Curriculum  /  Math  /  3rd Grade  /  Unit 3: Multiplication and Division, Part 2  /  Lesson 17

Multiplication and Division, Part 2

Lesson 17

Math

Unit 3

3rd Grade

Lesson 17 of 23

Objective

Multiply one-digit whole numbers by multiples of 10.

Common Core Standards

Core Standards

  • 3.NBT.A.3 — Multiply one-digit whole numbers by multiples of 10 in the range 10—90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
  • 3.OA.A.4 — Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
  • 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.)

Foundational Standards

  • 3.OA.A.1
  • 3.OA.A.2

Criteria for Success

  1. Multiply a one-digit number by a multiple of ten using base ten blocks, a number line, or the associative property. 
  2. Make use of structure by using a basic fact to solve its corresponding one-digit by multiple of ten fact (MP.7). 
  3. Determine the unknown whole number in an equation that involves multiplication by a multiple of ten. 

Tips for Teachers

  • Make sure to be precise in language use when discussing how basic multiplication facts are related to multiplication by multiples of ten (e.g., how $$2\times4$$ is related to $$2\times40$$). Avoid saying "add a zero," and instead discuss how the units shift. This serves two purposes: (1) it doesn’t conflate two operations, multiplication with addition, and (2) it is aligned to the work they’ll do in later grades of seeing how digits shift places when multiplying or dividing numbers by powers of ten, including decimals, where in fact "adding a zero" after a decimal point won’t change its value.
  • This lesson focuses on the additional cluster work of multiplying by multiples of tens (3.NBT.3) but simultaneously supports the major work of the grade in other domains, including the use of the associative property as a strategy to multiply (3.OA.5) and practice with fluency of one-digit numbers (3.OA.7). 

Lesson Materials

  • Optional: Base ten blocks (24 tens 2 hundreds per student or small group) — Students might not need these depending on their reliance on concrete materials. Students could also use Paper base ten blocks instead. See Anchor Task 1 Notes for more information.
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Anchor Tasks

25-30 minutes

Problem 1

There are 6 tables in Mrs. Potter's classroom. There are 4 students sitting at each table. Each student has a dime to use as a place marker on a board game. 

a.   What is the value of the dimes at each table? 

b.   What is the value of the dimes in Mrs. Potter’s classroom?

Guiding Questions

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Student Response

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References

Illustrative Mathematics How Many Colored Pencils?

How Many Colored Pencils?, accessed on Nov. 1, 2018, 11:07 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

a.   Solve.

  1.  

$$2\times 4=$$ _____

$$7\times 3 =$$ _____

$$5\times 8=$$ _____
  1.  

$$2\times 40=$$ _____

$$70\times 3 =$$ _____

$$5\times 80=$$ _____

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

Guiding Questions

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Student Response

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References

Howard County Public School System 3.NBT.3 - About the Math, Learning Targets, and Rigor — Preferred Tasks: Multiples of 10 Patterns

3.NBT.3 - About the Math, Learning Targets, and Rigor is made available by the Howard County Public School System under a CC BY-NC-SA 4.0 license. © 2013-2014 Elementary Mathematics Office Howard County Public School System. Accessed Nov. 1, 2018, 11:10 a.m..

Modified by Fishtank Learning, Inc.

Problem 3

Solve. Show or explain your work.

a.   ____ $$=3\times 30$$

b.   $$80\times 4=$$ ____

c.   ____ $$=6\times 50$$

d.   $$8\ \times$$ ____ $$=160$$

e.   ____ $$\times \ 7 = 630$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • How did #2a help you to solve #2b? What about #2c and #2d? 
  • Is Mr. Cortina correct in #3? What mistake did he make? 
  • In #6c, I wrote 30 as the answer. Do you agree or disagree with my answer? Why? What mistake did I make? 
  • How did you solve for the unknown values in #8?
  • What could be Claire’s number in #11? Is there more than one correct answer? What are some other possibilities? 
  • In #12, how did Gabriella convert the computation to an easier problem?
  • How does knowing your multiplication facts help you easily multiply by multiples of 10? 
  • Now that we know a strategy for multiplying with multiples of 10, how would we use the same process for multiplying with multiples of 100? What would be the same? What would change? 
  • How is this new strategy helpful for finding unknown, larger facts?

Target Task

5-10 minutes

Problem 1

Notecards come in packs of 20. How many notecards are there in 6 packs? 

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Student Response

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Problem 2

Nell says $$5\times60$$ is $$30$$. 

  • Identify the error in Nell’s reasoning. 
  • Find the correct product. Show or explain your work. 

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

Multiply one-digit whole numbers by two-digit whole numbers using the associative and distributive properties.

Lesson 18
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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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