Curriculum  /  Math  /  4th Grade  /  Unit 2: Multi-Digit Multiplication  /  Lesson 15

Multi-Digit Multiplication

Lesson 15

Math

Unit 2

4th Grade

Lesson 15 of 18

Objective

Multiply two-digit by two-digit numbers using two partial products 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. Understand that products can be computed by decomposing numbers into base-ten units, finding partial products of these base-ten units, then adding these partial products together based on the distributive property (e.g., $$36\times54=(36\times50)+(36\times4)$$). (Note that students need not know the term “distributive property.”)
  2. Multiply a two-digit whole number by a two-digit whole number using area models and the standard algorithm. 
  3. Assess the reasonableness of answers using mental computation and estimation strategies including rounding (MP.1).
  4. Solve one-step word problems involving multiplication of two-digit by two-digit numbers (on the Problem Set and Extra Practice Problems) (MP.4).
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Anchor Tasks

25-30 minutes

Problem 1

Joy started to solve the math problem 13 × 62 with an area model. Her work looked like this:

But, her classmate Sophia told her that instead of using four areas, she could solve it using only two and drew the area model below:

a.   How are Joy’s and Sophia’s area models similar? 

b.   How are Joy’s and Sophia’s area models different?

c.   Do you think Sophia’s method will work? Why or why not? 

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic H > Lesson 37 — Concept Development

Grade 4 Mathematics > Module 3 > Topic H > Lesson 37 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Joy and Sophia wrote the partial products from their area models as follows:

Calculation A Calculation B

a.   Which two numbers are being multiplied to get 6 in Calculation A? Which numbers are being multiplied to get 26 in Calculation B? How are the other partial products below calculated?

b.   Which calculation corresponds with Joy’s area model from Anchor Task 1? With Sophia’s 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

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

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.     $$42\times22$$

b.     $$35\times26$$

c.     $$24\times36$$

d.     $$56\times63$$

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic H > Lesson 37 — Concept Development

Grade 4 Mathematics > Module 3 > Topic H > Lesson 37 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes

Discussion of Problem Set

  • Look at #2c and #2d. What do you notice about their factors? What do you notice about their products? 
  • How did you determine the total amount of money the store made in #4? How did you round the total? How is that different from the way we’ve rounded in the unit thus far? 
  • Look at #6c and #6d. What do you notice about their factors? What do you notice about their products? 
  • Did you use any strategies from Lesson 13 to solve any problems on today’s Problem Set? For example, #6a or #6c?

Target Task

5-10 minutes

Problem 1

Which method can be used to solve 14 × 23?

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Student Response

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Problem 2

Solve. Assess the reasonableness of your answer.

a.   92 × 41

b.   86 × 53

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

Abstract the formulas for the area and perimeter of a rectangle and apply those formulas in real-world and mathematical problems involving multiplication, addition, and subtraction.

Lesson 16
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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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