Representing Quantitative Relationships
Lesson
Represent and Analyze
Quantitative Relationships
[
OBJECTIVE
]
•
The student will represent and analyze
quantitative relationships in graphs, tables,
and equations.
[
MY
SKILLS
]
•
Unit rates
•
Plotting points in the coordinate plane
•
Equations
[
ESSENTIAL
QUESTIONS
]
1.
Explain the meaning of an independent
variable.
2.
Explain the meaning of a dependent variable.
3.
Explain how you can use the information
given in an equation to model the relationship
using a table and coordinate plane.
[Warm-Up]
Begin by completing the warm-up for this
lesson.
REPRESENT AND ANALYZE
QUANTITATIVE RELATIONSHIPS
SOLVE Problem – Introduction
[
LESSON
]
SOLVE
Jennie helps her grandmother every week one
day after school. Her grandmother gives her $15
every week. Write an equation that can be used
to represent the relationship between the total
she earns (
y
) and the number of weeks worked
(
x
). Create a table to model the relationship for 4
weeks, 8 weeks, 12 weeks, and 16 weeks and
graph the relationship on a coordinate plane.
[
LESSON
]
SOLVE
S
Study the Problem
Underline the question.
[
LESSON
]
SOLVE
Jennie helps her grandmother every week one
day after school. Her grandmother gives her $15
every week. Write an equation that can be used
to represent the relationship between the total
she earns (
y
) and the number of weeks worked
(
x
). Create a table to model the relationship for 4
weeks, 8 weeks, 12 weeks, and 16 weeks and
graph the relationship on a coordinate plane.
[
LESSON
]
SOLVE
S
Study the Problem
Underline the question.
This problem is asking me to find
the equation, table and graph to represent the
relationship between the number of weeks
worked and Jennie’s earnings.
VARIABLES
Variables
When we write and evaluate expressions that have
unknown values we can use a __________ to
represent the unknown value.
variable
A variable is a ________ that we can use to
represent any number. We use the term variable
because the value _________ based on the
expression.
letter
changes
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
What information do we know?
He mows 2 lawns each day.
What information do we not know?
How many days he mows and the total lawns mowed.
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
How can we represent the relationship between the
two values?
By using variables
What are the two most common letters we use to
represent unknown values?
x
and
y
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
What is the relationship between the number of
days and the number of lawns?
Brian mows ___ lawns for every ___ day.
2
1
Let’s read that statement again:
Brian mows 2 lawns for every 1 day.
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
What information do we know from the problem?
Brian mows two lawns per day.
Will we represent that value with a variable?
Explain your answer.
No, because that is a
constant
value.
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
What is one unknown in our problem?
The number of days mowed
Identify the words in the problem that describe that
unknown.
every day
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
Explain how that is an unknown.
We know that he mows 2 lawns every day, but we do
not know how many days he mows.
Circle the words that describe the unknown.
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
What is the second unknown in the problem?
The total lawns mowed
Circle the words that describe this unknown.
Variables
When we are working with two variables in a situation,
one of them changes and one is affected by the change.
Example: As your feet grow in length, you must buy a
bigger shoe. These values vary from person to person.
In the shoe situation, which variable changes?
The length of the foot
Explain this.
The foot growth happens and determines what size
shoes you must have.
Variables
What two letters are we using to represent the variables
or values that change?
x
and
y
We use the variable __ to represent the value that
changes.
x
In our foot/shoe scenario, which value changes?
The length of the foot
Variables
What two letters are we using to represent the variables
or values that change?
x
and
y
We use the variable __ to represent the value that is
affected by the change.
y
In our foot/shoe scenario, which value is affected by
the change of the foot size?
The shoe size
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
We have two variables circled in the problem.
The number of days
Which variable changes?
x
What letter will we use to represent that variable?
x
– number of
days Brian
mows
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
The variable that changes is called the
independent variable
.
x
– number of
days Brian
mows
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
We have two variables circled in the problem.
Which variable is affected by the number of days
Brian mows?
y
What letter will we use to represent that variable?
x
– number of
days Brian
mows
y
– total
lawns mowed
the total lawns
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
x
– number of
days Brian
mows
y
– total
lawns mowed
The variable “
y
” is affected by the change in the first
variable. This is called the
dependent variable
because its value
changes
based on the value of the
independent variable.
Variables
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
x
– number of
days Brian
mows
y
– total
lawns mowed
What does this mean in the situation with Brian?
