Curriculum  /  Math  /  3rd Grade  /  Unit 3: Multiplication and Division, Part 2  /  Lesson 5

Multiplication and Division, Part 2

Lesson 5

Math

Unit 3

3rd Grade

Lesson 5 of 23

Objective

Introduce the associative property of multiplication.

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.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. Look for structure to understand 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.7). 
  2. Make use of structure by using the associative property to decompose a factor in a multiplication problem into a product of values, then multiplying the three values in any order (MP.7).

Tips for Teachers

  • Students will be informally introduced to associative notation in this lesson, but note that students will not be expected to use it or understand it yet, and thus it is not on the Problem Set.
  • Students need not use formal terms for the properties of operations, including the terms "associative" or "associative property." Thus, the term is used throughout teacher-facing materials but not the student-facing materials. Thus, this objective would require edits in order to be student-facing.
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Anchor Tasks

25-30 minutes

Problem 1

a.   How many stars are on both window curtains? Explain how you solved.

b.   Write a multiplication expression to represent how you found the total number of stars on both window curtains.

Guiding Questions

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Student Response

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References

Photo: Window Curtains Inside (Pixabay)

Problem 2

Debra is finding the number of pentagons in the following array. She marks the array like this:

a.   Explain what Debra did to find the number of pentagons in the array.

b.   Why do you think Debra used this strategy?

Guiding Questions

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Student Response

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Problem 3

Use the following array to answer Parts (a) and (b).

a.   Use Debra’s strategy from Anchor Task 2 to decompose the array into ones whose products you know from memory. Then find the total product represented by the array.

b.   Find a second way to decompose the array.

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • How did you use $$3\times7$$ to help you find $$6\times7$$ in #1b? Is there another fact you could have used to help you solve $$6\times7$$? What about $$2\times7$$? 
  • How did you find the total number of Ruby’s stamps in #3a? How did #2b help you?
  • How did you decompose the array in #4? What fact did you then use to help you solve $$9\times8$$? Could you have used $$9\times2$$ to help you? What about $$3\times8$$?

Target Task

5-10 minutes

Rishi is trying to find the total number of clouds in the following array.

 

Rishi says "I know 3 × 9 = 27, so I can use that to help me solve."

a.   Mark the array above to show how Rishi is thinking about it.

b.   Use the fact that $$3\times9=27$$ to find the total number of clouds in the array.

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

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

Lesson 6
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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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