unit 1- place value - jefferson parish public...

MATH 5 Updated 10/8/2017 8:44 PM

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Unit 1- PLACE VALUE UNDERSTANDING PLACE VALUE (10 DAYS)

PLACE VALUE PATTERNS- EXPONENTS- READING, WRITING, AND COMPARING DECIMAL FRACTIONS- ROUNDING DECIMAL FRACTIONS

1. Overview

Students will strengthen their understanding of place value. Content limits include up to billion and to the thousandths place for decimals. Students

are learning to compare, order, and round these numbers. To do all of this, students must understand the concept of place value—that the value of a

digit depends on its place in the number.

Students will be introduced to whole number exponents with a focus on powers of 10. Students understand why multiplying by a power of 10 shifts the

digits in a whole number or decimal that many places to the left. Students will extend the models and strategies they developed for working with whole

numbers in grades 1 through 4 to decimal values. Estimation strategies will be extended to multiply decimals with compatible numbers and rounding.

Students will mentally divide decimals using patterns of 10 and place value. (5th grade standards do not use a decimal as a divisor.) Children’s

understanding of place value and division of whole numbers influences how easily they make sense of dividing decimals. When a decimal is divided by a

power of 10 (10, 100, 1,000, etc.), the pattern is to move the decimal point (in the number being divided) one place to the left for each zero in the power

of 10. For example, to divide 56.76 ÷ 10, move the decimal point one place to the left. 56.76 ÷ 10 = 5.676. Estimation strategies will also be used in

this topic to divide decimals with compatible numbers and rounding.

Students will read, write, expand, compare and round decimal fractions to the thousandths place using a number line.

Manipulatives/Materials: place-value charts, fraction models: strips, 10 x 10 x 10 cube, comparing and ordering decimals, problem solving: look for a

pattern


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FOCUS

STANDARDS 5.NBT.A.1 Recognize that in a multi – digit number, a digit in one place represents 10 times as much as it

represents in the place to its right and 1

10 of what it represents in the place to its left.

5.NBT.A.2 Explain and apply patterns in the number of zeroes of the product when multiplying a number by

powers of 10. Explain and apply patterns in the values of the digits in the product or the quotient, when a

decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

5.NBT.A.3 Read, write, and compare decimals to thousandths. o (5.NBT.A.3a) Read and write decimals to thousandths using base-ten numerals, number names, and

expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1

10) + 9 x (

1

100) + 2 x (

1

1000).

o (5.NBT.A.3b) Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.NBT.A.4 Use place value understanding to round decimals to any place

5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real-world problems.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regulatory in repeated reasoning.

FOUNDATIONAL

STANDARDS

4.NBT.A.1 4.NBT.A.3 4.NF.C.5 4.NF.C.6 4.NF.C.7 4.MD.A.1 4.MD.B.2


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1. Resources

e n V i s i o n M A T H E U R E K A M A T H R E A D Y T E A C H E R T O O L B O X

Topic 1: Lessons 1-1, 1-2, 1-3, 1-4, 1-5

Topic 6: Lesson 6-1 Topic 7: Lesson 7-1

Topic 13: Lessons 13-4. 13-5. 13-6

Module 1: Topic A Lessons 1-4

Module 1: Topic B Lessons 5-6

Module 1: Topic C Lessons 7-8

Unit 1, Lessons 1 and 3

A D D I T I O N A L S U P P O R T I N G R E S O U R C E S

LearnZillion:

Lessons: Understand the value of a digit using a place value chart: https://LearnZillion.com/lesson_plans/5022 Compare the value of the digits in a multi-digit whole number: https://LearnZillion.com/lesson_plans/5046 Use number lines to show increases in place value with each shift to the left in a multi-digit number: https://LearnZillion.com/lesson_plans/8205 Lesson:

Solve problems using place value understanding: https://LearnZillion.com/lesson_plans/2732

Illustrative Mathematics: Task:

5.NBT – Are these equivalent to 9.52?: https://www.illustrativemathematics.org/content-standards/5/NBT/A/tasks/1813

https://learnzillion.com/lesson_plans/5022




https://www.illustrativemathematics.org/content-standards/5/NBT/A/tasks/1813


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3. Activities for Understanding

SUGGESTIONS Place Value

Students will write numbers. Ask students to take out a piece of lined paper and turn it sideways. Have students use a pencil to draw 11 horizontal lines to create a grid with 10 rows. Have students draw a colored line to mark every third vertical row so that the ones, thousands, millions, and billions periods are separated. Call out the following numbers by name and have students work together to write them in the grid: 1; 10; 100; 1,000; 10,000; 100,000; 1,000,000; 10,000,000; 100,000,000; 1,000,000,000. Starting with 1, ask volunteers to read the numbers again.

Decimal Place Value

Students will write decimal numbers. Divide the class into three groups. On the chalkboard, draw four blanks and a decimal as shown here: _. _ _ _ Ask students in each group to come to the chalkboard and carry out the following directions:

-Place a 5 in the tenths place. -Place a 7 in the thousandths place. -Place a 4 in the ones place. -Place a 6 in the hundredths place. -Repeat with at least two other numbers.

Patterns in the Powers of Ten:

Students will multiply a number by a power of 10. In table groups, students will share a stack of ten multiplication

problems involving decimals multiplied by powers of 10 on premade index cards. As a group, students will solve all

ten problems and will identify patterns when each decimal number is multiplied by a power of 10. Students will

follow up with a written paragraph articulating and defending the patterns they have discovered.

Around the World:

Students will read decimal numbers after mentally multiplying the numbers by a power of 10. Students may work

in small groups or whole class for this activity. Take a seat where all students can see you. Pick a student to be the

first challenger, and have him/her stand behind the student to his/her right. Those are the first two players. Hold

up the decimal multiplied by a power of 10. The first player to correctly name the decimal first (in standard form)

gets to move on to challenge the next student (to his/her right). The winner is the student who moved “around

the world” to arrive back at his/her seat.


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Comparing and Ordering Decimals Students will create decimal numbers and compare. Ask students to fold a piece of paper in fourths in both

directions to create 16 sections, then tear the paper into the sections. Have students write numbers 0 to 9 on separate pieces and a decimal point on another piece. Next, have the students write five digits of their choice on the remaining 5 pieces. Write two numbers on the board with a common digit in the ones place and three decimal places, such as 5.738 and 5.694. Ask students to tell which number is greater and then to build a new number that falls between the two.


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UNIT 2- DECIMALS TOPIC 2 – ADDING AND SUBTRACTING DECIMALS (12 DAYS)

ADDING, SUBTRACTING, MULTIPLYING, DIVIDING DECIMALS

I. Overview

Students will develop an in-depth understanding of place value and number sense, and extend their understandings of addition and subtraction with

decimals to the thousandths place. Students will also use estimation skills when solving problems that involve the rounding of numbers.

Students will begin development of multiplication of decimals to hundredths will include concrete models or drawings, place value strategies, and the

standard algorithm.

The development of division of decimals to hundredths will include place value strategies and the standard algorithm. However, exposure to dividing

decimals within a word problem will help students to develop the reasonableness of quotients.