The ______________ of lawns mowed is determined by
________________ he mows.
total number
how many days
IDENTIFYING VARIABLES IN A TABLE
Identifying Variables in a Table
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
x
– number of
days Brian
mows
Identify the independent variable, or
x
-value.
the number of days Brian mows
y
– total
lawns mowed
Identify the dependent variable, or
y
-value.
the total lawns mowed
Identifying Variables in a Table
We can represent the relationship between these
two values in a table.
Identifying Variables in a Table
What is the label for the first column?
Days Brian mows
Days Brian Mows
Identifying Variables in a Table
Let’s use our paper square to represent the days.
Place one paper square on the work space.
Identifying Variables in a Table
Days Brian Mows
What variable is used to represent the days Brian
mows?
The independent or
x
-value
Identifying Variables in a Table
What is the label for the second column?
Total Lawns Mowed
Days Brian Mows
Total Lawns Mowed
Identifying Variables in a Table
Let’s use our yellow tiles to represent the number of
lawns mowed.
Identifying Variables in a Table
How many lawns did Brian mow in one day?
two
Place two yellow unit tiles on the paper square.
Identifying Variables in a Table
What variable is used to represent the total lawns
mowed?
The dependent or
y
-value
Days Brian Mows
Total Lawns Mowed
Identifying Variables in a Table
What information do we know?
He mows two lawns every day.
Days Brian Mows
Total Lawns Mowed
Identifying Variables in a Table
What is the first value given in the
x
-column?
1
Days Brian Mows
Total Lawns Mowed
Identifying Variables in a Table
Explain what this value of “1” represents.
It means that Brian mowed one day.
Days Brian Mows
Total Lawns Mowed
Identifying Variables in a Table
What do we know about the number of lawns Brian
will mow in 1 day?
He mows 2 lawns in one day.
Days Brian Mows
Total Lawns Mowed
Identifying Variables in a Table
What number is written in the
y
-column where
x
is
equal to 1?
2
Days Brian Mows
Total Lawns Mowed
Identifying Variables in a Table
What does this mean?
When Brian mows one day, he will mow 2 lawns.
Days Brian Mows
Total Lawns Mowed
Identifying Variables in a Table
Example: Brian mows two lawns every day. How many
total lawns will he mow during summer vacation?
x
– number of
days Brian
mows
Let’s read the scenario about Brian again.
y
– total
lawns mowed
Identifying Variables in a Table
Does our first row of information in the table match
our scenario?
Yes, because the problem tells us that for every 1 day, he
mows 2 lawns.
Days Brian Mows
Total Lawns Mowed
Identifying Variables in a Table
What is the next row of the
x
-column?
2
Days Brian Mows
Total Lawns Mowed
Identifying Variables in a Table
If we are using the paper squares to represent the
days he mows, how many paper squares do we use?
2
Days Brian Mows
Total Lawns Mowed
Identifying Variables in a Table
Let’s place 2 paper squares on the work space.
How many lawns does Brian mow each day?
2
How many yellow tiles do we place on each square?
2
Identifying Variables in a Table
What is the total number of yellow tiles in the 2
squares?
4
What does this represent?
Brian mows 4 lawns in 2 days.
Identifying Variables in a Table
What value do we record in the
y
-column in the row
where Brian mows 2 days?
4
Days Brian Mows
Total Lawns Mowed
4
Identifying Variables in a Table
What does this represent?
Brian mows 4 lawns in 2 days.
Days Brian Mows
Total Lawns Mowed
4
Identifying Variables in a Table
What is the next row of the
x
-column?
3
Days Brian Mows
Total Lawns Mowed
4
Identifying Variables in a Table
If we are using the paper squares to represent the
days he mows, how many paper squares do we use?
3
Days Brian Mows
Total Lawns Mowed
4
Identifying Variables in a Table
Let’s place 3 paper squares on the work space.
How many lawns does Brian mow each day?
2
How many yellow tiles do we place on each square?
2
Identifying Variables in a Table
What is the total number of yellow tiles in the 3
squares?
6
What does this represent?
Brian mows 6 lawns in 3 days.
Identifying Variables in a Table
What value do we record in the
y
-column in the row
where Brian mows 3 days?
6
Days Brian Mows
Total Lawns Mowed
4
6
Identifying Variables in a Table
What is the next row of the
x
-column?
4
Days Brian Mows
Total Lawns Mowed
4
6
Identifying Variables in a Table
If we are using the paper squares to represent the
days he mows, how many paper squares do we use?
