Curriculum  /  Math  /  4th Grade  /  Unit 2: Multi-Digit Multiplication  /  Lesson 10

Multi-Digit Multiplication

Lesson 10

Math

Unit 2

4th Grade

Lesson 10 of 18

Objective

Multiply two-, three-, and four-digit numbers by one-digit numbers and assess the reasonableness of the product.

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 two-, three-, or four-digit whole number by a one-digit whole number using the partial products algorithm and/or the standard algorithm. 
  2. Assess the reasonableness of answers using mental computation and estimation strategies including rounding (MP.1).
  3. Solve one-step word problems involving multiplication of up to four-digit by one-digit numbers (on the Problem Set and Extra Practice Problems) (MP.4).

Tips for Teachers

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 2 in the context of a word problem.

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Anchor Tasks

25-30 minutes

Problem 1

Here are two algorithms for finding the value of 64 × 2. 

Patrice’s method Jerome’s method

a.   How is Patrice’s method similar to and different from Jerome’s method?

b.   How do you think Jerome found the product 128?

Guiding Questions

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Student Response

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References

Two Algorithms to Multiply — Grade 4 Unit 6 Lesson 11 Activity 1

Problem 2

Patrice solved the problem 813 × 7 using the partial products algorithm, as shown below: 

Jerome solved in a different way from Patrice. Here is what he did:

First, he found the partial product of 3 ones and 7, which is 21 ones, or 2 tens 1 one. He wrote the ones digit, 1, under the equal bar, and the 2 tens on the equal bar above the tens place in smaller handwriting. Then, he found the partial product of 1 ten and 7, which was 7 tens. Because he had the 2 tens from the first partial product, he added those tens together and wrote 9 in the tens place in the product. Because he had accounted for the 2 tens from his first partial product, he crossed it off.  Finally, he found the partial product of 8 hundreds and 7, which was 56 tens. He wrote 56 in the hundreds and tens place in the product.

 

a.   How is Patrice's method similar to and different from Jerome's method?

b.   What are the advantages and disadvantages of Patrice's method? Of Jerome's method? 

Guiding Questions

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Student Response

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Problem 3

Try using the standard algorithm to solve. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer. 

a.   $$54\times6$$

b.   $$9\times673$$

c.   $$1,605\times4$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Look at #1. Which problems were particularly difficult to solve? Why? 
  • Look at #2. Were there any answers you could eliminate right away as being unreasonable? 
  • Look at #4. Where did the 3 come from? What value does it have—ones? Tens? Hundreds? Thousands? What is the final product? 
  • Look at #5. What is a possible number that Casey multiplies 178 by? Are there other possibilities? How did you find them? What product do they result in?
  • Did you use any strategies from Lesson 6 to solve any problems on today’s Problem Set? For example, #1d?

Target Task

5-10 minutes

Problem 1

Anika begins to solve 562 × 4 below.

Complete the algorithm that Anika has started.

Student Response

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Problem 2

Solve. Assess the reasonableness of your answer.

a.   81 × 5

b.   6 × 2,348

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 two-digit multiples of 10 by two-digit multiples of 10. Estimate multi-digit products by rounding numbers to their largest place value.

Lesson 11
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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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