Unit 3.2 Modeling Multiplication and Division · multiplication or division you must consider key words and relationships defined in the problem. • The inverse relationship of multiplication

3rd Grade Mathematics

Modeling Multiplication and Division: Relationships and Properties

Pacing: 48 Days Unit Overview

In this unit, students will: 1.) Begin to understand the concepts of multiplication and division and 2.) Learn the basic facts of multiplication and their related division facts. Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Throughout the unit, students will have extensive practice distinguishing between real life situations that require multiplication or division. In Grade 2 students have added groups of objects by skip-counting and using repeated addition (2.OA.4). In this unit students connect these concepts to multiplication and division by interpreting and representing products and quotients. Students begin developing these concepts by working with numbers with which they are more familiar, such as 2s, 5s, and 10s, then develop strategies to work with less familiar groupings. Since multiplication is a critical area for Grade 3, students will build on these concepts throughout the year, working towards fluency by the end of the year. In this unit, students will use concrete objects or pictures to help conceptualize and solve problems (MP.1). As the unit progresses, students will be required to implement multiple strategies to solve the same problem. They use arrays and other representations to model multiplication and division (MP.4) and contextualize given expressions (MP.2).

Prerequisite Skills Vocabulary Mathematical Practices 1) Add groups of objects by skip counting and using repeated

addition

2) Fluently add and subtract number within 20.

3) Recognize that the multiplication symbol means “groups of”

4) Identify odd and even numbers

5) Skip count by two, threes, fives, and tens

6) Determine reasonableness of answers using estimation

7) Describe the inverse relationship of addition and subtraction

8) Construct a picture/visual representing repeated addition to find the total number of objects represented

Equal groups Factor Multiplication Repeated addition Product Divisor Partition Dividend Division Equal shares Groups Quotient Inverse operations Commutative Property Identity Property Zero Property Distributive Property

Associative Property

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

MP.2: Reason abstractly and quantitatively

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

MP.4: Model with mathematics

MP.5: Use appropriate tools strategically

MP.6: Attend to precision

MP.7: Look for and make use of structure

MP.8: Look for and express regularity in repeated reasoning

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Common Core State Standards

According to the PARCC Model Content Framework, Standards 3.OA.3 and 3.OA.7 should serve as opportunities for in-depth focus: 3.OA.3—“Word problems involving equal groups, arrays, and measurement quantities can be used to build students’ understanding of and skill with multiplication and division...” 3.OA.7—“Finding single-digit products and related quotients is a required fluency for grade 3. Reaching fluency will take much of the year for many students.”

The key advance in multiplication and division concepts between third and fourth grade is: “In grade 3, students studied multiplication in terms of equal groups, arrays and area. In grade 4, students extend their concept of multiplication to

make multiplicative comparisons (4.OA.1).”

3.NBT.3: Multiply by

Multiples of 10

3.MD.3: Scaled Picture and Bar Graphs

3.OA.1: Interpret Products of Whole Numbers

3.OA.2: Interpret Quotients of Whole Numbers

3.OA.3: Multiplication and Division Fact Word Problems

3.OA.4: Unknowns in Multiplication and Division Equations 3.OA.5: Apply Properties of Operations to Multiply and Divide 3.OA.6: Understand Division as an Unknown Factor Problem

3.OA.7: Fluently Multiply and Divide within 100 3.OA.8: Two-Step Word Problems

3.OA.9: Patterns in Addition and Multiplication 3.MD.2: Solve Word Problems with Mass and Volume and Estimate Mass and

Volume

Major Standards (70%)

Additional Standards (10%)

Supporting Standards (20%)

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Progression of Skills 2nd Grade 3rd Grade 4th Grade

2.OA.4: Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns

3.OA.1: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

4.OA.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 � 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.

N/A 3.OA.2: Interpret whole-number quotients of whole numbers, e.g.,

interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

N/A

N/A 3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

4.OA.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted

N/A 3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

4.OA.2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

N/A 3.OA.6: Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

4.OA.4: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

N/A 3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.

