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

Lesson 9.29.2 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use a table and a graph to determine and analyze the relationship between two variable quantities, 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.

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 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

1Complete each step, then write the final answer.
The line starts at (0, 0).
A train moves at the same speed the whole time. Its graph of (hours, kilometers) passes through (6, 270). How far does it go each hour? What is the point for 10 hours?
1. 1What does the point (6, 270) mean?
2. 2How many kilometers does the train go each hour?
3. 3What is the point for 10 hours? Give the kilometers.
Final answer:
2Complete each step, then write the final answer.
Both trams use the same scale factor.
Tram A goes 900 feet each minute. Tram B goes 1,200 feet each minute. Both start at 0. After 5 minutes, how much farther has Tram B gone?
1. 1What do you multiply 1 minute by to get 5 minutes?
2. 2Multiply both trams' feet by 5. Write each point.
3. 3How much farther has Tram B gone?
4. 4Why is Tram B's line steeper on the graph?
Final answer:
3Complete each step, then write the final answer.

Go to 1 first, then scale up.
A graph of (hours, dollars) passes through (4, 34). The pay is the same each hour. What is the point for 1 hour? Give the dollars.
Show your work
Final answer:
4Complete each step, then write the final answer.

Go to 1 first, then scale up.
A graph of (bags, pounds) passes through (6, 15). Every bag weighs the same. How many bags weigh 25 pounds?
Show your work
Final answer:
5Complete each step, then write the final answer.

Go to 1 first, then scale up.
Leo's savings account earns the same interest each year. The graph of (years, interest) passes through (2, 36). How much interest does Leo earn in 5 years?
Show your work
Final answer:
6Circle the letter of the best answer. Show how you know.
Scale the unit rate to test each column.
A table shows (minutes, pages): (2, 6), (4, 12) and (5, 16). One row does not fit the same rate. Which row?
1. A(5, 16)
2. B(4, 12)
3. C(2, 6)
Show your work

Explain your thinkingTram B's line is steeper than Tram A's line. What does a steeper line tell you about a relationship?

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