Manipulatives/Materials: number lines, place-value charts, hundred grid, number disks/tiles, number cards, markers or crayons, dice (number cubes),

area models/arrays, decimal grids, base-ten rods and unit cubes, tenths models, bar models, calculators (optional), scissors, number cubes, paper clips,

color tiles, center activity game-boards

FOCUS

STANDARDS 5.NBT.A.2 Explain and apply patterns in the number of zeroes of the product when multiplying a number by



5.NBT.A.3 Read, write, and compare decimals to thousandths.

o (5.NBT.A.3a) Read and write decimals to thousandths using base-ten numerals, number names, and

expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1

10) + 9 x (

1

100) + 2 x (

1

1000).


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o (5.NBT.A.3b) Compare two decimals to thousandths based on meanings of the digits in each place, using

>, =, and < symbols to record the results of comparisons.

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; justify the reasoning used with a written explanation.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.6 Attend to precision.

MP.7 Look for and make use of structure.

MP.8 Look for and express regulatory in repeated reasoning.

FOUNDATIONAL

STANDARDS 4.NBT.A.3 4.NBT.B.4


2. Resources


Topic 2: Lesson 2-4, 2-6, 2-7, 2-

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Topic 6: Lessons 6-2, 6-3, 6-4, 6-

5

Topic 3: Lesson 3-4

Topic 7: Lessons 7-4

Module 1: Topic D Lessons 9-10 Module 1: Topic E Lessons 11-12 Module 1: Topic F Lessons 13-16

Unit 1, Lesson 4 Unit 1, Lessons 7 and 8

Unit 1, Lesson 9


Guidebook: Lesson:

Number Cards: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/5th-grade-instructional-tasks.pdf?sfvrsn=5

http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/5th-grade-instructional-tasks.pdf?sfvrsn=5


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LearnZillion: Lesson:

Multiple video lessons for 5.NBT: https://LearnZillion.com/resources/74912-5th-grade-numbers-and-operations-in-base-ten-5-nbt Multiply decimals to the hundredths by using fractions: https://LearnZillion.com/lesson_plans/8804

Illustrative Mathematics: Tasks:

5.NBT – The Value of Education: https://www.illustrativemathematics.org/content-standards/5/NBT/B/7/tasks/1293



SUGGESTIONS

Rounding Whole Numbers:

Students will use a number line to round whole numbers to the closest multiple of ten, hundred, or thousand. Have each student draw a number line labeling the far left and right mark with a given multiple. When given four or five numbers, they will copy them onto the number line indicating that the numbers are closest to the left or to the right. As an extension to this activity, have students justify their reasoning for how they rounded the numbers.

Rounding Decimals: http://games4gains.com/blogs/teaching-ideas/45489732-roll-it-rounding-game

Students will create 3-digit decimal numbers and round to the nearest tenth or hundredth. Students will work in pairs with a free printable game board, dice, and markers. Once dice are rolled, the numbers can be placed in any order and marker is placed on game board decimal number that accurately indicates the rounded number. Players continue taking turns until one player creates a line of 4 in a row of his/her own counters on the game board.

Adding and Subtracting Decimals:

Students will use estimation skills to add and subtract decimals. Working in small groups, each group will be given a grocery store sales flier. Each group must buy at least five different items and spend as close to $20 as possible, without going over. Direct each group to list the items they will purchase, the estimated cost of each item, and how many of each item they will buy. Have students add the estimates to make sure that they have not exceeded the $20 limit. Have students add the exact amounts to see whether the total is actually less than $20.

https://learnzillion.com/resources/74912-5th-grade-numbers-and-operations-in-base-ten-5-nbt


http://games4gains.com/blogs/teaching-ideas/45489732-roll-it-rounding-game


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Mental Computation for Multiplying Decimals: Students will use manipulatives to provide a concrete representation of numbers and operations to help answer

mental computation questions. Pairs of students will be provided with base-ten rods and unit cubes. Rods will

represent one whole and the unit cube, one tenth. A question involving decimal numbers will be written on the

board. Students will use the base-ten materials to help them solve the problem; exchanging a tens rod for 10 unit

cubes (or vice versa) when necessary. Challenge students to find more than one method of solving the problem.

Ask student to explain their thinking in how they found the solution. Provide additional problems as time permits.

http://eworkshop.on.ca

How Much Money?

Students will use multiplication or mental math to determine their answers. Students will divide to check their

answers to see the relationship between the two methods and to check for accuracy.

https://www.georgiastandards.org/Georgia-Standards/Frameworks/5th-Math-Unit-3.pdf

Place the Point!

Students will use estimation to determine where to place the decimal point in several quotients. The digits remain

the same; however, the value will change. In this task, students will only use estimation to find the quotients.

Students will justify each response and check their answers using a calculator.


Clip and Cover (TE 171B)

Students will divide decimals by a power of 10 (10, 100, or 1,000). The first player to get any three connected

rectangles in a row or column wins!

Toss and Talk (TE 175B)

Students will divide decimal numbers. The first to connect four rectangles wins!

http://eworkshop.on.ca/




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UNIT 3- MUTLIPLICATION TOPIC 3 – MULTIPLYING WHOLE NUMBERS (29 DAYS)

MENTAL STRATEGIES FOR MULTI-DIGIT MULTIPLICATION- USING THE STANDARD ALGORITHM TO MULTIPLY WHOLE NUMBERS OR DECIMAL

NUMBERS- MEASUREMENT WORD PROBLEMS USING MULTIPLICATION

I. Overview

Students will extend their understanding of multiplication using the Distributive Property, basic facts, place value, and patterns. Students will use mental

math and estimation strategies, including compatible numbers to easily multiply multi-digit decimal fractions and/or multi-digit whole numbers. Students

will develop accuracy, efficiency, and flexibility when multiplying multi-digit decimal numbers as well as multi-digit whole numbers. These strategies help

students transition to using the standard algorithm to multiply with ease.

Students will continue development of multiplication of decimals to hundredths to include concrete models or drawings, place value strategies, and the

standard algorithm.

Manipulatives/Materials: place-value charts, color counters, place value disks/tiles, rectangular arrays, area models, Teaching Tool 15 (or grid paper),

Teaching Tool 18 (optional), grid paper, rulers, base-ten blocks

FOCUS




5.NBT.A.2 Explain and apply patterns in the number of zeroes of the product when multiplying a number by powers of 10. Explain and apply patterns in the values of the digits in the product or the quotient, when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; justify the reasoning used with a written explanation.


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5.OA.A.1 Use parentheses or brackets in numerical expressions, and evaluate expressions with these symbols.

5.OA.A.2 Write simple expressions that record calculations with whole numbers, fractions, and decimals, and

interpret numerical expressions without evaluating them.

5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real-world problems.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.2 Reason abstractly and quantitatively.



FOUNDATIONAL

STANDARDS

4.NBT.B.4 4.NBT.B.5 4.NBT.B.6 4.MD.A.1

4.MD.A.2

MENTAL STRATEGIES FOR MULTI-DIGIT MULTIPLICATION- USING THE STANDARD ALGORITHM TO MULTIPLY WHOLE NUMBERS OR DECIMAL

NUMBERS- MEASUREMENT WORD PROBLEMS USING MULTIPLICATION

2. Resources


Topic 3: Lessons 3-1, 3-2, 3-3, 3-5, 3-6, 3-7, 3-8, 3-9, 3-10 **Topic 3 Lesson 4 is NOT taught with Topic 3. It will be taught later with Topic 6.

