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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. Use a scale factor of 3 to make an equivalent ratio. Multiply the first number by 3. What is it? (6) Multiply the second number by 3. What is it? (15) Jay adds 3 to each number and gets 5:8. Why is that not equivalent? (Multiplying by 3 makes 3 copies of 2:5. Adding 3 to each number does not make copies, so the comparison changes.)

   Show your work
2. 2

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

   1. A7.5 pages
   2. B30 pages
   3. C34 pages
   4. D120 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. A6 minutes
   2. B9 minutes
   3. C12 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. A2.4 cups
   2. B4 cups
   3. C5 cups
   4. D6 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. A3
   2. B5
   3. C12
   4. D45

   Why is that the answer?
2. 6

   Think it throughHow many cups of strawberries are needed?

   1. A5
   2. B10
   3. C12
   4. D15

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

   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$18
   2. B$20
   3. C$24
   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. A30 miles per gallon
   2. B32.5 miles per gallon
   3. C33 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, 20 minutes
   3. CPrinter B, 24 minutes
   4. DPrinter A, 24 minutes

   How do you know?

Be honest — this tells your teacher what to do next