Curriculum  /  Math  /  3rd Grade  /  Unit 3: Multiplication and Division, Part 2  /  Lesson 22

Multiplication and Division, Part 2

Lesson 22

Math

Unit 3

3rd Grade

Lesson 22 of 23

Objective

Identify other patterns in the multiplication table.

Common Core Standards

Core Standards

  • 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

  • 2.OA.C.3

Criteria for Success

  1. Look for and express regularity in repeated reasoning in the multiplication table to deduce that an odd number times an odd number results in an odd product, an even number times an odd number results in an even product, and an even number times an odd number results in an even product (MP.8). 
  2. Look for and express regularity in repeated reasoning in the multiplication table to deduce that $$n\times n$$ is a sum of the first $$n$$ odd numbers (e.g., $$16=4\times4=1+3+5+7$$) (MP.8). 
  3. Look for and express regularity in repeated reasoning to find other patterns in the multiplication table (MP.8). 
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Anchor Tasks

25-30 minutes

Problem 1

Do you think there are more odd or even products on the multiplication table? Why? 

Guiding Questions

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Student Response

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Problem 2

a.   Shade all of the squares that are a product of the same two factors. In other words, shade the product of $$1\times 1$$, $$2\times 2$$, etc.

× 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 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100

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

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • How do the patterns you discovered in #1 for odd and even products help you when multiplying?
  • Look at the arrays you drew for #2. If you drew an array for $$7\times7$$, how many little squares would you add to the array that you drew for $$6\times6$$? How do you know?
  • In #2c, you proved that $$9\times9$$ is the sum of the first $$9$$ odd numbers. Is $$10\times10$$ the sum of the first $$10$$ odd numbers? Where can you see the odd numbers on the two-colored multiplication table? Can you state a rule that this pattern shows using $$n$$ to represent a number? (Guide students to see that $$n\times n$$ is the sum of the first $$n$$ odd numbers. These types of problems are included in the Extra Practice Problems.)

Target Task

5-10 minutes

Problem 1

Sondra says $$3\times223=696$$. Use what you know about the product of two odd numbers to explain why Sondra is wrong.  

Student Response

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Problem 2

Explain two ways you could find the next number in the highlighted diagonal below. You don’t need to actually compute it!

× 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 64 72 80  
9 9 18 27 36 45 54 63 72 81 90  
10 10 20 30 40 50 60 70 80 90 100  
                       

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

Identify arithmetic patterns and explain them using properties of operations.

Lesson 23
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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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