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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: Store A sells 2 pens for $6. Store B sells 3 pens for $12. Which store has the better deal? Divide Store A's table by 2. What does 1 pen cost? ($3, because $6 ÷ 2 = $3.) Divide Store B's table by 3. What does 1 pen cost? ($4, because $12 ÷ 3 = $4.) Why compare the price for 1 pen, not the total prices? (The stores sell different numbers of pens. The price for 1 pen makes the comparison fair.)

   Show your work
2. 2

   Warm restartA ratio table for 3:2 gives the points (3, 2) and (6, 4). Which point also lies on the same graph?

   1. A(2, 3)
   2. B(8, 6)
   3. C(9, 6)
   4. D(9, 5)

   How do you know?
3. 3

   Warm restartThe graph of a set of equivalent ratios always passes through which point?

   1. A(0, 0)
   2. B(0, 1)
   3. C(1, 1)
   4. D(1, 0)

   How do you know?
4. 4

   Warm restartOn a graph of cups of juice (x) to cups of water (y), the point (4, 10) is plotted. What ratio does that point show?

   1. A4:10
   2. B4:14
   3. C10:4
   4. D14:10

   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 Mario's price per pizza?

   1. A$4.50
   2. B$8.33
   3. C$9.00
   4. D$18.00

   Why is that the answer?
2. 6

   Think it throughWhat is Sal's price per pizza?

   1. Aabout $7.50
   2. Babout $8.33
   3. Cabout $9.00
   4. Dabout $12.50

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

   Think it throughWhich shop is the better deal?

   1. AMario's, because $18 is less than $25
   2. BMario's, because 2 is less than 3
   3. CSal's, because $8.33 per pizza is less than $9.00
   4. DThey cost the same

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

   Back to the modelThe two recipes use different amounts, so you cannot compare them directly. How did building equivalent ratios let you compare them fairly?

Use the words

Fill each blank with a word from the bank.

• A rate that tells the amount for exactly one unit, like 5 miles per 1 hour, is a ___.
• Two ratios that make the same comparison are ___ ___.
• To decide which ratio is greater or if they are equal is to ___ them.
• Writing a ratio with smaller numbers that compares the same way, like 6:9 = 2:3, is to ___ it.

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 Compare Ratios is thinking the ratio with the bigger raw number automatically wins — like assuming Chef Tran's 8 tablespoons of cocoa must be more chocolatey than Chef Reyes's 6 tablespoons, without checking that the milk amounts (14 oz vs.
2. 10

   Say moreYou scaled both recipes to 35 oz of milk: Chef Reyes became 21:35 and Chef Tran became 20:35. How does scaling to a common denominator let you compare the recipes fairly?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Two chefs each mixed cocoa and milk to make the cups of hot cocoa shown. Each used a different ratio of cocoa to milk.

   Show your work

Last check

These two come from Lesson 3.4. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A bakery sells 4 muffins for $10 and another bakery sells 6 muffins for $14. Which bakery has the lower price per muffin?

   1. AThe first bakery
   2. BSame price
   3. CCannot determine
   4. DThe second bakery

   Explain your choice.
2. 13

   From Lesson 3.4Explain your thinking — A ratio table shows cups of rice to cups of water: (1, 2), (2, 4), (3, 6). If you plot these points, the line passes through which point?

   1. A(4, 6)
   2. B(5, 10)
   3. C(5, 8)
   4. D(6, 10)

   How do you know?
3. 14

   From Lesson 3.4Which point would NOT be on this line?

   1. A(4, 8)
   2. B(5, 12)
   3. C(6, 12)
   4. D(10, 20)

   How do you know?

Be honest — this tells your teacher what to do next