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: On a graph of equivalent ratios, y divided by x is the same for every point, and the line passes through the origin.

Model to copy — Example · Does the point belong?

  1. The points (2, 5) and (4, 10) are on a graph of equivalent ratios. Is the point (6, 14) on the same line?
  2. Write the point (2, 5) in the table.
  3. Find the scale factor from 2 to 6: 6 ÷ 2 = 3
  4. Multiply y by the same factor: 5 × 3 = 15
  5. Compare it with the point (6, 14): 14 ≠ 15
  6. No. For x = 6, the line has y = 15. The point (6, 14) is not on the line.

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. Sugar is x and flour is y. Write and plot the ordered pairs. What scale factor takes 1 cup of sugar to 2 cups? (2) Multiply the flour by 2. How many cups of flour? (6) Write the ordered pairs for 1, 2 and 3 cups of sugar. ((1, 3), (2, 6), (3, 9)) Why does the line go through (0, 0)? (0 cups of sugar goes with 0 cups of flour. Zero times 3 is still zero.)
    Show your work
  2. 2

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

    1. A5:10
    2. B6:12
    3. C6:15
    4. D8:15

    How do you know?

  3. 3

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

    1. A6:10
    2. B8:10
    3. C12:15
    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. A7.5 oz
    2. B17 oz
    3. C20 oz
    4. D30 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(5, 12)
    3. C(6, 12)
    4. D(10, 20)

    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

Coordinate plane (Plano cartesiano)Ordered pair (Par ordenado)Linear pattern (Patrón lineal)Proportional (Proporcional)Origin (Origen)Ratio table (Tabla de razones)Unit rate point (Punto de tasa unitaria)

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(4, 6)
    2. B(5, 10)
    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. A7
    2. B8
    3. C10
    4. D12

    How do you know?

  3. 14

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

    1. A5:4
    2. B6:4
    3. C9:6
    4. D30:20

    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: On a graph of equivalent ratios, y divided by x is the same for every point…
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