Grade 6 Mathematics · Pre-UnitStandard MPP.3

Lesson 1.61.6 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can describe my problem-solving process, name strategies for getting unstuck, and identify the behaviors that make our class a community of math thinkers, explain how I can tell, and judge a case I have not seen before.

Why This Matters This is your challenge small group for Lesson 1.6. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

Start hereWords for this lesson

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

WordWhat it meansExample
representationSpanish: representación A way of showing a problem — a drawing, table, equation, or model — that helps you see it. The same 12 shown three ways: a tape diagram, a table, and 3 × 4.
strategySpanish: estrategia A plan of attack for a problem — and something you can switch when you get stuck. “I will draw a tape diagram first, then divide” — chosen before computing.
critiqueSpanish: criticar constructivamente To examine an idea and say what is convincing or not — about the idea, never about the person. “That step assumes the boxes are full — how do we know?”
community agreementSpanish: acuerdo comunitario A rule the whole class agrees to so that everyone can learn together. “We take turns sharing, and we critique ideas, not people.”

How it worksWorked example

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

The big rack has 6 times as many wheels as the small rack. The big rack has 96 wheels. Every bike has 2 wheels. How many bikes are on the small rack?

  1. Make sense: name what you know and need.
  2. Divide to undo “6 times as many.”: 96 ÷ 6 = 16
  3. Divide by 2 wheels per bike: 16 ÷ 2 = 8
  4. Check by working forward: 8 × 2 = 16; 16 × 6 = 96
  5. The small rack holds 8 bikes.

Now you trySame steps, your turn

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

One rack holds 5 bikes. Each bike has 2 wheels. A bigger rack has 4 times as many wheels. How many wheels are on the bigger rack? Use get-unstuck moves.

Answer:

Say it and write itSentence starters

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

Word bank representationstrategycritiquecommunity agreement

Watch out!A common mistake

Treating 'stuck' as a stop sign instead of a signal

Grade 6 Mathematics · Pre-UnitStandard MPP.3

Lesson 1.61.6 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can describe my problem-solving process, name strategies for getting unstuck, and identify the behaviors that make our class a community of math thinkers, explain how I can tell, and judge a case I have not seen before.

Why This Matters This is your challenge small group for Lesson 1.6. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  1. 1Complete each step, then write the final answer.
    Big rack????56 wheelsSmall rack?
    56 wheels split into 4 equal groups.

    The big rack has 4 times as many wheels as the small rack. The big rack has 56 wheels. Every bike has 2 wheels. How many bikes are on the small rack?

    1. 1Undo “4 times as many”: 56 ÷ 4. How many wheels on the small rack?
    2. 2Divide by 2 wheels per bike. How many bikes?
    3. 3Check by working forward.
    Final answer:
  2. 2Complete each step, then write the final answer.
    Shelf B??????72 ballsShelf A?

    Shelf B has 6 times as many balls as Shelf A. Shelf B has 72 balls. Each box on Shelf A holds 3 balls. How many boxes are on Shelf A?

    1. 1How many balls are on Shelf A?
    2. 2How many boxes are on Shelf A?
    3. 3Lu wrote 72 − 6 = 66. Why is that wrong?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Box B has 5 times as many pens as Box A. Box B has 45 pens. How many pens are in Box A?

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

    Rack B has 6 times as many wheels as Rack A. Rack B has 108 wheels. Every bike has 2 wheels. How many bikes are on Rack A?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A big tank has 8 times as many fish as a small tank. The big tank has 96 fish. How many fish are in the small tank?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Rack B has 4 times as many wheels as Rack A. Rack B has 64 wheels. Eli says Rack A has 60 wheels. How many wheels does Rack A really have?

    Show your work
    Final answer:

Explain your thinkingHow do you decide to multiply or divide in a “times as many” problem? Use Eli's problem.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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