# Calculus Project Ideas

Instructor: John Hamilton

John has tutored algebra and SAT Prep and has a B.A. degree with a major in psychology and a minor in mathematics from Christopher Newport University.

Teach your high school students about calculus with these helpful project ideas to be done in pairs and groups. They will learn to communicate and cooperate, while utilizing their analytical abilities.

## Why Calculus?

Since 1699, the debate has been raging as to whether Newton or Leibniz invented calculus. Nonetheless, the complex mathematical discipline known as calculus examines change as well as motion and has been used for everything from chemistry to engineering to the space shuttles. The following three projects, designed for either pairs or groups, will challenge your high schoolers as they learn about the mathematical fundamentals of calculus, and learn some real-world applications as well.

## Calculus Design Your Own Amusement Park Ride

Materials: online access, paper, projector, slides, writing utensils

• Who says calculus can't be fun? Talented engineers and designers actually utilize calculus when creating their thrill rides. After all, calculus involves the study of motion. Divide your students into four groups. Tell them:
• Group One, you will be Team Gravity Rides and Roller Coasters
• Group Two, you will be Team Flat Rides and Bumper Cars
• Group Three, you will be Team Vertical Rides and Ferris Wheels
• Group Four, you will be Team Drop Towers
• Now, have your students meet in their groups to research and eventually design their rides on paper. As an option, they can use various materials to design the actual rides from their drawings.
• When they are through, have your students meet in one large group and debate as to which type of ride is the best. Don't just let them say 'roller coasters', but have them justify their answers with facts.
• As an option, have each group give slideshow presentations to explain their creations.

Discussion Question: Are derivatives or integrals more beneficial in designing these exciting rides? Why?

## Calculus Science Fair Booths

Materials: colored markers, construction paper (one large sheet and two small sheets per pair), glue, online devices, scissors, tape

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