4.NBT.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division

2.OA.3: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

4.OA.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain why the numbers will continue to alternate

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Big Ideas Students Will… • What is multiplication/division? In what

real world contexts do we use multiplication and division?

• What is the relationship between multiplication and division? ( e.g. both represent the manipulation of equal-sized groups; they are inverse operations, etc.)

• How does understanding the relationship between multiplication and division, as well as their properties, help me multiply and divide efficiently?

• What do the numbers in multiplication and division problems represent? How does understanding these numbers help us interpret, represent and solve mathematical equations?

• How can we solve for unknown whole

numbers in multiplication and division problems? Why is learning this process important to us as mathematical thinkers?

• What strategies can I use to become

fluent with multiplication and division facts?

• How can I use equations to represent one-

and two-step word problems?

Know/Understand Be Able To… • Multiplication represents repeated addition of groups. • A rectangular array can represent a multiplication

problem. • The product of a multiplication problem may represent

the combination of a number of groups with multiple objects in each group.

• Division is the splitting of a number into equal groups. • Division represents repeated subtraction. • The quotient resulting from a division problem represents

the number of times one group of objects is split equally among another group.

• A symbol can represent an unknown number in a math problem.

• To identify whether an operation in a word problem is multiplication or division you must consider key words and relationships defined in the problem.

• The inverse relationship of multiplication and division • A division problem is a multiplication problem with an

unknown factor. • A symbol can represent an unknown whole number in a

math problem relating three whole numbers. • The concepts behind the commutative property of

multiplication, the associative property of multiplication, and the distributive property

• An equation may represent information from a two-step word problem.

• Arithmetic patterns exist and can be identified using a variety of strategies.

• Categories on a scaled picture or scaled bar graph can be compared to each other to determine how many more or less of that category.

• What operation(s) are required from "how many more" and "how many less" word problems.

• The relationship between place value and multiplication. • The relationship between the associative property of

multiplication and decomposing large numbers to solve multiplication problems.

• Interpret the product of whole numbers using rectangular arrays and pictures.

• Draw equal groups of objects to represent a multiplication expression.

• Find the quotient of a division problem by identifying how many equal groups can be made out of a certain number of objects.

• Interpret the quotient of a division problem by describing what it means in the context of a problem.

• Use repeated subtraction to understand a quotient by finding the number of equal groups within a number.

• Use arrays, manipulatives, and drawings to represent and solve multiplication and division problems.

• Create multiplication and division equations to represent the information in word problems.

• Solve for an unknown whole number in a multiplication or division equation with the unknown number in any position.

• Apply properties of operations to multiply and divide • Find an unknown factor in a division problem using

multiplication. • Multiply and divide within 100 quickly, accurately, and

efficiently using multiple strategies. • Create equations to represent and solve a two-step word

problem. • Solve equations to find an unknown number • Assess the reasonableness of answers when solving two-

step equations by using mental math and estimation • Identify, extend, and explain arithmetic patterns. • Solve one-step addition, subtraction, multiplication, and

division word problems involving masses or volumes • Interpret, translate, and represent data as a scaled picture

graph and scaled bar graph to represent a data set • Determine a scale for a scaled picture or scaled bar graph

in order to convert data correctly. • Use information from scaled picture or bar graphs to

solve "how many more" and "how many less" problems. • Multiply one-digit factors by multiples of 10 up to 90.

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Unit Sequence Student Friendly

Objective SWBAT…

Key Points/ Teaching Tips

Exit Ticket Instructional Resources

1

Use visual models to demonstrate understanding of multiplication as equal groups.

• Students should practice interpreting, creating, and evaluating visual models of multiplication and writing corresponding multiplication equations.

1. There are 4 pretzels in each bag. How many pretzels are in 6 bags?

a. 4 x 6 = _____ b. There are _____ pretzels altogether.

