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

Lesson 9.29.2 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can use a table and a graph to determine and analyze the relationship between two variable quantities — 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
graphSpanish: gráfica	A picture on a coordinate plane that shows how two quantities are related.	points that rise in a line
table of valuesSpanish: tabla de valores	A list of matched pairs of values that shows a relationship using numbers.	months 1, 2, 4 beside cost 24.95, 49.90, 99.80 — one row per pair.
ordered pairSpanish: par ordenado	Two numbers written as (x, y) that name one point on a graph. The independent variable comes first.	(3, 12)
axisSpanish: eje	One of the two number lines that frame a graph. Each axis is labeled with a quantity from the problem.	x-axis and y-axis
coordinatesSpanish: coordenadas	The numbers in an ordered pair that tell how far to move along each axis to reach a point.	x-coordinate, y-coordinate
Rate of changeSpanish: Tasa de cambio	How much y changes each time x goes up by one.	Up $4 for each hour.

How it worksWorked exampleturning a table into points on a graph

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

A rental site charges $7 per movie. Make a table for 1, 2, and 3 movies, then list the points to plot.

Independent: number of movies (x). Dependent: total cost (y).
Multiply each x by the rate: 1 → 7 · 2 → 14 · 3 → 21
Write each row as an ordered pair (x, y): (1, 7), (2, 14), (3, 21).
Plot each pair: move right along the x-axis first, then up to the y value.

Answer: Points to plot: (1, 7), (2, 14), and (3, 21). They rise in a straight path.

Now you trySame steps, your turn

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

A subway car holds 40 riders. Make a table for 1, 2, and 4 cars, then list the points to plot.

Independent: (x). Dependent: (y).
Multiply each x by riders: 1 → · 2 → · 4 →
Write each row as an ordered pair: ( __ , __ ), ( __ , __ ), ( __ , __ ).
Plot each pair: move first, then to the y value.

Answer:three ordered pairs to plot

Say it and write itSentence starters

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

The independent variable is , so it goes on the axis.
The ordered pair ( , ) means that .
To plot a point I move first, then .
As x increases, y , so the points .

Word bank graphordered paircoordinatesaxisplotpointtableinputoutputrateincreasesorigin

Watch outA common mistake

Reversing the coordinates of a point — writing (cost, tickets) instead of (tickets, cost). The independent variable always comes first in the ordered pair.

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

Lesson 9.29.2 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 use a table and a graph to determine and analyze the relationship between two variable quantities — one step at a time, with support.

Part 1Understand the ideamodels and meaning

1Complete each step, then write the final answer.
Each column becomes one point.
A car travels 50 miles each hour. Find the point on the graph for 3 hours. What does that point mean?
1. 1Which quantity is independent: hours or miles?
2. 2How many miles in 1 hour? Write it in the first column.
3. 3What do you multiply 1 hour by to get 3 hours?
4. 4Multiply the miles by 3 too. What is the point for 3 hours?
Final answer:
2Circle the letter of the best answer. Show how you know.
Read each column as (hours, dollars).
Mia earns $15 each hour. What does the point (4, 60) mean on her graph of (hours, dollars)?
1. AMia earns $60 for 4 hours.
2. BMia earns $4 for 60 hours.
3. CMia earns $60 each hour.
Hint The first number is hours. The second number is dollars.
Show your work

Part 2Apply itreal-world problems

3Complete each step, then write the final answer.
Each ticket adds $9.
Each movie ticket costs $9. Make ordered pairs for 1, 2 and 3 tickets. Then find the point for 4 tickets.
1. 1Find the cost of 1, 2 and 3 tickets.
2. 2Write each pair with tickets first.
3. 3What is the cost of 4 tickets? Write the point (4, ?).
4. 4Describe the pattern of the points.
Final answer:
4Complete each step, then write the final answer.

Use the same scale factor on both rows.
Pens cost $2 each. The graph of (pens, total cost) passes through (5, ?). What is the missing number?
Show your work
Hint The ? is the total cost of 5 pens.
Final answer:
5Complete each step, then write the final answer.

Use the same scale factor on both rows.
A tram climbs 1,500 feet each minute. The graph shows (minutes, feet). What is the point for 6 minutes? Give the feet.
Show your work
Hint Minutes go first. Multiply to find the feet for 6 minutes.
Final answer:
6Complete each step, then write the final answer.

Go to 1 first, then scale up.
Mia earns money babysitting. Her table shows (hours, dollars): (2, 30), (3, 45) and (5, 75). How much does she earn for 1 hour?
Show your work
Hint Pick one row. Divide the dollars by the hours.
Final answer:

Explain your thinkingWhy does the number of hours go first in each ordered pair? What would the point (60, 4) mean?

Sentence starter Hours go first because ___. · The point (60, 4) would mean ___.

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