Multi-Digit Multiplication

Lesson 17

Math

Unit 2

4th Grade

Lesson 17 of 18

Objective


Solve two-step word problems involving multiplication, addition, and subtraction.

Common Core Standards


Core Standards

  • 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

  • 4.NBT.B.4
  • 3.OA.D.8

Criteria for Success


  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. Represent word problems using equation(s) with a letter standing for the unknown quantity (see Tips for Teachers) (MP.2).
  4. Assess the reasonableness of an answer (MP.1).

Tips for Teachers


  • 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.
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Anchor Tasks


Problem 1

Act 1: Look at the following image -

a.   What do you notice? What do you wonder?

b.   How big was the winning pumpkin? How much money did the winner earn? Make an estimate. 

Guiding Questions

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References

Problem 2

Act 2: Use the following information to determine how much the winner earned -

  • A typical pumpkin weighs an average of 25 pounds.
  • The pumpkin at the Topsfield Fair was 83 times larger than a typical pumpkin.
  • The winner earned $3 per pound as his prize.

Guiding Questions

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Problem 3

Act 3: See the solution shown in the original news article. Was your answer reasonable? Why or why not?

Guiding Questions

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Problem 4

Act 4 (sequel): Here is another winner of a pumpkin weight contest -

How much money did this winner earn?

Guiding Questions

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References

Problem Set


Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

  • How did you determine which equation was correct in #1? Did anyone use their equation to answer Part B?
  • What equation(s) did you write to represent #3? Are there other possibilities?
  • How did you determine whether you answer was reasonable in #5 Part B?

Target Task


Stan, Denise, and Tyrell all collect coins. Stan has 137 coins in his collection. Denise has 4 times as many coins in her collection as Stan does. Tyrell has 218 more coins in his collection than Denise does. 

  • Write an equation or equations to find how many coins Tyrell has. Use a letter for the unknown value in your equation(s). 
  • How many coins does Tyrell have?
  • Show or explain your work. 

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.

Extra Practice Problems

Answer Keys

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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.

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Lesson 16

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Lesson 18

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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