2. Kevin has 3 bags of candy. There are 4

candies in each bag. a. Draw a picture to represent the

situation. b. Write a multiplication sentence to

represent the situation.

3. The picture below shows 2 groups of pencils. Does the picture below show 2 x 3? Explain why or why not.

My Math Chapter 4, Lesson 1 “Engage NY Lesson1.1” (Appendix C)

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2 Use visual models to represent and identify factors as the size of the group or the number of groups.

• Students should learn the definitions of “factors” and “product” and begin to develop an understanding of “multiplication” that includes equal groups.

• Students should begin to distinguish

between real world situations that require multiplication versus addition and justify their reasoning based on equal groups.

1. There are 3 stars in each group. How many stars are in 4 groups?

a. Number of groups: _____ b. Size of each group: _____ c. Multiplication equation: __________ d. There are _____ stars altogether.

2. Kevin has 5 bags of oranges. There are 6

oranges in each bag. a. Draw a picture to represent the

situation. b. How many groups are there? c. What is the size of each group? d. Write a multiplication sentence to

represent the situation.

3. Which statement can be represented by the expression 4 x 8?

a. A teacher put 8 chairs at each of 4 tables.

b. Tom buys 4 red markers and 8 black markers.

4. There are 8 ducks in the pond, then 4 more ducks join them.

“Engage NY Lesson1.3” (Appendix C) “What’s My Product?” (Appendix C)

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3 Model multiplication using repeated addition on a number line and write related addition and multiplication number sentences.

• Students’ understanding of “multiplication” should expand to include repeated addition of equal groups.

• Each arrow “bump” on the

number line should represent one equal group and expand the range of the size of one group. Students may benefit from drawing smaller “bumps” to count the size of the groups with precision.

1. Write an addition sentence and a multiplication sentence to represent the picture above:

_____ + _____ + _____ = _____

_____ x _____ = _____

2. Use the number line below to model the total

number of smiley faces using repeated addition:

4. Explain the relationship between

multiplication and addition in complete sentences.

My Math Chapter 4 Lesson 2 *Modify resource to include representing repeated addition on a number line

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4 Construct rectangular arrays to represent a multiplication problem and to model the Commutative Property of Multiplication.

• On 4 square Do Now, assess students’ ability to construct a simple (5 by 2) array in the “I’m ready to tackle today’s objective” box

• Inquiry Based Lesson: • Start with the task “Seating

Arrangements” and give students 24 tiles or counters to model their solutions (within a mixed group, with a partner or independently). Provide time for students to share their different solutions

• Use this task to lead into a mini-lesson, modeling the different combinations of factors that were possible to create an array of 24

• Use this model to introduce the Commutative Property of multiplication (i.e. an array of 8 x 3 and 3 x 8 both equal 24) – when modeling the combinations it would be helpful to write these pairs side by side in a table so students can see how each set of factors can be written in two different ways

• Explicitly teach how to distinguish between rows and columns.

• Students should be able to physically rotate their arrays (either manipulatives or pictures) to model the Commutative Property of Multiplication.

1. Write an addition sentence and a multiplication sentence to represent the picture below:

____ + ____ + ____ + ____ = ____

____ x ____ = ____

2. Write another addition sentence and

multiplication sentence to represent the picture.

__ + __ + __ + __ + __ + __ + __ + __ = __

____ x ____ = ____

3. In the multiplication table below, shade four

factors and two products that demonstrate the Commutative Property of Multiplication. Explain your reasoning in complete sentences.

“Seating Arrangement” (Appendix C) *Inquiry-based hook My Math Chapter 4 Lesson 4 *Note: For students who require remediation, use lesson 3 to review arrays (a concept that was taught in 2nd grade) EngageNY Lesson 1.2 (Appendix C)

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5 Use manipulatives and visual models to demonstrate understanding of division as partitioning a number into equal groups.

