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.

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.

Lesson 10.4 — Math is Ingenuity: With each pedal rotation, the bicycle travels the length of the perimeter of the wheel. The front wheel is large so the bicycle travels a greater distance with one pedal rotation.

  1. Lesson 10.5 — Math is Boundless: Math can be used to create beautiful designs. These designs often have repetition, patterns, and rhythm — and the pattern unit lets you predict what comes next.
  2. Lesson 10.6 — Math is Mine: We are all doers of math and use math in our daily lives. Our math stories continue to grow and evolve as we grow and advance.

Now you trySame steps, your turn

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

From 10.4: The smallest rear gear has 12 teeth, and the pedal gear still turns 48 teeth per rotation.

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 outA common mistake

Treating your math story as finished — writing the same answers you wrote in Lesson 1-1 instead of looking for what actually changed. The story grows and evolves; a retrospective that copies September has missed the point.

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.

  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 10.4) On the Penny Farthing, what is the ratio of pedal rotations to front-wheel rotations?

    1. A1 to 1
    2. B1 to 2
    3. C1 to 4
    4. D2 to 1

    Hint The pedals are attached directly to the front wheel.

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    (Lesson 10.4) How far does the Penny Farthing travel with each pedal rotation?

    1. AThe height of the rider
    2. BThe length of the pedal
    3. CIt does not move a fixed distance
    4. DThe length of the perimeter of the front wheel

    Hint Picture the wheel rolling one full turn on the ground.

    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    (Lesson 10.5) In geometric design, what is repetition?

    1. AA set of different shapes arranged randomly
    2. BShapes that vary in size and order of appearance
    3. CThe same object or shape repeated multiple times
    4. DAny drawing that uses color

    Hint The word itself is a clue: something repeats.

    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    (Lesson 10.5) A border shows: pink circle, purple square, blue triangle, pink circle, purple square, blue triangle. What are the next three shapes?

    1. ABlue triangle, purple square, pink circle
    2. BPink circle, blue triangle, purple square
    3. CPink circle, purple square, blue triangle
    4. DIt is impossible to predict

    Hint Find the chunk that repeats.

    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    (Lesson 10.6) In Lesson 1-1 you estimated the Ferris wheel: 20 cars each holding about 4 people. About how many riders was that?

    1. AAbout 5
    2. BAbout 24
    3. CAbout 80
    4. DAbout 400

    Hint This is the very first estimate of the year — 20 groups of 4.

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