Place Value, Rounding, Addition, and Subtraction

Lesson 19

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Objective

Solve multi-step word problems involving addition and 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. 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, using a letter to represent the unknown (MP.4).
  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 by using the relationship between addition and subtraction to check answers (MP.1).

Tips for Teachers

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  • 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.
  • 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.

Remote Learning Guidance

This lesson does not have any identified priority Anchor Tasks, but students should complete the Problem Set independently rather than skipping the lesson entirely. Find more guidance on adapting our math curriculum for remote learning here.

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  • Problem Set
  • Student Handout Editor
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Anchor Tasks

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Problem 1

Act 1: Look at the image below.

How many pieces of candy are there?

Guiding Questions

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References

Photo: Untitled by @julianasteiner (W Magazine)

Problem 2

Act 2: Use the following information to solve.

  • 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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Problem 3

Act 3: Reveal the answer.
There were 5,716 pieces left at the end of the show.

Guiding Questions

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Problem Set & Homework

  • Problem Set

    • Problem Set Answer Key
  • Homework

    • Homework Answer Key

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

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In one year a factory used 11,650 meters of cotton, 4,950 fewer meters of silk than cotton, and 3,500 more meters of wool than silk.

a.   How many meters in all were used of the three fabrics? Show or explain your work.

b.   Assess the reasonableness of your answer.

Mastery Response

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References

Additional Practice

Unit Practice

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