Proportional Relationships in Mathematics
11.26.2018
Ticket in the
Door
Ticket in the
Door Review
Current lesson:
Test
Proportionality
Wrap-up
3 + p = 8
x − 7 = 13
m − 9 = −13
m + 4 = −12
Agenda
Ticket in the Door
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P
ROPORTIONALITY
USING
G
RAPHS
AND
T
ABLES
Exercise for Practices
P
ROPORTIONALITY
USING
GRAPHS
AND
T
ABLES
INTRODUCTION
https://www.youtube.com/watch?v=HwJPkXOboB
k
https://www.youtube.com/watch?v=USmit5zUGas
https://www.youtube.com/watch?v=0JCoSeFKW_
Y&list=PL7df-
zRnuvQWxyb2j60R3DjbV7xExH1Hy
F
ORMAT
YOUR
PAPER
FOR
C
ORNELL
NOTES
Topic: Understanding
Proportional
Relationships
E.Q. How do I
determine when a
proportional
relationship exist?
Topic/E.Q.
Cornell Note Example
P
ROPORTIONAL
R
ELATIONSHIPS
We can use our knowledge of ratios and
proportions to determine if there is a proportional
relationship between different elements.
Relationships are usually represented using a
graph or a table.
We can use the graphs and tables to test the
proportionality.
U
SING
A
TABLE
In order to tell from a table if there is a
proportional relationship or not, you can check to
see if the ratio
y : x
is the same.
The ratio
y : x
is also known as the
constant of
proportionality
.
You must reduce the ratios to accurately
compare!
EX .Tell if the following tables represent a
proportional relationships.
•
This is a proportional
relationship because the y: x
ratios are all equal!
•
The constant of
proportionality is 2/1 (or 2)
EX .Tell if the following tables represent a
proportional relationships.
•
This is NOT a proportional
relationship because the y: x
ratios are not all equal!
P
RACTICE
Are the following tabled representing
proportional relationships?
Q
UICK
R
EVIEW
OF
G
RAPHING
Ordered Pair - A pair of numbers (x , y)used to
locate a point on a coordinate plane.
Also called a
point.
Using the table below, create a list of ordered
pairs.
(1,4) , (3,8), (2,6), (8,10)
When we plot points on the grid (coordinate
plane), we start at the origin then count :
1.
right or left on the
x-axis and then
1.
up or down on the
y-axis.
Q
UICK
R
EVIEW
OF
G
RAPHING
x-axis
y-axis
Origin (0,0)
Plot the following points (write the ordered pairs
on the grid)
(1,4) and (2,8)
Q
UICK
R
EVIEW
OF
G
RAPHING
x
y
0 1 2 3 4 5 6 7 8
0 1 2 3 4 5 6 7 8
(1,4)
(2,8)
U
SING
A
G
RAPH
We can test for proportionality on a graph by
looking for various properties.
1.
A proportional graph will always go through the
origin (0,0)
2.
A proportional graph will be a straight line.
3.
If you list points (ordered pairs) from a graph,
you can create ratios and see if they are
constant (equal).
In order to tell if a graph is proportional the line must go
through the origin and be a straight line.
•
Straight line ?
Yes
•
Passes through (0,0)?
Yes
•
This is a
proportional
relationship!
In order to tell if a graph is proportional the line must go
through the origin and be a straight line.
•
Straight line ?
Yes
•
Passes through (0,0)?
No
•
This is
NOT
a
proportional relationship!
In order to tell if a set of ordered pairs is proportional, graph
them or look at the ratio of
y
to
x
.
Tell if the following set of ordered pairs represents
a proportional relationship.
•
(x, y) ordered pairs are used to make ratios
•
y: x = y/x
4/8 = 1/2
5/10 = 1/2
2.5/5 = 1/2
6/12 = 1/2
T
h
i
s
i
s
a
p
r
o
p
o
r
t
i
o
n
a
l
r
e
l
a
t
i
o
n
s
h
i
p
b
e
c
a
u
s
e
t
h
e
r
a
t
i
o
s
a
r
e
c
o
n
s
t
a
n
t
•
To determine if the following equations show a proportional
relationship, put a zero in for x and solve for y.
•
if y is zero then it is a proportional relationship because
it goes through the origin.
y
=
3
x
+
1
y
=
1
0
x
U
SING
AN
E
QUATION
y = 3(0) + 1
y= 0 + 1
y= 1
Not Proportional
y = 10(0)
y= 0
Proportional
G
RAPHING
P
ROPORTIONAL
R
ELATIONSHIPS
1. Given a table
Create a list of ordered pairs
Plot the points on the grid
Connect using a ruler
Label axis
2. Given an equation
Create a table
Create a list of ordered pairs
Plot the points
Connect using a ruler
Label axis
G
RAPHING
GIVEN
A
TABLE
(1,3)
(0,0)
(2,6)
Ordered pairs:
(0,0), (1,3), (2,6)
Hours
Miles
G
RAPHING
G
IVEN
AN
E
QUATION
y = 2x
1. Create a table by substituting value into x and
solving for y. (need three points)
2. Ordered Pairs
(0,0), (1,2), (2,4)
3. Plot the points on the grid.
(0,0), (1,2), (2,4)
4. Connect the points
G
RAPHING
G
IVEN
AN
E
QUATION
R
EFERENCE
http://sunvalleycharterschool.com/teacher_blog/fil
e/8th%20G%20PPT%20-
%20Proportionality_Using_Graphs_and_Tables.p
pt.
