Lesson 4: Math is IngenuityMPP.4

I can…

I can use ratios and models to explain how the Penny Farthing and gear-driven bicycles were ingenious solutions to a real problem.

Key words

• ingenuity — Coming up with different, and sometimes unique, solutions to problems.
• rotation — One full turn of a wheel, gear, or pedal all the way around.
• gear — A toothed wheel that passes motion to another toothed wheel through a chain.
• ratio — A comparison of two quantities, like pedal rotations to wheel rotations.
• equivalent ratios — Ratios that make the same comparison using different numbers.

Steps

1. A later bicycle design uses a chain: the pedal gear has 48 teeth, and the largest rear gear has 32 teeth.
2. For each rotation of the 48-tooth pedal gear, the wheel gear also turns 48 teeth.
3. The 32-tooth gear needs to turn 32 teeth to make one full rotation, so I find the equivalent ratio: 48 ÷ 32 = 1.5.
4. The rear wheel makes 1.5 rotations for each pedal rotation — this gear makes it easier to pedal at slower speeds or go uphill.

Try it

Explain to a partner why the Penny Farthing's front wheel was so large.

Check your answer

Check with your guided notes.

Sentence starter

I know ___ because ___.

Goal: I can explain a gear ratio using the words rotation, teeth, and 'for each ___, the wheel turns ___.'