# Multi-Digit Division

## Objective

Solve multi-step word problems involving all four operations and assess the reasonableness of answers.

## 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.

?

• 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. Interpret the remainder in the context of a problem (MP.1).
4. 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 unit 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, Math, Grade 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.

#### 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.

#### Fishtank Plus

Subscribe to Fishtank Plus to unlock access to additional resources for this lesson, including:

• Problem Set
• Student Handout Editor
• Google Classrom Integration
• Vocabulary Package

?

### Problem 1

Act 1: Watch the video Act 1 -

How long will it take to fill up all four jars?

#### Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

#### 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 The Match Foundation, Inc.

### Problem 2

Act 2: Use the following information to solve -

 Original jar: 8 ounces Rest of the jars:

#### Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

#### 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 The Match Foundation, Inc.

### Problem 3

Act 3: Reveal the answer -

Watch Dill 'er Up (Act-3).

#### Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

#### 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 The Match Foundation, Inc.

## Problem Set & Homework

#### Discussion of Problem Set

• Look at #1. How did you interpret the remainder?
• Look at #2 Part B. If someone thought that the boxes would cost \$98, what error do you think that person made? Why?
• What did the remainder represent in #4? How did the remainder come into play in Part A? In Part B?

?

On Saturday the owner of a pet store gave away a goldfish to every sixth customer and a clownfish to every ninth customer. A total of 130 customers came to the store on Saturday.

• What is the total number of fish the owner gave away? Show your work.
• How many additional customers would need to have come for 1 more goldfish to be given away? Explain your answer.

#### References

PARCC Released Items Math Spring Operational 2016 Grade 4 Released ItemsQuestion #28

Math Spring Operational 2016 Grade 4 Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed Dec. 22, 2017, 1:50 p.m..

?