4
Days Brian Mows
Total Lawns Mowed
4
6
Identifying Variables in a Table
How many yellow tiles do we place on each square?
2
Identifying Variables in a Table
What is the total number of yellow tiles in the 4
squares?
8
Identifying Variables in a Table
What value do we record in the
y
-column in the row
where Brian mows 4 days?
8
Days Brian Mows
Total Lawns Mowed
4
6
8
Identifying Variables in a Table
Is there a value in the table we did not represent?
Yes
What was the value?
x
Explain why we could not represent the
x
-value with
the concrete model.
x
is a variable, not a constant value.
Identifying Variables in a Table
Days Brian Mows
Total Lawns Mowed
4
6
8
What pattern do you see between the values in the
x
- and
y
-columns?
The values in the
y
-column are always 2 times the
x
-value.
Identifying Variables in a Table
Explain how we can represent 2 times the value of
x
.
2
x
Explain your answer.
The relationship between the values in the
x
-column
and the
y
-column can be described as multiplying by 2.
Identifying Variables in a Table
We can write the relationship between two values
as an equation.
How do we find the value of
y
in each row?
Multiply the
x
value by 2.
How can we write an
equation
to represent the
relationship?
y
= 2
x
IDENTIFYING VARIABLES IN A
GRAPH
Identifying Variables in a Graph
Let’s complete the values in the second column.
4
6
8
Identifying Variables in a Graph
What is the title of the third column?
4
6
8
Ordered Pair
Identifying Variables in a Graph
What values are represented in the ordered pair?
4
6
8
(
x
,
y
)
Identifying Variables in a Graph
What is the ordered pair for Row 1?
4
6
8
(1, 2)
(1, 2)
Identifying Variables in a Graph
What is the
x
-value in Row 2?
4
6
8
2
What is the
y
-value in Row 2?
4
What is the ordered pair for Row 2?
(2, 4)
(2, 4)
(1, 2)
Identifying Variables in a Graph
What is the
x
-value in Row 3?
4
6
8
3
What is the
y
-value in Row 3?
6
What is the ordered pair for Row 3?
(3, 6)
(2, 4)
(1, 2)
(3, 6)
Identifying Variables in a Graph
What is the
x
-value in Row 4?
4
6
8
4
What is the
y
-value in Row 4?
8
What is the ordered pair for Row 4?
(4, 8)
(2, 4)
(1, 2)
(3, 6)
(4, 8)
Identifying Variables in a Graph
What is the label for the
x
-axis?
4
6
8
Number of days
(2, 4)
(1, 2)
(3, 6)
(4, 8)
Identifying Variables in a Graph
What is the label for the
y
-axis?
4
6
8
Total number of lawns
(2, 4)
(1, 2)
(3, 6)
(4, 8)
Identifying Variables in a Graph
Let’s plot the first
point (1, 2).
Identify the
x
-value.
1
Explain how to plot
the
x
-value.
Move 1 space on
the
x
-axis.
Identifying Variables in a Graph
(1, 2)
Explain how to plot
the
y
-value.
Move from the 1
space on the
x
-axis
up two spaces.
Plot the point (1, 2)
Plot the other points
from the table.
Identifying Variables in a Graph
What value represents
the number of days?
x
-value
Explain how the
x
-values
increase in the table and
graph.
By 1
Identifying Variables in a Graph
What value represents
the total number of
lawns?
y
-value
Explain how the
y
-values
increase in the table and
graph.
By 2
Identifying Variables in a Graph
What equation can be
used to represent this
relationship?
y
= 2
x
Is there a relationship
between the number of
days and the number of
lawns?
Yes
Identifying Variables in a Graph
Can we connect the
coordinate points with a
line?
Yes
What is the starting point
of the line?
The origin
Identifying Variables in a Graph
Explain your answer.
The origin is the starting
point because before he
started (day zero) he
would have mowed zero
lawns.
Is it possible to interpret
data on the graph
between points?
Yes
Identifying Variables in a Graph
This is an example of
continuous data
.
What does it mean to be
continuous?
It happens all the
time.
Identifying Variables in a Graph
Can we make a prediction
about how many lawns
Brian would mow in 30
days?
Yes, we can substitute the
value of 30 for
x
in the
equation
y
= 2
x
to
determine that he will
mow 60 lawns in 30 days.
Identifying Variables in a Graph
Let’s complete the values in the second column.
8
12
16
Identifying Variables in a Graph
What is the title of the third column?
Ordered Pair
8
12
16
Identifying Variables in a Graph
What values are represented in the ordered pair?
