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

Lesson 9.19.1 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

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.

Why This Matters This is your support small group for Lesson 9.1. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
independent variableSpanish: variable independiente The quantity that is subject to choice. It does not depend on the other quantity. hours studied
dependent variableSpanish: variable dependiente The quantity that changes in response to the independent variable. quiz score
depends onSpanish: depende de One quantity depends on another when changing the first causes the second to change. Score depends on study time.
quantitySpanish: cantidad Something that can be counted or measured. minutes, dollars, laps
relationshipSpanish: relación How two quantities change together. more time → higher score
Table of valuesSpanish: Tabla de valores A list of matched input and output pairs. x: 2, 4 paired with y: 14, 28

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A bike rental costs $5 for each hour. Name the variables.

  1. The quantities are hours rented and total cost.
  2. Cost changes when hours change.
  3. “Total cost depends on hours rented” makes sense.

Answer: hours = independent; cost = dependent

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Claire burned 123 Calories on a 30-minute jog. She burned 246 Calories on a 60-minute jog. Which quantity is independent? Which is dependent?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The independent variable is because you it.
  • The dependent variable is because it .
  • depends on .
  • If the changes, then the changes in response.

Word bank independentdependentvariablequantitydepends oninputoutputcauserespondchoosechangesrelationship

Watch out!A common mistake

Naming the variables backward

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

Lesson 9.19.1 Small Group · Group 1

Group 1Supported practice

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

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.

Why This Matters This is your support small group for Lesson 9.1. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.

  1. 1Complete each step, then write the final answer.
    Pages readMinutes
    1015
    2030
    Dev's reading log.

    Dev chooses how many pages to read each night. He records how many minutes it takes. Which quantity is independent? Which is dependent?

    1. 1What are the two quantities?
    2. 2Which one does Dev choose: pages or minutes?
    3. 3Which one responds to his choice?
    4. 4Finish the sentence: ___ depends on ___.
    Final answer:
  2. 2Complete each step, then write the final answer.
    ApplesTotal cost ($)
    12
    36
    510

    Apples cost $2 each. Kim chooses how many apples to buy. Which quantity is independent? Which is dependent?

    1. 1Which quantity does Kim choose?
    2. 2Which quantity changes because of her choice?
    3. 3As the number of apples goes up, what happens to the cost?
    Final answer:
  3. 3Circle the letter of the best answer. Show how you know.

    Lin chooses how many dogs to walk. She earns money for each dog. Which is the dependent variable?

    1. AThe money Lin earns
    2. BThe number of dogs
    3. CBoth are dependent

    Hint Ask: which quantity does Lin choose? The other one is dependent.

    Show your work
  4. 4Complete each step, then write the final answer.

    Ravi chooses how many hours to practice piano each week. His teacher gives his song a score. Is the score independent or dependent?

    Show your work

    Hint Did Ravi choose the score, or did the score respond to his practice?

    Final answer:
  5. 5Complete each step, then write the final answer.
    Minutes15Pages12?× ?× ?
    The printer prints 12 pages each minute.

    A printer prints 12 pages each minute. You choose how long to run it. How many pages are printed in 5 minutes?

    Show your work

    Hint Minutes is the independent variable. Pages depend on minutes. Multiply.

    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.

    Which pair of quantities does NOT change together?

    1. AA student's height and the color of her shirt
    2. BHours worked and money earned
    3. CGallons of gas and the cost of the gas

    Hint For each pair, ask: if one changes, does the other change because of it?

    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 ___.

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