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.

Start hereWords for this lesson

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

Word	What it means	Example
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?

Find the riders in a full hour: 80 × 6 = 480
Scale 100% down to 25%: ÷ 4: 480 ÷ 4 = 120
Check a second way: start with one turn: 80 ÷ 4 = 20; 20 × 6 = 120
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 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 10.610.6 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

1Complete each step, then write the final answer.
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:
2Complete each step, then write the final answer.
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:
3Complete each step, then write the final answer.

25% of the number is 45.5.
45.5 is 25% of what number?
Show your work
Final answer:
4Complete each step, then write the final answer.

Bridge through 10% to reach 20%.
Find 20% of 345.
Show your work
Final answer:
5Complete each step, then write the final answer.

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:
6Complete each step, then write the final answer.

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.

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