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

Lesson 10.610.6 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can look back at my answers from Lesson 1-1, describe how my math biography has changed this year, and recognize ways we are all doers of math, 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 10.6. 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
math biographySpanish: biografía matemática The story of your relationship with math — and how it has changed over time. September: “I am not a math person.” June: “I can explain why it works.”
reflectSpanish: reflexionar To look back at what you did, felt, and learned, and think about what it means. Looking back at the tram problem: what worked, what you would change.
growthSpanish: crecimiento The change between what you could do before and what you can do now. In Unit 1 you estimated 80 riders; now you find 480 riders per hour.
confidenceSpanish: confianza Trusting yourself to try a problem, even when the first attempt might fail. Starting a hard problem before you are sure it will work.
communitySpanish: comunidad The people and places around you — where math shows up outside the classroom. The people and places where math shows up — home, work, the neighborhood.

How it worksWorked example

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

A Ferris wheel carries about 80 riders per turn and makes 6 turns an hour. On a rainy day, it is only 25% full. About how many riders ride in one hour?

  1. Find the riders in a full hour: 80 × 6 = 480
  2. Scale 100% down to 25%: ÷ 4: 480 ÷ 4 = 120
  3. Check a second way: start with one turn: 80 ÷ 4 = 20; 20 × 6 = 120
  4. About 120 riders ride in one hour on a rainy day.

Now you trySame steps, your turn

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

In September, we wrote 78.5 = 70 + 8.5 and 78.5 = 80 − 1.5. Use this year's tools to write 78.5 in new ways. Then explain why two of them match.

Answer:

Say it and write itSentence starters

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

Word bank math biographyreflectgrowthconfidencecommunity

Watch out!A common mistake

Treating your math story as finished

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

Lesson 10.610.6 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can look back at my answers from Lesson 1-1, describe how my math biography has changed this year, and recognize ways we are all doers of math, 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 10.6. 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.
    Percent100%25%Riders per turn72?÷ ?÷ ?
    A full turn is 100%: about 72 riders.

    A Ferris wheel carries about 72 riders per turn and makes 5 turns an hour. On a windy day it is only 25% full. About how many riders ride in one hour?

    1. 1What do you divide 100% by to get 25%?
    2. 2Do the same to 72. How many riders per turn at 25%?
    3. 3Multiply by 5 turns. About how many riders in one hour?
    4. 4Check a second way: find 25% of a full hour, 72 × 5.
    Final answer:
  2. 2Complete each step, then write the final answer.
    Percent75%25%100%Riders135??÷ ?÷ ?× ?× ?
    Bridge through 25% to reach 100%.

    On a cool night, the wheel carried 135 riders in one hour. That was 75% of a full hour. How many riders ride in a full hour?

    1. 1What do you divide 75% by to get 25%?
    2. 2Do the same to 135. How many riders is 25%?
    3. 3Multiply 25% by 4 to get 100%. How many riders is 100%?
    4. 4Why does 75% of 180 = 135 prove the answer?
    Final answer:
  3. 3Complete each step, then write the final answer.
    Percent25%100%Amount45.5?× ?× ?
    25% of the number is 45.5.

    45.5 is 25% of what number?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    Percent100%10%20%Amount345??÷ ?÷ ?× ?× ?
    Bridge through 10% to reach 20%.

    Find 20% of 345.

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    Percent100%25%75%Riders in 1 hour???÷ ?÷ ?× ?× ?
    Full hour first, then bridge through 25%.

    In September, a class estimated a Ferris wheel holds about 96 riders. It makes 6 turns an hour. On weekdays it is 75% full. About how many riders ride in one weekday hour?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    Percent100%10%40%Amount85??÷ ?÷ ?× ?× ?
    Bridge through 10% to reach 40%.

    Rosa says 40% of 85 is 34. Ben says it is 85 ÷ 4 = 21.25. Who is right? What is 40% of 85?

    Show your work
    Final answer:

Explain your thinkingWhy can you trust an answer more when two different methods agree? Use the windy-day Ferris wheel.

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