Curriculum  /  Math  /  3rd Grade  /  Unit 3: Multiplication and Division, Part 2  /  Lesson 1

Multiplication and Division, Part 2

Lesson 1

Math

Unit 3

3rd Grade

Lesson 1 of 23

Objective

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

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
  • 3.OA.B.6

Criteria for Success

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

Tips for Teachers

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

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Anchor Tasks

25-30 minutes

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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Student Response

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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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Student Response

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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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Student Response

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Problem Set

15-20 minutes

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

5-10 minutes

Problem 1

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

Student Response

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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

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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

Understand the zero and identity properties of multiplication.

Lesson 2
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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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