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.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 9.1–9.3: 9.1 Explore Relationships Between Two Variables, 9.2 Analyze Graphs of Relationships Between Two Variables, 9.3 Write Equations to Represent Relationships Between Two Variables. Work one example from each lesson, then prove you're caught up in the 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 example

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

Write an equation for the pairs (1, 6), (2, 12), (5, 30).

  1. 6 ÷ 1 = 6, 12 ÷ 2 = 6, 30 ÷ 5 = 6.
  2. The rate is 6 every time.
  3. Check: 6 × 5 = 30.

Answer: y = 6x

Now you trySame steps, your turn

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

You choose how many movie tickets to buy. Is the total cost independent or dependent?

Answer:

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 out!A common mistake

Writing the equation with addition

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.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 9.1–9.3: 9.1 Explore Relationships Between Two Variables, 9.2 Analyze Graphs of Relationships Between Two Variables, 9.3 Write Equations to Represent Relationships Between Two Variables. Work one example from each lesson, then prove you're caught up in the mixed practice.

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

    Leo chooses how many plants to water. He measures the cups of water he uses. Which is the dependent variable: plants or cups?

    Show your work

    Hint Leo chooses the plants. The other quantity responds.

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

    Gina chooses how many songs to download. Each song costs $1. Is the number of songs independent or dependent?

    Show your work

    Hint Did Gina choose the number of songs?

    Final answer:
  3. 3Complete each step, then write the final answer.
    Tickets15Total cost ($)6?× ?× ?
    Use the same scale factor on both rows.

    Each ticket costs $6. Write the point for 5 tickets: (5, ?). What is the missing number?

    Show your work

    Hint The ? is the cost of 5 tickets.

    Final answer:
  4. 4Complete each step, then write the final answer.
    Time (hours)14Total cost ($)7?× ?× ?
    Use the same scale factor on both rows.

    A bike rents for $7 each hour. What is the point for 4 hours on the graph of (hours, total cost)? Give the total cost.

    Show your work

    Hint Hours go first. Multiply to find the total cost.

    Final answer:
  5. 5Complete each step, then write the final answer.
    Time (hours)1hTotal cost ($)5?× h× h
    Scale the 1-unit column by the variable.

    A table shows 1 hour costs $5, 2 hours cost $10 and 3 hours cost $15. Let h = hours and c = total cost. Complete the equation: c = ___h.

    Show your work

    Hint How much does 1 hour cost? That number goes in the blank.

    Final answer:
  6. 6Complete each step, then write the final answer.
    Pens18Total cost ($)2?× ?× ?
    Use the same scale factor on both rows.

    Pens cost $2 each. Let p = pens and c = total cost. Write an equation. What do 8 pens cost?

    Show your work

    Hint Write c = 2p. Then put 8 in for p.

    Final answer:
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