Topic 6: Lesson 6-1, 6-2, 6-4 Topic 13: 13-1, 13-2, 13-3, 13-4,

13-7

Module 2: Topic A Lessons 1-2



Module 2: Topic D Lesson 13-15



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LearnZillion Lesson:

Use Area Models for Multiplication: https://learnzillion.com/lesson_plans/8122-use-area-models-for-multiplication Use Partial Products for Multiplication: https://learnzillion.com/lesson_plans/8117-use-partial-products-for-multiplication Use the Standard Algorithm for Multiplication: https://learnzillion.com/lesson_plans/8041-use-the-standard-algorithm-for-multiplication

Illustrative Mathematics:

Task:

5.NBT – Elmer’s Multiplication Error: https://www.illustrativemathematics.org/content-standards/5/NBT/B/5/tasks/1812

MENTAL STRATEGIES FOR MULTI-DIGIT MULTIPLICATION- USING THE STANDARD ALGORITHM TO MULTIPLY WHOLE NUMBERS OR

DECIMAL NUMBERS- MEASUREMENT WORD PROBLEMS USING MULTIPLICATION


SUGGESTIONS

Multiplying Whole Numbers: Background Students will use multiple strategies to find the product of multi-digit whole numbers. This activity helps build an

understanding that multiples of 10 and 100 are not just adding a zero. The teacher will need base ten blocks (or a

pictorial representation) and grid paper available for the students. Students will be asked to model problems, such as 80 x 20. Have students conclude that it would be difficult to draw 80 squares by 20 squares. Model how to make an 8 by 2 array on the grid paper. Show how each box represents 10, instead of 1. Then, count by 10 to get the product. It is important to relate the problem to how the numbers are decomposed (Distributive Property). NC Mathematics Lessons for Learning (page 42) http://maccss.ncdpi.wikispaces.net/file/view/5thgrade%20Lessons%204Learning%2022616.pdf/585433849/5thgrade%20Lessons%204Learning%2022616.pdf

https://learnzillion.com/lesson_plans/8122-use-area-models-for-multiplication

https://learnzillion.com/lesson_plans/8117-use-partial-products-for-multiplication

https://learnzillion.com/lesson_plans/8041-use-the-standard-algorithm-for-multiplication

https://www.illustrativemathematics.org/content-standards/5/NBT/B/5/tasks/1812

http://maccss.ncdpi.wikispaces.net/file/view/5thgrade%20Lessons%204Learning%2022616.pdf/585433849/5thgrade%20Lessons%204Learning%2022616.pdf



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Distributive Property (TE page 72B) Students write two equal expressions using their knowledge of area. Show (or give) students Teaching Tool 15 for

Distributive Property. Have students write numerical expressions using only numbers shown on the rectangle to find the

area of the unshaded rectangle. If they need help ask, “How can you find the length of the unmarked side in the

unshaded rectangle?” Guide students to write a second expression that will have the same value. This is an example of

the Distributive Property. It states that multiplying a sum (or difference) by a number is the same as multiplying each

number in the sum (or difference) by that number and adding (or subtracting) the products:

a × (b + c) = (a × b) + (a × c) a × (b – c) = (a × b) – (a × c)

Area Models (TE page 78B and TE page 80B)

Students will use area models to multiply. Students will draw rectangles to model decomposing factors to find products.

Using partial products, students will find the total area of the model. If students struggle seeing the area model by

drawing rectangles, provide graph or grid paper.

Multiplication Mix-up

Students will generate numbers and multiply. Using a deck of cards, the ace represents one and all other cards carry their numerical values. Remove the face cards. Working in groups of 3, deal each player three cards. Each player must use two of the cards to make a two digit number. The third card will be the multiplier. The player with the largest product gets the cards. NC Mathematics Lessons for Learning (page 21) http://maccss.ncdpi.wikispaces.net/file/view/5thgrade_GAMES_8.22.14.pdf/519548106/5thgrade_GAMES_8.22.14.pdf

http://maccss.ncdpi.wikispaces.net/file/view/5thgrade_GAMES_8.22.14.pdf/519548106/5thgrade_GAMES_8.22.14.pdf


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Unit 4- Division DIVISION WITH MUTLI-DIGIT WHOLE NUMBERS- DIVISION WITH DECIMAL FRACITONS (19 DAYS)

MENTAL STRATEGIES FOR MULTI-DIGIT DIVISION- PARTIAL QUOTIENTS TO DIVIDE MULTI-DIGIT WHOLE NUMBERS AND DECIMAL

FRACTIONS- MEASUREMENT WORD PROBLEMS FOR DIVISION

I. Overview

Students will extend their understanding of division through basic facts, place value, and patterns. Students will use various estimation strategies, such as

rounding and compatible numbers to mentally divide whole numbers with one-digit divisors. Students will find whole number quotients with remainders

using a variety of strategies. To develop understanding of division, the use of story context is critical in problem solving including a remainder that must

be interpreted.

Students will extend their understanding of division of whole numbers to two-digit divisors through basic facts, place value, and patterns. Students will

continue to use estimation strategies by using compatible numbers. To understand the process for dividing whole numbers by 2-digit divisors, students

will create arrays/area models. In lessons 5-5, 5-6, and 5-7, the standard algorithm is used to teach division; however, other strategies may be suggested

through use of activities to develop conceptual understanding of two-digit divisors.

Manipulatives/Materials: place value charts, place value chips/tiles, base-ten models, area models, rectangular arrays, grids, area model worksheet,

multiplication chart for facts (optional), number cubes, rectangular arrays, grid paper, calculators (optional), color tiles, paper clips, center activity game

boards

FOCUS




5.NBT.A.2 Explain and apply patterns in the number of zeroes of the product when multiplying a number by




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5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, subtracting multiples of the divisor, and/or the relationship between multiplication and division. Illustrate and/or explain the calculation by using equations, rectangular arrays, area models, or other strategies based on place value.

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and

strategies based on place value, properties of operations, and/or the relationship between addition and

subtraction; justify the reasoning used with a written explanation.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.1 Make sense of problems and persevere in solving them.



FOUNDATIONAL

STANDARDS 4.NBT.B.4 4.NBT.B.6



2. Resources


Topic 4: Lessons 4-1, 4-2 Topic 5: Lessons 5-3, 5-4, 5-5, 5-

6, 5-7

Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5

Module 2: Topic E

Lessons 16-18 Module 2: Topic F Lessons19-23

Module 2: Topic G Lessons 24-27

Module 2: Topic H Lessons 28-29

Unit 1, Lesson 6


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Find whole number quotients with up to 4-digit dividend and 2-digit divisors: https://LearnZillion.com/resources/72204-find-whole-number-quotients-with-up-to-4-digit-dividends-and-2-digit-divisors-5-nbt-b-6

Illustrative Mathematics: Task:

Multiple tasks link for 5.NBT: https://www.illustrativemathematics.org/5.NBT.A 5.MD Minutes and Days: https://www.illustrativemathematics.org/content-standards/5/NBT/B/6/tasks/878




SUGGESTIONS

Constructing Task: What is 2500 ÷ 300?

