Place Value, Rounding, Addition, and Subtraction

Lesson 15

Objective

Solve multi-step word problems involving addition and assess the reasonableness of answers.

Materials and Resources

Common Core Standards

Core Standards

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  • 4.NBT.B.4 — Fluently add and subtract multi-digit whole numbers using the standard algorithm.

  • 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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  • 3.NBT.A.2

  • 3.OA.D.8

Criteria for Success

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  1. Solve two- and multi-step word problems involving addition, using a letter to represent the unknown (MP.4).
  2. Assess the reasonableness of answers by choosing a place to round the given values to, rounding them, and using those to compute the solution (MP.1).

Tips for Teachers

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  • Lesson 15 is the first lesson of the year where students will solve two- and multi-step word problems using a letter to represent the unknown. This begs the question: should students be able to represent a two- or multi-step problem with a single equation or are many equations acceptable? As Bill McCallum states, “it’s a good question and a good discussion, but the standards are largely silent on the answer… I don’t read the standard as requiring that every single word problem be accompanied by an equation, merely that students should have experience writing equations for word problems” (Parenthesis in equations that represent multi-step word problems, Mathematical Musings). 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 multi-step word problems involving addition within 1,000,000 and assess the reasonableness of their answers using rounding, thus connecting standards 4.OA.3, 4.NBT.3, and 4.NBT.4.
  • Let students work on each problem on 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 solution.

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Anchor Tasks

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Problem 1

The city flower shop sold 14,594 pink roses on Valentine’s Day. They sold 7,857 more red roses than pink roses. 

  1. How many red roses did they sell? Show or explain your work. 
  2. Use your answer in Part (a) to write a second problem for your classmates to solve.

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic D > Lesson 12Concept Development

Grade 4 Mathematics > Module 1 > 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.

Problem 2

On Saturday, 32,736 more bus tickets were sold than on Sunday. On Sunday, only 17,295 tickets were sold. How many people bought bus tickets over the weekend?

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic D > Lesson 12Concept Development

Grade 4 Mathematics > Module 1 > 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..

Problem 3

Last year, Big Bill’s Department Store sold many pairs of footwear. 118,214 pairs of boots were sold, 37,092 more pairs of sandals than pairs of boots were sold, and 124,417 more pairs of sneakers than pairs of boots were sold.  How many pairs of footwear were sold last year?

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic D > Lesson 12Concept Development

Grade 4 Mathematics > Module 1 > 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..

Discussion of Problem Set

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  • Look at #1. What would happen to your estimate if you rounded all of the values to the nearest hundred? 
  • Did anyone determine that their answer was not reasonable based on your estimate for any of these problems? What did that cause you to do? 

Target Task

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In January, Scott earned $8,999. In February, he earned $2,387 more than in January. In March, Scott earned the same amount as in February. 

  1. Choose a place value to round to, then use those rounded values to estimate the amount Scott earned altogether during those three months. 
  2. Exactly how much did Scott earn in those three months?
  3. Assess the reasonableness of your answer in (b). Use your estimate from (a) to explain. 

References

Mastery Response

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