Curriculum  /  Math  /  4th Grade  /  Unit 3: Multi-Digit Division  /  Lesson 13

Multi-Digit Division

Lesson 13

Math

Unit 3

4th Grade

Lesson 13 of 16

Objective

Solve multi-step word problems involving all four operations.

Common Core Standards

Core Standards

  • 4.MD.A.3 — Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
  • 4.NBT.B.6 — Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • 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

  • 4.NBT.B.4
  • 4.NBT.B.5
  • 3.OA.D.8

Criteria for Success

  1. Make sense of a three-act task and persevere in solving it (MP.1).
  2. Solve multi-step word problems involving all four operations (MP.4).
  3. Represent word problems using equation(s) with a letter standing for the unknown quantity (see Lesson 12's Tips for Teachers) (MP.2).
  4. Interpret the remainder in the context of a problem (MP.1). 
  5. Assess the reasonableness of an answer (MP.1).

Tips for Teachers

  • The three-act task in this lesson depends a bit on students understanding the relationships between units of time, and arguably touches on the idea of unit conversion. Since students know the relationships between different units of time from Grade 2 (2.MD.7a) and have worked a bit with word problems involving time in Grade 3 (3.MD.1), this shouldn’t be too far of a stretch. 
  • “To compute and interpret remainders in word problems (4.OA.A.3), students must reason abstractly and quantitatively (MP.2), make sense of problems (MP.1), and… search for the structure (MP.7) in problems with similar interpretations of remainders” (PARCC Model Content Frameworks, Mathematics, Grades 3–11).
  • This lesson provides an opportunity to connect two domains in the grade, 4.OA and 4.NBT, since students will be solving two-step word problems involving addition, subtraction, multiplication, and division and assessing the reasonableness of their answers using rounding, thus connecting standards 4.OA.3, 4.NBT.3, 4.NBT.4, 4.NBT.5, and 4.NBT.6.
  • Let students work on each problem in 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 answer.
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Anchor Tasks

25-30 minutes

Problem 1

Act 1: Watch the video Act 1.

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

b.   How long will it take to fill up all four jars? Make an estimate.

Guiding Questions

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Student Response

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References

Questioning My Metacognition Dill ‘Er Up

Dill ‘Er Up by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Jan. 18, 2018, 9:36 a.m..

Modified by Fishtank Learning, Inc.

Problem 2

Act 2: Use the following information to determine how long it will take to fill up all four jars - 

Original jar: 8 ounces

Rest of the jars: 

Guiding Questions

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Student Response

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References

Questioning My Metacognition Dill ‘Er Up

Dill ‘Er Up by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Jan. 18, 2018, 9:36 a.m..

Modified by Fishtank Learning, Inc.

Problem 3

Act 3: Watch Dill 'er Up (Act-3) to see the solution. Was your estimate reasonable? Why or why not?

Guiding Questions

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Student Response

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References

Questioning My Metacognition Dill ‘Er Up

Dill ‘Er Up by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Jan. 18, 2018, 9:36 a.m..

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes

Discussion of Problem Set

  • Look at #2. How did you interpret the remainder? 
  • What did the remainder represent in #5? How did the remainder come into play in Part A? How did you choose which equation represented the situation in Part B? 

Target Task

5-10 minutes

A radio station is running a contest. Every seventh person to call into the radio station gets a free ticket to a concert. Every fifth person to call into the radio station gets a free ticket to a comedy show. The radio station received 194 calls. 

  • What is the total number of tickets the radio station gave away? Show your work. 
  • How many additional callers would need to call in in order for 1 more concert ticket to be given away? Explain 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.

Next

Identify and extend growing number patterns.

Lesson 14
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Lesson Map

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

Topic A: Understanding and Interpreting Remainders

Topic B: Division of up to Four-Digit Whole Numbers by One-Digit Whole Numbers

Topic C: Multi-Step Word Problems and Patterns

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