Explore the concept of proportionality using graphs, tables, and ratios. Learn how to determine if a relationship is proportional by analyzing ratios y:x and the constant of proportionality. Practice exercises and examples provided for better comprehension.
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Presentation Transcript
11.26.2018 Agenda Ticket in the Door Ticket in the Door Ticket in the Door Review Current lesson: Test Proportionality Wrap-up 3 + p = 8 x 7 = 13 m 9 = 13 m + 4 = 12
PROPORTIONALITY USING GRAPHS AND TABLES Exercise for Practices
PROPORTIONALITY USING GRAPHS AND TABLES INTRODUCTION https://www.youtube.com/watch?v=HwJPkXOboB k https://www.youtube.com/watch?v=USmit5zUGas https://www.youtube.com/watch?v=0JCoSeFKW_ Y&list=PL7df- zRnuvQWxyb2j60R3DjbV7xExH1Hy
FORMAT YOUR PAPER FOR CORNELL NOTES Topic/E.Q. Cornell Note Example Topic: Understanding Proportional Relationships E.Q. How do I determine when a proportional relationship exist?
PROPORTIONAL RELATIONSHIPS We can use our knowledge of ratios and proportions to determine if there is a proportional relationship between different elements. Relationships are usually represented using a graph or a table. We can use the graphs and tables to test the proportionality.
USING A TABLE In order to tell from a table if there is a proportional relationship or not, you can check to see if the ratio y : x is the same. The ratio y : x is also known as the constant of proportionality. You must reduce the ratios to accurately compare!
EX .Tell if the following tables represent a proportional relationships. This is a proportional relationship because the y: x ratios are all equal! x y y:x =y/x 10/5 = 2/1 16/8 = 2/1 20/10 = 2/1 28/14 = 2/1 42/21 = 2/1 5 10 8 16 The constant of proportionality is 2/1 (or 2) 10 20 14 28 21 42
EX .Tell if the following tables represent a proportional relationships. This is NOT a proportional relationship because the y: x ratios are not all equal! x y y:x =y/x 9/6 = 3/2 15/10 = 3/2 20/4 = 5/1 21/14 = 3/2 42/21 = 2/1 6 9 10 15 4 20 14 21 22 44
PRACTICE Are the following tabled representing proportional relationships? X Y X Y 4 6 1 4 6 9 2 8 10 15 3 9
QUICK REVIEWOF GRAPHING Ordered Pair - A pair of numbers (x , y)used to locate a point on a coordinate plane. Also called a point. Using the table below, create a list of ordered pairs. X Y (1,4) , (3,8), (2,6), (8,10) 1 4 3 8 2 6 8 10
QUICK REVIEWOF GRAPHING When we plot points on the grid (coordinate plane), we start at the origin then count : right or left on the x-axis and then up or down on the y-axis. 1. 1. y-axis x-axis Origin (0,0)
QUICK REVIEWOF GRAPHING Plot the following points (write the ordered pairs on the grid) y 0 1 2 3 4 5 6 7 8 (1,4) and (2,8) (2,8) (1,4) x 0 1 2 3 4 5 6 7 8
USINGA GRAPH We can test for proportionality on a graph by looking for various properties. A proportional graph will always go through the origin (0,0) A proportional graph will be a straight line. If you list points (ordered pairs) from a graph, you can create ratios and see if they are constant (equal). 1. 2. 3.
In order to tell if a graph is proportional the line must go through the origin and be a straight line. Straight line ? Yes Passes through (0,0)? Yes This is a proportional relationship!
In order to tell if a graph is proportional the line must go through the origin and be a straight line. Straight line ? Yes Passes through (0,0)? No This is NOT a proportional relationship!
In order to tell if a set of ordered pairs is proportional, graph them or look at the ratio of y to x. Tell if the following set of ordered pairs represents a proportional relationship. ( ) ( ) ( 8, 4 , 10, 5 , 5, 2.5 , 12, 6 ) ( ) (x, y) ordered pairs are used to make ratios y: x = y/x This is a proportional relationship because the ratios are constant 4/8 = 1/2 5/10 = 1/2 2.5/5 = 1/2 6/12 = 1/2
USINGAN EQUATION To determine if the following equations show a proportional relationship, put a zero in for x and solve for y. if y is zero then it is a proportional relationship because it goes through the origin. y = 10x y = 3x + 1 y = 3(0) + 1 y = 10(0) y= 0 + 1 y= 0 y= 1 Not Proportional Proportional
GRAPHING PROPORTIONAL RELATIONSHIPS 1. Given a table Create a list of ordered pairs Plot the points on the grid Connect using a ruler Label axis 2. Given an equation Create a table Create a list of ordered pairs Plot the points Connect using a ruler Label axis
GRAPHINGGIVENATABLE Hours X 0 Miles Y 0 (2,6) 1 3 Miles (1,3) 2 6 Ordered pairs: (0,0), (1,3), (2,6) Hours (0,0)
GRAPHING GIVENAN EQUATION y = 2x 1. Create a table by substituting value into x and solving for y. (need three points) X y=2x Y 0 y= 2(0)= 0 0 1 y= 2(1) = 2 2 2 y=2(2) = 4 4 2. Ordered Pairs (0,0), (1,2), (2,4)
GRAPHING GIVENAN EQUATION 3. Plot the points on the grid. (0,0), (1,2), (2,4) 4. Connect the points
REFERENCE http://sunvalleycharterschool.com/teacher_blog/fil e/8th%20G%20PPT%20- %20Proportionality_Using_Graphs_and_Tables.p pt.