(
x
,
y
)
8
12
16
Identifying Variables in a Graph
What is the ordered pair for Row 1?
(1, 4)
8
12
16
8
12
16
Identifying Variables in a Graph
What is the
x
-value in Row 2?
2
What is the
y
-value in Row 2?
8
What is the ordered pair for Row 2?
(2, 8)
(2, 8)
8
12
16
(2, 8)
Identifying Variables in a Graph
What is the
x
-value in Row 3?
3
What is the
y
-value in Row 3?
12
What is the ordered pair for Row 3?
(3, 12)
(3, 12)
8
12
16
(2, 8)
(3, 12)
Identifying Variables in a Graph
What is the
x
-value in Row 4?
4
What is the
y
-value in Row 4?
16
What is the ordered pair for Row 4?
(4, 16)
(4, 16)
Identifying Variables in a Graph
What is the label for the
x
-axis?
Number of Packs of Pencils
8
12
16
(2, 8)
(3, 12)
(4, 16)
Identifying Variables in a Graph
What is the label for the
y
-axis?
Total Number of Pencils
8
12
16
(2, 8)
(3, 12)
(4, 16)
Identifying Variables in a Graph
Let’s plot the first
point (1, 4).
Identify the
x
-value.
1
Explain how to plot
the
x
-value.
Move 1 space on
the
x
-axis.
Identifying Variables in a Graph
Let’s plot the first
point (1, 4).
Explain how to plot
the
y
-value.
Move from the 1
space on the
x
-axis
up to the 4 on the
y
-axis.
Plot the points
Identifying Variables in a Graph
What value represents
the number of packs of
pencils?
x
-value
Explain how the
x
-values
increase in the table and
graph.
By 1
Identifying Variables in a Graph
What value represents
the total number of
pencils?
y
-value
Explain how the
y
-values
increase in the table and
graph.
By 4
Identifying Variables in a Graph
What equation can be
used to represent this
relationship?
y
= 4
x
Is the relationship
between the coordinates
proportional?
Yes, because they could
be connected with a
straight line passing
through the origin.
Identifying Variables in a Graph
In this situation can we
represent the data with a
line? Explain your answer.
No, because the pencils
are in packages, and it is
not possible to buy part
of a package.
Identifying Variables in a Graph
There are some real-life
situations where the data
points cannot be connected
because the relationship
between the two values can
only be represented by
specific points, not all the
values on the line. This is an
example of
discrete data
.
Identifying Variables in a Graph
Can we make a prediction
about how many pencils
would be in 12 packs?
Explain your answer.
Yes, we can substitute
the value of 12 for
x
in
the equation
y
= 4
x
to
determine that there are
48 pencils in 12 packs.
REPRESENT AND ANALYZE
QUANTITATIVE RELATIONSHIPS
SOLVE Problem – Completion
[
LESSON
]
SOLVE
Jennie helps her grandmother every week one
day after school. Her grandmother gives her $15
every week.
Write an equation that can be used
to represent the relationship between the total
she earns (
y
) and the number of weeks worked
(
x
).
Create a table to model the relationship for 4
weeks, 8 weeks, 12 weeks, and 16 weeks and
graph the relationship on a coordinate plane.
[
LESSON
]
SOLVE
S
Study the Problem
Underline the question.
This problem is asking me to find
the equation, table and graph to represent the
relationship between the number of weeks
worked and Jennie’s earnings.
O
Organize the Facts
Identify the facts.
[
LESSON
]
SOLVE
Jennie helps her grandmother every week one
day after school. Her grandmother gives her $15
every week. Write an equation that can be used
to represent the relationship between the total
she earns (
y
) and the number of weeks worked
(
x
). Create a table to model the relationship for 4
weeks, 8 weeks, 12 weeks, and 16 weeks and
graph the relationship on a coordinate plane.
O
Organize the Facts
Identify the facts.
Eliminate the unnecessary facts.
[
LESSON
]
SOLVE
Jennie helps her grandmother every week one
day after school. Her grandmother gives her $15
every week. Write an equation that can be used
to represent the relationship between the total
she earns (
y
) and the number of weeks worked
(
x
). Create a table to model the relationship for 4
weeks, 8 weeks, 12 weeks, and 16 weeks and
graph the relationship on a coordinate plane.
O
Organize the Facts
Identify the facts.
Eliminate the unnecessary facts.
List the necessary facts.
