# Multiplication and Division of Whole Numbers

## Objective

Solve word problems involving multi-digit multiplication and division.

## Common Core Standards

### Core Standards

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• 5.NBT.B.5 — Fluently multiply multi-digit whole numbers using the standard algorithm.

• 5.NBT.B.6 — Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.

• 5.OA.A.1 — Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

• 5.OA.A.2 — Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

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• 4.NBT.B.4

• 4.NBT.B.5

• 4.NBT.B.6

• 5.NBT.A.1

• 5.NBT.A.2

• 4.OA.A.3

## Criteria for Success

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1. Make sense of a three-act task and persevere in solving it (MP.1).
2. Solve multi-step word problems involving multiplication and division, including those that require the interpretation of the remainder (MP.1, MP.4).
3. Solve multi-step word problems involving all four operations, including those that require the interpretation of the remainder (MP.1, MP.4).
4. Write an expression or equation to represent a real-world context, including using a letter to represent an unknown (MP.2).
5. Assess the reasonableness of an answer (MP.1).

## Tips for Teachers

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• Today’s lesson provides a nice coherence between all of the standards in this unit (and thus, between different domains). Students solve word problems that require them to apply their newly acquired multi-digit multiplication and division skills (5.NBT.5, 5.NBT.6) and, in some cases, are asked to represent those word problems with expressions that they then evaluate to solve (5.OA.1, 5.OA.2).
• Students are not asked to write an expression or equation to represent an unknown for either Anchor Task but are asked to do so on the Problem Set. This is because the unknowns in the computations in Anchor Tasks #1 and #2 are not the solution to the contextual problem, since both problems require not just the computation but also an interpretation of the remainder. If you think students need additional work on writing expressions or equations based on contextual problems, change Anchor Task #2 to not require the interpretation of the remainder and ask students to do so.

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### Problem 1

Act 1: Look at the following images:

How many cans of spray paint were needed to complete the mural?

#### Guiding Questions

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### Problem 2

Act 2: Use the following information to solve.

The mural is 55 feet by 35 feet, and a spray paint can covers 12 square feet of wall space.

#### Guiding Questions

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### Problem 3

Act 3: Reveal the answer.

161 cans of spray paint were needed to complete the mural.

#### Guiding Questions

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### Problem 4

On Saturday, the owner of a department store gave away a \$15 gift card to every 25th customer. A total of 8,879 customers came to the store on Saturday. What is the total value of the gift cards the owner gave away? How many additional customers would need to have come in for another gift card to be given away?

#### Guiding Questions

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#### 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..

Modified by The Match Foundation, Inc.

## Discussion of Problem Set

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• Look at #3a. What was your expression? Is there more than one correct way to write the expression? How can you prove that these various expressions are equivalent?
• Look at #4. How did you take the gate into account when figuring out the cost of the fencing?

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Solve. Show or explain your work.

Sixteen students in a drama club want to attend a play. The ticket price is ${35}$ for each student, and the transportation and meals for everyone will cost ${960}$.

To pay for the trip, the students design sweatshirts to sell for a profit of ${18}$ per sweatshirt. If each student sells the same number of sweatshirts, how many sweatshirts must each student sell so that there will be enough money to pay for the entire cost of the trip?

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