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5-8

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## Gears and Proportions

Students learn about proportions and ratios through learning about the gears on a bike.

### Overview

In this Cyberchase activity, students are introduced to the way bicycle gears work and the relationships between the sizes of front and rear gears, gear ratios and relative speeds of the bicycle wheels. Students later list gear combinations and ratios for bicycles of different speeds.

5-8

1 hour

### Media Resources

Bianca Gets in Gear QuickTime Video

### Part I: Learning Activity

1. Read the following to your students: "Have you ever ridden a bicycle with multiple gears? In this activity, you will consider how mathematics can help us understand how gears work. In a Cyberchase video segement, Bianca buys a fast new bicycle to keep up with her friend Kelly when they go riding in the park."

2. Ask if any of the students can explain what happens when they change gears during a bike ride. Ask them to discuss whether a geared bike is easier to ride than a bike with no gears.

3. Play the Bianca Gets in Gear QuickTime Video . Tell students to watch as Bianca visits the bike shop and to pay attention to the shop owner's explanation of gears.

4. Distribute the Gearing Up handout .

5. Ask the students to complete the handout. (Note: This activity will be enhanced if your students can examine a geared bicycle directly. We suggest that the class go out to the bike rack and look at a geared bike. If any of the students have a bicycle at school, perhaps a student could bring a bicycle into the classroom so students can examine the gears, gearshifters and derailleurs, and how they work.)

6. Discuss with students the relationships between the front and rear gears and how mathematics is involved in the motion of the bicycle gears.

### Part II: Assessment

Assessment: Level A (proficiency): From a set of gear combinations and gear ratios, students are asked to identify high and low gear ratio values. They are asked to determine what it means to compare gear ratios.

Assessment: Level B (above proficiency): Students are asked to list gear combinations for a12-speed bike and to rank the gear ratios in terms of relative speeds per pedal turn.

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