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

Lesson 9.39.3 Small Group · Group 1

Group 1 · Set BSecond form · new problems, same idea

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
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Learning target With my small group, I can write an equation from a table or a graph to model the relationship between the dependent and independent variables — one step at a time, with support.

Remember9.3 Small Group · Group 1

To write an equation, find how much one unit costs, then write total equals rate times amount, like c = 15h. An equation shows the whole pattern in a table. It works for any number, not only the numbers in the table.

Words: equation (ecuación)variable (variable)rate (tasa)represent (representar)define the variables (definir las variables)

  1. 1Complete each step, then write the final answer.
    Time (hours)1hTotal cost ($)12?× h× h
    Scale the 1-unit column by the variable.

    A table shows 1 hour costs $12, 2 hours cost $24 and 3 hours cost $36. 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:
  2. 2Complete each step, then write the final answer.
    Weight (pounds)1pTotal cost ($)3?× p× p
    Scale the 1-unit column by the variable.

    A table shows 1 pound of apples costs $3, 2 pounds cost $6 and 3 pounds cost $9. Let p = pounds and c = total cost. Complete the equation: c = ___p.

    Show your work

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

    Final answer:
  3. 3Complete each step, then write the final answer.
    0123456071421283542Days (x)Cups of food (y)(0, 0)(2, 14)(3, 21)(5, 35)

    A graph shows cups of dog food. It goes through (2, 14), (3, 21) and (5, 35). Let x = days and y = cups. Complete the equation: y = ___x.

    Show your work

    Hint No point shows 1 day. Divide the cups by the days to find the cups for 1 day.

    Final answer:
  4. 4Complete each step, then write the final answer.
    Time (hours)4112Total cost ($)26??÷ ?÷ ?× ?× ?
    Go to 1 first, then scale up.

    A table shows 4 hours cost $26, 6 hours cost $39 and 10 hours cost $65. Let h = hours and c = total cost. Write an equation. Then find the cost of 12 hours.

    Show your work

    Hint No row shows 1 hour. Divide a cost by its hours to find the rate.

    Final answer:

Explain your thinkingLeo wrote c = 6 + h. Why does the rate multiply the hours instead of being added once?

Sentence starter The rate multiplies because every hour ___. · I can check an equation with the row ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help