Students will explore why dividing by zero is undefined. Start with a whole group discussion on division and zero. Discuss the relationship between multiplication and division and the product when one of the factors is zero. Students will work with partners/groups to critically think and justify. https://www.georgiastandards.org/Georgia-Standards/Frameworks/4th-Math-Unit-2.pdf

Constructing Task: Compatible Numbers to Estimate Students will use compatible numbers to divide. They will use a recording worksheet to evaluate the reasonableness of a

division problem with one-digit divisor in a story context. https://www.georgiastandards.org/Georgia-Standards/Frameworks/4th-Math-Unit-2.pdf

Dividing using an Area Model

Students will interpret a division problem with a one-digit divisor that has been completed using an area model. Provide students with a printable worksheet that shows how an area model was used to divide. After a class discussion, have students complete a problem on their own. http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/58773

https://learnzillion.com/resources/72204-find-whole-number-quotients-with-up-to-4-digit-dividends-and-2-digit-divisors-5-nbt-b-6

https://learnzillion.com/resources/72204-find-whole-number-quotients-with-up-to-4-digit-dividends-and-2-digit-divisors-5-nbt-b-6

https://www.illustrativemathematics.org/5.NBT.A

https://www.illustrativemathematics.org/content-standards/5/NBT/B/6/tasks/878




http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/58773


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Clip and Cover Center Activity (TE p121B) Students will use patterns to divide multiples of 10, 100, and 1,000 by factors of 10. Students will toss number cubes and

divide the number on the left of the worksheet by the number on the right of the worksheet. They will explain how to use

patterns to divide. Then, they will find and cover the quotient. The first player to get any three connected rectangles in a

row or column wins.

Area Model for Division (TE p124B)

Students use grid paper to find the quotient involving two-digit divisors. Give students one sheet of grid paper. Read the

problem: A parking lot holds 270 cars. Each row holds 18 cars. How many rows are in this parking lot? Using the grid

paper, students will then work with decomposing the divisor and making arrays to discover the quotient as they solve the

problem.

2-Digit Quotients Tic-Tac-Toe (TE 133B) Students will practice dividing two-digit divisors. Working in pairs, each pair of students will need a number cube and color

squares. The first player will roll a number cube. The number rolled will represent the number of tens in a two-digit

divisor. The second roll will represent the ones in the same two-digit divisor. Next, the student will explain how to divide

792 by the two-digit divisor (created from the number cube). Cover the answer on the chart. Players switch roles. The

first player to cover a row, column, or diagonal in one of the four sections of the game board wins. There are different

levels of difficulty available.

Division of Whole Numbers: Dealing with Remainders

Students will use multiple strategies to find the quotient of two whole numbers including remainders. Students will illustrate

and explain a division calculation in a variety of ways. Students will divide up to four-digit whole numbers by one- and two-

digit divisors. (pg. 61)


Constructing Task: Division Four in a Row

Students will divide numbers up to 4-digit dividends by 1- or 2-digit divisors. This task challenges students with game

boards that contain simple 4-digit numbers in the dividend box or multiples of 10 (i.e., 10, 20, … 90) in the divisor box.


Constructing Task: Are These All 365 ÷ 15? Students will analyze different division situations. The three word problems in this task represent situations where division

can be used to solve different kinds of problems: measurement, partitive, and repeated subtraction strategies.







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UNIT 5- FRACTIONS UNDERSTANDING FRACTIONS (36 DAYS)

EQUIVALENT FRACTIONS- ADDING AND SUBTRACTING FRACTIONS- MULTIPLYING AND DIVIDING FRACTIONS- NUMERICAL EXPRESSIONS I. Overview

Students extend their understanding of equivalent fractions developed in 4th grade and their ability to rewrite fractions in an equivalent form to find

common denominators. Students will use multiplication or division to develop equivalent fractions including simplest form. They should know that

multiplying the denominators will always give a common denominator but may not result in the smallest denominator. This process should come after

students have used visual fraction models (area models, number lines, etc.) to build understanding before moving into the standard algorithm. The use

of visual fraction models allows students to reason about a common denominator prior to using the algorithm. Students will estimate and evaluate word

problems with addition and subtraction of unlike fractions using mathematical explanations, including words, pictures, numbers, or equations. Students

should use benchmark fractions to estimate and examine the reasonableness of their answers.

Students will convert improper fractions as mixed numbers and mixed numbers as improper fractions using number lines and/or visual fraction models.

Students will use models and computational procedures to add and subtract mixed numbers with unlike denominators. This process allows students to

reason prior to using the algorithm. Students will use benchmark fractions to estimate sums and differences. Students will accurately evaluate word

problems with addition and subtraction of unlike mixed numbers using mathematical explanations, including words, pictures, numbers, or equations.

Students should use benchmark fractions to estimate and to examine the reasonableness of their answers.

Manipulatives/Materials: area models, number lines, fractions models/strips, hundreds chart, fraction bars, bar models

FOCUS

STANDARDS 5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given

fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

5.NF.A.2 Solve word problems involving addition and subtraction of fractions. o (5.NF.A.2a) Solve word problems involving addition and subtraction of fractions referring to the same whole,

including cases of unlike denominators. o (5.NF.A.2b) Use benchmark fractions and number sense of fractions to estimate mentally and justify the

reasonableness of answers.


19

FOCUS

STANDARDS 5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given

fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

5.NF.A.2 Solve word problems involving addition and subtraction of fractions. o (5.NF.A.2a) Solve word problems involving addition and subtraction of fractions referring to the same whole,

including cases of unlike denominators. o (5.NF.A.2b) Use benchmark fractions and number sense of fractions to estimate mentally and justify the

reasonableness of answers.

STANDARDS FOR

MATHEMATICAL

PRACTICE



MP.3 Construct viable arguments and critique the reasoning of others.

MP.5 Use appropriate tools strategically.



FOUNDATIONAL

STANDARDS

4.NF.A.1 4.NF.A.2

TOPIC 9 AND 10- FRACTIONS

2. Resources


Topic 9: Lessons 9-1, 9-2, 9-3,

9-4, 9-5, 9-6, 9-7, 9-8, 9-9

Topic 10: 10-1, 10-3, 10-4, 10-5, 10-6, 10-7

Remediation Lessons: Topic A

Lessons 1-2


Remediation Lesson: Topic C Lesson 8


Unit 2, Lesson 10 Unit 2, Lesson 11


20

Module 3: Topic D Lesson 13, 15

Enrichment Lessons: Topic D Lessons 14, 16


Guidebook: Lessons:

Rainfall Amounts: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/5th-grade-instructional-tasks.pdf?sfvrsn=5 Milk and Cookies: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/5th-grade-extended-contructed-response-

tasks.pdf?sfvrsn=7 LearnZillion:

Lesson:

Add and subtract fractions and mixed number with unlike denominators using area model: https://learnzillion.com/resources/72258-add-and-subtract-fractions-and-mixed-numbers-with-unlike-denominators-using-area-models

