Multi-Digit Multiplication

Lesson 1

Objective

Solve multiplicative comparison problems. Distinguish multiplicative comparison from additive comparison.

Common Core Standards

Core Standards

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  • 4.OA.A.1 — Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

  • 4.OA.A.2 — Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Foundational Standards

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  • 3.OA.A.1

  • 3.OA.A.3

Criteria for Success

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  1. Solve multiplicative comparison word problems with a larger unknown (MP.4).
  2. Write an equation to represent a multiplicative comparison word problem with a larger unknown (MP.2).
  3. Distinguish between additive comparison and multiplicative comparison.

Tips for Teachers

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  • Students will have additive comparison problems mixed in with multiplicative comparison problems with a larger unknown on the Problem Set and Homework. This is to ensure students are making sense of the mathematics more generally (MP.1) instead of generalizing that multiplication can be used to solve all problems and, more specifically, to ensure students are drawing a distinction between these two problem types since their language is very similar. 
  • All of the lessons in Topics A and B are opportunities to review multiplication within 100 (3.OA.7). While the main goals of Topics A and B are the objectives aligned to grade-level content standards, they also serve as an opportunity for teachers to diagnose students’ fluency with multiplication and division within 100 and review facts as needed. If in this lesson or future ones you notice that students need additional practice with their multiplication facts through 10 x 10, you could infuse games like Carolina Clip It, Charlotte Speedway Race, and Multiplication Cover-Up from Building Conceptual Understanding and Fluency Through Games, Grade 4 by the North Carolina Department of Public Instruction, into various times in the day. The game Damult Dice on the blog math4love also a nice one that can potentially involve up to 12 x 12 multiplication (4.OA.3a).

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 1 (benefits from discussion) and Anchor Task 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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Problem 1

Mrs. Ingall wants to know how long her bookshelf is. She can’t find a ruler, but she knows her copy of The Twits is 4 inches wide. So, how long do you think her bookshelf is?

Guiding Questions

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Problem 2

Jaylene is collecting books. She has 7 comic books. She has 3 times as many science books as comic books. How many science books does she have? Represent the situation as an equation to solve. 

Guiding Questions

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Problem 3

Your parents want to give you a larger allowance! Your current allowance is $8 a week. They give you two options:

  • Option 1: You can get $2 more for your allowance moving forward.
  • Option 2: You can get two times as much for your allowance moving forward.

a. Which option earns more money? How much more?

b. Which option will you choose? Explain why.

Guiding Questions

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References

Illustrative Mathematics Delayed Gratification

Delayed Gratification, accessed on Dec. 14, 2018, 1:33 p.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 The Match Foundation, Inc.

Problem Set & Homework

Discussion of Problem Set

  • Which equation matches Tameca’s situation in #1? How could you change the language of the situation so that the equation that matched was 6 + 3 = 9? 
  • Look at #3. How did you solve? How was this different from many of the other problems in the Problem Set? 
  • How did you solve in #5? How did you know to multiply even though the problem doesn’t say “times as many”? 
  • If #6 said, “Jaquan has five times more marbles than Evelyn,” how many marbles would Jaquan have? 
  • Look at #8. Which salad should Danielle eat? Why? Could you have answered that question without even finding exactly how many peanuts are in the purple bowl? How?
  • How are the two verbal statements in #9 different? How would their equations be different?

Target Task

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Problem 1

Rebecca is walking down the street. It takes her 10 minutes to get to the 7-Eleven. It takes her 2 times as long to walk back home. How long did it take her to get back home?

Problem 2

Sasha has 6 red M&Ms. She has 3 more green M&Ms than red M&Ms. How many green M&Ms does she have? 

Problem 3

An animal weighs 4 pounds. A bald eagle weighs 3 times as much as this animal. How many pounds does the bald eagle weigh?

Mastery Response

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Additional Practice

Unit Practice

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