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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: Let's change 1/5 into a fraction out of 100, then a decimal and a percent. What do we multiply the denominator 5 by to get 100? (20) Now multiply the numerator by that same 20: 1 × 20 = ? (20) So 1/5 = 20/100. 20 out of 100 is what percent? (20%) And as a decimal? (0.2) Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartOn a 100-square grid, 37 squares are shaded. What percent of the grid is shaded?

   1. A37%
   2. B0.37%
   3. C63%
   4. D3.7%

   How do you know?
3. 3

   Warm restartPercent means 'per ___'.

   1. A100
   2. B10
   3. C1
   4. D1,000

   How do you know?
4. 4

   Warm restartA tape diagram is split into 4 equal parts and 3 parts are shaded. What percent is shaded?

   1. A75%
   2. B34%
   3. C43%
   4. D30%

   How do you know?

You answered these out loud. Now write them.

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

1. 5

   Think it through'3/5 off' means 3 of the 5 equal parts come off the price. Which friend is right?

   1. AThe friend who said 35% off
   2. BThe friend who said 60% off
   3. CBoth are the same amount
   4. DNeither — 3/5 is not a percent

   Why is that the answer?
2. 6

   Think it throughWrite 3/5 as a decimal.

   1. A0.35
   2. B0.6
   3. C3.5
   4. D0.53

   How do you know? Give a second reason as well.
3. 7

   Think it throughThe game costs $40 and 3/5 comes off. How much is taken off?

   1. A$14
   2. B$24
   3. C$16
   4. D$35

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelWhat number did you multiply by to turn each denominator into 100, and how did that fraction out of 100 give you the percent?

Use the words

Fill each blank with a word from the bank.

• Three equivalent ways to name the same part of a whole are ___, ___ and ___.
• A ratio that compares a number to 100, written with a % sign, is a ___.
• A number that uses a point to show parts of a whole is a ___.
• Having the same value but written a different way is being ___.

Explain the thinking

1. 9

   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: A common mistake in Relate Fractions, Decimals, and Percents is treating the numerator and denominator as the percent's digits — turning 3/5 into "35%" by just reading the 3 and the 5.
2. 10

   Say moreHow did you turn a fraction like 3/5 into a fraction out of 100, and then into a decimal and a percent?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Some middle school students are running a canned food drive. Their goal is to collect 100 cans each week for the local food pantry. So far this week, students have brought in 75 cans.

   Show your work

Last check

These two come from Lesson 4.1. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain 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%

   Explain your choice.
2. 13

   From Lesson 4.1Explain your thinking — Four out of every ten voters chose the tiger. What percent chose the tiger, and how do you know?

   1. A40%, because 4 out of 10 equals 40 out of 100
   2. B4%, because 4 voters chose the tiger
   3. C10%, because the ratio is out of 10
   4. D14%, because 4 + 10 = 14

   How do you know?
3. 14

   From Lesson 4.1A percent of 150% tells you the amount is…

   1. A1.5 times the whole
   2. BHalf the whole
   3. C150 items
   4. DImpossible

   How do you know?

Be honest — this tells your teacher what to do next