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

Lesson 9.19.1 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable, explain how I can tell, and judge a case I have not seen before.

Why This Matters This is your challenge small group for Lesson 9.1. 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.

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 2

Group 2Challenge practice

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

Learning target I can recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable, explain how I can tell, and judge a case I have not seen before.

Why This Matters This is your challenge small group for Lesson 9.1. 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.

Part 1Understand the ideamodels and meaning
  1. 1Complete each step, then write the final answer.
    MonthsTotal cost ($)
    125
    250
    375

    A gym charges $25 each month. Jo chooses how many months to join. The gym has 8 trainers. What does the total cost depend on?

    1. 1Which quantity does Jo choose?
    2. 2What is the total cost for 4 months?
    3. 3Why do the 8 trainers not belong in this relationship?
    Final answer:
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    MinutesPages read
    3012
    3014
    3011
    Three nights. Dev picks 30 minutes each time.

    Dev reads every night. This time he decides to read for exactly 30 minutes. He records how many pages he reads. Which quantity is independent? Which is dependent?

    1. 1What does Dev choose this time?
    2. 2What does he measure?
    3. 3Name the independent and dependent variables.
    Final answer:
  2. 3Complete each step, then write the final answer.

    A recipe uses 3 eggs for each cake. A baker chooses how many cakes to make. Which is the dependent variable: cakes or eggs?

    Show your work
    Final answer:
  3. 4Complete each step, then write the final answer.

    Rosa wants exactly 20 roses. She records how many minutes it takes to pick them. Is the number of roses independent or dependent here?

    Show your work
    Final answer:
  4. 5Complete each step, then write the final answer.
    Loaves1120Flour cost$0.75?× ?× ?
    Each loaf uses $0.75 of flour.

    A bakery spends $0.75 on flour for each loaf of bread. This week it bakes 120 loaves. How much does it spend on flour?

    Show your work
    Final answer:
  5. 6Circle the letter of the best answer. Show how you know.

    A movie theater is open 12 hours every day. On Monday it sells 150 tickets. On Tuesday it sells 210 tickets. Do the hours open depend on the tickets sold?

    1. ANo. The hours stay 12 when the tickets change.
    2. BYes. Selling more tickets means more hours.
    3. CYes. The hours are the dependent variable.
    Show your work

Explain your thinkingCan the same quantity be independent in one story and dependent in another? Use Dev's reading to explain.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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