6.AT.3a Group 2 · Challenge

Practice Set · Part 1

Determine Equivalent Ratios Using Graphs

Pick up where we left off

Name: Date: Group:

Where we left off

Our goal: I can graph the values from a ratio table as points on the coordinate plane, explain what each part stands for, and build one for a situation I have not seen before.

The big idea: The points from equal ratios form a straight line that passes through the origin (0, 0) — and you can say why it is true, and where it would stop being true.

Model to copy — Watch me

  1. The recipe uses 2 ounces of sauce for every 1 sundae.
  2. I put sundaes on the x-axis and ounces of sauce on the y-axis.
  3. For 1 sundae I need 2 ounces, so I plot the ordered pair (1, 2): right 1, up 2.
  4. For 2 sundaes I need 4 ounces, so I plot (2, 4): right 2, up 4.
  5. When I connect (1, 2), (2, 4), (3, 6), they form a straight line through the origin (0, 0).

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 recipe uses 1 cup of sugar for every 3 cups of flour. For 1 cup of sugar, the ordered pair is (1, 3): right 1, up 3. For 2 cups of sugar, what is the pair? It is (2, 6): right 2, up 6. Now prove it: say why that move had to work at all — not just that it did.
    Show your work
  2. 2

    Warm restartA ratio table for 2:5 starts with 2:5, 4:10. What is the third row?

    1. A6:12
    2. B6:15
    3. C8:15
    4. D5:10

    How do you know?

  3. 3

    Warm restartWhich row does NOT belong in a ratio table for 4:5?

    1. A8:10
    2. B12:15
    3. C6:10
    4. D16:20

    How do you know?

  4. 4

    Warm restartA ratio table shows 3:7, 6:14, and 9:21. What is the next row?

    1. A10:24
    2. B12:24
    3. C12:28
    4. D15:28

    How do you know?

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

Practice Set · Part 2

Determine Equivalent Ratios Using Graphs

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 throughThe graph shows 1 taco uses 2 oz of salsa. How much salsa for 15 tacos?

    1. A30 oz
    2. B17 oz
    3. C7.5 oz
    4. D20 oz

    Why is that the answer?

  2. 6

    Think it throughWhy do the points form a straight line through (0, 0)?

    1. ABecause the quantities are proportional — the same ratio holds for every pair
    2. BBecause the owner sold the same number of tacos every day
    3. CBecause all graphs of data are straight
    4. DBecause salsa is measured in ounces

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

  3. 7

    Think it throughWhich point would NOT be on this line?

    1. A(4, 8)
    2. B(10, 20)
    3. C(6, 12)
    4. D(5, 12)

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

  4. 8

    Back to the modelWhat pattern do the plotted points make? How does the graph show the ratio of 1 sundae to 2 ounces of sauce?

3.4 Small Group · Group 2 · Practice SetPart 2 of 4
6.AT.3a Group 2 · Challenge

Practice Set · Part 3

Determine Equivalent Ratios Using Graphs

Words and reasoning

Word bank · Banco de palabras

Graph Ratio Tables (Representar tablas de razones en una gráfica)Coordinate plane (Plano cartesiano)Ordered pair (Par ordenado)Linear pattern (Patrón lineal)Proportional (Proporcional)Origin (Origen)Ratio table (Tabla de razones)

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 Graph Ratio Tables is writing the ordered pair in the wrong order — putting the second table value first instead of matching (x, y) to the table's column order.
  2. 10

    Say moreAfter plotting (1,2), (2,4), (3,6)... what pattern do you notice, and how does it show the chocolate-sauce ratio?

  3. 11

    Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Chef Reyes keeps a table for sundae sauce: 1 sundae takes 2 ounces of chocolate sauce, 2 sundaes take 4 ounces, and 3 sundaes take 6 ounces. She starts plotting the (sundaes, ounces) pairs on a coordinate grid.

    Show your work
3.4 Small Group · Group 2 · Practice SetPart 3 of 4
6.AT.3a Group 2 · Challenge

Practice Set · Part 4

Determine Equivalent Ratios Using Graphs

Show what you know

Last check

These two come from Lesson 3.3. If they are shaky, that is the lesson to revisit — not this one.

  1. 12

    Show what you knowExplain your thinking — A ratio table shows cups of rice to cups of water: (1, 2), (2, 4), (3, 6). If you plot these points, the line passes through which point?

    1. A(5, 10)
    2. B(4, 6)
    3. C(5, 8)
    4. D(6, 10)

    Explain your choice.

  2. 13

    From Lesson 3.3Explain your thinking — A salad dressing recipe uses 2 tablespoons of oil for every 5 tablespoons of vinegar. How many tablespoons of oil are needed for 20 tablespoons of vinegar?

    1. A8
    2. B10
    3. C7
    4. D12

    How do you know?

  3. 14

    From Lesson 3.3Which pair is NOT equivalent to 3:2?

    1. A9:6
    2. B6:4
    3. C30:20
    4. D5:4

    How do you know?

Be honest — this tells your teacher what to do next

I can…Not yetGetting thereGot it
I can graph the values from a ratio table as points on the coordinate plane, explain what each part stands for, and build one for a situation I have not seen before.
I can explain why it works: The points from equal ratios form a straight line that passes through the origin (0, 0)…
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