•
Jennie
earns $15 per week
•
Total earned (
y
) and number of weeks (
x
)
•
Table with 4 weeks, 8 weeks, 12, weeks, 16
weeks
L
Line Up a Plan
Write in words what your plan of action will
be.
Write an equation that shows the relationship
between the number of weeks that Jennie
works and the amount of money she earns.
Write the given information about the weeks
in a table and fill in the missing values using
the equation. Graph the (
x
,
y
) values from
the table on a coordinate plane.
Choose an operation or operations.
Multiplication
V
Verify Your Plan with Action
Estimate your answer.
There will be a relationship between the weeks
she works and the money she makes. The
data is discrete so the graph will be made of
points that are not connected by a line.
Carry out your plan.
$60
$120
$180
$240
(4, 60)
(8, 120)
(12, 180)
(16, 240)
V
Verify Your Plan with Action
Carry out your plan.
(4, 60)
(8, 120)
(12, 180)
(16, 240)
E
Examine Your Results
Does your answer make sense?
(Compare your answer to question.)
Yes, I represented the relationship with an
equation, table, and graph.
Is your answer reasonable?
(Compare your answer to the estimate.)
Yes, because I graphed the relationship, and
the data is discrete and not connected by a
line.
Is your answer accurate?
(Check your work.)
Yes
Write your answer in a complete sentence.
The equation that represents the relationship
between Jennie’s weeks worked and the total
amount she earns is
y
= 15
x
.
REPRESENT AND ANALYZE
QUANTITATIVE RELATIONSHIPS
Closure
[
ESSENTIAL
QUESTIONS
]
1.
Explain the meaning of an independent
variable.
The independent variable is the
variable that can be changed.
[
ESSENTIAL
QUESTIONS
]
2.
Explain the meaning of a dependent
variable.
The dependent variable is the variable
that is affected by the change in the
independent variable.
[
ESSENTIAL
QUESTIONS
]
3.
Explain how you can use the information
given in an equation to model the
relationship using a table and coordinate
plane.
Choose values for the
x
-coordinates and
write them in the table. Substitute the
x
-
values into the equation and fill in the table
with the
y
-values. Write a coordinate pair
for each
x
- and
y
-value and plot the
coordinates on the coordinate plane.
Variable
Equation
Dependent Variable
Independent Variable
Constant
Discrete Data
Continuous Data
Lesson
Represent and Analyze
Quantitative Relationships
Explore how to represent and analyze quantitative relationships using graphs, tables, and equations. Practice with unit rates, plotting points in a coordinate plane, and understanding independent and dependent variables. Develop skills in creating equations, tables, and graphs to model relationships between variables. Engage with essential questions to deepen your understanding of quantitative relationships and their applications.
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Presentation Transcript
Lesson Represent and Analyze Quantitative Relationships
[OBJECTIVE] The student will represent and analyze quantitative relationships in graphs, tables, and equations.
[MYSKILLS] Unit rates Plotting points in the coordinate plane Equations
[ESSENTIALQUESTIONS] 1. Explain the meaning of an independent variable. 2. Explain the meaning of a dependent variable. 3. Explain how you can use the information given in an equation to model the relationship using a table and coordinate plane.
[Warm-Up] Begin by completing the warm-up for this lesson.
SOLVE Problem Introduction REPRESENT AND ANALYZE QUANTITATIVE RELATIONSHIPS
[LESSON] SOLVE Jennie helps her grandmother every week one day after school. Her grandmother gives her $15 every week. Write an equation that can be used to represent the relationship between the total she earns (y) and the number of weeks worked (x). Create a table to model the relationship for 4 weeks, 8 weeks, 12 weeks, and 16 weeks and graph the relationship on a coordinate plane.
[LESSON] SOLVE S Study the Problem Underline the question.
[LESSON] SOLVE Jennie helps her grandmother every week one day after school. Her grandmother gives her $15 every week. Write an equation that can be used to represent the relationship between the total she earns (y) and the number of weeks worked (x). Create a table to model the relationship for 4 weeks, 8 weeks, 12 weeks, and 16 weeks and graph the relationship on a coordinate plane.
[LESSON] SOLVE S Study the Problem Underline the question. This problem is asking me to find the equation, table and graph to represent the relationship between the number of weeks worked and Jennie s earnings.
Variables When we write and evaluate expressions that have unknown values we can use a __________ to represent the unknown value. variable A variable is a ________ that we can use to represent any number. We use the term variable because the value _________ based on the expression. letter changes
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? What information do we know? He mows 2 lawns each day. What information do we not know? How many days he mows and the total lawns mowed.
