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

Which statement best captures what this lesson means by 'Math is Ingenuity'?

Check your answer

Math can help us come up with creative solutions to everyday problems

From the Penny Farthing's giant wheel to gear ratios, math powered each creative improvement — that is the lesson's summary.

Sentence starter

I know ___ because ___.

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