6.AT.1 Group 2 · Challenge

Practice Set · Part 1

Understand Ratios

Pick up where we left off

Name: Date: Group:

Where we left off

Our goal: I can write and describe a ratio that compares two quantities, explain what each part stands for, and build one for a situation I have not seen before.

The big idea: A ratio compares two quantities, and the order you write them in matters. You can write a ratio in words or with a colon, and you can draw it with a tape diagram or a double number line — and you can say why it is true, and where it would stop being true.

Model to copy — Watch me

  1. Chef Reyes uses 3 cups of apple juice for every 2 cups of sparkling water.
  2. I am comparing two amounts: apple juice and sparkling water.
  3. I write apple juice to sparkling water, in that order, as 3 to 2, or 3:2.
  4. I can also draw the ratio. On a tape diagram I give apple juice 3 equal parts and sparkling water 2 equal parts, so one batch is 5 parts in all.
  5. Those same 5 parts show a second ratio: apple juice to the whole fruit drink is 3 to 5.
  6. On a double number line I line the two amounts up: 5 cups of fruit drink pairs with 3 cups of apple juice, and 10 cups of fruit drink pairs with 6 cups of apple juice.

Start here

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. What two amounts are we comparing? We write apples to oranges in order: 4 to 1, or 4:1. Now draw it: 4 equal parts for apples beside 1 part for oranges, 5 parts of fruit in all. So apples to total fruit is 4 to 5. Now prove it: say why that move had to work at all — not just that it did.
    Show your work
  2. 2

    Warm restartWhat is the reciprocal of 3/4?

    1. A4/3
    2. B3/4
    3. C1/4
    4. D7/4

    How do you know?

  3. 3

    Warm restartWhat is 4 ÷ 1/2?

    1. A8
    2. B2
    3. C4 1/2
    4. D1/8

    How do you know?

  4. 4

    Warm restartWhat is 3/4 ÷ 1/2?

    1. A3/8
    2. B1 1/2
    3. C2/3
    4. D1/2

    How do you know?

3.1 Small Group · Group 2 · Practice SetPart 1 of 4
6.AT.1 Group 2 · Challenge

Practice Set · Part 2

Understand Ratios

Keep going

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. A15
    2. B12
    3. C5
    4. D20

    Why is that the answer?

  2. 6

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

    1. APart-to-part, because it compares two separate groups
    2. BPart-to-whole, because it compares mains to all dishes
    3. CA rate, because it uses different units
    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. A3 to 5
    2. B3 to 2
    3. C15 to 10
    4. D2 to 5

    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?

3.1 Small Group · Group 2 · Practice SetPart 2 of 4
6.AT.1 Group 2 · Challenge

Practice Set · Part 3

Understand Ratios

Words and reasoning

Word bank · Banco de palabras

Understand Ratios (Comprender razones)Ratio (Razón)Comparison (Comparación)Part-to-part (Parte a parte)Part-to-whole (Parte a todo)Colon notation (Notación con dos puntos)Tape diagram (Diagrama de cintas)Double number line (Recta numérica doble)

Use the words

Fill each blank with a word from the bank.

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
3.1 Small Group · Group 2 · Practice SetPart 3 of 4
6.AT.1 Group 2 · Challenge

Practice Set · Part 4

Understand Ratios

Show what you know

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. B8:5
    3. C5:8
    4. D13:5

    Explain your choice.

  2. 13

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

    1. A10.58
    2. B105.8
    3. C1.058
    4. D10.48

    How do you know?

  3. 14

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

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

    How do you know?

Be honest — this tells your teacher what to do next

I can…Not yetGetting thereGot it
I can write and describe a ratio that compares two quantities, explain what each part stands for, and build one for a situation I have not seen before.
I can explain why it works: A ratio compares two quantities, and the order you write them in matters…
I can justify my answer to a skeptic and connect it to a second strategy or representation.

One question I want to ask my group next time