# Glide Ratio # Use Appropriate Tools

Today you will explore and compare glide ratios of things that fly.

In this unit, you have used tape diagrams, double number lines, ratio tables, and graphs to represent ratios, make comparisons, and solve ratio problems.

Whenever you work with ratios, you should think about the tools that are available to you and choose the one(s) that you think will be the most useful.

• How do you think your work in previous lessons might help you represent and compare ratios?
• Watch this video as Jan, Carlos, and Mia use appropriate tools to explore wingspan and glide ratios.

VIDEO: Mathematical Practice 5

## Opening

Solve problems about glide ratios using appropriate tools.

# White-Backed Vultures

White-backed vultures have a glide ratio of 75:5. The ratio tells us that this kind of vulture can glide 75 feet forward for every 5 feet that it descends.

Choose a tool that you think will be useful for representing and comparing equivalent glide ratios for the white-backed vulture. (The Double Number Line Tool and Ratio Table Tool are provided below; however, you can use any tool that you feel will be the most useful.)

• Using your chosen tool, represent equivalent glide ratios for the white-backed vulture.
• Explain where you "see" the ratios in your representation and what each ratio means.

INTERACTIVE: Double Number Line Tool

INTERACTIVE: Ratio Table Tool

When representing and comparing the glide ratios, pay attention to which numbers you use for the forward distances and which you use for the vertical descent distances.

# Paragliders and Sailplanes

Sailplanes have a glide ratio of 150:3.

Paragliders have a glide ratio of 24:4.

• Choose either the sailplane or the paraglider. Use the same tool you used with the white-backed vulture to represent equivalent glide ratios for the sailplane or the paraglider.
• Explain the meaning of each of the ratios. INTERACTIVE: Double Number Line Tool

INTERACTIVE: Ratio Table Tool

## Hint:

When representing the glide ratios, pay attention to which numbers you use for the forward distances and which you use for the vertical descent distances.

# Compare Glide Ratios

Based on their glide ratios, which of these can glide farther from a given altitude:

• The white-backed vulture or the sailplane or the paraglider?

When representing and comparing the glide ratios, pay attention to which numbers you use for the forward distances and which you use for the vertical descent distances.

# Prepare a Presentation

Explain what a glide ratio is.

Explain which tool you chose to represent glide ratios and why you chose that tool.

Explain how the representations you made support your answer about whether the vulture or the sailplane/paraglider can glide farther from a given altitude.

# Challenge Problem

As you can see in the photograph, the northern flying squirrel has its own wing suit! This wing suit is similar to a wing suit that humans have developed. The squirrel has a glide ratio similar to the glide ratio of the man-made wing suit: both ratios are approximately 2:1.

• Imagine that the squirrel jumps from one tree to another, from a branch 140 feet off the ground to a branch 30 feet off the ground. How far apart are the two trees?
• Another set of trees is 120 feet apart. The squirrel jumps from one tree branch to another and lands on a branch that is 10 feet off the ground. How high was the branch that the squirrel jumped from? # Ways of Thinking: Make Connections

Take notes about your classmates' representations and the strategies they used for comparing glide ratios.

• Which tool do you think is the most useful for comparing glide ratios? Why?
• Which tool would be the most useful for determining the distance a bird can travel before reaching the ground if you only know its starting height and glide ratio?
• Which tool did you work from to make your graph?

# Summary of the Math: Represent and Compare Glide Ratios

Write a summary about representing and comparing glide ratios and the tools that help you do this.

• Do you define glide ratio ?
• Do you describe different ways to represent ratios?
• Do you describe the different tools you can use to represent glide ratios?
• Do you explain how you can use these representations to compare glide ratios?