Curriculum  /  Math  /  3rd Grade  /  Unit 3: Multiplication and Division, Part 2  /  Lesson 4

Multiplication and Division, Part 2

Lesson 4

Math

Unit 3

3rd Grade

Lesson 4 of 23

Objective

Introduce the distributive 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.NBT.A.2
  • 3.OA.A.1
  • 3.OA.A.2

Criteria for Success

  1. Look for structure to understand that when multiplying two numbers, either number can be decomposed into a sum of values and multiplied by the other factor, then added together (e.g., $$5\times4=(3\times4)+(2\times4)$$) (MP.7).
  2. Make use of structure by using the distributive property to decompose a factor in a multiplication problem into a sum of values, multiplying those values separately by the other factor, then adding those products together to get the overall product (MP.7). 

Tips for Teachers

  • Students will be informally introduced to distributive notation in this lesson, but 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 "distributive" or "distributive 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

Each box of tissues costs $2.

a.   What is the cost for 3 boxes? What is the cost for 5 boxes? What is the cost for 8 boxes?

b.   What do you notice about your answers to Part (a)? What do you wonder?

Guiding Questions

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Student Response

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Problem 2

Shawn is finding the number of diamonds in the following array. He marks the array like this:

a.   Explain what Shawn did to find the number of diamonds in the array.

b.   Why do you think Shawn 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 Shawn’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

  • In #1c, I think I can find $$3\times3$$ and then double that product to find the number of objects in the whole array. Do you agree or disagree? Why? 
  • In #1d, I think I can find $$10\times6$$ and then subtract a group of 6 to find the product of 9 and 6. Do you agree or disagree? Why? 
  • In #2 and #3, how did you find Matt’s total cards? How was that total related to the number of cards he first had and the number of cards he added? 
  • How did you decompose your arrays in #4? Why did you choose to decompose them in that way? Was there more than one way to decompose them? 
  • What did you always do to the products of the decomposed arrays to find the product of the larger array? 

Target Task

5-10 minutes

Decompose the following array in a way that will help you find its total number of objects. Then show how you find the total number of objects.

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

Introduce the associative property of multiplication.

Lesson 5
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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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