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# The World's Highest and Lowest Locations

# The World’s Highest and Lowest Locations

# Above and Below Sea Level

## Overview

Students watch a video showing the highest and lowest locations on each of the continents. Then they create a diagram (a number line) for a book titled *The World’s Highest and Lowest Locations*. Students show four of the highest elevations and four of the lowest elevations in the world on their diagrams.

# Key Concepts

- A complete number line has both positive numbers (to the right of 0) and negative numbers (to the left of 0).
- Negative numbers are written with a minus sign—for example, –12, which is pronounced “negative 12.”
- Positive numbers can be written with a plus sign for emphasis, such as +12, but a number without a sign, such as 12, is always interpreted as positive.
- Every number except 0 is either positive or negative. The number 0 is neither positive nor negative.

# Goals and Learning Objectives

Create a number line to show elevations that are both above and below sea level.

# Elevations Around the World

# Lesson Guide

Have students watch the video.

Ask the following questions:

- What did you notice about the locations you saw in the video? (Elicit that each location either had a very high elevation or a very low elevation.)
- What does
*above sea level*mean? - What does
*below sea level*mean? - How can you create a number line to show the elevations of some of the locations?

Have students talk with a partner about how they might represent the elevations on a number line diagram.

ELL: When showing video, be sure that ELLs can follow the explanations in the video. Ask students if they need to watch it a second time. Pause the playback, as necessary, to allow ELLs time to process the information if the pace of the video is too fast for them. Consider asking some questions before moving on, to be sure that students understand the video.

SWD: Students with disabilities may have difficulty determining the relevant information for this task. Provide students with a note-taking organizer as they watch the video that includes the names of different locations and spaces for their elevations.

## Opening

# Elevations Around the World

Watch this video of the Math News discussing the highest and lowest locations on each of the continents.

- What do the terms
*above sea level*and*below**sea level*mean? - How can a number line help you show the elevations of some of the locations you saw in the video?

VIDEO: The World’s Highest and Lowest Locations

# Math Mission

# Lesson Guide

Discuss the Math Mission. Students will create a number line that represents elevations above and below sea level.

## Opening

Create a number line that represents elevations above sea level and below sea level.

# The World’s Highest and Lowest Locations

# Lesson Guide

Have students read their assignment. Ask a few questions to make sure students understand the task:

- What is the title of the book you have been commissioned to write?
*(Answer: The World’s Highest and Lowest Locations)* - What are you going to create for the book?
*(Answer: a number line diagram)* - What are the types of locations that you will show on your number line? How many of each type will you show?
*(Answer: elevations above and below sea level; four elevations of each type)*

Students will need to watch the video at least one more time to choose their locations. Have the students pause the video on the summary screen at the end of the video and choose their four highest and lowest locations.

As students are working, look for different kinds of number lines to show in Ways of Thinking:

- Vertical number lines that show positive elevations above 0 and negative elevations below 0
- Horizontal number lines that show positive elevations to the right of 0 and negative elevations to the left of 0

ELL: Consider presenting some of the questions in writing to support ELLs.

When eliciting answers orally, be aware of the difficulties some ELLs have in expressing themselves in a foreign language. For example, if you hear that they say the right things but use the wrong grammar structure, show signs of agreement and softly rephrase, using the correct grammar (using the student’s own words as much as possible).

If students are struggling, check that ELLs are following the Intervention questions.

In order for these Interventions to be supportive for ELLs, be sure ELLs are clear about the task and understand the vocabulary in the questions. Allow them to use dictionaries if needed.

# Interventions

**Student has difficulty getting started.**

- Describe the task in your own words to your partner.
- What does 0 represent on your number line?
- Where will you place the four locations above sea level on your number line?
- Where will you place the four locations below sea level on your number line?
- What is the highest elevation? What is the lowest elevation? What scale will you use on your number line?

**[common error] Student does not scale the number line correctly. The scale on the number line is incorrect. The distance between tick marks is not the same.**

- Where is sea level on your number line?
- What scale are you using on your number line?
- Does it make sense to mark every foot of elevation? Every 10 feet of elevation? What is a good interval to use?

**[common error] Student has an incorrect solution. All elevations are on the same side of 0 on the number line.**

- Where is sea level on your number line? What number does sea level represent?
- Where are the elevations that are above sea level on your number line?
- Where are the elevations that are below sea level on your number line?

**Student has a solution.**

- Explain how you interpreted the task.
- Why did you choose this scale for the number line?
- Is it easier to compare the elevations using a horizontal or a vertical number line? Why?

