Place Value, Rounding, Addition, and Subtraction

Lesson 18

Math

Unit 1

4th Grade

Lesson 18 of 19

Objective


Solve multi-step word problems involving subtraction, using rounding to assess the reasonableness of answers.

Common Core Standards


Core Standards

  • 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

  • 3.NBT.A.2
  • 3.OA.D.8

Criteria for Success


  1. Solve two- and multi-step word problems involving addition and subtraction (MP.4).
  2. Represent word problems using equation(s) with a letter standing for the unknown quantity (see Tips for Teachers) (MP.2).
  3. 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


  • 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.
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Anchor Tasks


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 Fishtank Learning, Inc.

Problem 2

On June 1, Home Depot had 367,962 air conditioners in stock. With the first heat wave of the season coming, they sold 193,584 of them the first week in June. They got more air conditioners in the second week of June, resulting in them having 256,741 air conditioners in stock by June 15. How many air conditioners did Home Depot receive in the second week of June?

Guiding Questions

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Problem 3

There were 12,345 people at a concert on Saturday night. This was 1,795 more people than attended the concert on Sunday night. How many people attended the concert on both nights? Assess the reasonableness of your answer.

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


Answer Keys

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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


Juliette made $83,769 last year. She made $4,218 selling her embroidery on Etsy and $3,421 selling her embroidery on eBay. The rest of the money she made at her main job as an engineer. 

a.   How much money did Juliette make last year as an engineer? 

b.   Is your answer in Part A reasonable? Use rounding to support your conclusion. 

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

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Lesson 17

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Lesson 19

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Place Value of Multi-Digit Whole Numbers

Topic B: Reading, Writing, and Comparing Multi-Digit Whole Numbers

Topic C: Rounding Multi-Digit Whole Numbers

Topic D: Multi-Digit Whole-Number Addition and Subtraction

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