# Gallery Problems

## Overview

# Gallery Overview

Allow students who have a clear understanding of the content in the unit to work on Gallery problems of their choosing. You can use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.

# Gallery Description

**Tiling a Floor**

Students determine which size tiles are cheaper to use to tile a floor with given dimensions.

**Adam's Homework**

Students find and correct an error in a whole number division problem.

**Then and Now**

Students solve comparison problems involving census data from 1940 and 2010.

**Graphical Multiplication**

Given points *m* and *p* on a number line, students must locate *m* × *p*.

**When Does Zero Matter?**

Students must determine how the placement of 0 affects the value of a number.

# Tiling a Floor

# Answers

For the $\frac{3}{4}$ foot by $\frac{3}{4}$ foot tiles, there would be $12\xf7\frac{3}{4}$, or 16, tiles along each edge for a total of 16 x 16, or 256 tiles. The total cost would be 256 x $3.89, or $999.84.

For the $1\frac{1}{3}$ foot by $1\frac{1}{3}$ foot tiles, there would be $12\xf71\frac{1}{3}$, or 9, tiles along each edge for a total of 9 x 9, or 81 tiles. The total cost would be 81 x $8.75, or $708.

- $472.50 ÷ $8.75 per tile = 54 tiles.

## Work Time

# Tiling a Floor

Jack wants to tile a 12 foot by 12 foot room. He is considering two sizes of square tiles. The tiles with side length $\frac{3}{4}$ foot cost $3.89 each. The tiles with side length$1\frac{1}{3}$ foot cost $8.75 each.

- For which size tile will the total cost of tiling the room be less? How much less will it be? Show all your work and explain how you found your answers.
- Jack’s friend bought the $1\frac{1}{3}$ foot tiles and spent $472.50 on the tiles. How many tiles did she buy?

# Adam's Homework

# Answers

You can tell Adam made a mistake because the remainder, 16, is greater than his divisor, 9.

**Work Time**

# Adam's Homework

This is Adam’s homework. Read the problem. Then look at his work.

- Ricky has 133 goldfish. He wants to put them into 9 fish tanks. If he distributes the fish equally among the fish tanks, how many fish should he put in each tank?
- How can you tell, just by looking, that Adam did not follow the usual rules of long division?
- Solve the problem using the usual rules of long division. Label each number in your solution to show what it represents.

# Then and Now

# Answers

- Approximately 134.2 million
- 2.5 times more
- About $33,269

**Work Time**

# Then and Now

Every 10 years, the United States government conducts a census. The census attempts to accurately determine the population. It also gathers information about topics such as jobs and education. The questions below are based on results from the 1940 and 2010 censuses. (Source: census.gov)

- The U.S. population in 2010 was 308.7 million. This is about 2.3 times the 1940 population. What was the approximate 1940 population?
- In 2010, about 10% (0.10) of working Americans were involved in manufacturing. In 1940, about 0.25 of working Americans were involved in manufacturing. The decimal 0.25 is how many times the decimal 0.10?
- In 1940, the median income for working men was $956. In 2010, the median income for working men was about 34.8 times this amount. What was the median income for working men in 2010?

# Graphical Multiplication

# Answers

**Work Time**

# Graphical Multiplication

- Copy this picture. Then locate the product
*m*x*p*as precisely as you can.

# When Does Zero Matter?

# Answers

Explanations, examples, and counterexamples will vary.

Always True or Sometimes True?

- Always True. Example: $356\to 0356$
- Always True. Example: $\mathrm{3,567}\to \mathrm{35,067}$
- Sometimes True. Counterexample: $5.2\to 5.20$
- Sometimes True
- Sometimes True. Counterexample: $6.2\times 10=62$
- Sometimes True. Counterexample: $1.4\xf710=0.14$
- Always True. Check examples with a calculator
- Sometimes True. Counterexample: $\frac{10}{100}=0.1$

**Work Time**

# When Does Zero Matter?

Work with a partner.

- Take turns choosing a card. Decide whether the statement on the card belongs in the “Always True” or “Sometimes True” column.
- Explain to your partner how you made your decision. Your partner should either agree with your explanation or challenge it if he or she thinks your explanation is not clear, correct, and complete.
- When you both agree, move the card into the appropriate column.