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© 21st Century Math Projects Project Title: Walkathon Championship Standard Focus: Algebra & Functions Time Range: 2-3 Days Supplies: Tape Measures, Stopwatch, Measured course or track. Topics of Focus: - Solving Radical Functions

Benchmarks: 1. Create equations and inequalities in one variable and use them to solve Creating Equations A-CED problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Reasoning with 2. Solve simple rational and radical equations in one variable, and give examples Equations and A-REI showing how extraneous solutions may arise. Inequalities

Procedures:

A.) Students will complete “Walk on the Wild Side”. In this assignment, students will use a biological formula to determine the walking speed of different animals.

B.) Students will complete “Tortoise and the Hare”. In this assignment, students will continue using the formula, but will be comparing different animal species to see which can walk the fastest. Students will need to convert from metric to standard units or vice versa.

C.) Students will complete “Walkathon Championship”. Students will measure the lengths of their legs with a tape measure and determine their maximum theoretical walking speed.

Either on a track or in a field measure out distance for a start and finish line (or better yet, have your students do it). A 50 foot track might be about perfect for this. With a stopwatch time the students. They will use this to calculate their actual speed. The student with the closest actual speed to their theoretical speed will win this challenge.

© 21st Century Math Projects Walk on the Wild Side We know that the cheetah is the fastest land animal on Earth, but what if it were not allowed to run? Biologists model maximum walking speed by the equation 푠 = √푔퐿, where g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2) and L is the length of the leg (in metric or standard units). In the situations below, use this information to answer the questions.

(Hint: It will be useful to know 1 m = 3.23 ft for conversions)

1. Find the maximum walking speed of a giraffe with legs 6.03 feet long.

2. Find the maximum walking speed of a coyote with legs 0.46 m long. How much faster can a giraffe walk than a coyote?

3. If an elephant’s leg is 68 inches long, what is its maximum walking speed?

4. The length of a leg of a typical horse is 98 cm long, what is the maximum walking speed of the horse?

5. If the maximum walking speed of a red kangaroo is 4.31 m/s, how long is its leg?

6. If the maximum walking speed of a groundhog is 3.10 ft/s, how long is its leg? Is its leg longer or shorter than the red kangaroo?

© 21st Century Math Projects Tortoise & the Hare and other Races It’s time for animals to face off to prove who the fastest walker in all of wildlife is. Determine the winner of each race. There are three different heats (small mammals, big mammals and big cats), but everything will start with a pair of celebrity… Celebrity race Tortoise Hare (Galapagos) (Jackrabbit) Leg Length: 0.384 m Leg Length: 0.787 feet

Who is the faster racer? How much faster did they walk?

Small Mammals race Opossum Raccoon Wolverine Leg Length: 0.29 ft Leg Length: 6 inches Leg Length: 0.21 m

Who is the faster racer? How much faster did they walk?

Big Mammals race American Bison Black Rhino Brown Bear Hippopotamus Leg Length: 2.54 ft Leg Length: 0.844 m Leg Length: 26.3 in Leg Length: 68.3 cm

Who is the faster racer? How much faster did they walk?

Big Cats race Cheetah Lion (African) Tiger (Siberian) Leg Length: 1.54 ft Leg Length: 0.567 m Leg Length: 23.16 in

Who is the faster race? How much faster did they walk?

Walkathon Championship A gold medal is on the line today. Who is the best walker in your class? After a careful analysis of the equation 푠 = √푔퐿, where g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2) and L is the length of the person’s leg (in metric or standard units), one could probably figure out that the fastest walker will be the person with the longest legs, BUT this championship has a different wrinkle.

There are two parts to this challenge: a person’s theoretical speed (based on the length of their leg) and their actual speed based on a competition. The winner of the Walkathon Championship will be the person whose actual walking speed is the closest to their theoretical walking speed!

Theoretical Walking Speed – Actual Walking Speed = Score

Theoretical Actual Measure the length of your leg from your hip to On a measured course, walk as fast as you your heel (or the top of your foot). possibly can (no running).

Length: Distance:

Use the length of your leg to calculate your Time: maximum walking speed.

Use the length the course and your time calculate your walking speed.

Max Max Theoretical Actual Speed: Speed:

- = (Max Theoretical Speed) (Max Actual Speed) Score

Are you satisfied with your performance? Are you surprised by the result?

Thank you for being my Math Friend!

If you liked this 21st Century Math Project You might like others. (Click the logo)

Math it Up. Boomdiggy.

Walk on the Wild Side We know that the cheetah is the fastest land animal on Earth, but what if it were not allowed to run? Biologists model maximum walking speed by the equation 푠 = √푔퐿, where g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2) and L is the length of the leg (in metric or standard units). In the situations below, use this information to answer the questions.

(Hint: It will be useful to know 1 m = 3.23 ft for conversions)

1. Find the maximum walking speed of a giraffe with legs 6.03 feet long.

13.89 ft/s

2. Find the maximum walking speed of a coyote with legs 0.46 m long. How much faster can a giraffe walk than a coyote? 2.12 m/s or 6.86 ft/s thus a giraffe can walk 7.03 ft/s faster.

3. If an elephant’s leg is 68 inches long, what is its maximum walking speed?

13.47 ft /s

4. The length of a leg of a typical horse is 98 cm long, what is the maximum walking speed of the horse?

3.10 m/s

5. If the maximum walking speed of a red kangaroo is 4.31 m/s, how long is its leg?

1.90 m

6. If the maximum walking speed of a groundhog is 3.10 ft/s, how long is its leg? Is its leg longer or shorter than the red kangaroo? 0.30 ft or 0.09 m so a kangaroo leg is 1.81 m longer.

