Grade 6 Mathematics · Unit 9: Relationships Between Two VariablesStandard 6.AT.11

Lesson 9.19.1 Small Group · Group 1

Group 1 · Set BSecond form · new problems, same idea

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Learning target With my small group, I can recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable — one step at a time, with support.

Remember9.1 Small Group · Group 1

Ask who chooses: the chosen quantity is the independent variable, and the quantity that responds is the dependent variable. The independent variable is the quantity someone chooses. The dependent variable changes because of that choice.

Words: independent variable (variable independiente)dependent variable (variable dependiente)depends on (depende de)quantity (cantidad)relationship (relación)

  1. 1Complete each step, then write the final answer.

    Sam chooses how many hours to work. He earns money for each hour. Which quantity is the dependent variable: hours worked or money earned?

    Show your work

    Hint Which quantity does Sam choose? The other quantity is the dependent variable.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Nora chooses how many laps to swim. She records her time. Is the time independent or dependent?

    Show your work

    Hint Nora chooses one quantity. The other one responds.

    Final answer:
  3. 3Circle the letter of the best answer. Show how you know.

    Water flows into a tank. You choose how many minutes the water runs. Which sentence is correct?

    1. AThe gallons in the tank depend on the minutes.
    2. BThe minutes depend on the gallons in the tank.
    3. CThe minutes and the gallons do not change together.

    Hint Which quantity do you choose? Put it after the words "depend on".

    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    Ana decides to earn exactly $30 babysitting. She records how many hours it takes. Which is the independent variable this time?

    1. AThe money Ana decides to earn
    2. BThe hours it takes
    3. CNeither one changes

    Hint Read carefully. What does Ana decide first?

    Show your work

Explain your thinkingWhat question can you ask to find the independent variable in any story? Use Ravi's piano practice to explain.

Sentence starter I ask: which quantity ___? · The score depends on ___ because ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help