Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3a

Lesson 3.43.4 Small Group · Group 2

Group 2 · Set BSecond challenge form · new problems, same idea

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target 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.

Why This Matters This is your challenge small group for Lesson 3.4. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

Remember3.4 Small Group · Group 2

On a graph of equivalent ratios, y divided by x is the same for every point, and the line passes through the origin. Every point on a graph of equivalent ratios has the same unit rate, so we can test if a point belongs.

Words: Coordinate plane (Plano cartesiano)Ordered pair (Par ordenado)Linear pattern (Patrón lineal)Proportional (Proporcional)Origin (Origen)

  1. 1Complete each step, then write the final answer.
    x-valuey-value________________________

    The points (2, 6) and (4, 12) are on a graph of equivalent ratios. What y-value goes with x = 7?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.
    x-valuey-value________________

    The points (3, 6) and (5, 10) are on a graph of equivalent ratios. What is the y-value when x = 9?

    Show your work
    Final answer:
  3. 3Circle the letter of the best answer. Show how you know.
    01234567123456789101112Apples (lb)Cost ($)(0, 0)(2, 3)
    Find the cost of 1 pound, then test each point.

    A store's graph shows pounds of apples as x and cost in dollars as y. It goes through (0, 0) and (2, 3). Which point is also on the graph?

    1. A(6, 9)
    2. B(4, 5)
    3. C(3, 4)
    4. D(5, 6)
    Show your work
  4. 4Complete each step, then write the final answer.
    x-valuey-value________________________________
    Line A: first two columns. Line B: last two.

    Two lines go through (0, 0). Line A goes through (4, 6). Line B goes through (6, 8). At x = 12, how much greater is the y-value of line A than line B?

    Show your work
    Final answer:

Explain your thinkingHow can you tell if a point is on a graph of equivalent ratios without drawing it? Use (8, 27) to explain.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help