Start here

You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: The Green-Team recycled 216 pounds of material; 8.6% was metal. Round both: 8.6% is about 10%, and 216 is about 220. 10% of 220 = 0.1 × 220 = 22. About 22 pounds of metal. Compatible numbers work too: 10% of 200 = 20. Both estimates agree — around 20 pounds. Now prove it: say why that move had to work at all — not just that it did.

   Show your work

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 2

   Think it throughFor the question 'of the USED storage, what percent are photos,' what is the whole (100%)?

   1. A4 GB, the used storage
   2. B6 GB, the total storage
   3. C3.5 GB, the photos themselves
   4. D10 GB, adding the total and used storage together

   Why is that the answer?
2. 3

   Think it throughOn a double number line built for a whole of 4 GB, what amount lines up with the 75% mark?

   1. A3 GB
   2. B4.5 GB
   3. C3.5 GB
   4. D1 GB

   How do you know? Give a second reason as well.
3. 4

   Think it throughPhotos take up 3.5 of the 4 GB of used storage. About what percent of the used storage is photos?

   1. AAbout 87%
   2. BAbout 58%
   3. CAbout 35%
   4. DAbout 99%

   Explain your thinking. What would have to change for a different choice to be right?
4. 5

   Back to the modelMargaret's phone has 6 GB total and 4 GB used. On the double number line, 4 GB lands between the 50% mark (3 GB) and the 75% mark (4.5 GB), closer to 4.5. Why does that make 'about 70%' a reasonable estimate instead of an exact one?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• Treating 24% as 25% because quarters are easy
• Changing 216 pounds to 200 pounds to divide easily
• Using 10% of a number and scaling from there
• Swapping 81 for 80 before multiplying
• Placing 4 GB between the 50% and 75% marks
• Using 10% and 200 for 8.6% of 216

Use the words

Fill each blank with a word from the bank.

• A reasoned answer close enough to be useful is an ___.
• A friendly percent used as a landmark, like 10% or 25%, is a ___ ___.
• Numbers close to the originals that are easy to compute with are ___ ___.
• Two parallel lines pairing amounts with their percents form a ___ ___ ___.

Explain the thinking

1. 6

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: Keeping the same whole for every question — when the problem says 'of the used storage,' the whole changes from 6 GB to 4 GB, and estimates anchored to the old whole are wrong before any arithmetic happens.
2. 7

   Say moreYou sorted moves like 'treating 24% as 25%' and 'changing 216 pounds to 200 pounds' into benchmark percent versus compatible numbers. What's the difference between those two strategies?
3. 8

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A phone's storage screen shows a bar nearly full: 6 GB total, with photos taking the biggest colored stripe and small slivers for mail, messages, and documents.

   Show your work

Last check

These two come from Lesson 4.2. If they are shaky, that is the lesson to revisit — not this one.

1. 9

   Show what you knowExplain your thinking — Estimate 19% of 412 using benchmarks or compatible numbers.

   1. AAbout 80
   2. BAbout 8
   3. CAbout 200
   4. DAbout 40

   Explain your choice.
2. 10

   From Lesson 4.2Explain your thinking — Which shows 0.45 as a fraction and a percent?

   1. A9/20 and 45%
   2. B45/10 and 4.5%
   3. C4/5 and 45%
   4. D9/20 and 4.5%

   How do you know?
3. 11

   From Lesson 4.2So what do you actually pay for the game?

   1. A$16
   2. B$24
   3. C$26
   4. D$40

   How do you know?

Be honest — this tells your teacher what to do next