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Animal scientists noticed patterns in the size of an animal and its speed.

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CCSS: 4.OA.A.2; MP1, MP3, MP4

TEKS: 4.5A

How Fast Can They Go?

Scientists use math to learn more about animals’ top speeds

A cheetah is the world’s fastest land animal. But why? For decades, scientists have wondered why some animals are speedier than others.

Many scientists have tried to predict animals’ top speeds. But doing so is harder than you might think. Does an elephant run at 360 miles per hour? No way. But math equations commonly used to predict animals’ speeds produced outlandish numbers like that.

Scientists in Germany tried something new. Ulrich Brose studies biodiversity, or the different kinds of life in an ecosystem. He and his team used data from 472 animals to develop new equations.

First, the scientists calculated the maximum speed that different animal species could travel based on their weight. This included land mammals, birds, and sea animals.

A cheetah is the world’s fastest land animal. But why? For decades, scientists have wondered. They want to know why some animals are speedier than others.

Many scientists have tried to predict animals’ top speeds. But doing so is harder than you might think. Does an elephant run at 360 miles per hour? No way. But math equations commonly used to predict animals’ speeds produced outlandish numbers like that.

Scientists in Germany tried something new. Ulrich Brose studies biodiversity. That’s the different kinds of life in an ecosystem. He and his team used data from 472 animals. They developed new equations.

First, the scientists calculated the maximum speed that different animal species could travel. They did it based on the animal’s weight. The study included land mammals, birds, and sea animals.

iStockPhoto/Getty Images

Tuna swim 3 times faster than hippos run!

Then, they used an equation to find how quickly each species could accelerate, or get faster during a period of time. Acceleration depends on an animal’s weight, how it stores energy, and whether the animal runs, flies, or swims.

The scientists proved that medium-sized animals—like the cheetah—go the fastest. That’s because they can use stored energy to move quickly before their muscles tire out.

This isn’t true for larger animals, such as elephants. Their muscles run out of energy before they can reach their theoretical top speed.

All animals move at different speeds depending on whether they are hunting, eating, or exploring. The study’s results give scientists a framework they can use in the future. The models also hold fascinating clues for extinct animals, such as dinosaurs. “The Tyrannosaurus rex was not a fast runner,” says Brose. “We could have escaped one!”

Then, they used an equation to find how quickly each species could accelerate. This means getting faster during a period of time. Acceleration depends on an animal’s weight. It also depends on how it stores energy. Whether the animal runs, flies, or swims is important too.

The scientists proved that medium-sized animals go the fastest. An example is the cheetah. It can use stored energy to move quickly before its muscles tire out.

This isn’t true for larger animals. An example is the elephant. Its muscles run out of energy before it can reach its theoretical top speed.

All animals move at different speeds depending on what they are doing. For example, they could be hunting, eating, or exploring. The study’s results give scientists a framework. They can use this in the future. The models also hold fascinating clues for extinct animals, such as dinosaurs. “The Tyrannosaurus rex was not a fast runner,” says Brose. “We could have escaped one!”

Humans and polar bears have the same maximum speed of 24 mph. An average polar bear weighs about 600 pounds. An average adult human weighs 150 pounds. Which equation shows how many times more a polar bear weighs than a human?

A. 150 × ? = 600

B. 600 – 150 = ?         

C. 150 ÷ ? = 600

D. 600 + ? = 150  

Humans and polar bears have the same maximum speed of 24 mph. An average polar bear weighs about 600 pounds. An average adult human weighs 150 pounds. Which equation shows how many times more a polar bear weighs than a human?

A. 150 × ? = 600

B. 600 – 150 = ?         

C. 150 ÷ ? = 600

D. 600 + ? = 150 

A house cat can run about 40 feet in 1 second. A mouse can run 10 feet in 1 second. How many times faster is a house cat than a mouse? Write and solve an equation using the variable b as the unknown.

A house cat can run about 40 feet in 1 second. A mouse can run 10 feet in 1 second. How many times faster is a house cat than a mouse? Write and solve an equation using the variable b as the unknown.

A mosquito’s top speed is 4 mph. You want to find how many times faster a human is compared with a mosquito. Write what you know and what you want to find out. What is the variable?

A mosquito’s top speed is 4 mph. You want to find how many times faster a human is compared with a mosquito. Write what you know and what you want to find out. What is the variable?

Write an equation using a variable to represent the problem. Then solve it.

Write an equation using a variable to represent the problem. Then solve it.

Express your answer in words as a complete sentence.

Express your answer in words as a complete sentence.

A rat can move at about 6 mph. An American cockroach moves at about half that speed. Write two equations for the speed of an American cockroach, using the variable s.

A rat can move at about 6 mph. An American cockroach moves at about half that speed. Write two equations for the speed of an American cockroach, using the variable s.

Solve your equations. What does s represent?

Solve your equations. What does s represent?

A cheetah is the fastest land animal. A shortfin mako shark is the fastest marine animal. A cheetah runs about twice as fast as a shortfin mako shark swims. What math terms do you notice in these statements?

A cheetah is the fastest land animal. A shortfin mako shark is the fastest marine animal. A cheetah runs about twice as fast as a shortfin mako shark swims. What math terms do you notice in these statements?

A shortfin mako shark’s top speed is 35 mph.

A cheetah’s top speed is 70 mph. A student sets up the following equation to solve for how many times faster a cheetah is than a mako shark:

70 mph – 35 mph = r

What did the student do wrong? Fix the mistake and write the correct equation.

A shortfin mako shark’s top speed is 35 mph.

A cheetah’s top speed is 70 mph. A student sets up the following equation to solve for how many times faster a cheetah is than a mako shark:

70 mph – 35 mph = r

What did the student do wrong? Fix the mistake and write the correct equation.

What is the value of r? How can you use the information in part A to check your work?

What is the value of r? How can you use the information in part A to check your work?

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