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

Lesson 10.410.4 Small Group · Group 1

Group 1 · Set BSecond form · new problems, same idea

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
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Learning target With my small group, I can use ratios and models to explain how the Penny Farthing and gear-driven bicycles were ingenious solutions to a real problem — one step at a time, with support.

Remember10.4 Small Group · Group 1

In a ratio table, the rear gear's teeth make 1 turn. Scale to the pedal gear's teeth to find the wheel turns for one pedal turn. A gear ratio tells how many times the rear wheel turns for each turn of the pedals.

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________________

    The pedal gear has 48 teeth. The rear gear has 16 teeth. How many times does the rear wheel turn for each pedal turn?

    Show your work

    Hint Put 16 teeth and 1 turn in the first column. What do you multiply 16 by to get 48?

    Final answer:
  2. 2Complete each step, then write the final answer.
    Teeth turnedWheel turns________________

    The pedal gear has 56 teeth. The rear gear has 14 teeth. How many times does the rear wheel turn for each pedal turn?

    Show your work

    Hint Put 14 teeth and 1 turn in the first column. What do you multiply 14 by to get 56?

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

    An egg beater has a handle gear with 45 teeth. It turns a small gear with 9 teeth. How many times does the small gear spin for each turn of the handle?

    Show your work

    Hint This works like a bike. Put 9 teeth and 1 spin in the first column. Scale to 45 teeth.

    Final answer:
  4. 4Complete each step, then write the final answer.
    Teeth turnedWheel turns________________
    3 pedal turns move 3 × 48 = 144 teeth.

    The pedal gear has 48 teeth. The rear gear has 36 teeth. A rider makes 3 pedal turns. How many times does the rear wheel turn?

    Show your work

    Hint Find how many teeth 3 pedal turns move. Put 36 teeth and 1 turn in the first column. Then scale up.

    Final answer:

Explain your thinkingWhy do we divide the pedal teeth by the rear teeth? Use a 40-tooth pedal gear and a 20-tooth rear gear.

Sentence starter One pedal turn moves ___ teeth on the rear gear. · The scale factor from ___ teeth to ___ teeth is the wheel turns.

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