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

Lesson 9.39.1–9.3 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 9.1–9.3 by using each lesson's big idea in mixed practice.

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. Miguel picks the number of MONTHS — nothing else decides it for him.
dependent variableSpanish: variable dependiente The quantity that changes in response to the independent variable. Total cost = $24.95 × months — the cost RESPONDS to the months.
depends onSpanish: depende de One quantity depends on another when changing the first causes the second to change. “Total cost depends on the number of months.” Responder first, chooser last.
quantitySpanish: cantidad Something that can be counted or measured. 24.95 dollars per month, 12 months — each is a number with a meaning.
relationshipSpanish: relación How two quantities change together. 1 month → $24.95, 2 months → $49.90: the two quantities move together.
graphSpanish: gráfica A picture on a coordinate plane that shows how two quantities are related. Points (1, 45), (2, 90), (3, 135) climbing left to right — cost by tickets.

How it worksWorked examplewriting an equation from a table

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

A table shows x: 1, 2, 3, 4 hours worked and y: 18, 36, 54, 72 dollars earned. Write an equation.

  1. Define the variables: x = hours worked, y = total dollars earned.
  2. Check each row for one rate: 18 ÷ 1, 36 ÷ 2, and 54 ÷ 3 all give 18.
  3. The constant rate is 18 dollars per hour, so y is 18 times x.
  4. Write it: y = 18x. Test the last row: 18 × 4 → 72, which matches.

Answer: y = 18x, where x is hours worked and y is total dollars earned.

Now you trySame steps, your turn

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

A table shows x: 1, 2, 3, 4 bags of sand and y: 11, 22, 33, 44 pounds. Write an equation.

  1. Define the variables: x = , y = .
  2. Check each row for one rate: ÷ 1, ÷ 2, ÷ 3 all give .
  3. The constant rate is pounds per bag, so y is times x.
  4. Write it: y = x. Then test the last row of the table to check.
Answer:equation in the form y = ______x

Say it and write itSentence starters

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

  • In my equation, x stands for and y stands for .
  • The constant rate is because every y value is .
  • My equation is y = , which means .
  • I checked my equation by substituting for x.

Word bank equationvariablerateconstantdefinesubstitutetimespertablerowrelatecheck

Watch outA common mistake

Writing the equation with addition — c = 24.95 + m — instead of multiplication. The fee is charged EVERY month, so the total is the rate times the number of months; always test the equation against a row of the table.

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

Lesson 9.39.1–9.3 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 9.1–9.3 by using each lesson's big idea in mixed practice.

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

    (Lesson 9.1) Akela chooses how many hours of sunlight each tray gets. Which is the INDEPENDENT variable?

    1. APlant height
    2. BNumber of trays
    3. CHours of sunlight
    4. DNumber of seeds

    Hint Which quantity did Akela get to decide?

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

    (Lesson 9.1) In Akela's experiment, which is the DEPENDENT variable?

    1. AHours of sunlight
    2. BThe kind of seed
    3. CPlant height
    4. DThe size of the tray

    Hint Which quantity RESPONDED to the other?

    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    (Lesson 9.2) Football tickets cost $45 each. What is the total cost of 3 tickets?

    1. A$45
    2. B$48
    3. C$90
    4. D$135

    Hint What is the cost of ONE ticket?

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

    (Lesson 9.2) Which ordered pair belongs on the ticket graph for 2 tickets?

    1. A(2, 90)
    2. B(2, 45)
    3. C(2, 47)
    4. D(90, 2)

    Hint Which quantity goes first in the ordered pair?

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

    (Lesson 9.3) Recreation World charges $24.95 per month. What is the total cost of 2 months of membership?

    1. A$24.95
    2. B$26.95
    3. C$49.90
    4. D$74.85

    Hint What does ONE month cost?
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help