Add and subtract fractions and mixed numbers with unlike denominators using fraction bars: https://learnzillion.com/resources/72928-add-and-subtract-fractions-and-mixed-numbers-with-unlike-denominators-5-nf-a-1

Solve Word problems involving addition and subtraction of fractions referring to the same whole: https://learnzillion.com/resources/72413-solve-word-problems-involving-addition-and-subtraction-of-fractions-referring-to-the-same-whole-2

Solve word problems involving addition and subtraction of fractions with unlike denominators: https://learnzillion.com/resources/72846-solve-word-problems-involving-the-addition-and-subtraction-of-fractions-with-unlike-denominators

Lesson:

Understanding Mixed Numbers and Improper Fractions: https://learnzillion.com/resources/72268-understand-fractions-as-a-division-of-the-numerator-by-the-denominator

Add and subtract fractions and mixed number with unlike denominators using area model: https://learnzillion.com/resources/72258-add-and-subtract-fractions-and-mixed-numbers-with-unlike-denominators-using-area-models

Add and subtract fractions and mixed numbers with unlike denominators using fraction bars: https://learnzillion.com/resources/72928-add-and-subtract-fractions-and-mixed-numbers-with-unlike-denominators-5-nf-a-1


http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/5th-grade-extended-contructed-response-tasks.pdf?sfvrsn=7


https://learnzillion.com/resources/72258-add-and-subtract-fractions-and-mixed-numbers-with-unlike-denominators-using-area-models


https://learnzillion.com/resources/72928-add-and-subtract-fractions-and-mixed-numbers-with-unlike-denominators-5-nf-a-1


https://learnzillion.com/resources/72413-solve-word-problems-involving-addition-and-subtraction-of-fractions-referring-to-the-same-whole-2

https://learnzillion.com/resources/72413-solve-word-problems-involving-addition-and-subtraction-of-fractions-referring-to-the-same-whole-2

https://learnzillion.com/resources/72846-solve-word-problems-involving-the-addition-and-subtraction-of-fractions-with-unlike-denominators

https://learnzillion.com/resources/72846-solve-word-problems-involving-the-addition-and-subtraction-of-fractions-with-unlike-denominators

https://learnzillion.com/resources/72268-understand-fractions-as-a-division-of-the-numerator-by-the-denominator

https://learnzillion.com/resources/72268-understand-fractions-as-a-division-of-the-numerator-by-the-denominator






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Discovery Education: Lesson 6: Adding and Subtracting Fractions with Like Denominators (Video and Teacher’s Guide):

https://app.discoveryeducation.com/learn/videos/bdfb91c4-79e8-4cfd-b8d5-d32369fca081

Lesson 8: Adding and Subtracting Fractions with Unlike Denominators (Video and Teacher’s Guide): https://app.discoveryeducation.com/learn/videos/4784C6F1-DAE3-4200-8533-FF51194A9A39?hasLocalHost=false


Tasks: 5.NF – Egyptian Fractions: https://www.illustrativemathematics.org/content-standards/5/NF/A/1/tasks/839 5.NF – Mixed Numbers with Unlike Denominators: https://www.illustrativemathematics.org/content-standards/5/NF/A/1/tasks/847 5. NF – Finding Common Denominators to Add: https://www.illustrativemathematics.org/content-standards/5/NF/A/1/tasks/848 5.NF – Finding Common Denominators to Subtract: https://www.illustrativemathematics.org/content-standards/5/NF/A/1/tasks/859

5.NF – Fractions on a Line Plot: https://www.illustrativemathematics.org/content-standards/5/NF/A/1/tasks/1563

Technology Tools

http://www.visualfractions.com/add.htm A set of interactive tools that allows students to represent fraction addition with measurement (lines) and

area (circles) models.

https://www.conceptuamath.com/app/tool/adding-fractions-with-uncommon-denominators

Highly interactive tool that allows students/teachers to represent fraction addition with number lines and area models and also allows the user to

input a customized word problem.

http://www.k-5mathteachingresources.com/ This site offers simple contextual problems to use to extend and to support students in their

understanding of fraction computation and all problems are correlated to CCSS.

https://app.discoveryeducation.com/learn/videos/bdfb91c4-79e8-4cfd-b8d5-d32369fca081

https://app.discoveryeducation.com/learn/videos/4784C6F1-DAE3-4200-8533-FF51194A9A39?hasLocalHost=false

https://www.illustrativemathematics.org/content-standards/5/NF/A/1/tasks/839





http://www.visualfractions.com/add.htm

https://www.conceptuamath.com/app/tool/adding-fractions-with-uncommon-denominators

http://www.k-5mathteachingresources.com/


22

TOPIC 9 AND 10- FRACTIONS


SUGGESTIONS

Game: Color the Door (page 44) Students will create their own door design using fraction playing cards. NC Mathematics Fifth Grade Games:

http://maccss.ncdpi.wikispaces.net/file/view/5thgrade_GAMES_8.22.14.pdf/519548106/5thgrade_GAMES_8.22.14.pdf Game: Rolling, Rolling, Rolling (page 48)

Students will create equivalent fractions. NC Mathematics Fifth Grade Games: http://maccss.ncdpi.wikispaces.net/file/view/5thgrade_GAMES_8.22.14.pdf/519548106/5thgrade_GAMES_8.22.14.pdf

Constructing Task: The Wishing Club (page 62)

Students will add fractions using equivalent fractions. https://www.georgiastandards.org/Georgia-Standards/Frameworks/5th-Math-Unit-4.pdf

Online Single or Partner Game: Racing Bikes Students will add fractions with like denominators or easily found equivalents. Students may choose from boards with

1

2 &

1

4 or

1

2,

1

4, &

1

8 . http://www.counton.org/games/map-fractions/racing/

Constructing Task: Fraction Addition and Subtraction (page 69)

Students will add fractions using common and unlike denominators through the use of various manipulatives. https://www.georgiastandards.org/Georgia-Standards/Frameworks/5th-Math-Unit-4.pdf

Practice Task: Up and Down the Number Line (page 84)

Students will add and subtract fractions. https://www.georgiastandards.org/Georgia-Standards/Frameworks/5th-

Math-Unit-4.pdf

Practice Task: Create Three (page 90) Students will add and subtract fractions and mixed numbers with unlike denominators.


Frosty Fractions

Students will add fractions with like and unlike denominators. http://www.counton.org/games/map-fractions/frosty/

Hiking Trail

Students will determine equivalents to add and subtract with unlike denominators. (page 49)






http://www.counton.org/games/map-fractions/racing/





http://www.counton.org/games/map-fractions/frosty/



23

Gardening Fractions Students will solve single-step and multi-step practical problems involving addition and subtraction with fractions and

mixed numbers and explain their work.

http://www.doe.virginia.gov/instruction/mathematics/professional_development/institutes/2012/3-

5/grade5_task_gardening_fractions.pdf

http://www.doe.virginia.gov/instruction/mathematics/professional_development/institutes/2012/3-5/grade5_task_gardening_fractions.pdf

http://www.doe.virginia.gov/instruction/mathematics/professional_development/institutes/2012/3-5/grade5_task_gardening_fractions.pdf


24

TOPIC 14 – FRACTION LINE PLOTS

I. Overview

Students will learn how to draw line plots using fractional numbers, interpret points, and recognize outliers. Students will interpret and make line plots

and frequency tables and collect data from a survey. When solving problems involving data represented on a line plot, students combine their

understandings of the representation of the data and the operations needed to solve the problem.

