Curriculum  /  Math  /  3rd Grade  /  Unit 3: Multiplication and Division, Part 2  /  Lesson 8

Multiplication and Division, Part 2

Lesson 8

Math

Unit 3

3rd Grade

Lesson 8 of 23

Objective

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

Common Core Standards

Core Standards

  • 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.C.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.
  • 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

  • 3.OA.A.1
  • 3.OA.A.2

Criteria for Success

  1. Understand and explain that when multiplying three or more numbers, those multiplications can be performed in any order (e.g., $$3\times5\times2$$ can be found by $$3\times5=15$$ then $$15\times2=30$$, or by $$5\times2=10$$ then $$3\times10=30$$) (MP.3).
  2. Use parentheses to indicate which operations are performed in what order when demonstrating the associative property. 
  3. Make use of structure by using the associative property to decompose the 6 in a multiplication problem into a product of 2 and 3, then multiply the three values in any order (MP.7).
  4. Look for structure in the multiplication table to see the pattern between the 3s facts and the 6s facts (and optionally the 2s facts and 6s facts) and explain that pattern using the associative property (MP.7). 
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Anchor Tasks

25-30 minutes

Problem 1

a.   Solve.

$$3\times6$$

$$3\times(3\times2)$$

$$(3\times3)\times2$$

b.   What do you notice? What do you wonder?

Guiding Questions

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Student Response

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Problem 2

a.   Solve.

  1.  

$$(7\times3)\times2$$

$$7\times(3\times2)$$

$$7\times6$$
  1.  

$$(7\times2)\times3$$

$$7\times(2\times3)$$

$$7\times6$$

b.   Use the reasoning in Part (a-i) to explain how you could use $$4\times3$$ to solve $$4\times6$$.

c.   Use the reasoning in Part (a-ii) to explain how you could use $$5\times2$$ to solve $$5\times6$$.

Guiding Questions

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Student Response

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Problem 3

Decompose 6 into a product of two factors in the following expression and multiply the numbers in the order that makes sense to you.

$$6\times8$$

Guiding Questions

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Student Response

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Problem 4

Explain how the relationship we just explored is shown on the multiplication table below.

× 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56     80
9 9 18 27 36 45 54 63     90
10 10 20 30 40 50 60 70 80 90 100

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • What is the value of the three expressions in #1? What does that mean in terms of their relationship to one another? 
  • Is Libby’s reasoning correct or incorrect in #2? Why? 
  • Many of the numbers that we had to multiply by two in #3 were quite large. Why is multiplying by two easy, even with large numbers? 
  • Are the equations in #5 true or false? How did you explain your answer? Can you use the strategy we used in today’s lesson to support your answer? 
  • How did you decompose the 6 in #6? Could you have decomposed the other factor? Why? 
  • How can decomposing 6 into smaller factors help to solve multiplication problems involving 6? 

Target Task

5-10 minutes

Enok says he can find the value of $$6\times7$$ by thinking of it as $$2\times(3\times7)$$.

a.   Show or explain why Enok’s strategy works.

b.   What is the value of $$6\times7$$? Show or explain your work.

Student Response

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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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

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

Lesson 9
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Introduction to The Properties of Operations

Topic B: Multiplication and Division by 6 and 7

Topic C: Multiplication and Division by 8 and 9

Topic D: Multiplication and Division by Values Greater than 10

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

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