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

Lesson 9.1Explore Relationships Between Two Variables

Set B · Version ASecond form · supported 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.

Why This Matters Akela planted three trays of bean seeds for a science experiment. Each tray sat in a different spot, so each got a different amount of sunlight per day. After three weeks she measured the average plant height in every tray. Two quantities in that experiment are related: change the sunlight and the height changes with it. One of them Akela chose, and the other one answered back. Today you will name which quantity is the independent one and which depends on it, and you will find pairs like this in a jogging tracker and a pizza shop.

RememberExplore Relationships Between Two Variables

Independent & Dependent Variables When two quantities are related, one of them depends on the other. Naming which is which is the whole job of this lesson.

  1. Independent Variable (x): The input / cause that is chosen or changes freely.
  2. Dependent Variable (y): The output / effect that depends on the independent variable.
  3. Sentence check: 'The (dependent) depends on the (independent)'

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

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Sort each quantity: independent or dependent?

    Groups: Independent variable (input) Dependent variable (output)
    • Hours of sunlight a tray of seedlings gets
    • Months of gym membership
    • Minutes spent jogging
    • Height the seedlings grow
    • Total cost of the membership
    • Calories burned on the jog

    Hint Use the sentence check: 'The ___ depends on the ___.' The first blank is dependent.

  2. 2Complete the table. Show how you found each value.

    Claire burns Calories at a steady rate: 30 minutes burns 123 Calories. Complete the table.

    Minutes jogged (independent)ThinkingCalories burned (dependent)
    30
    60
    90

    Hint 60 minutes is twice 30 minutes, so it burns twice the Calories.

    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    If Claire runs exactly 3 miles and records how long it takes, which is the independent variable now?

    1. ATime it takes
    2. BHer speed
    3. CDistance (3 miles)
    4. DCalories burned

    Hint What did Claire decide in advance this time?

    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    A ticket costs $8. Which equation represents "8 tickets cost $56"?

    1. A8t = 56
    2. Bt + 8 = 56
    3. Ct − 8 = 56
    4. Dt ÷ 8 = 56
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    Solve: 4x = 32

    1. Ax = 8
    2. Bx = 28
    3. Cx = 36
    4. Dx = 128
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    Maya needs at least 20 points to win a prize. Which inequality shows this?

    1. Ap ≥ 20
    2. Bp > 20
    3. Cp ≤ 20
    4. Dp < 20
    Show your work

Explain your thinkingTake a card you and your partner put in different columns. Say the sentence 'The ___ depends on the ___' out loud both ways — which version is true, and how does that settle which variable is independent?

Sentence starter The ___ depends on the ___, so ___ is the independent variable.

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

Lesson 9.1Explore Relationships Between Two Variables

Set B · Version BSecond form · core 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.

Why This Matters Akela planted three trays of bean seeds for a science experiment. Each tray sat in a different spot, so each got a different amount of sunlight per day. After three weeks she measured the average plant height in every tray. Two quantities in that experiment are related: change the sunlight and the height changes with it. One of them Akela chose, and the other one answered back. Today you will name which quantity is the independent one and which depends on it, and you will find pairs like this in a jogging tracker and a pizza shop.

  1. 1Circle the letter of the best answer. Show how you know.

    Solve: x + 7 = 19

    1. Ax = 7
    2. Bx = 12
    3. Cx = 19
    4. Dx = 26
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    At a local pizza shop a customer can order up to three toppings on a large pizza. The shop has 6 employees. The shop spends $1.15 on cheese and $1.95 on sauce for each pizza it makes. The number of pizzas made each week determines other costs at the shop. Which variable is the independent variable in this relationship?

    1. Athe cost of cheese used
    2. Bthe number of pizzas made
    3. Cthe number of employees
    4. Dthe number of toppings allowed
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    At a local pizza shop a customer can order up to three toppings on a large pizza. The shop has 6 employees. The shop spends $1.15 on cheese and $1.95 on sauce for each pizza it makes. Which two quantities have a dependent relationship in this scenario?

    1. Anumber of employees and number of pizzas made
    2. Bcost of cheese and number of pizzas made
    3. Cnumber of toppings allowed and cost of sauce
    4. Dnumber of employees and number of toppings allowed
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    At a local pizza shop a customer can order up to three toppings on a large pizza. The shop has 6 employees. The shop spends $1.15 on cheese and $1.95 on sauce for each pizza it makes. The shop makes 20 pizzas in a week. Which of these does NOT depend on the number of pizzas sold?

    1. Athe total cost of cheese
    2. Bthe number of employees
    3. Cthe total cost of sauce
    4. Dthe total spent on cheese and sauce combined
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A dog walker charges by the hour. Which sentence is correct?

    1. AThe number of hours depends on the total charge, so the charge is the independent variable.
    2. BBoth quantities are independent variables.
    3. CThe total charge depends on the number of hours, so hours is the independent variable.
    4. DNeither quantity depends on the other.
    Show your work

Explain your thinkingTake a card you and your partner put in different columns. Say the sentence 'The ___ depends on the ___' out loud both ways — which version is true, and how does that settle which variable is independent?

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