- License:
- Creative Commons Attribution Non-Commercial
- Language:
- English
- Media Formats:
- Downloadable docs, Text/HTML

# Gallery Problems

## Overview

# Gallery Overview

Allow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then 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

## Diving

Chen stands on top of a cliff, and a woman scuba diver dives in the ocean below. Students will determine their positions on a vertical number line that represents distance above and below sea level.

## Negative Numbers?

Students will read about five students’ opinions about negative numbers and decide whose opinions they agree with, whose they disagree with, and why. Students will also share their own ideas about negative numbers.

## Temperatures in January

A map shows the lowest temperatures recorded in January since 2008 for five cities. Students will locate these temperatures on a number line and compare the temperatures.

## Greenwich Mean Time

Students will use positive and negative numbers and Greenwich Mean Time to find the times of different cities around the world.

## Numbers Timeline

Students will research the history of negative numbers and absolute value and create a timeline to show what they learned.

## Rational Numbers and Absolute Value Video

Students will create a video about rational numbers and absolute value.

# Diving

# Answers

## Work Time

# Diving

In this diagram, the vertical number line represents distances above and below sea level. Sea level is at 0 meters.

- Chen is standing on top of a cliff that is 20 meters above sea level. Write his position as a positive number on the number line.
- The diver is swimming 10 meters below sea level. Write her position as a negative number on the number line.
- The sea floor is 50 meters below the cliff top. Write this point as a negative number on the number line.
- Suppose the diver swims to a position that is 5 meters above the sea floor. Write her position as a positive or negative number on the number line.

# Negative Numbers?

# Answers

- Answers will vary.
- Answers will vary.
- Answers will vary.
- Answers will vary. Possible answers: temperature, latitude, longitude, altitude, or negative cash flow
- Answers will vary.

**Work Time**

# Negative Numbers?

Jason, Emma, Denzel, Carlos, and Chen were discussing negative numbers.

Jason: “I think negative numbers are like ordinary numbers but with a negative sign.”

Emma: “Negative numbers are amounts less than 0.”

Chen: “I think of negative numbers as movements on a number line.”

Denzel: “Negative numbers are like debts, when you owe money, and positive numbers are like credits, when you have money.”

Carlos: “I do not think there is any such thing as a negative number. You can’t count negative numbers.”

- Whose ideas do you agree with? Explain why you agree. Use drawings or diagrams if you wish.
- Whose ideas do you disagree with? Explain why you disagree. Use drawings or diagrams if you wish.
- Do you have another way of thinking about negative numbers? Write your idea.
- Write at least two ways that negative numbers appear in the world around you.
- How could you convince Carlos that negative numbers exist?

# Temperatures in January

# Answers

- Denver had the lowest temperature, –25°F.
- Rosa is wrong. Possible answer: Since –3°F is farther away from 0°F than –2°F, –3°F is colder.

**Work Time**

# Temperatures in January

This map shows five cities in the United States and their lowest recorded January temperatures (in degrees Fahrenheit) since 2008. Use the map to answer the following questions.

Draw a number line and place a point on the number line for the temperature of each city. Label each point with the temperature and the name of the city.

Which city had the lowest January temperature?

Rosa said that the lowest January temperature recorded in Portland is colder than the lowest January temperature recorded in New York. Do you agree? Explain how you know.

# Greenwich Mean Time

# Answers

- Answers will vary. Possible answers: Los Angeles is 1 hour behind Denver. Cairo is 7 hours ahead of New York City. Sydney is 10 hours ahead of London.
- It will be 2 a.m. the next day in London and 11 a.m. the next day in Tokyo when it is 8 p.m. in Chicago.

**Work Time**

# Greenwich Mean Time

Since 1884, people on Earth have used the time of the meridian at Greenwich, England—known as Greenwich Mean Time—as the basis for standard time around the globe. The time at different places varies from 12 hours ahead of Greenwich Mean Time to 12 hours behind it, as shown on the map. Greenwich is near London. Regions whose time zone is shown in two colors are halfway between the time zones represented by those colors. For example, New Delhi is 5$\frac{1}{2}$ hours ahead of Greenwich Mean Time.

- Examine and interpret the map. Write three statements about the time in three different cities.
On the number line, label each city you discussed in problem 1 next to the number that represents its time zone. Use positive numbers for time zones ahead of Greenwich Mean Time and negative numbers for time zones behind it.

Use the number line from problem 2 to find what time it is in London and Tokyo when it is 8:00 p.m. in Chicago.

Complete the table. Find the times in the other cities when it is 8:00 p.m. in Chicago. Then find the number of hours each city is ahead of or behind London.

HANDOUT: Greenwich Mean Time

# Numbers Timeline

# Answers

- Answers will vary. Have students present their timelines to the class.

**Work Time**

# Numbers Timeline

- Research the history of negative numbers and absolute value.
- Create a timeline to show the information you found.
- Be prepared to present your timeline to the class.

# Rational Numbers and Absolute Value Video

# Answers

- Videos will vary. Have students present their videos to the class.

**Work Time**

# Rational Numbers and Absolute Value Video

Create a video about rational numbers and absolute value.

- Think about the key concepts about rational numbers and absolute value.
- Develop a story line that encompasses those concepts.
- Film and edit the video.