Manipulatives/Materials: number lines, frequency tables

FOCUS

STANDARDS 5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (

1

2,

1

4,

1

8). Use operations

on fractions for this grade to solve problems involving information presented in line plots.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP.5 Use appropriate tools strategically.

FOUNDATIONAL

STANDARDS 4.MD.B.4 3.NF.A.2


25


2. Resources


Topic 14: Lessons 14-1 (Using Whole Numbers), 14-3, 14-4 (Using Fractions)

Module 4: Topic A Lesson 1

Unit 4, Lesson 23 Unit 5, Lesson 29


LearnZillion: Lesson: Solve problems involving line plots: https://learnzillion.com/resources/72715-solve-problems-involving-measurement-data-in-fractions-of-a-unit-

displayed-line-plots-5-md-b-2

Illustrative Mathematics: Tasks:

Fractions on a Line Plot: https://www.illustrativemathematics.org/content-standards/5/MD/B/2/tasks/1563



SUGGESTIONS

Sing a Song: Students will use data to develop a line plot. Students will analyze that data to determine an average time by

equally redistributing each data point. https://www.georgiastandards.org/Georgia-Standards/Frameworks/5-Math-Unit-6.pdf

Survival Badge:

Students will create line plots based on given data. https://www.georgiastandards.org/Georgia-Standards/Frameworks/5-Math-Unit-6.pdf

Data Research and Collection:

Students will create a tally chart based on data collected. Instruct students to research 5 hurricane preparation tips. Then, have students survey at least 25 people and record which tip people found the most important to follow. Students will display their data in a tally chart and write a question that relates to the data.

https://learnzillion.com/resources/72715-solve-problems-involving-measurement-data-in-fractions-of-a-unit-displayed-line-plots-5-md-b-2

https://learnzillion.com/resources/72715-solve-problems-involving-measurement-data-in-fractions-of-a-unit-displayed-line-plots-5-md-b-2

https://www.illustrativemathematics.org/content-standards/5/MD/B/2/tasks/1563

https://www.georgiastandards.org/Georgia-Standards/Frameworks/5-Math-Unit-6.pdf





26

TOPIC 11 – FRACTIONS

I. Overview

Students develop an understanding of multiplying a fraction by a fraction, a fraction by a whole number, mixed numbers with drawing models. In 5th

grade, students experience division problems with whole number divisors and unit fraction dividends (fractions with a numerator of 1), or with unit

fraction divisors and whole number dividends. Students extend their understanding of the meaning of fractions, how many unit fractions are in a whole,

and their understanding of multiplication and division as involving equal groups or shares and the number of objects in each group/share. Students are

expected to demonstrate their understanding using concrete materials, drawing models, and explaining their thinking when working with fractions in

multiple contexts.

In Topic 11, students will also tile the area of a rectangle and relate the fractional lengths to the formula for area of a rectangle. Students will also

examine how numbers change when multiplying by a fraction less than one, a fraction equal to one, or a mixed number/improper fraction (scaling or

resizing).

Manipulatives/Materials: Fraction models/strips, Patty paper (optional), number lines, grid paper, candy bars (optional)

FOCUS

STANDARDS

5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a

b = a ÷ b). Solve word problems

involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

o (5.NF.B.4a) Interpret the product (𝑚

𝑛) x q as m parts of a partition of q into n equal parts; equivalently, as

the result of a sequence of operations, m x q ÷ n. o (5.NF.B.4b) Construct a model to develop understanding of the concept of multiplying two fractions and

create a story context for the equation. o (5.NF.B.4c) Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the

appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.

o (5.NF.B.4d) Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.


27

5.NF.B.5 Interpret multiplication as scaling (resizing), by: o (5.NF.B.5a) Comparing the size of a product to the size of one factor on the basis of the size of the other

factor, without performing the indicated multiplication. o (5.NF.B.5b) Explaining why multiplying a given number by a fraction greater than 1 results in a product

greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case).

o (5.NF.B.5c) Explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.

o (5.NF.B.5d) Relating the principle of fraction equivalence a

b =

(n x a)

(n x b) to the effect of multiplying

a

b by 1.

5.NF.B.6 Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Division of a fraction by a fraction is not a requirement at this grade.)

o (5.NF.B.7a) Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

o (5.NF.B.7b) Interpret division of a whole number by a unit fraction, and compute such quotients. o (5.NF.B.7c) Solve real-world problems involving division of unit fractions by non-zero whole numbers and

division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

STANDARDS FOR

MATHEMATICAL

PRACTICE


MP.3 Construct viable arguments and critique the reasoning of others.

MP.4 Model with mathematics.


FOUNDATIONAL

STANDARDS

3.OA.A.1 3.OA.A.2 3.OA.B.6 4.OA.A.1 4.OA.A.2


28

4.MD.A.2 4.NF.A.1 4.NF.B.4


2. Resources


Topic 11: Lessons 11-1, 11-2, 11-3, 11-4, 11-5, 11-6, 11-7, 11-8, 11-9, 11-10

Module 4: Topic B Lessons 2/3

Remediation Lesson: Topic B Lesson 4

Module 4: Topic C Lessons 6-7, 9

Module 4: Topic D Lessons 10-12

Module 4: Topic E Lessons 13-20

Module 4: Topic F Lessons 21, 22/23, 24

Module 4: Topic G Lessons 25-30/31

Unit 2, Lessons 12 – 18


Guidebook: Lessons:

Baking Cookies: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/5th-grade-extended-contructed-response-tasks.pdf?sfvrsn=7

Colored Jugs: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/5th-grade-instructional-tasks.pdf?sfvrsn=5





29


Interpreting fractions as division: https://learnzillion.com/resources/72736-interpreting-fractions-as-division-of-the-numerator-by-the-denominator Answer division problems using fractions: https://learnzillion.com/resources/72546-interpret-a-fraction-as-division-and-answer-division-problems-

using-fractions-5-nf-b-3

Multiply Fractions: https://learnzillion.com/resources/72323-multiply-fractions Solve problems involving multiplication of fractions and mixed numbers: https://learnzillion.com/resources/73064-solve-problems-involving-

multiplication-of-fractions-and-mixed-numbers-5-nf-b-6 Divide whole numbers by unit fractions and viceversa: https://learnzillion.com/resources/72437-divide-whole-numbers-by-unit-fractions-and-unit-

fractions-by-whole-numbers-5-nf-b-7

Divide whole numbers by fractions: https://learnzillion.com/resources/72969-divide-whole-numbers-by-fractions Solve word problems with division of fractions: https://learnzillion.com/resources/72698-solve-real-world-problems-involving-division-of-whole-

numbers-by-unit-fractions Illustrative Mathematics:

