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

Lesson 9.4Working Backward to a Goal

Apply Day · Set BSecond form · new problems, same idea

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Learning target I can write an equation to represent the relationship between two variable quantities and use it to solve a real problem.

Remember9.4 · Part II

Analyzing & Applying Two-Variable Relationships

  1. Connect the four representations: Scenario, Table, Graph, and Equation
  2. Substitute given values into the equation to make predictions and solve problems
  3. Interpret coordinates and rate of change in the real-world context

Words: solution (solución)substitute (sustituir)at least (al menos)predict (predecir)justify (justificar)

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

    Last year the student council washed 34 cars and raised $408. How much did they charge per car?

    1. A$10
    2. B$12
    3. C$34
    4. D$374
    per 1
  2. 2Complete each step, then write the final answer.

    (Lesson 9.4) A gym membership costs $9 per month, so the equation is c = 9m. Use it to find the cost c of 6 months.

    1. 1Substitute the months: c = 9 × ___.
    2. 2Multiply: 9 × 6 = ___.
    Final answer:
  3. 3Complete each step, then write the final answer.

    A gym membership costs $9 per month, so the equation is c = 9m. Use it to find the cost c of 5 months.

    1. 1Substitute the months: c = 9 × ___.
    2. 2Multiply: 9 × 5 = ___.
    Final answer:
  4. 4Circle the letter of the best answer. Show how you know.

    The goal is $500 at $12 per car. Using 12n = 500, at least how many cars must be washed?

    1. A40 cars
    2. B41 cars
    3. C42 cars
    4. D50 cars
    per 1
  5. 5Complete each step, then write the final answer.

    A gym membership costs $9 per month, so the equation is c = 9m. Use it to find the cost c of 5 months.

    1. 1Substitute the months: c = 9 × ___.
    2. 2Multiply: 9 × 5 = ___.
    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.

    The solution to one problem was 41.7 cars. Would producing or washing a PARTIAL car make sense?

    1. ANo — cars come in whole numbers, so round up to the next whole car
    2. BYes — 0.7 of a car is a real amount you can wash
    3. CNo — so round down and accept a smaller total
    4. DYes — the equation is wrong if it gives a decimal
    Show your work
  7. 7Circle the letter of the best answer. Show how you know.

    The assembly line produces 2.5 cars per hour. How many cars does it produce in one 8-hour shift?

    1. A10.5 cars
    2. B16 cars
    3. C20 cars
    4. D25 cars
    per 1
  8. 8Circle the letter of the best answer. Show how you know.

    Let h = hours of operation and c = cars produced. Which equation represents the assembly line?

    1. Ac = 2.5h
    2. Bc = 2.5 + h
    3. Ch = 2.5c
    4. Dc = h ÷ 2.5
    Show your work
  9. 9Circle the letter of the best answer. Show how you know.

    Using the table (1 hour, 2.5 cars; 8 hours, 20 cars; 16 hours, 40 cars), how many cars are produced in 24 hours?

    1. A26.5 cars
    2. B40 cars
    3. C50 cars
    4. D60 cars
    Show your work
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help