Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ
MPs
Applied MP
* Embedded MP
Procedural Lesson
Grade 6 · Unit 5 · Lesson 16
MC: 6.EE.9
Steps:
1. Identify the independent & dependent
variables.
2. Write an equation.
3. Make a t-chart (or input-output table)
and solve for at least 3 values of each
variable.
4. Graph.
5. Check your solution on the graph.
Vocabulary Notes
Independent variable: a variable whose value does
not depend on another variable in the equation
Dependent variable: a variable whose value is based
on the value of another variable in the equation
Example:
d
= 60
t
dependent independent
variable variable
In this equation,
d
stands for distance and
t
stands
for time. This is the distance formula. In this
equation, the speed is a constant of 60 mph (like a
car on cruise control). If
t
= 1 hour, then
d
= 60 miles;
if
t
= 2 hours, then
d
= 120 miles. Time (
t
) is the
independent variable because as it changes, it
affects the distance. Time change does not depend
on the distance, because the clock “just keeps
moving.” The distance traveled depends on the time;
therefore, distance (
d
) is the dependent variable.
The relationship between
distance and time can be
represented in a table
(sometimes called a t-chart or an
input-output table).
t
(
x
-axis)
d
(
y
-axis)
1 60
2 120
3 180
1 2 3 4 5 6 7 8
*
* *
*
*
Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ
/
Directions: Identify the independent and dependent variables. Create a table of values
(t-chart) to solve the problem. Write the equation. Graph the solution to check your work.
1. At an average speed of 50 miles per hour, how long will it take to travel 450
miles without stops?
Solution: ___________________________
Independent variable: ______________
Dependent variable: ________________
Equation: __________________________
Equation:
____________
Independent Variable
(x-axis)
____________
Dependent Variable
(y-axis)
Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ
/
2. A club is selling large rolls of wrapping paper for a fundraiser. The club
gets to keep $15 for every roll they sell. How many rolls of wrapping paper
do the members need to sell to raise $330?
Solution: ___________________________
Independent variable: ______________
Dependent variable: ________________
Equation: __________________________
MP3: How will you test to see if your equation works?
MP4: How might it help to create a visual?
Equation:
____________
Independent Variable
(x-axis)
____________
Dependent Variable
(y-axis)
Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ
Directions: Identify the independent and dependent variables. Create a table of values
(t-chart) to solve the problem. Write the equation. Graph the solution to check your work.
1. A race car averages 125 mph on a race track. How long will it take to
complete a 500 mile race?
Solution: ___________________________
Independent variable: ______________
Dependent variable: ________________
Equation: __________________________
Equation:
____________
Independent Variable
(x-axis)
____________
Dependent Variable
(y-axis)
Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ
2. Miranda walks at a rate of 3 mph. How long will it take to walk 5 miles?
Solution: ___________________________
Independent variable: ______________
Dependent variable: ________________
Equation: __________________________
Equation:
____________
Independent Variable
(x-axis)
____________
Dependent Variable
(y-axis)
Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ
Name: ____________________________
Date: ______________________________
1. Ezekiel is driving from California to Colorado. He will drive 1,200 miles. If
Ezekiel averages 50 mph, how many hours will he drive?
Solution: ___________________________
Independent variable: ______________
Dependent variable: ________________
Equation: __________________________
Directions: Identify the independent and dependent variables. Create a table of values
(t-chart) to solve the problem. Write the equation. Graph the solution to check your work.
Equation:
____________
Independent Variable
(x-axis)
____________
Dependent Variable
(y-axis)
Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ
2. Joyce is driving from Utah to Texas. She will drive 1,500 miles. If Joyce
drives an average of 60 mph, how many hours will she drive?
Solution: ___________________________
Independent variable: ______________
Dependent variable: ________________
Equation: __________________________
Equation:
____________
Independent Variable
(x-axis)
____________
Dependent Variable
(y-axis)
Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ
Name: ____________________________
Date: ______________________________
3. If a tortoise walks at an average speed of 0.25 miles per hour, how many
hours will it take the tortoise to travel 2.5 miles?
Solution: ___________________________
Independent variable: ______________
Dependent variable: ________________
Equation: __________________________
Equation:
____________
Independent Variable
(x-axis)
____________
Dependent Variable
(y-axis)
Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ
4. A basketball player scores 3 points for each basket made during the three-
point shooting contest. How many baskets must she make to earn 42
points?
Solution: ___________________________
Independent variable: ______________
Dependent variable: ________________
Equation: __________________________
Equation:
____________
Independent Variable
(x-axis)
____________
Dependent Variable
(y-axis)
Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ
Directions: Read and answer each question.
1. Matthew said that if you double the length of one side of a square, the
area doubles. Is Matthew correct? Use charts, graphs, or diagrams to
support your answer.
2. Matthew said that if you double the length of one side of a square, the
perimeter doubles. Is Matthew correct? Use charts, graphs, or diagrams
to support your answer.
Extension Activity
*
MP4: How can you relate this to something in real life?
Rectangle #1 and Rectangle #2 are the same size (1 cm × 2 cm). Then the
length of Rectangle #1 is doubled. In Rectangle #2, the length and the width
are doubled. Compare the perimeters of the rectangles. Use tables and
graphs. What is the relationship between the perimeters of the rectangles
when the parts are doubled? Doubled again?
Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ
Recap today’s lesson with one or more of the following questions:
MP3: How will you test to see if your equation worked?
MP4: How might it help to create a visual?
Reaching Consensus
*MP3: Do you agree/disagree with what said?
Student Presentations
*MP6: How do you know your answers are correct/reasonable?
Copyright © Swun Math Grade 6 Unit 5 Lesson 16 P SJ