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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: Diamond wants to drink 4 liters of water. Her bottle holds 500 milliliters. How many times does she fill the bottle? What scale factor takes 1 liter to 4 liters? (4) Multiply 1,000 mL by 4. How many milliliters is that? (4,000 mL) How many times does she fill the 500 mL bottle? (8 times, because 4,000 ÷ 500 = 8.) Why must we change liters to milliliters before we divide? (The bottle is measured in milliliters. Both amounts must use the same unit. 4 ÷ 500 would mix two units.)

   Show your work
2. 2

   Warm restartRecipe A uses 2 lemons for 4 cups of water. Recipe B uses 3 lemons for 4 cups of water. Which recipe is more lemony?

   1. ARecipe A
   2. BThey are the same
   3. CRecipe B
   4. DYou cannot tell

   How do you know?
3. 3

   Warm restartWhich ratio is greater: 3:4 or 5:8?

   1. A5:8
   2. B3:4
   3. CThey are equal
   4. DCannot determine

   How do you know?
4. 4

   Warm restartChef A uses 2 cups of cheese for every 8 crackers. Chef B uses 3 cups of cheese for every 9 crackers. Who uses more cheese per cracker?

   1. AChef A
   2. BChef B
   3. CThey use the same amount
   4. DCannot determine

   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 throughHow many inches are in 4 feet?

   1. A3 inches
   2. B16 inches
   3. C44 inches
   4. D48 inches

   Why is that the answer?
2. 6

   Think it throughA bottle holds 500 milliliters. How many bottles make 4 liters?

   1. A4
   2. B8
   3. C500
   4. D2,000

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

   Think it throughYou convert 96 ounces to pounds (16 ounces = 1 pound). Should the number get bigger or smaller?

   1. ABigger, because 96 is already large
   2. BSmaller, because pounds are the larger unit
   3. CIt stays the same
   4. DYou cannot tell without the ratio table

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

   Back to the modelWhy does converting to a smaller unit always make the NUMBER bigger, even though the amount stays exactly the same?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• Feet → inches
• Inches → feet
• Liters → milliliters
• Milliliters → liters
• Pounds → ounces
• Ounces → pounds
• Quarts → cups
• Cups → quarts

Use the words

Fill each blank with a word from the bank.

• The ratio that trades one unit for another is a ___ ___.
• A ratio comparing an amount to exactly ___ unit is a unit ratio.
• To change a measurement to another unit without changing the amount is to ___.
• Inches and feet belong to the customary ___ ___; centimeters and meters to the metric one.

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 converting within a measurement system is choosing the operation by habit instead of by unit size — multiplying every time.
2. 10

   Say moreYou sorted ratio pairs into equivalent and not equivalent. How does ratio reasoning, like cross-multiplying, prove that 4:7 and 12:21 are equivalent?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Chef Reyes lines up two trays of vinaigrette at the tasting table. Tray A mixes 3 tablespoons of vinegar with 9 tablespoons of oil. Tray B mixes 5 tablespoons of vinegar with 15 tablespoons of oil.

   Show your work

Last check

These two come from Lesson 3.5. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — There are 4 cups in 1 quart. A soup recipe calls for 5 quarts of broth. How many cups is that, and why?

   1. A1.25 cups, because I divide 5 by 4
   2. B5 cups, because the amount does not change
   3. C9 cups, because I add 5 + 4
   4. D20 cups, because cups are smaller so I multiply: 5 × 4

   Explain your choice.
2. 13

   From Lesson 3.5Explain 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

   How do you know?
3. 14

   From Lesson 3.5Which 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

   How do you know?

Be honest — this tells your teacher what to do next