Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step. 🔊 Listen 💡 Hint

   Try it together — then prove it:

   1. A wire is 4 yards long. How many feet long is it? Use 1 yard = 3 feet.
   2. Find the scale factor from 1 yard to 4 yards. (4)
   3. Multiply 3 feet by 4. How many feet? (12 feet)
   4. Why do we multiply to change yards to feet? (A foot is shorter than a yard. It takes more feet to make the same length.)

   Show your work
2. 2

   Quick reviewWhich ratio is equivalent to 8:12? 🔊 Listen 💡 Hint

   1. A2:3
   2. B4:8
   3. C8:16
   4. D12:8

   How do you know?
3. 3

   Quick reviewFill in the missing value: 5:9 = 20:___ 🔊 Listen 💡 Hint

   1. A24
   2. B32
   3. C36
   4. D45

   How do you know?
4. 4

   Quick reviewA ratio table shows 7:4 and 21:12. What was each part of 7:4 multiplied by? 🔊 Listen 💡 Hint

   1. A3
   2. B4
   3. C7
   4. D14

   How do you know?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughHow many inches are in 1 foot? 🔊 Listen 💡 Hint

   1. A10
   2. B12
   3. C16
   4. D36

   Why is that the answer?
2. 6

   Think it throughHow many inches tall is the 7-foot cabinet? 🔊 Listen 💡 Hint

   1. A19
   2. B70
   3. C82
   4. D84

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

   Think it throughWill the cabinet fit through the 80-inch doorway? 🔊 Listen 💡 Hint

   1. ANo, because 84 > 80
   2. BYes, because 84 < 80
   3. CYes, because 7 feet is small
   4. DYou cannot tell without the width

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

   Back to the modelHow do you decide whether to multiply or divide when converting units? 🔊 Listen 💡 Hint

Use the words

Fill each blank with a word from the bank.

• A ratio equal to 1 that relates two units, like 12 inches / 1 foot, is a ___.
• A standard amount used to measure, like a foot or a gram, is a ___.
• Two measurements that name the same amount, like 1 foot and 12 inches, are ___.
• A comparison of two quantities is a ___.

Explain the thinking

1. 9

   Find the mistakeRead the mistake. Explain what went wrong, then show the correct step. 🔊 Listen 💡 Hint

   The mistake: A common mistake in Convert Measurement Units is applying the conversion factor in the wrong direction — for example, converting 4 feet to inches by dividing (4 ÷ 12 = 0.
2. 10

   Say moreHow did you use a conversion factor like '1 ft = 12 in' to fill in the ratio table, and how did you decide whether to multiply or divide? 🔊 Listen 💡 Hint
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Evelyn is visiting family in Canada. The highway sign she sees says 100 kilometers per hour, and she is used to speed limits posted in miles per hour. 🔊 Listen 💡 Hint

   Show your work

Last check

These two come from Lesson 3.9. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Which is the correct conversion of 5 yards to inches? 🔊 Listen 💡 Hint

   1. A15 inches
   2. B60 inches
   3. C180 inches
   4. D540 inches

   Explain your choice.
2. 13

   From Lesson 3.9Explain your thinking — A store sells 5 notebooks for $8. At this rate, how much would 15 notebooks cost? 🔊 Listen 💡 Hint

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

   How do you know?
3. 14

   From Lesson 3.9Why must both ingredients be multiplied by the same factor? 🔊 Listen 💡 Hint

   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

   How do you know?

Check your progress

Choose the box that best describes how you feel about each skill.