Curriculum  /  Math  /  4th Grade  /  Unit 1: Place Value, Rounding, Addition, and Subtraction  /  Lesson 19

Place Value, Rounding, Addition, and Subtraction

Lesson 19

Math

Unit 1

4th Grade

Lesson 19 of 19

Objective

Solve multi-step word problems involving addition and 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. Make sense of a three-act task and persevere in solving it (MP.1). 
  2. Solve two- and multi-step word problems involving 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 answers by choosing a place to round the given values to, rounding them, and using those to compute the solution or by using the relationship between addition and subtraction to check answers (MP.1).

Tips for Teachers

  • As mentioned in Lessons 15 and 18, 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.
  • Today's lesson is the first one in which students will solve a 3-Act Task in 4th grade. To learn more about this lesson structure, read Dan Meyer's blogpost, The Three Acts of a Mathematical Story.
  • 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 and 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

25-30 minutes

Problem 1

Act 1: Look at the image below and answer the questions that follow. 

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

b.   How many pieces of candy are there? Make an estimate.

Guiding Questions

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Student Response

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References

Photo: Untitled by @julianasteiner (W Magazine)

Problem 2

Act 2: Use the following information to determine how many pieces of candy there are after the third month.

  • There were 15,750 pieces of candy at the beginning of the show, which ran for three months.
  • In the first month, 4,116 pieces were eaten.
  • 1,478 fewer pieces were eaten in the second month than in the first month. 
  • 1,060 more pieces were eaten in the third month than in the second month.

Guiding Questions

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Student Response

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Problem 3

Act 3: There were 5,298 pieces left at the end of the show. Was your estimate reasonable? Why or why not?

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Look at #3. How did drawing a double tape diagram help you to visualize the problem?
  • Why is there more than one right way to solve, for example, #5?
  • How are the problems alike? How are they different?
  • How was your solution the same and different from those that were demonstrated by your peers?
  • Did you see other solutions that surprised you or made you see the problem differently?
  • Why is it helpful to assess for reasonableness after solving?
  • How were the tape diagrams helpful in estimating to test for reasonableness? Why is that?

Target Task

5-10 minutes

In 2018, there were 13,910 McDonald’s restaurants, 7,205 fewer Wendy’s restaurants than McDonald’s, and 625 more Burger King restaurants than Wendy’s in the United States.

a.   How many of all three restaurants were there in all in 2018? Show or explain your work. 

b.   Assess the reasonableness of your answer.

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.

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.

Lesson Map

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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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