Curriculum  /  Math  /  3rd Grade  /  Unit 2: Multiplication and Division, Part 1  /  Lesson 11

Multiplication and Division, Part 1

Lesson 11

Math

Unit 2

3rd Grade

Lesson 11 of 21

Objective

Build fluency with multiplication and division facts using units of 4.

Common Core Standards

Core Standards

  • 3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
  • 3.OA.A.2 — Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
  • 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.B.6 — Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
  • 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.

Criteria for Success

  1. Skip-count by fours. 
  2. Solve multiplication, division, and missing factor problems involving four by skip-counting. (Note: this includes problems where 4 is listed as the first factor, implying the use of the commutative property.)

Tips for Teachers

  • As mentioned in previous lessons, there are three main levels of ways students can represent and solve multiplication and division problems, two of which are the focus of this unit:
    • Level 1: Making and counting all of the quantities involved in a multiplication or division, and 
    • Level 2: Skip-counting, or repeated counting on a given number.

To achieve fluency, the goal is to help students move along this progression, eventually to the point of "just knowing" products and quotients. 

  • To help students develop facility with skip-counting by 4, you can use the same process described in Lesson 6. Instead of having students say all the numbers in the count sequence, have them hum, clap, or make some sort of noise in place of the number names that aren’t part of the count sequence, just thinking about what those numbers are instead. So, students would do: <clap> <clap> <clap> "four!" <clap> <clap> <clap> "eight!" <clap> <clap> <clap> "twelve!" etc. Then, they can remove the interspersed sounds and just say the skip-counting sequence. This provides a nice scaffold for students to use a placeholder for those numbers not in the count sequence before removing them entirely.
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Anchor Tasks

25-30 minutes

Problem 1

How many?

Guiding Questions

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Student Response

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References

flickr Photo: iPhone Home Screens, August 7, 2014 by Lee Bennett

iPhone Home Screens, August 7, 2014 by Lee Bennett by Lee Bennett is made available on flickr under a CC BY-NC-SA 2.0 license. Accessed Oct. 12, 2018, 9:59 a.m..

Problem 2

Solve. 

a.   $$4\times 9 = $$ ___

b.   ___ $$= 24 \div 4$$

c.   ___ $$\times\:4 =12$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • How did the skip-counting sequence in #1 help you solve the other problems on the Problem Set?
  • What do you notice about #3b and #3c? What do you wonder? 
  • In #7, 3 is the first factor in all problems. How did you solve without knowing the other factor's skip-counting sequence? 
  • Is division commutative? In other words, will switching the order of the values in a division expression result in an equivalent expression? How do you know?
  • Write the twos skip-counting sequence. Write the fours skip-counting sequence. What do you notice? What do you wonder? 

Target Task

5-10 minutes

Solve.

a.   $$8\times 4 =$$ _____

b.   _____ $$= 28 \div 4$$

c.   $$4\:\times $$ ____ $$=8$$

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

Solve one-step word problems involving multiplication and division using units of 3 and 4.

Lesson 12
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Lesson Map

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Topic A: The Meaning of Multiplication and Division

Topic B: Multiplication and Division by 2, 5, and 10

Topic C: Multiplication and Division by 3 and 4

Topic D: More Complex Multiplication and Division Problems

Topic E: Scaled Picture and Bar Graphs

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