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

Lesson 9.39.3 Small Group · Group 2

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, explain what each part stands for, and build one for a situation I have not seen before.

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 examplewriting an equation from a table

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A table shows x: 1, 2, 3, 4 hours worked and y: 18, 36, 54, 72 dollars earned. Write an equation.

  1. Define the variables: x = hours worked, y = total dollars earned.
  2. Check each row for one rate: 18 ÷ 1, 36 ÷ 2, and 54 ÷ 3 all give 18.
  3. The constant rate is 18 dollars per hour, so y is 18 times x.
  4. Write it: y = 18x. Test the last row: 18 × 4 → 72, which matches.

Answer: y = 18x, where x is hours worked and y is total dollars earned.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A table shows x: 1, 2, 3, 4 bags of sand and y: 11, 22, 33, 44 pounds. Write an equation.

  1. Define the variables: x = , y = .
  2. Check each row for one rate: ÷ 1, ÷ 2, ÷ 3 all give .
  3. The constant rate is pounds per bag, so y is times x.
  4. Write it: y = x. Then test the last row of the table to check.
Answer:equation in the form y = ______x

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 outA common mistake

Writing the equation with addition — c = 24.95 + m — instead of multiplication. The fee is charged EVERY month, so the total is the rate times the number of months; always test the equation against a row of the table.

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

Lesson 9.39.3 Small Group · Group 2

Group 2Challenge 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, explain what each part stands for, and build one for a situation I have not seen before.

Part 1Understand the ideamodels and meaning
  1. 1Complete each step, then write the final answer.

    A plumber charges a $40 visit fee plus $25 for each hour. Let h = hours and c = total cost. Write an equation. What does a 3-hour job cost?

    Show your work
    Final answer:
  2. 2Circle 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. 3Complete each step, then write the final answer.
    Games (g)Total cost (c)
    1$10
    2$16
    3$22
    Look at how the cost changes.

    A bowling alley charges $10 for 1 game, $16 for 2 games and $22 for 3 games. Let g = games and c = total cost. Write an equation.

    1. 1How much does each game add?
    2. 2Test the shortcut c = 10g with 2 games. Does it work?
    3. 31 game costs $10, and $6 pays for the game. What is the fixed fee?
    4. 4Write the equation: rate times games, plus the fee.
    Final answer:
  2. 4Complete each step, then write the final answer.
    01234502468101214161820Toppings (t)Total cost (c)(0, 5)(1, 8)(2, 11)(4, 17)
    The line starts at $5, not at 0.

    A graph shows the cost of a pizza. It goes through (0, 5), (1, 8), (2, 11) and (4, 17). Let t = toppings and c = total cost. Write an equation.

    1. 1What does the point (0, 5) mean?
    2. 2How much does each topping add?
    3. 3Write the equation.
    4. 41 topping costs $8. Why is the equation not c = 8t?
    Final answer:
  3. 5Complete each step, then write the final answer.
    Time (hours)217Total cost ($)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:
  4. 6Complete each step, then write the final answer.

    A gym charges $35 for 1 month, $55 for 2 months and $75 for 3 months. Let m = months and c = total cost. Complete the equation: c = 20m + ___.

    Show your work
    Final answer:

Explain your thinkingHow can you tell from a table whether the equation is c = rate × h or c = rate × h + fee? Use one row to prove it.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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