Tasks: 5.NF – Connor and Makayla Discuss Multiplication: https://www.illustrativemathematics.org/content-standards/5/NF/B/4/tasks/321 5.NF – Cornbread Fundraiser: https://www.illustrativemathematics.org/content-standards/5/NF/B/4/tasks/2078 Additional Tasks to support 5.NF instruction: https://www.illustrativemathematics.org/5.NF.B.4



SUGGESTIONS

NC Mathematics Fifth Grade Games Students will build fluency with multiplication of fractions.

http://maccss.ncdpi.wikispaces.net/file/view/5thgrade_GAMES_8.22.14.pdf/519548106/5thgrade_GAMES_8.22.14.pdf Parts of a whole (page 28) The Whole Matters (page 38) Greatest Product (page 42)

Constructing/Practice Task: Sharing Candy Bars (page 29 and 38)

Students will make sense of a fraction as division. https://www.georgiastandards.org/Georgia-Standards/Frameworks/5th-Math-Unit-4.pdf

https://learnzillion.com/resources/72736-interpreting-fractions-as-division-of-the-numerator-by-the-denominator

https://learnzillion.com/resources/72546-interpret-a-fraction-as-division-and-answer-division-problems-using-fractions-5-nf-b-3

https://learnzillion.com/resources/72546-interpret-a-fraction-as-division-and-answer-division-problems-using-fractions-5-nf-b-3

https://learnzillion.com/resources/72323-multiply-fractions

https://learnzillion.com/resources/73064-solve-problems-involving-multiplication-of-fractions-and-mixed-numbers-5-nf-b-6

https://learnzillion.com/resources/73064-solve-problems-involving-multiplication-of-fractions-and-mixed-numbers-5-nf-b-6

https://learnzillion.com/resources/72437-divide-whole-numbers-by-unit-fractions-and-unit-fractions-by-whole-numbers-5-nf-b-7

https://learnzillion.com/resources/72437-divide-whole-numbers-by-unit-fractions-and-unit-fractions-by-whole-numbers-5-nf-b-7

https://learnzillion.com/resources/72969-divide-whole-numbers-by-fractions

https://learnzillion.com/resources/72698-solve-real-world-problems-involving-division-of-whole-numbers-by-unit-fractions

https://learnzillion.com/resources/72698-solve-real-world-problems-involving-division-of-whole-numbers-by-unit-fractions

https://www.illustrativemathematics.org/content-standards/5/NF/B/4/tasks/321

https://www.illustrativemathematics.org/content-standards/5/NF/B/4/tasks/2078

https://www.illustrativemathematics.org/5.NF.B.4





30

Constructing/Practice Task: Comparing MP3s (page 96) Students will practice with multiplication of fractions as an area model. https://www.georgiastandards.org/Georgia-

Standards/Frameworks/5th-Math-Unit-4.pdf Constructing Task: Reasoning with Fractions (page 116)

Students will determine the effect on a product, of multiplying a number by a factor greater than 1 and less than 1. https://www.georgiastandards.org/Georgia-Standards/Frameworks/5th-Math-Unit-4.pdf

NC Mathematics Lessons for Learning: Introduction for Dividing Fractions (page 72) Students will create a visual representation for division and justify their reasoning when developing a strategy for

division. http://maccss.ncdpi.wikispaces.net/file/view/5thgrade%20Lessons%204Learning%2022616.pdf/585433849/5thgrade%20Lessons%204Learning%2022616.pdf

Constructing Task: Dividing with Unit Fractions (page 134)

The student will investigate dividing whole numbers with unit fractions. https://www.georgiastandards.org/Georgia-Standards/Frameworks/5th-Math-Unit-4.pdf

NC Mathematics Fraction Unit (use at the end of the Topic)

http://maccss.ncdpi.wikispaces.net/file/view/5thGradeUnit.pdf/295516386/5thGradeUnit.pdf








http://maccss.ncdpi.wikispaces.net/file/view/5thGradeUnit.pdf/295516386/5thGradeUnit.pdf


31

TOPIC 8 – NUMERICAL EXPRESSIONS, PATTERNS, AND RELATIONSHIPS

I. Overview

Students will write algebraic expressions using variables and will translate words into expressions. Students need experiences with multiple expressions

that use grouping symbols throughout the year to develop an understanding of when and how to use parentheses and brackets. In Topic 8, students use

these symbols to add, subtract, multiply, and divide whole numbers. Students also need exposure using these symbols to add, subtract, multiply, and

divide decimals and fractions (see pg. 4 of the Companion Document for Teachers Grade 5). Students are expected to know the order in which to

execute the operations in simple expressions with no grouping symbols. At the end of Topic 8, students will determine a rule that establishes a pattern

that identifies a relationship between two quantities. In addition, students will extend tables with given rules.

Manipulatives/Materials: Base-ten rods and unit cubes

FOCUS

STANDARDS 5.OA.A.1 Use parentheses or brackets in numerical expressions, and evaluate expressions with these symbols.

5.OA.A.2 Write simple expressions that record calculations with whole numbers, fractions, and decimals, and interpret numerical expressions without evaluating them.

5.OA.A.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

STANDARDS FOR

MATHEMATICAL

PRACTICE


FOUNDATIONAL

STANDARDS 4.OA.C.5


32


2. Resources


Topic 8: Lessons 8-1, 8-2, 8-3,

8-4, 8-5, 8-6, 8-7, 8-8

Module 4: Topic H Lessons 32-33



LearnZillion:

Lesson: Use parentheses and interpret and evaluate expressions with parentheses: https://learnzillion.com/resources/72624-use-parentheses-and-

interpret-and-evaluate-expressions-with-parentheses

Write, interpret, describe, and reason about expressions: https://learnzillion.com/resources/72836-write-interpret-describe-and-reason-about-expressions-5-oa-a-2

Identify the relationship between two numerical patterns: https://learnzillion.com/lesson_plans/6758-identify-the-relationship-between-two-numerical-patterns


Tasks:

5.OA – Sidewalk Patterns: https://www.illustrativemathematics.org/content-standards/5/OA/B/3/tasks/1895 Discovery Education:

Patterns and Rules (Video, Blackline Masters and Teacher’s Guide): https://app.discoveryeducation.com/learn/videos/77F5D099-533A-46C8-9093-D26422F1592C?hasLocalHost=false

https://learnzillion.com/resources/72624-use-parentheses-and-interpret-and-evaluate-expressions-with-parentheses

https://learnzillion.com/resources/72624-use-parentheses-and-interpret-and-evaluate-expressions-with-parentheses

https://learnzillion.com/resources/72836-write-interpret-describe-and-reason-about-expressions-5-oa-a-2

https://learnzillion.com/resources/72836-write-interpret-describe-and-reason-about-expressions-5-oa-a-2

https://learnzillion.com/lesson_plans/6758-identify-the-relationship-between-two-numerical-patterns

https://learnzillion.com/lesson_plans/6758-identify-the-relationship-between-two-numerical-patterns

https://www.illustrativemathematics.org/content-standards/5/OA/B/3/tasks/1895

https://app.discoveryeducation.com/learn/videos/77F5D099-533A-46C8-9093-D26422F1592C?hasLocalHost=false

https://app.discoveryeducation.com/learn/videos/77F5D099-533A-46C8-9093-D26422F1592C?hasLocalHost=false


