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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 bowl has 4 apples and 1 orange. Write the ratio of apples to oranges and the ratio of apples to all the fruit. Write the ratio of apples to oranges. (4:1) Fill the Total row. Write the ratio of apples to all the fruit. (4:5) Both ratios start with 4. Why is the second number different? (4:1 compares a part to a part. 4:5 compares a part to the whole bowl.)

   Show your work
2. 2

   Warm restartWhat is the reciprocal of 3/4?

   1. A1/4
   2. B3/4
   3. C4/3
   4. D7/4

   How do you know?
3. 3

   Warm restartWhat is 4 ÷ 1/2?

   1. A1/8
   2. B2
   3. C4 1/2
   4. D8

   How do you know?
4. 4

   Warm restartWhat is 3/4 ÷ 1/2?

   1. A1 1/2
   2. B1/2
   3. C2/3
   4. D3/8

   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 throughKeeping the 3:2 ratio, how many main dishes go with 10 side dishes?

   1. A5
   2. B12
   3. C15
   4. D20

   Why is that the answer?
2. 6

   Think it throughWhat kind of ratio is 3 mains to 2 sides?

   1. APart-to-whole, because it compares mains to all dishes
   2. BA rate, because it uses different units
   3. CPart-to-part, because it compares two separate groups
   4. DNot a ratio at all

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

   Think it throughWith 15 mains and 10 sides, what is the ratio of mains to TOTAL dishes?

   1. A2 to 5
   2. B3 to 5
   3. C3 to 2
   4. D15 to 10

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

   Back to the modelWhat makes something a ratio? How did you decide which statements to sort into each group?

Use the words

Fill each blank with a word from the bank.

• A comparison of two quantities, like 3 to 5, is a ___.
• Showing how two amounts relate to each other is a ___.
• A ratio that compares one part of a group to another part is a ___ ratio.
• A ratio that compares one part of a group to the total is a ___ ratio.

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 Understand Ratios is writing the ratio in the wrong order: when asked for the ratio of apple juice to sparkling water in a recipe that uses 3 cups of apple juice for every 2 cups of sparkling water, some students write 2:3 (sparkling water to apple juice) because they list the ingredients in whatever order comes to mind rather than the order the question asks for.
2. 10

   Say moreWhen you sorted the board statements, what made something a ratio instead of NOT a ratio (like '12 cookies on the tray')?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The recipe card shows the ingredients needed to make one batch of sparkling cranberry-apple fruit drink.

   Show your work

Last check

These two come from Lesson 2.12. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A bag of trail mix contains 8 peanuts and 5 raisins. What is the ratio of raisins to total pieces?

   1. A5:13
   2. B5:8
   3. C8:5
   4. D13:5

   Explain your choice.
2. 13

   From Lesson 2.12Explain your thinking — What is 4.6 × 2.3?

   1. A1.058
   2. B10.48
   3. C10.58
   4. D105.8

   How do you know?
3. 14

   From Lesson 2.12A student answered $238.00. What went wrong?

   1. AThey added instead of multiplying
   2. BThey rounded too early
   3. CThey used the wrong price
   4. DThey put the decimal point in the wrong place

   How do you know?

Be honest — this tells your teacher what to do next