Grade 6 Mathematics · Unit 10: Math Is...Standard MPP.3

Lesson 10.610.4–10.6 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 10.4–10.6 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 10.4–10.6: 10.4 Math is Ingenuity, 10.5 Math is Boundless, 10.6 Math is Mine. Work one example from each lesson, then prove you're caught up in the mixed practice.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
ingenuitySpanish: ingenio Coming up with different, and sometimes unique, solutions to problems. The Penny Farthing's huge wheel, then chains and gears — two clever fixes.
rotationSpanish: rotación One full turn of a wheel, gear, or pedal all the way around. One full turn of the pedal — 360° all the way around.
gearSpanish: engranaje A toothed wheel that passes motion to another toothed wheel through a chain. A 48-tooth pedal gear pulling a 12-tooth wheel gear through the chain.
ratioSpanish: razón A comparison of two quantities, like pedal rotations to wheel rotations. 48 pedal teeth to 12 wheel teeth — 4 wheel turns for every pedal turn.
equivalent ratiosSpanish: razones equivalentes Ratios that make the same comparison using different numbers. 1 : 4 and 3 : 12 describe the same gear, at different sizes.
repetitionSpanish: repetición The same object, shape, or form repeated multiple times. The same tile, over and over, all the way along the border.

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

The pedal gear has 48 teeth. The rear gear has 12 teeth. How many times does the rear wheel turn for each pedal turn?

  1. Write the rear gear: 12 teeth make 1 turn: 12 : 1
  2. One pedal turn moves 48 teeth. Find the scale factor: 48 ÷ 12 = 4
  3. Multiply the wheel turns by 4 too: 1 × 4 = 4
  4. The rear wheel turns 4 times for each pedal turn.
  5. A border repeats: circle, square, triangle. What is shape number 20?
  6. Find the complete units and the leftover shapes: 6 × 3 = 18; 20 − 18 = 2
  7. Use the remainder to name the shape: remainder 2 → 2nd shape → square
  8. Shape number 20 is a square.
  9. A Ferris wheel has 20 cars with about 4 riders each. It makes 6 turns an hour. About how many riders can it carry in one hour?
  10. Find the riders for one turn: 20 × 4 = 80
  11. Scale 1 turn to 6 turns: × 6: 80 × 6 = 480
  12. The wheel can carry about 480 riders in one hour.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

The pedal gear has 30 teeth. The rear gear has 15 teeth. How many times does the rear wheel turn for each pedal turn?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • In September I thought math was .
  • Now I think because .

Word bank ingenuityrotationgearratioequivalent ratiosrepetition

Watch out!A common mistake

Treating your math story as finished

Grade 6 Mathematics · Unit 10: Math Is...Standard MPP.3

Lesson 10.610.4–10.6 Catch-Up

Catch-UpSkill bridge

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can show I am caught up on Lessons 10.4–10.6 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 10.4–10.6: 10.4 Math is Ingenuity, 10.5 Math is Boundless, 10.6 Math is Mine. Work one example from each lesson, then prove you're caught up in the mixed practice.

  1. 1Complete each step, then write the final answer.
    Teeth turnedWheel turns________________

    The pedal gear has 24 teeth. The rear gear has 6 teeth. How many times does the rear wheel turn for each pedal turn?

    Show your work

    Hint Put 6 teeth and 1 turn in the first column. What do you multiply 6 by to get 24?

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

    The pedal gear has 35 teeth. The rear gear has 7 teeth. How many times does the rear wheel turn for each pedal turn?

    Show your work

    Hint Put 7 teeth and 1 turn in the first column. What do you multiply 7 by to get 35?

    Final answer:
  3. 3Complete each step, then write the final answer.

    Circle, square, triangle repeat in that order. What is shape number 9?

    Show your work

    Hint Divide 9 by 3. What does the remainder tell you?

    Final answer:
  4. 4Complete each step, then write the final answer.

    Star, heart, star, heart repeat. What is shape number 11?

    Show your work

    Hint The pattern unit is 2 shapes. Divide 11 by 2.

    Final answer:
  5. 5Complete each step, then write the final answer.
    Turns13Riders??× ?× ?
    Find the riders for one turn first.

    A Ferris wheel has 10 cars with about 4 riders each. It makes 3 turns an hour. About how many riders can it carry in one hour?

    Show your work

    Hint First find the riders for one turn. Then use the turns in one hour.

    Final answer:
  6. 6Complete each step, then write the final answer.
    Percent100%50%Amount57?÷ ?÷ ?
    100% is the whole: 57.

    What is 50% of 57?

    Show your work

    Hint 50% means half. Split 57 into 2 equal parts.

    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help