1.94 m/s or 6.27 ft/s 5.02 ft/s.

Who is the faster racer? How much faster did they walk? The tortoise is theoretically a faster walker by 1.25 ft/s.

Small Mammals race Opossum Raccoon Wolverine Leg Length: 0.29 ft Leg Length: 6 inches Leg Length: 0.21 m

3.05 ft/s 4 ft/s 1.43 m/s or 4.63 ft/s

Who is the faster racer? How much faster did they walk? The wolverine won the race. They were 0.63 ft/s faster than the raccoon.

Big Mammals race American Bison Black Rhino Brown Bear Hippopotamus Leg Length: 2.54 ft Leg Length: 0.844 m Leg Length: 26.3 in Leg Length: 68.3 cm 9.02 ft/s 2.876 m/s or 9.29 ft/s 8.37 ft/s 2.59 m/s or 8.36 ft/s

Who is the faster racer? How much faster did they walk? Black Rhino won the race. They were 0.27 ft/s faster than the bison.

Big Cats race Cheetah Lion (African) Tiger (Siberian) Leg Length: 1.54 ft Leg Length: 0.567 m Leg Length: 23.16 in 7.02 ft/s 2.36 m/s or 7.63 ft/s 7.86 ft/s

Who is the faster racer? How much faster did they walk? The tiger would win the race. They were 0.23 ft/s faster than the tiger.

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Teacher Guide Walkathon Championship -- Square Root Functions Project

Can your actual walking rate meet your theoretical rate?

Lesson Duration: 2-3 Days

Lesson Type: POL

Audience: Classmates, Teachers Overview

A gold medal is on the line today. Who is the best walker in your class? Walking speed of humans and animals can be modeled by square root functions so move your feet and crown a champion!

-- In “Walk on the Wild Side”, students will use a biological formula to determine the walking speed of different animals.

-- In “Tortoise and the Hare”, students will continue using the formula, but will be comparing different animal species to see which can walk the fastest. Students will need to convert from metric to standard units or vice versa.

-- In “Walkathon Championship”, students will measure the lengths of their legs with a tape measure and determine their maximum theoretical walking speed.

Measure out a distance either on a track or in a field for a start and finish line (or better yet, have your students do it). A 50 foot track might be about perfect for this. With a stopwatch time the students. They will use this to calculate their actual speed. The student with the closest actual speed to their theoretical speed will win this challenge.

Common Core Standards

CCSS.Math.Content.HSA-CED.A.1 CCSS.Math.Content.HSA-REI.A.2 21st Century Skills

Information Media Literacy Critical Thinking/Problem Solving Skills Collaboration Skills

Lesson Plan

Step 1: Walk on the Wild Side

Students will complete Walk on the Wild Side.

In this assignment, students will use a biological formula to determine the walking speed of different animals.

The formula does include a square root, and the students do have to evaluate and solve the expression.

Note: The Complete PDF and Answer Key is downloadable in the Teacher Resources above. Step 2: Tortoise and the Hare

Students will complete Tortoise and the Hare.

In this assignment, students will continue using the biological formula, but will be comparing different animal species to see which can walk the fastest.

To add complexity, students will need to convert from metric to standard units or vice versa.

Once they complete Tortoise and the Hare, your students can then complete the Rank & Reason tasks where they must rank the fastest animals in each race.

Students can complete the Rank & Reason by logging in individually or by logging in as a group (using the Group option under Advanced Features).

Alternative ways of completing the ranking are to project the ranking below on the board for students to come up, drag an option and then justify verbally to the class; or to use the printable version of the activity in the Teacher Resources above. Students will be able to compare with other students or with the class average and see other justifications. This feature can be turned off under Advanced Options.

The orders should be:

Small mammals: Wolverine, Raccoon, Opossum Big mammals: Black Rhinoceros, American Bison, Brown Bear, Hippopotamus Big Cat: Tiger, Lion, Cheetah Step 3: Walkathon Championship

Students will complete Walkathon Championship.

First, students will measure the lengths of their legs with a tape measure and calculate their maximum theoretical walking speed.

Either on a track or in a field measure out distance for a start and finish line (or better yet, have your students do it). A 50 foot track might be about perfect for this.

With a stopwatch, time the students. They will use this to calculate their actual speed.

The student with the closest actual speed to their theoretical speed will win the Walkathon Championship.

Student naturally will try to push the limits of "walking", skipping, jogging have to disqualify the time. Walkathon Championship -- Square Root Functions Project Instructions

1) Cut out along each of the dashed lines below. 2) Review the different items in bold and discuss them with your teammates. 3) Rearrange the items to re-order your ranking for the discussion question below, and then number them 1 – 3. 4) Now fill in the justification for each item to explain your ranking. 5) When you have finished, compare your rankings/justifications with other teams. It’s okay to go back and re-rank your answers after discussing them with other teams.

Discussion Question

Which big cat is the fastest walker? Drag the fastest to the top of the list and order the rest accordingly.

Ranking No. Justification: Explain why your team has ranked this here

Cheetah Ranking No. Justification: Explain why your team has ranked this here

Lion

Ranking No. Justification: Explain why your team has ranked this here

Tiger

Discussion Question:

Which big cat is the fastest walker? Drag the fastest to the top of the list and order the rest accordingly.