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.

Start hereWords for this lesson

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

Word	What it means	Example
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.

Define the variables: x = hours worked, y = total dollars earned.
Check each row for one rate: 18 ÷ 1, 36 ÷ 2, and 54 ÷ 3 all give 18.
The constant rate is 18 dollars per hour, so y is 18 times x.
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.

Define the variables: x = , y = .
Check each row for one rate: ÷ 1, ÷ 2, ÷ 3 all give .
The constant rate is pounds per bag, so y is times x.
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 1

Group 1Supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

1Complete each step, then write the final answer.
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:
2Complete each step, then write the final answer.
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:
3Complete each step, then write the final answer.

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:
4Complete each step, then write the final answer.

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:
5Complete each step, then write the final answer.

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:
6Circle the letter of the best answer. Show how you know.
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 ___.

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