Curriculum  /  Math  /  4th Grade  /  Unit 2: Multi-Digit Multiplication  /  Lesson 13

Multi-Digit Multiplication

Lesson 13

Math

Unit 2

4th Grade

Lesson 13 of 18

Objective

Multiply two-digit numbers by two-digit numbers using a variety of mental strategies.

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 two-digit numbers by two-digit numbers using a variety of mental strategies, including: 
    1. Finding partial products and adding them together (e.g., $$28\times25=(20+8)\times25=(20\times25)+(8\times25)$$)
    2. Adjusting one number to  a benchmark or “friendly” number (e.g., $$28\times25=(30-2)\times25=(30\times25)-(2\times25)$$)
    3. Doubling and halving (e.g., $$28\times25=14\times50$$)
    4. Breaking factors into smaller factors (e.g., $$28\times25=28\times5\times5$$).
  2. Understand and explain why various mental strategies work (MP.3). 

Tips for Teachers

  • This lesson explores strategies students may use for particular computational problems before they jump into generalizable methods and algorithms in later lessons. As Bill McCallum notes on his blog Mathematical Musings, “the distinction between a strategy and an algorithm is that an algorithm is general, it works in all possible cases, whereas a strategy might be specialized” (Algorithms Grades 2-5, Mathematical Musings).  He goes on to say that the progression toward fluency with any computation begins with strategies, then algorithms (note the plurality), then the standard algorithm. 
  • The first page of the Problem Set provides an array of Number Talks, similar to Anchor Task #2. You may decide to use these tasks in a similar way to Anchor Task #2, using them as a whole class and restricting the use of paper and pencil, forcing the use of mental math to solve and therefore encouraging the use of the mental strategies discussed in the lesson. Or, if Anchor Tasks #1 and #2 take up much of the lesson block, you can use them as a source for problems to be spread out over various parts of the day in the future so that students can gradually develop the use of each strategy.
  • Similar to the Problem Set, the first page of the Extra Practice Problems provides an array of Number Talks, similar to Anchor Task #2. If you use the Extra Practice Problems as homework, you may decide to send students home with instructions for guardians about how to have a Number Talk with their child. Or, you could save the first page as a source for problems to be spread out over various parts of the day in the future so that students can gradually develop the use of each strategy.
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Anchor Tasks

25-30 minutes

Problem 1

Four different students solved the problem $$28\times25$$. Your teacher will assign you one of their strategies below. Explain what the student did and whether the strategy they used works. Be prepared to share your thinking. 

Student A

Student B

Student C

Student D

Guiding Questions

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Student Response

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Problem 2

Solve.

3 $$\times $$ 16

10 $$\times $$ 16

13 $$\times $$ 10

13 $$\times $$ 6

13 $$\times $$ 16

6 $$\times $$ 30

40 $$\times $$ 30

46 $$\times $$ 30

46 $$\times $$ 29

2 $$\times $$ 45 $$\times $$ 6

5 $$\times $$ 12 $$\times $$ 9

4 $$\times $$ 5 $$\times $$ 3 $$\times $$ 9

12 $$\times $$ 45

8 $$\times $$ 60

16 $$\times $$ 30

32 $$\times $$ 15

Guiding Questions

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Student Response

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References

Problem Set

15-20 minutes

Discussion of Problem Set

  • What is the correct choice for #2? How do you know that without needing to compute it?
  • Were there specific strategies that you found yourself relying on repeatedly in #3? 
  • Which strategies seem to be useful for all computations? Which ones seem to be useful just in specific cases?

Target Task

5-10 minutes

Solve. Show or explain your work.

a.   35 × 42

b.   19 × 54

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 by two-digit numbers using four partial products.

Lesson 14
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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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