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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 is marked in milliliters. The conversion factor is 1,000 mL : 1 L. On a double number line, every 1 liter above matches 1,000 milliliters below. Milliliters are smaller, so multiply: 4 × 1,000 = 4,000. So 4 liters = 4,000 milliliters. Her bottle holds 500 milliliters. How many fills? Solve ? × 500 = 4,000. Since 8 × 500 = 4,000, she fills the bottle 8 times. Now prove it: say why that move had to work at all — not just that it did.

   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 B
   2. BRecipe A
   3. CThey are the same
   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. BThey use the same amount
   3. CCannot determine
   4. DChef B

   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. A48 inches
   2. B16 inches
   3. C3 inches
   4. D44 inches

   Why is that the answer?
2. 6

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

   1. A8
   2. B4
   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. ASmaller, because pounds are the larger unit
   2. BBigger, because 96 is already large
   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.

• Feet into inches stays inside the ___ measurement system.
• 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 ___.

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. A20 cups, because cups are smaller so I multiply: 5 × 4
   2. B1.25 cups, because I divide 5 by 4
   3. C9 cups, because I add 5 + 4
   4. D5 cups, because the amount does not change

   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 second bakery
   2. BThe first bakery
   3. CSame price
   4. DCannot determine

   How do you know?
3. 14

   From Lesson 3.5Which shop is the better deal?

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

   How do you know?

Be honest — this tells your teacher what to do next