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

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
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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. 1Complete each step, then write the final answer.
    Minutes1?Boxes545× ?× ?
    The machine fills 5 boxes each minute.

    A machine fills 5 boxes every minute. Let m = minutes and b = boxes. How many minutes does it take to fill 45 boxes?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.
    Hours1?Bikes3.5280× ?× ?
    The factory makes 3.5 bikes each hour.

    A factory makes 3.5 bikes every hour. Let h = hours and b = bikes. How many hours does the factory need to make 280 bikes?

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

    An elevator holds at most 1,200 pounds. A cart on it weighs 150 pounds. Each box weighs 40 pounds. Let b = boxes. What is the greatest number of boxes it can carry?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    Hours1?Miles60210× ?× ?
    The train goes 60 miles each hour.

    A train travels 60 miles each hour. Let h = hours and d = distance in miles. How many hours does it take to travel 210 miles?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    Ms. Lee has $150. She must buy a $12 pump and 7 basketballs that all cost the same. Let p = price of one ball. What is the most each ball can cost, to the cent?

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

    Suppose the variable s counts 8-hour SHIFTS instead of hours. Which equation gives the cars produced?

    1. Ac = 2.5s
    2. Bc = 8s
    3. Cc = 10.5s
    4. Dc = 20s
    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
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