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: Sheng's car is now worth $26,600. That is 70% of what his parents paid for it. What did they pay for the car? What amount goes with 70% in the first column? (26,600) Divide both by 7. What amount matches 10%? (3,800) What do you multiply 10% by to reach 100%? (× 10) Do the same to the other row. What is the whole? (38,000) Why must the price they paid be more than $26,600? ($26,600 is only 70% of the price. The whole is 100%, so it must be bigger.)

   Show your work
2. 2

   Warm restartWhat is 10% of 320?

   1. A3.2
   2. B32
   3. C64
   4. D320

   How do you know?
3. 3

   Warm restartWhat is 50% of 84?

   1. A34
   2. B42
   3. C50
   4. D168

   How do you know?
4. 4

   Warm restartWhat is 20% of 150?

   1. A20
   2. B30
   3. C35
   4. D75

   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$42 is 60% of the original price. What was the original price?

   1. A$25.20
   2. B$60
   3. C$70
   4. D$102

   Why is that the answer?
2. 6

   Think it throughWhich equation finds the whole when 75 minutes is 15% of the school day?

   1. A0.15d = 75
   2. Bd = 0.15 × 75
   3. C75d = 0.15
   4. Dd = 75 + 15

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

   Think it throughIf the percent given is less than 100%, the whole must be…

   1. ASmaller than the part
   2. BLarger than the part
   3. CEqual to the part
   4. DImpossible to find

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

   Back to the modelHow can you tell, before doing any arithmetic, whether the answer should be bigger or smaller than the number you were given?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• $42 is 60% of what number?
• What is 60% of $70?
• 75 minutes is 15% of the school day. How long is the day?
• 15% of a 500-minute day is how many minutes?
• A car worth $26,600 is 70% of its original price. What did it cost?
• What is 70% of $38,000?

Use the words

Fill each blank with a word from the bank.

• How much of the base you get — your answer — is the ___.
• The full amount a percent is measured against is always ___%.
• Two parallel lines pairing amounts with their percents form a ___ ___ ___.
• The percent number sentence is part = ___ × ___.

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 when finding the whole is multiplying by the percent instead of dividing.
2. 10

   Say moreTo find the whole when 60% is $42, one strategy finds 10% first. Why is 10% such a useful stepping stone, and how does it get you to 100%?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Three hundred middle school students voted for one of three snacks to add to the cafeteria menu, and the graph shows the PERCENT of students who chose each snack. Today the question runs the other way: if you knew only how many students picked one snack and what percent that was, could you work back to the total?

   Show your work

Last check

These two come from Lesson 4.4. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A sweater's sale price is $42, which is 60% of the original price. What was the original price?

   1. A$25.20, because 0.6 × 42 = 25.20
   2. B$60, because the percent is 60
   3. C$70, because 42 ÷ 0.6 = 70
   4. D$102, because 42 + 60 = 102

   Explain your choice.
2. 13

   From Lesson 4.4Explain your thinking — What is 45% of 360?

   1. A45
   2. B162
   3. C180
   4. D315

   How do you know?
3. 14

   From Lesson 4.4Check with a benchmark: what is 10% of 1,500?

   1. A1.5
   2. B15
   3. C100
   4. D150

   How do you know?

Be honest — this tells your teacher what to do next