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

Lesson 9.39.3 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

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.

Why This Matters This is your support small group for Lesson 9.3. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
equationSpanish: ecuación A mathematical sentence with an equals sign that shows two amounts are the same. y = 5x
variableSpanish: variable A letter that represents a quantity that can change, or vary. x, y, c, h
rateSpanish: tasa A fixed amount of one quantity for every one unit of the other quantity. $3 for each pound
representSpanish: representar To show a relationship using a tool such as a table, a graph, or an equation. The same membership shown as a table, a graph, AND c = 24.95m.
define the variablesSpanish: definir las variables To state exactly what quantity each letter in an equation stands for. c = total cost
ConstantSpanish: Constante A number in an equation that never changes. the 5 in y = 5x

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.

A canoe rents for $15 per hour. Write an equation for the total cost of a canoe rental.

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 9.39.3 Small Group · Group 1

Group 1Supported practice

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

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.

Why This Matters This is your support small group for Lesson 9.3. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.

  1. 1Complete each step, then write the final answer.
    Time (hours)1hTotal cost ($)8?× h× h
    Scale the 1-unit column by the variable.

    A bike rents for $8 per hour. Let h = hours and c = total cost. Write an equation for the total cost.

    1. 1Which quantity depends on the other: hours or total cost?
    2. 2What is the cost in the 1-hour column?
    3. 3What do you multiply 1 hour by to get h hours?
    4. 4Multiply the cost by h too. Complete: c = ___h.
    Final answer:
  2. 2Complete each step, then write the final answer.
    012345691827364554Tickets (t)Total cost (c)(0, 0)(1, 9)(2, 18)(4, 36)
    The cost goes up $9 for each ticket.

    A graph shows the cost of movie tickets. It goes through (1, 9), (2, 18) and (4, 36). Let t = tickets and c = total cost. Write an equation. Then find the cost of 6 tickets.

    1. 1Read the point (1, 9). What does 1 ticket cost?
    2. 2Write the equation for the total cost.
    3. 3Use the equation. What do 6 tickets cost?
    Final answer:
  3. 3Complete each step, then write the final answer.
    Books1bTotal cost ($)4?× b× b
    Scale the 1-unit column by the variable.

    A table shows 1 book costs $4, 2 books cost $8 and 3 books cost $12. Let b = books and c = total cost. Complete the equation: c = ___b.

    Show your work

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

    Final answer:
  4. 4Complete each step, then write the final answer.
    Time (months)1mTotal cost ($)12.99?× m× m
    Scale the 1-unit column by the variable.

    A music plan costs $12.99 for 1 month, $25.98 for 2 months and $38.97 for 3 months. Let m = months and c = total cost. Complete the equation: c = ___m.

    Show your work

    Hint Subtract one row's cost from the next row's cost. That is how much each month adds.

    Final answer:
  5. 5Complete each step, then write the final answer.
    Time (hours)15Money earned ($)11?× ?× ?
    Use the same scale factor on both rows.

    Ana earns $11 for each hour she babysits. Let h = hours and e = money earned. Write an equation. How much does she earn in 5 hours?

    Show your work

    Hint Say it in words first: money earned = $11 times the hours. Then put 5 in for h.

    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.
    Time (hours)12hTotal cost ($)612?× 2× 2
    Scaling multiplies; it does not add.

    A table shows 1 hour costs $6, 2 hours cost $12 and 3 hours cost $18. Leo writes c = 6 + h. Which equation is correct?

    1. Ac = 6h
    2. Bc = 6 + h
    3. Ch = 6c

    Hint Test each equation with 2 hours. Which one gives $12?

    Show your work

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 ___.

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