Grade 6 Mathematics · Unit 10: Math Is...Standard MPP.4

Lesson 10.410.4 Small Group · Group 2

Group 2 · Set BSecond challenge form · new problems, same idea

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Learning target I can use ratios and models to explain how the Penny Farthing and gear-driven bicycles were ingenious solutions to a real problem, explain why the method works, and use it on a problem I have not seen before.

Remember10.4 Small Group · Group 2

Teeth turned and wheel turns form equivalent ratios, so a ratio table can predict wheel turns or work backward to design a gear. You can work backward from a gear ratio to find how many teeth a gear needs.

Words: ingenuity (ingenio)rotation (rotación)gear (engranaje)ratio (razón)equivalent ratios (razones equivalentes)

  1. 1Complete each step, then write the final answer.
    Teeth turnedWheel turns________________________
    Each pedal turn moves 36 teeth.

    A pedal gear has 36 teeth. The rear gear has 24 teeth. The rider makes 4 pedal rotations. How many rotations does the rear wheel make?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.
    Teeth turnedWheel turns________________________

    A pedal gear has 35 teeth. A designer wants the rear wheel to turn 2.5 times for each pedal turn. How many teeth must the rear gear have?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.
    Teeth turnedSmall gear spins________________

    In a windmill, a big gear with 64 teeth turns a small gear. The small gear spins 4 times for each turn of the big gear. How many teeth does the small gear have?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    Teeth turnedWheel turns________________________
    Gear X. Make one for gear Y too.

    A pedal gear has 36 teeth. Rear gear X makes the wheel turn 1.5 times per pedal turn. Rear gear Y makes it turn 3 times. How many more teeth does gear X have than gear Y?

    Show your work
    Final answer:

Explain your thinkingA shop says a smaller rear gear always makes a bike better. When is a small rear gear better, and when is a big one better?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help