• Students should become comfortable with the word “partition,” as it will appear again in the unit on fractions.

Partition 15 counters into 3 equal groups. 1. How many counters are in each group? 2. Write a division sentence to model the

situation: ____ ÷ ____ = ____ 3. Ali drew a picture to model 20 ÷ 4 = 5.

4. Is her picture accurate? Give at least 2

reasons to explain why or why not.

My Math Chapter 5 Lessons 1 - 2

6 Interpret the unknown in division as the number of groups or the size of the group.

• Students must be able to identify whether a problem gives them the number of groups or the size of the groups.

• Students should learn division

vocabulary: “dividend,” “divisor,” and “quotient” and recognize that only the divisor or the quotient can refer to the number or size of groups.

• Students should be required to label

their answers when possible (i.e. the best response for exit ticket question #2 is “7 stacks,” as opposed to “7” or “7 erasers”).

1. Use the picture below to answer parts a and b:

a. Write a division sentence in which

the solution tells the size of the group.

b. Write a division sentence in which the solution tells the number of groups.

2. Alyssa has 14 erasers. She puts them in

stacks of 2. How many stacks does she have? Draw a picture and write a division sentence to support your answer.

Write a division problem in which the number of equal groups is given.

EngageNY Lessons 1.4-1.5 “Appendix C)

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7

Model division using repeated subtraction on a number line and write related subtraction and division number sentences.

• Each arrow “bump” on the number line should represent one equal group and span the size of one group. Students may benefit from drawing smaller “bumps” to count the size of the groups with precision.

1. Fill in the blanks to represent the picture above:

_____ ÷ _____ = _____

2. Use the number line below to model the total number of smiley faces using repeated addition:

2. Explain the relationship between division

and subtraction in complete sentences.

My Math Chapter 5 Lesson 3

8 Use arrays to model related multiplication and division facts. Describe the relationship between multiplication and division.

• Students should continue to use manipualtives (i.e. tiles, counters, etc) to model multiplication sentences in the form of arrays

• Given the definition of division as an unknown factor problem, build the lesson around relating an array that represents a multiplication sentence to an unknown factor or division problem

Create an array to show 6 x 4: Write a related division sentence that matches this array: Explain multiplication and division are related to each other:

My Math Chapter 5 Lesson 4 “Engage NY Lesson 1.6” (Appendix C)

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9 Apply the inverse relationship between multiplication and division to write and solve equations based on a given fact family

Students should understand that an equation (unlike an expression) has an equals sign. Either an equation or an expression may include a variable to stand in for an unknown. Students should relate the terms “dividend,” “divisor,” and “quotient” to the terms “factor” and “product.” Students should learn the definition of “inverse operations.” Students should use the Commutative Property of Multiplication as a foundation for their understanding of fact families.

1. Write four different number sentences using the following numbers: 2, 4, and 8. In one equation, label the factors and the product. In a different equation, label the dividend, divisor, and quotient.

2. For a school field trip, 72 students will be traveling in 9 vans. Each van will hold an equal number of students. The equation below shows one way to determine the number of students that will be in each van:

72 ÷ 9 = ? Write an equation using a different operation to show the number of students in each van. Using words and an array, explain why multiplication and division are inverse operations.


10

Match expressions with multiplication and division situations. Create a visual model to accompany the expression

• Students should define an “expression” as a number or combination of numbers and operations without an equals sign (My Math Chapter 9, Lesson 5).

• Attend to precision when

distinguishing between addition and multiplication expressions, as well as between division and subtraction

• Students should recognize “each” as

a key word indicating multiplication or division.

• Students should be justifying their

answers with language of repeated groups or partitioning into equal groups.