# Mathematical Practices

**Mathematical Practice 1: Make sense of problems and persevere in solving them.**

Students must make sense of the situation in order to represent it on a number line. Watch for the different strategies students use to set up their number lines. How do they label their number lines? Do they understand that 0 represents sea level? What intervals do they use between tick marks? Do they use a horizontal or a vertical number line to represent the elevations?

**Mathematical Practice 6: Attend to precision.**

Look for students who attend to precision when marking the points for each elevation. Do students accurately depict each elevation? Do they plot elevations above sea level to the right or above 0? Do they plot elevations below sea level to the left or below 0? Are intervals between tick marks the same distance?

# Possible Answers

**Horizontal Number Line**

[common error] Number line that has all elevations on same side of 0

**Vertical Number Line**

# Challenge Problem

# Possible Answers

- Students will draw a vertical or horizontal number line; see examples above.
- Explanations will vary. Sample explanations:
- On my number line, 0 represents sea level. I made a vertical number line, so elevations above 0 are above sea level and elevations below 0 are below sea level.
- I made a horizontal number line. The numbers to the right of 0 are the elevations above sea level. The numbers to the left of 0 are the elevations below sea level.

- Explanations will vary. Sample explanation: Positive numbers are used to represent elevations above sea level and negative numbers represent elevations below sea level.

## Work Time

# The World's Highest and Lowest Locations

You have been asked to write a book called *The World’s Highest and Lowest Locations.*

From *The World’s Highest and Lowest Locations* video, choose four locations above sea level and four locations below sea level to include in a diagram for the book.

- Either use the handout or draw your own number line in your notebook.

VIDEO: The World’s Highest and Lowest Locations

HANDOUT: The World's Highest and Lowest Locations

# Challenge Problem

- If you drew a horizontal number line for your book, now draw a vertical number line. If you drew a vertical number line for your book, now draw a horizontal number line.
- Explain how your number line represents elevations above and below sea level.
- Explain how you use the number system to show elevations above and below sea level.

Hint: First locate sea level on the number line.

# Make Connections

# Lesson Guide

Have students share their number lines with the class.

Point out at least two number lines that are done correctly. One should be a vertical number line and the other should be a horizontal one.

- How did [student] make sense of the problem?
- What is similar about their number lines?
- What is different?
- Where is sea level on each number line?
- Where are the elevations that are above sea level on the number lines?
- Where are the elevations that are below sea level on the number lines?
- What do you like about the number lines that are horizontal?
- What do you like about the number lines that are vertical?

**[common error]** Some students may put the elevations above and below sea level on the same side of 0 (sea level) on their number line. If any student did that, show their work. (If no one did, draw one on the board where the elevations above and below sea level are on the same side of sea level.) Ask the class if the number line works and have them make suggestions on what to do to make it work.

- Does this number line work to show the elevations that are above sea level and the elevations that are below sea level? Explain why or why not.

Be sure to honor students who show work that needs to be corrected. Tell students that this is a common error that anyone can make and that by sharing their work, students help prevent others from making similar errors. It is important to create a classroom atmosphere where students freely show their work without worrying about whether it is right or wrong.

ELL: Be sure that all students (including ELLs) participate in the group share, and monitor that ELLs do not shy away from this activity. It is important that ELLs share aloud so that they can hear their own voice and get used to talking in front of large groups.

Encourage ELLs to use their English speaking skills in class. At the same time, allow students to use their language of origin to clarify concepts during partner work. New ELL students may benefit from partners who speak the same language of origin.

## Performance Task

# Ways of Thinking: Make Connections

Take notes about how a number line can represent the highest and lowest elevations in the world.

As your classmates present, ask questions such as:

- Where is sea level on your number line?
- Where are elevations above sea level on your number line?
- Where are elevations below sea level on your number line?
- How did you know where to place each elevation on your number line?
- Compare this number line to number lines you have worked with in the past. How are they alike? How are they different?

# Reflect On Your Work

# Lesson Guide

Have each student write a brief reflection before the end of class. Review the reflections. If any wonderings look interesting enough to pursue later, make a note of them.

To get students started, give them some examples of things that you wondered about during the lesson.

- I wonder what other situations I can show on a number line using both negative and positive numbers?
- I wonder what other situations are best shown using a horizontal number line?
- I wonder what other situations are best shown using a vertical number line?

ELL: To help ELLs organize their thoughts, give them additional time to discuss with a partner before writing. Allow ELLs who share the same language of origin to discuss in this language if they want, and to use a dictionary (or dictionaries).

## Work Time

# Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**What I am wondering about is …**