Place Value, Rounding, Addition, and Subtraction

Lesson 18

Objective

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

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 and subtraction, 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 or using the relationship between addition and subtraction to check answers (MP.1).

Tips for Teachers

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  • As noted in 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 multi-step word problems involving subtraction 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.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 3 (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

A company has three locations with 70,010 employees altogether. The first location has 34,857 employees. The second location has 17,595 employees. How many employees work in the third location? 

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic E > Lesson 16Concept Development

Grade 4 Mathematics > Module 1 > Topic E > Lesson 16 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

Owen’s goal is to have 1 million people visit his new website within the first four months of it being launched. Below is a chart showing the number of visitors each month. How many more visitors does he need in Month 4 to reach his goal?

Month Month 1 Month 2 Month 3 Month 4
Visitors 228,211 301,856 299,542  

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic E > Lesson 16Concept Development

Grade 4 Mathematics > Module 1 > Topic E > Lesson 16 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

There were 12,345 people at a concert on Saturday night. On Sunday night, there were 1,795 fewer people at the concert than on Saturday night. How many people attended the concert on both nights?

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 1 > Topic E > Lesson 16Concept Development

Grade 4 Mathematics > Module 1 > Topic E > Lesson 16 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 Set & Homework

  • Problem Set

    • Problem Set Answer Key
  • Homework

    • Homework Answer Key

Discussion of Problem Set

  • How did your estimate help you determine that your exact answer was reasonable in #1?
  • In #2, how close was your actual answer to your estimate?  
  • In #3, to which place did you round? Why?
  • How did your tape diagram help you solve #5?
  • How do you determine what place value to round to when finding an estimate?
  • What is the benefit of checking the reasonableness of your answer?
  • Describe the difference between rounding and estimating.

Target Task

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Quarterback Brett Favre passed for 71,838 yards between the years 1991 and 2011. His all-time high was 4,413 passing yards in one year. In his second-highest year, he threw 4,212 passing yards. How many passing yards did Brett Favre throw in the remaining years? Is your answer reasonable? Explain. 

References

Mastery Response

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Additional Practice

Unit Practice

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