Multi-Digit Multiplication

Lesson 22

Objective

Solve two-step word problems involving multiplication, addition, and subtraction and assess the reasonableness of answers.

Common Core Standards

Core Standards

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  • 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.

  • 4.OA.A.3 — Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Foundational Standards

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  • 4.NBT.B.4

  • 3.OA.D.8

Criteria for Success

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  1. Make sense of a three-act task and persevere in solving it (MP.1).
  2. Solve two-step word problems involving multiplication, addition, and subtraction (MP.4). 
  3. Assess the reasonableness of an answer (MP.1).

Tips for Teachers

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  • As noted in Unit 1 Lesson 15, it isn’t especially clear whether students are expected to interpret, understand, and/or write one equation that represents a two- or multi-step word problem. As the Progressions state, “some problems might easily be represented with a single equation, and others will be more sensibly represented by more than one equation or a diagram and one or more equations” (OA Progression, p. 29). Thus, it is left to the teacher to decide what “easily” and “sensibly” means for your students, and when to make the transition to representing some two- and multi-step word problems with one step of representation/one equation, which you could do here or wait for subsequent lessons and units to do so. As some general guidance, it seems reasonable to expect every student to be able to write an equation for all one-step problems, two-step problems where the unknown is isolated on one side of the equal sign in the equation without needing to manipulate it, and some multi-step problems with the same parameters by the end of the year. For example, see #2 of Mathematics Common Core Sample Questions Grade 4, #5c of MCAS Spring 2016 Grade 4 Mathematics Test, and #11 of PARCC Math Spring 2017 Grade 4 Released Items.
  • This lesson provides an opportunity to connect two domains in the grade, 4.OA and 4.NBT, since students will be solving two-step word problems involving addition, subtraction, and multiplication and assessing the reasonableness of their answers using rounding, thus connecting standards 4.OA.3, 4.NBT.3, 4.NBT.4, and 4.NBT.5.
  • Let students work on each problem in the Problem Set independently and circulate to see whether students are solving correctly. If not, come back together to discuss how/what to draw on a tape diagram, then allow them to try again on their own. Encourage students to use a strategy of their choice to assess the reasonableness of their answer.

Remote Learning Guidance

This lesson does not have any identified priority Anchor Tasks, but students should complete the Problem Set independently rather than skipping the lesson entirely. Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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Problem 1

Show this news article from the Salem News to students. Include only the title to the bottom of the photograph. Block out the weight of the pumpkin, and the amount of prize money the winner won.

Ask students, "How big was the winning pumpkin? How much money did the winner earn?

Guiding Questions

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Problem 2

Act 2: Use the following information to solve:

  • A typical pumpkin weighs an average of 25 pounds.
  • The pumpkin at the Topsfield Fair was 82 times larger than a typical pumpkin.
  • He earned $3 per pound as his prize.

Guiding Questions

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Problem 3

Show the original news article to students with no information blocked out.

How did you solve? Was your answer reasonable?

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Problem 4

Act 4 (sequel):

Show student this article from the LA times, including the title through the 4th sentence. Block out the amount of money the man won.

Ask students, "How much money did this winner earn?"

Guiding Questions

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Problem Set & Homework

Discussion of Problem Set

  • How did you solve #2? Are there other strategies you could have used to solve? 
  • How did you know what to do when you saw the word “tripled” in #3?
  • Look at #6. I think we could multiply 814 by 9 and subtract 143 to solve. Do you agree or disagree? 
  • What are the advantages of knowing several methods for solving a multiplication problem?

Target Task

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Solve. Show or explain your work. 

Jennifer has 256 beads. Stella has 3 times as many beads as Jennifer. Tiah has 104 more beads than Stella. How many beads does Tiah have?

References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic D > Lesson 12Exit Ticket

Grade 4 Mathematics > Module 3 > Topic D > Lesson 12 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 The Match Foundation, Inc.

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Additional Practice

Unit Practice

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