wins.

*You may adapt this game to increase the number of digits to compare.**Formal assessment opportunity – have students record each round using symbols to compare the numbers.***Informal assessment opportunity – circulate as students are playing and note who is not comparing accurately.

Sample assessment opportunities from the EverydayMathematics, CCSS ed., 2012:

Sample assessment created from math-aids.com: