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

Lesson 9.3Equations from Situations

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can write an equation from a table or a graph to model the relationship between the dependent and independent variables.

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. c = 24.95m means the total cost equals $24.95 times the number of months
variableSpanish: variable A letter that represents a quantity that can change, or vary. In c = 24.95m, the m can be 1, 2, or 12 — it varies.
rateSpanish: tasa A fixed amount of one quantity for every one unit of the other quantity. $24.95 for every 1 month — the amount attached to one unit.
representSpanish: representar To show a relationship using a tool such as a table, a graph, or an equation. graph → equation
define the variablesSpanish: definir las variables To state exactly what quantity each letter in an equation stands for. “Let m = months and c = total cost” — written before you solve.
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.

A pet sitter earns $9 each day. Write an equation for dollars e earned in d days.

  1. Define: d = days, e = dollars earned.
  2. Rate: $9 for each day, so e = 9d.
  3. Test d = 5: e = 9 × 5 = 45.

Answer: e = 9d; 5 days earns $45

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • I let stand for and stand for .
  • In words, the total equals times .
  • My equation is , so when x is , y is .
  • This rule multiplies instead of adds because .

Word bank equationvariableconstant ratepermultiplyaddsubstituterepresentgraphpointtotaldefine

Watch out!A common mistake

Writing the equation with addition

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

Lesson 9.3Equations from Situations

Apply Day · Version ASupported practice

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

Learning target I can write an equation from a table or a graph to model the relationship between the dependent and independent variables.

  1. 1Complete 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:
  2. 2Complete 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. 3Complete each step, then write the final answer.
    Tickets1tTotal cost ($)6?× t× t
    Scale the 1-unit column by the variable.

    A table shows 1 ticket costs $6, 2 tickets cost $12 and 4 tickets cost $24. Let t = tickets and c = total cost. Complete the equation: c = ___t.

    Show your work

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

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

Lesson 9.3Equations from Situations

Apply Day · Version BCore practice

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

Learning target I can write an equation from a table or a graph to model the relationship between the dependent and independent variables.

  1. 1Circle 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
    Show your work
  2. 2Complete each step, then write the final answer.
    Time (hours)217Total cost ($)34?119÷ ?÷ ?× ?× ?
    Go to 1 first, then scale up.

    A table shows 2 hours cost $34, 5 hours cost $85 and 7 hours cost $119. Let h = hours and c = total cost. Complete the equation: c = ___h.

    Show your work
    Final answer:
  3. 3Complete 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
    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
Grade 6 Mathematics · Unit 9: Relationships Between Two VariablesStandard 6.AT.11

Lesson 9.3Equations from Situations

Apply Day · ChallengeExtension

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

Learning target I can write an equation from a table or a graph to model the relationship between the dependent and independent variables.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    Table A: when x = 1, 2, 3, y = 7, 14, 21. Table B: when x = 1, 2, 3, y = 7, 9, 11. Which equation matches Table B?

    1. Ay = 2x + 5
    2. By = 7x
    3. Cy = x + 6
    4. Dy = 9x
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    A spin studio charges $7.50 for each class. Let n be the number of classes a member takes and let c be the total cost in dollars. Which equation represents the relationship?

    1. Ac = 7.5 + n
    2. Bn = 7.5c
    3. Cc = n ÷ 7.5
    4. Dc = 7.5n
    Show your work
  2. 3Complete each step, then write the final answer.

    A skating rink charges $9 for 1 hour, $13 for 2 hours and $17 for 3 hours. Let h = hours and c = total cost. Complete the equation: c = 4h + ___.

    Show your work
    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