Multiplication and Division, Part 1

Lesson 8

Math

Unit 2

3rd Grade

Lesson 8 of 21

Objective


Build fluency with division facts using units of 2, 5, and 10.

Common Core Standards


Core Standards

  • 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.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. Solve division and unknown factor problems involving twos, fives, and tens by skip-counting, i.e.:
    • Keeping track on their papers or on their fingers of how many twos, fives, or tens have been counted,
    • Stopping the skip-counting sequence when they reach the dividend, and
    • Knowing that the number of twos, fives, or tens that they counted is the solution. 

Tips for Teachers


  • As mentioned in Lesson 6, 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. 

  • As mentioned in Lesson 6, skip-counting to solve a division problem is easier than skip-counting to solve a multiplication problem can be more challenging than skip-counting to solve a division problem. "For $$8\times3$$, you know the number of 3s and count by 3 until you reach 8 of them. For $$24\div 3$$, you count by 3 until you hear 24, then look at your tracking method to see how many threes you have. Because listening for 24 is easier than monitoring the tracking method for 8 threes to stop at 8, dividing can be easier than multiplying" when using a skip-counting strategy to solve (OA Progression, p. 25).
  • As a supplement to the Problem Set, students can play the first version of "What's your Number?" from the Independent Work tab in 3.OA.4 - About the Math, Learning Targets, and Rigor by the Howard County Public School System.
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Anchor Tasks

25-30 minutes


Problem 1

Maureen says the skip-counting sequence "10, 20, 30, 40, 50, 60" to help her solve a problem.

a.   What multiplication problem might Maureen be trying to solve? How do you know?

b.   What if Maureen was solving a division problem? What problem might that have been?

Guiding Questions

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Student Response

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Problem 2

Solve. 

a.    $$12\div2 =$$ _____

b.    _____ $$=35\div 5$$

c.    $$90\div 10=$$  _____

d.    _____ $$\times\:5 = 45$$

e.    $$2 \:\times$$ _____ $$=16$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • I think the answer in #3f is 8. Do you agree or disagree? What mistake did I make? 
  • What do you notice about #11a and #11d? What do you wonder? 
  • 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? 

Target Task

5-10 minutes


Solve.

a.   $$90 \div 10 =$$ _____

b.   ____ $$\times\space 2 = 8$$

c.   $$40 = 5\space\times $$ _____

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 2, 5, and 10.

Lesson 9
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

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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