33



SUGGESTIONS

Words to Expressions Game Students will translate algebraic expressions from words to numbers and symbols. Write three word forms of

an algebraic expression on a whiteboard (or state orally). The students have to record the correct expression on paper in numerical form, and evaluate the expression. Students with the correct answers receive points. The student(s) with the highest points after a certain time period wins the game! http://www.stroseoflimanyc.org

Target

Students will use order of operations and grouping symbols to evaluate given numbers to reach a target solution. Draw a bullseye with a target number in the center and five various numbers around the outer circles on the whiteboard. Challenge students to use all the numbers with operations and parentheses to get the target number. If they use all numbers, they get a bullseye and receive 10 points. If the students use only 4 numbers, they receive 4 points, three numbers, 3 points etc. Students can keep track of their points over the course of multiple days. http://www.stroseoflimanyc.org

Build the Rule

Students will use concrete objects to model the concept of input and output, and identify the function rule. (page 164) http://mason.gmu.edu/~jsuh4/impact/PFAEntire.pdf

Guess My Rule

Students will solve problems involving functional relationships. (page 166) http://mason.gmu.edu/~jsuh4/impact/PFAEntire.pdf

http://www.stroseoflimanyc.org/

http://www.stroseoflimanyc.org/

http://mason.gmu.edu/~jsuh4/impact/PFAEntire.pdf

http://mason.gmu.edu/~jsuh4/impact/PFAEntire.pdf


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UNIT 6- VOLUME AND AREA VOLUME AND AREA (8 DAYS)

UNDERSTANDING VOLUME, CALCULATING VOLUME, AREA OF RECTANGULAR FIGURES

I. Overview

The major emphasis for measurement in grade 5 is volume. In Topic 12, students will work with concrete unit cubes and pictorial representation of solids

to develop the concept of volume. This is the first time that students begin exploring the concept of volume. Volume introduces a third dimension and

thus a significant challenge to students’ spatial structuring. Therefore, students may need a review of describing, classifying, and analyzing three-

dimensional figures by their faces, edges, and vertices. As students develop their understanding of volume they understand that a 1-unit by 1-unit by 1-

unit cube is the standard unit for measuring volume. This cube has a length of 1 unit, a width of 1 unit and a height of 1 unit and is called a cubic unit.

This cubic unit is written with an exponent of 3 (e.g., in3, m3). Students connect this notation to their understanding of powers of 10 in our place value

system. Models of cubic inches, cubic centimeters, cubic feet, etc. are helpful in developing an image of a cubic unit. Student’s estimate how many cubic

yards would be needed to fill the classroom or how many cubic centimeters would be needed to fill a pencil box. Last, students will measure volume by

counting unit cubes and applying the formula for rectangular prisms. Students will find volumes of irregular solids by breaking apart (decomposing) into

two rectangular prisms and using the additive strategy to determine the whole.

Manipulatives/Materials: unit cubes, 3-D models of solids

FOCUS

STANDARDS

5.MD.C.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. o (5.MD.C.3a) A cube with side length 1 unit, called a “unit cube”, is said to have “one cubic unit” of

volume, and can be used to measure volume. o (5.MD.C.3b) A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have

a volume of n cubic units.

5.MD.C.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.


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5.MD.C.5 Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. o (5.MD.C.5a) Find the volume of a right rectangular prism with whole-number side lengths by packing it with

unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

o (5.MD.C.5b) Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.

o (5.MD.C.5c) Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems.

STANDARDS FOR

MATHEMATICAL

PRACTICE



MP.4 Model with mathematics.

MP.6 Attend to precision.


FOUNDATIONAL

STANDARDS 3.MD.C.5 3.OA.B.5 4.MD.A.3


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TOPIC 12 – VOLUME AND AREA

2. Resources


Topic 12: Lessons 12-4, 12-5, 12-6, 12-7

Topic 11: Lesson 11-5

Module 5: Topic A Lesson 1-3


Enrichment Lessons: Topic B Lessons 8/9

Module 5: Topic C Lessons 10-14/15

Unit 4, Lessons 24 – 27


Guidebook: Lesson:

Fish Tanks: http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/5th-grade-instructional-tasks.pdf?sfvrsn=5


Understanding volume: https://learnzillion.com/resources/72937-understand-volume-as-an-attribute-of-three-dimensional-figures-measure-it-and-relate-it-to-multiplication-and-addition-5-md-c-3-5-md-c-4-5-md-c-5

Counting unit cubes: https://learnzillion.com/resources/73036-count-unit-cubes-to-measure-volume-5-md-c-4 More on understanding volume, counting unit cubes, and relating volume: https://learnzillion.com/resources/72937-understand-volume-as-an-

attribute-of-three-dimensional-figures-measure-it-and-relate-it-to-multiplication-and-addition-5-md-c-3-5-md-c-4-5-md-c-5 Relating volume to multiplication and addition: https://learnzillion.com/resources/72256-relating-volume-to-the-operations-of-multiplication-and-

addition-5-md-c-5 Discovery Education:

Example 1: Perimeter, Circumference, and Area (Video, Blackline Masters and Teacher’s Guide): https://app.discoveryeducation.com/learn/videos/00e2332a-7e61-46c0-8577-9bd654057fc3

Example 2: Volume and Capacity (Video, Blackline Masters and Teacher’s Guide): https://app.discoveryeducation.com/learn/videos/1f9c0b98-655b-4ae7-9a4a-1eaec5546256


https://learnzillion.com/resources/72937-understand-volume-as-an-attribute-of-three-dimensional-figures-measure-it-and-relate-it-to-multiplication-and-addition-5-md-c-3-5-md-c-4-5-md-c-5


https://learnzillion.com/resources/73036-count-unit-cubes-to-measure-volume-5-md-c-4



https://learnzillion.com/resources/72256-relating-volume-to-the-operations-of-multiplication-and-addition-5-md-c-5

https://learnzillion.com/resources/72256-relating-volume-to-the-operations-of-multiplication-and-addition-5-md-c-5

https://app.discoveryeducation.com/learn/videos/00e2332a-7e61-46c0-8577-9bd654057fc3

https://app.discoveryeducation.com/learn/videos/1f9c0b98-655b-4ae7-9a4a-1eaec5546256

https://app.discoveryeducation.com/learn/videos/1f9c0b98-655b-4ae7-9a4a-1eaec5546256


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TOPIC 12 – VOLUME AND AREA


SUGGESTIONS

Counting Cubes:

Students will view 3-D representations using a variety of visual perceptions to determine the amount of cubes in a given object. http://www.mathplayground.com

Differentiating Area and Volume: Students will build models to represent units of area and units of volume. This task is intended to address the

misconception that the term “square” applies only to a geometric figure with equal length sides. https://www.georgiastandards.org/Georgia-Standards/Frameworks/5-Math-Uni

Volume in Two Ways:

Students will be asked to compare different strategies for finding the volume for a rectangular prism. http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/70378

http://www.mathplayground.com/

https://www.georgiastandards.org/Georgia-Standards/Frameworks/5-Math-Uni

http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/70378

unit 1- place value - jefferson parish public...

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