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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: A ratio is 2:5. We want to make it bigger using a scale factor of 3. Multiply both by 3: 2 x 3 = 6 and 5 x 3 = 15. So 2:5 and 6:15 are equivalent ratios. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartA printer prints 30 pages every minute. How many pages does it print in 4 minutes?

   1. A120 pages
   2. B34 pages
   3. C7.5 pages
   4. D30 pages

   How do you know?
3. 3

   Warm restartA faucet fills 3 gallons every 2 minutes. How long does it take to fill 18 gallons?

   1. A12 minutes
   2. B9 minutes
   3. C6 minutes
   4. D36 minutes

   How do you know?
4. 4

   Warm restartA recipe uses 3 cups of flour for 12 muffins. How much flour is needed for 20 muffins?

   1. A5 cups
   2. B6 cups
   3. C4 cups
   4. D2.4 cups

   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 throughWhat is the scale factor from 3 cups of yogurt to 15 cups?

   1. A5
   2. B12
   3. C45
   4. D3

   Why is that the answer?
2. 6

   Think it throughHow many cups of strawberries are needed?

   1. A10
   2. B12
   3. C15
   4. D5

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

   Think it throughWhy must both ingredients be multiplied by the same factor?

   1. ASo the ratio stays 2:3 and the smoothie tastes the same
   2. BBecause 2 and 3 are both small numbers
   3. CBecause addition would be harder
   4. DSo the total is a whole number

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

   Back to the modelHow did you find the missing values in Chef Montoya's table? How can you PROVE two of your rows are equivalent ratios?

Use the words

Fill each blank with a word from the bank.

• Ratios that compare quantities in the same relationship are ___ ___.
• A comparison of two quantities is a ___.
• A ratio that compares two quantities with different units, like miles per hour, is a ___.
• An equation showing that two ratios are equal is a ___.

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 Equivalent Ratios is ADDING the scale factor to one part instead of MULTIPLYING both parts by it.
2. 10

   Say moreLooking at the tomatoes-to-broth table (3:2, 6:4, 9:6, 12:8), how can you PROVE these ratios are all equivalent?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Chef Kowalski's spice mix uses 3 teaspoons of paprika for every 5 teaspoons of cumin. For a bigger batch she measures out 18 teaspoons of paprika and 30 teaspoons of cumin.

   Show your work

Last check

These two come from Lesson 3.8. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A store sells 5 notebooks for $8. At this rate, how much would 15 notebooks cost?

   1. A$24
   2. B$18
   3. C$20
   4. D$40

   Explain your choice.
2. 13

   From Lesson 3.8Explain your thinking — A car travels 195 miles on 6 gallons of gas. What is the unit rate in miles per gallon?

   1. A32.5 miles per gallon
   2. B33 miles per gallon
   3. C30 miles per gallon
   4. D1,170 miles per gallon

   How do you know?
3. 14

   From Lesson 3.8Which printer is faster, and how long for 600 tickets?

   1. APrinter A, 20 minutes
   2. BPrinter B, 24 minutes
   3. CPrinter B, 20 minutes
   4. DPrinter A, 24 minutes

   How do you know?

Be honest — this tells your teacher what to do next