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

Lesson 9.3Write Equations to Represent Relationships Between Two Variables

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.

Why This Matters Miguel is interested in joining a recreation center. Recreation World charges the monthly fee shown on the flyer. How can Miguel determine the cost of being a member of Recreation World for any number of months?

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. Which quantity is independent — hours or total cost?

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 9.3Write Equations to Represent Relationships Between Two Variables

Level 0Most support · every hint printed

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.

Why This Matters Miguel is interested in joining a recreation center. Recreation World charges the monthly fee shown on the flyer. How can Miguel determine the cost of being a member of Recreation World for any number of months?

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

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

    In the equation c = 24.95m for the gym membership, what does m represent?

    1. AThe number of months of membership
    2. BThe total cost in dollars
    3. CThe monthly fee of $24.95
    4. DThe name of the gym
    Steps to try
    1. Which letters are variables here — and which quantity does each stand for?
    2. c is the cost. What is left for m?
    3. m counts the months.
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Recreation World charges $24.95 per month. What is the total cost of 2 months of membership?

    1. A$24.95
    2. B$26.95
    3. C$49.90
    4. D$74.85
    Steps to try
    1. What does ONE month cost?
    2. The second month adds another $24.95.
    3. Multiply 24.95 by 2.
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  2. 3Circle the letter of the best answer. Show how you know.

    A canoe rents for $15 per hour. Let h = hours and c = total cost. Which equation represents the relationship?

    1. Ac = 15h
    2. Bc = 15 + h
    3. Ch = 15c
    4. Dc = h − 15
    Steps to try
    1. Say it in words: the total cost equals $15 ___ the number of hours.
    2. Every hour adds an equal $15 — which operation is that?
    3. Test your choice with 2 hours: the total should be $30.
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Using c = 15h, what is the total cost of a 3-hour canoe rental?

    1. A$15
    2. B$18
    3. C$45
    4. D$75
    Steps to try
    1. Replace h with 3 in the equation.
    2. c = 15 × 3.
    3. Skip-count: 15, 30, …
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.

Explain your thinkingBoth equations charge by a rate. What do m and h each stand for in their own situation, and why would c = 24.95m be wrong for the canoe?

Sentence starter In ___, ___ stands for ___, so the rate ___ means ___.

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