Curriculum  /  Math  /  4th Grade  /  Unit 2: Multi-Digit Multiplication  /  Lesson 8

Multi-Digit Multiplication

Lesson 8

Math

Unit 2

4th Grade

Lesson 8 of 18

Objective

Multiply three-digit numbers by one-digit numbers.

Common Core Standards

Core Standards

  • 4.NBT.B.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Foundational Standards

  • 3.NBT.A.3
  • 4.NBT.A.1
  • 4.NBT.B.4
  • 3.OA.B.5
  • 3.OA.C.7

Criteria for Success

  1. Multiply a three-digit whole number by a one-digit whole number using area models and the partial products algorithm. 
  2. Estimate products by rounding factors to the largest place value. 
  3. Solve one-step word problems involving multiplication of three-digit by one-digit numbers (on the Problem Set and Extra Practice Problems) (MP.4).

Tips for Teachers

  • In this lesson, the partial products are listed in decreasing order. This is the way students are likely to write them given the way the area model tends to be set up. Also, “at any point before or after their acquisition of fluency, some students may prefer to multiply from the left because they find it easier to align subsequent products under the biggest product” (NBT Progression, p. 15). Thus, it is included here. But, students will see in Lesson 9 that the partial products can also be written in increasing order. If a student chooses to do so in this lesson, allow them to do so but wait to discuss this with the whole class until Lesson 9.  
  • Note that the last Criteria for Success is not addressed in the Anchor Tasks below, since each problem type involving multiplication has been explored in previous lessons. However, if it seems students need additional practice with any type (particularly multiplicative compare with larger unknown), then you can use the values in Anchor Task 3 in the context of a word problem.
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Anchor Tasks

25-30 minutes

Problem 1

The area model below can be used to find 7 × 851.

To find 7 × 851, 

a.   Decompose each number into its base-ten units and write them in the corresponding boxes of the model. 

b.   Write the area of each region in the model. Then find the area of the entire model. Show your reasoning.  

Guiding Questions

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Student Response

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References

Open Up Resources Grade 6 Unit 5 Lesson 8 (Teacher Version) — Activity 2, "Calculating Products of Decimals"

Grade 6 Unit 5 Lesson 8 (Teacher Version) is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Dec. 14, 2018, 4:02 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Ayana used an area model to solve 746 $$\times$$ 8.        

a.   Use the area model to find 746 $$\times$$ 8. 

b.   Ayana recorded her work in a different way, as shown below. 

  1. In Ayana’s calculation, how are each of the partial products obtained? For instance, where does the 5,600 come from?
  2. How are the partial products in Ayana’s calculation related to the numbers in the area model?

Guiding Questions

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Student Response

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References

Open Up Resources Grade 6 Unit 5 Lesson 7 (Teacher Version) — Activity 2, "Connecting Area Diagrams to Calculations with Whole Numbers"

Grade 6 Unit 5 Lesson 7 (Teacher Version) is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Dec. 14, 2018, 4:05 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Estimate the product. Then use any method to solve. 

a.   $$940\times5$$

b.   $$7\times589$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Did you draw an area model for #2b? How may sections did it have? Why? 
  • Look at #2d. What did you estimate the product to be? Do you still think your product is reasonable despite it being hundreds away from the actual product? Why was the estimate hundreds away from the actual product? 
  • How did you determine what the values of A, B, C, and D were in #4? 
  • Did you use any strategies from Lesson 6 to solve any problems on today’s Problem Set? For example, #5d?

Target Task

5-10 minutes

Problem 1

Ms. Jones is using the area model below to solve a problem.

Which equation is represented by the whole area model?

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Student Response

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Problem 2

Estimate. Then solve. Show or explain your work.

748 × 7

Student Response

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Problem 3

Isaac ran a lemonade stand all summer. He sold 571 lemonades. If each lemonade cost $3, how much money did Isaac make? 

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 four-digit numbers by one-digit numbers.

Lesson 9
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Lesson Map

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

Topic A: Multiplicative Comparison

Topic B: Multiplication of up to Four-Digit Whole Numbers by One-Digit Whole Numbers

Topic C: Multiplication of Two-Digit Whole Numbers by Two-Digit Whole Numbers

Topic D: Multi-Step Word Problems

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