Lesson 1 | Multiplication and Division, Part 2 | 3rd Grade Mathematics

Objective

Study commutativity to find known facts of 6, 7, 8, and 9.

Common Core Standards

Core Standards

The core standards covered in this lesson

3.OA.B.5 — Apply properties of operations as strategies to multiply and divide. Students need not use formal terms for these properties. Example: Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) Example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)

Operations and Algebraic Thinking

3.OA.B.5 — Apply properties of operations as strategies to multiply and divide. Students need not use formal terms for these properties. Example: Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) Example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)
3.OA.D.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.

Operations and Algebraic Thinking

3.OA.D.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.

Foundational Standards

The foundational standards covered in this lesson

3.OA.A.1

Operations and Algebraic Thinking

3.OA.A.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.
3.OA.A.2

Operations and Algebraic Thinking

3.OA.A.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.
3.OA.B.6

Operations and Algebraic Thinking

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

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Demonstrate and explain the commutativity of multiplication using models (MP.3).
Use the commutative property to see that there are many 6s, 7s, 8s, and 9s facts that students already know.
Fill in a multiplication table with known facts, narrowing down the number of facts still needed to be learned.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Students have likely fully internalized the commutative property, but this lesson serves as a reminder before discussing more complex properties of multiplication. It also reminds students of the facts they have already learned, as well as gives them encouragement to see how few facts they have yet to acquire. Lastly, it introduces the multiplication table, which students will use throughout the unit—first to make connections between rows on the multiplication table to see the application of the distributive and associative properties, and then to notice patterns inherent in the multiplication table itself at the end of the unit.

Lesson Materials

Optional: Blank Multiplication Table (1 per student) — See Anchor Task 2 for more information.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

Katia and Gerard are stocking shelves at the grocery store. Katia stocks 3 shelves with 7 boxes of cereal on each shelf. Gerard stocks 7 shelves with 3 boxes of cereal on each shelf.

Katia says they put the same number of cereal boxes on each shelf. Gerard says they didn’t, since they stocked a different number of boxes on each of a different number of shelves. Who do you agree with, Katia or Gerard? Explain.

Guiding Questions

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Problem 2

Fill in the facts you know on the multiplication table below.

×	1	2	3	4	5	6	7	8	9	10
1
2
3
4
5
6
7
8
9
10

Guiding Questions

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References

EngageNY Mathematics Grade 3 Mathematics > Module 3 > Topic A > Lesson 1 — Concept Development

Grade 3 Mathematics > Module 3 > Topic A > Lesson 1 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Solve.

a. $$4 \times 8 =a $$

b. $$18 = b \times 6$$

c. $$c= 35 \div 7$$

d. $$9 = 18 \div d$$

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

What multiplication equations did you write for #1? What other equations can you write that are represented by this array?
How did you to solve the equations in #4? Were there any for which the commutative property, or switching the order of the factors, helped you?
What did you notice in the multiplication table in #6? Why does that pattern exist?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Fill in the blanks to write two different equations that represent the array below.

Problem 2

Sunni wants to solve the problem below.

4 × 6 = ?

Explain how she can use the fact that 6 × 4 = 24 to help her solve.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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Lesson 2

Lesson Map

Topic A: Introduction to The Properties of Operations

Study commutativity to find known facts of 6, 7, 8, and 9.

3.OA.B.5 3.OA.D.9

Understand the zero and identity properties of multiplication.

3.OA.A.4 3.OA.B.5 3.OA.C.7 3.OA.D.9

Understand the role of parentheses and apply to solving problems.

3.OA.B.5 3.OA.D.8

Introduce the distributive property of multiplication.

3.OA.B.5 3.OA.D.9

Introduce the associative property of multiplication.

3.OA.B.5 3.OA.D.9

Topic B: Multiplication and Division by 6 and 7

Build fluency with multiplication and division facts using units of 6.

3.OA.A.4 3.OA.C.7

Build fluency with multiplication and division facts using units of 7.

3.OA.A.4 3.OA.C.7

Use the associative property as a strategy to multiply by units of 6.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Use the distributive property as a strategy to multiply by units of 6.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Use the distributive property as a strategy to multiply by units of 7.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Solve one- and two-step word problems involving units up to 7.

3.OA.A.3 3.OA.D.8

Topic C: Multiplication and Division by 8 and 9

Build fluency with multiplication and division facts using units of 8 and 9.

3.OA.A.4 3.OA.C.7

Use the associative property as a strategy to multiply by units of 8 and 9.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Use the distributive property as a strategy to multiply by units of 8 and 9.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Use the distributive property as a strategy to multiply by units of 8 and 9, including the subtractive use of the distributive property.

3.OA.B.5 3.OA.C.7 3.OA.D.9

Solve one- and two-step word problems involving units up to 9.

3.OA.A.3 3.OA.D.8

Topic D: Multiplication and Division by Values Greater than 10

Multiply one-digit whole numbers by multiples of 10.

3.NBT.A.3 3.OA.A.4 3.OA.B.5

Multiply one-digit whole numbers by two-digit whole numbers using the associative and distributive properties.

3.NBT.A.3 3.OA.A.4 3.OA.B.5

Topic E: Two-Step Word Problems and Patterns in Arithmetic

Solve two-step word problems involving all four operations.

3.OA.D.8

Solve two-step word problems involving all four operations, including multiplying one-digit whole numbers by multiples of 10.

3.NBT.A.3 3.OA.D.8

Identify patterns in single or multiple rows/columns of the multiplication table.

3.OA.C.7 3.OA.D.9

Identify other patterns in the multiplication table.

3.OA.D.9

Identify arithmetic patterns and explain them using properties of operations.

3.OA.D.9

Multiplication and Division, Part 2

Objective

Common Core Standards

Core Standards

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Foundational Standards

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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