(#1 and #2 are sample PARCC EOY assessment questions)

1. Which three statements can be represented by the expression 24 ÷ 4?

a. Jake makes 24 muffins. He gives away 4 muffins.

b. Collin has 24 toy trucks. He sorts them into groups of 4 trucks each.

c. Amira has 24 trading cards. She puts them into piles containing 4 cards each.

d. Rosemary puts 24 stickers in each book. She uses enough stickers to fill 4 books.

e. Steven fills a new bookshelf with 24 books. He puts the same number of books on each of the 4 shelves.

2. For one of the three statements you chose for #1, use words, numbers, and pictures to explain why the statement represents 24 ÷ 4.

My Math Chapter 9 Lessons 5-7

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3. Which two statements can be represented by the expression 4 x 8?

a. A teacher puts 8 chairs at each of 4 tables.

b. Tom buys 4 red markers and 8 black markers.

c. Marie shares her 8 marbles equally among 4 friends.

d. There are 4 rows of flowers. There are 8 flowers in each row.

e. There are 8 ducks in the pond. Then, 4 more ducks join them.

For one of the statements you did not choose for #3, use words, numbers, and pictures to explain why the statement does not represent 4 x 8.

11 Make sense of and persevere in solving real world problems involving multiplication and division. Model these problems using visuals, manipualtives, arrays, and/or equations.

• Students should ask themselves questions to determine whether to use multiplication or division for word problems, such as Do I know the total amount? Do I know the number of groups? Do I know the size of each group? By modeling and making sense of problems, students will be able to reason about which operation is necessary because

• Students should begin to write the

number sentence of the inverse operation as a way to check their work.

• Students should also practice

multiplication and division word problems with money.

1. Lucy has 28 craft sticks. She needs 7 sticks to make a puzzle. How many puzzles can Lucy make? Write an equation to represent the situation, and then use your favorite strategy to solve.

2. Maria makes 6 blueberry muffins. Each muffin has 5 blueberries. How many blueberries did she use in all? Write an equation to represent the situation, and then use your favorite strategy to solve.

3. Explain in complete sentences how you are able to decide whether to use multiplication or division to solve a single-step word problem.

My Math Chapter 5 Lesson 6 “Making Up Multiplication” (Appendix C)

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12 Flex Day (Instruction Based on Data) Recommended Resources:

Arrays on the Farm (Appendix C) Array Picture Cards (Appendix C)

Sharing or Grouping? (Appendix C) Sharing Marbles Equally (Appendix C)

Number Story Arrays (Appendix C) Division as Unknown Factor Problems (Appendix C)

My Math Chapter 5 Review (Pages 283 – 286)

13 Through repeated observations, infer the pattern in products when multiplying by 2. Use skip counting, arrays, visual models and repeated addition to multiply by 2 with fluency.

• Tip: Prior to this lesson (or on the do now), assess students’ prerequisite skills of identifying even/odd numbers

• Teaching Tip: Design this as an inquiry based lesson by:

• Begin with #3 (Independent practice) on page 297 – ask students to color in the row that shows the products of 2 and to identify a pattern and make a prediction

• Then, allow students to put their theory to the test using visual models, manipulatives and/or arrays

• For instance, if they predict that any number x 2 will always be even, they can use models to represent 11 x 2 or 15 x 2, and so on to “test” their theory

• Then, begin instruction by confirming that any number with a factor of 2 is in fact an even number. Encourage students to think about how this understanding helps them as mathematicians (i.e. it helps us judge the reasonableness of our work – if I ever multiply by 2 and get an odd number, I know I made a mistake!)

• emphasize fluency through skip-counting

1. Julia plants 2 rows of lilies. There are 9 lilies in each row. How many lilies are there altogether?

a. Write an equation with a ? to represent the unknown.

b. Draw an array to solve. c. Write the inverse equation to

check your work. 3. Describe the pattern that occurs when

you multiply by 2 and provide an example:


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14 Visually represent dividing by two to demonstrate that the quotient is now ½ of the dividend. For each division problem, write a related multiplication fact.