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? How can we represent the relationship between the two values? By using variables What are the two most common letters we use to represent unknown values? x and y
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? What is the relationship between the number of days and the number of lawns? Brian mows ___ lawns for every ___ day. 2 1 Let s read that statement again: Brian mows 2 lawns for every 1 day.
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? What information do we know from the problem? Brian mows two lawns per day. Will we represent that value with a variable? Explain your answer. No, because that is a constant value.
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? What is one unknown in our problem? The number of days mowed Identify the words in the problem that describe that unknown. every day
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? Explain how that is an unknown. We know that he mows 2 lawns every day, but we do not know how many days he mows. Circle the words that describe the unknown.
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? What is the second unknown in the problem? The total lawns mowed Circle the words that describe this unknown.
Variables When we are working with two variables in a situation, one of them changes and one is affected by the change. Example: As your feet grow in length, you must buy a bigger shoe. These values vary from person to person. In the shoe situation, which variable changes? The length of the foot Explain this. The foot growth happens and determines what size shoes you must have.
Variables What two letters are we using to represent the variables or values that change? x and y x We use the variable __ to represent the value that changes. In our foot/shoe scenario, which value changes? The length of the foot
Variables What two letters are we using to represent the variables or values that change? x and y y We use the variable __ to represent the value that is affected by the change. In our foot/shoe scenario, which value is affected by the change of the foot size? The shoe size
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? x number of days Brian mows We have two variables circled in the problem. Which variable changes? The number of days What letter will we use to represent that variable? x
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? x number of days Brian mows The variable that changes is called the independent variable.
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? y total lawns mowed x number of days Brian mows We have two variables circled in the problem. Which variable is affected by the number of days Brian mows? the total lawns What letter will we use to represent that variable? y
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? y total lawns mowed x number of days Brian mows The variable y is affected by the change in the first variable. This is called the dependent variable because its value changes based on the value of the independent variable.
Variables Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? y total lawns mowed x number of days Brian mows What does this mean in the situation with Brian? total number The ______________ of lawns mowed is determined by ________________ he mows. how many days
Identifying Variables in a Table Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? y total lawns mowed x number of days Brian mows Identify the independent variable, or x-value. the number of days Brian mows Identify the dependent variable, or y-value. the total lawns mowed
Identifying Variables in a Table (x) (y) 1 2 3 4 x 2 We can represent the relationship between these two values in a table.
Identifying Variables in a Table Days Brian Mows (x) (y) 1 2 3 4 x 2 What is the label for the first column? Days Brian mows
Identifying Variables in a Table Let s use our paper square to represent the days. Place one paper square on the work space.
Identifying Variables in a Table Days Brian Mows (x) (y) 1 2 3 4 x 2 What variable is used to represent the days Brian mows? The independent or x-value
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 What is the label for the second column? Total Lawns Mowed
Identifying Variables in a Table Let s use our yellow tiles to represent the number of lawns mowed.
Identifying Variables in a Table How many lawns did Brian mow in one day? two Place two yellow unit tiles on the paper square.
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 What variable is used to represent the total lawns mowed? The dependent or y-value
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 What information do we know? He mows two lawns every day.
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 What is the first value given in the x-column? 1
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 Explain what this value of 1 represents. It means that Brian mowed one day.
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 What do we know about the number of lawns Brian will mow in 1 day? He mows 2 lawns in one day.
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 What number is written in the y-column where x is equal to 1? 2
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 What does this mean? When Brian mows one day, he will mow 2 lawns.
Identifying Variables in a Table Example: Brian mows two lawns every day. How many total lawns will he mow during summer vacation? y total lawns mowed x number of days Brian mows Let s read the scenario about Brian again.
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 Does our first row of information in the table match our scenario? Yes, because the problem tells us that for every 1 day, he mows 2 lawns.
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 What is the next row of the x-column? 2
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 If we are using the paper squares to represent the days he mows, how many paper squares do we use? 2
Identifying Variables in a Table Let s place 2 paper squares on the work space. How many lawns does Brian mow each day? 2 How many yellow tiles do we place on each square? 2
Identifying Variables in a Table What is the total number of yellow tiles in the 2 squares? 4 What does this represent? Brian mows 4 lawns in 2 days.
Identifying Variables in a Table Days Brian Mows (x) (y) Total Lawns Mowed 1 2 3 4 x 2 4 What value do we record in the y-column in the row where Brian mows 2 days? 4