• Begin lesson with visual models to students can actually see that dividing by two is cutting an amount into two equal halves

• Require students to continue visually representing division by two using arrays, hundreds charts, pictures and/or manipulatives

• In this lesson, also emphasize fluency (students may use hundreds chart)

1. There are 14 mints in a box. Cecilia eats 2 mints each day. How many days does it take Cecilia to eat all of the mints in the box? o Write an equation with a ? to

represent the unknown. o Draw a number line or a tape

diagram to solve. o Write the inverse equation to check

your work.


15 Through repeated observations, infer the pattern in products when multiplying by 5. Use skip counting, arrays, visual models and repeated addition to multiply by 5 with fluency.

Students should explore this objective through the multiplication table and be aware of skip-counting patterns (the products in each row and column increase by the same amount) and the fact that when 5 is a factor, every other product will end in 0 or 5.

1. Rose has 6 ribbons. Each ribbon is 5 inches long. How many inches of ribbon does she have in all?


b. Draw a number line or a tape diagram to solve.

c. Write the inverse equation to check your work.

2. What is true about all products of 5? Show/explain:


16 Apply patterns in multiplying by 5s to determine if a given number will be divisible by 5. Divide by 5 with fluency and for each division problem, write a related multiplication fact.

• Introduce the term divisible (when one number can be divided evenly by another number and the quotient is one whole number)

• Encourage students to use the patterns they found in 5 products yesterday to determine whether or not a number will be divisible by 5 (tip: use this as a warm-up for the day’s lesson using a mix of numbers that are and are not divisible by 5)

Garrison collected 45 flags. He displays them in his room in 5 equal rows. How many flags does Garrison have in each row?

o Write an equation with a ? to represent the unknown.

o Draw an array to solve. o Write the inverse equation to check

your work.


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17 Apply skip-counting strategies and previously learned models to solve problems with multiplication and division by 10.

In this lesson, students only need to multiply 10 by 2-12 and divide 20-120 by 10. Students should explore this objective through the multiplication table and be aware of skip-counting patterns (the products in each row and column increase by the same amount) and the fact that when 10 is a factor every product ends in 0.

1. Byron has 40 pennies. He stacks them in groups of 10. How many stacks of pennies can Byron make?


b. Draw a picture or an array to solve.

c. Write the inverse equation to check your work.

2. Mia found 3 dimes. How much money did Mia find?


b. Draw a number line to solve. c. Write the inverse equation to

check your work. 1. What is true about all products of 10?

Show and explain how you know

My Math Chapter 6, Lessons 7 & 9

18 Use place value understanding and the Associative Property of Multiplication to solve problems with multiplication by multiples of 10.

• Students should define “multiple” in the context of multiples of ten. (they can represent multiples of 10 using multiple hundreds charts) – encourage students to describe “how many tens” compose each multiple

• Students may benefit from the use of place value blocks.

• Sample PARCC EOY assessment question:

Which two ways show how to find the value of 7 x 40? Select the two correct answers.

A. 7 x 4 B. 4 x 10 C. 7 x 4 x 10 D. 7 groups of 4 ones

E. 7 groups of 4 tens

1. A small plane (pictured below) has 20 rows of seats. Each row has 4 seats.

Write an equation to find the total number of seats on the plane.

2. Write a multiplication sentence that uses a multiple of 10 and has a product of 160.

(Hint: ___ x ___ x 10 = ___ x ___) 3. Jamila solves 20 x 5 by thinking about

10 tens. Explain her strategy.

My Math Chapter 6 Lesson 8 “Engage NY Lesson 3.19” https://learnzillion.com/lessons/2761-‐multiply-‐by-‐mutliples-‐of-‐10-‐by-‐breaking-‐apart-‐the-‐multiple-‐of-‐ten-‐into-‐2-‐factors

Unit 3.2 Modeling Multiplication and Division · multiplication or division you must consider key words and relationships defined in the problem. • The inverse relationship of multiplication

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