Constant vs' Varying Change

1
Constant vs. Varying Change
2
Consider the following
3
Consider the following
A new pencil is placed in an electric sharpener.
4
Study the following chart. Does this chart show
an increase or a decrease?
5
As time goes by, the length of the pencil is
decreasing.
Minus 2 inches
Minus 2 inches
Minus 2 inches
6
Is the rate of decrease constant or does the rate
vary?
7
This is a constant rate of decrease.The pencil
shrinks by 2 inches every ½ minute.
Minus 2 inches
Minus 2 inches
Minus 2 inches
8
A Pencils Changing Length In A Sharpener
10
How much time must pass before the pencil is gone?
Lengthofpencil
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
Time (in minutes)
9
A Pencils Changing Length In A Sharpener
10
Lengthofpencil
9
8
7
EXTEND THE GRAPH.
6
5
4
3
2
1
0
0
1
2
3
After 2 ½ minutes, the pencil will be gone.
Time (in minutes)
10
Consider the following
11
Consider the following
Jack puts 5 into his piggy bank every week.
12
Study the following chart. Does this chart show
an increase or a decrease?
13
As time goes by, Jacks savings is increasing.
Plus 5
Plus 5
Plus 5
14
Is the rate of increase constant or does the rate
vary?
15
This is a constant rate of increase.Jack gains
5 each week.
Plus 5
Plus 5
Plus 5
16
Jacks Savings
Numberofdollars
50
If Jack wants to have 45 in his piggy bank, for
how many weeks must he save?
45
40
35
30
25
20
15
10
5
0
0
2
4
3
5
1
Time (in weeks)
17
Jacks Savings
Numberofdollars
50
45
40
35
EXTEND THE GRAPH.
30
25
20
15
10
5
0
After 9 weeks, Jack will have 45.
0
2
4
3
5
1
6
7
8
9
Time (in weeks)
18
Consider the following
19
Consider the following
John works the concession stand at football games
20
Study the following chart. Does this chart show
an increase or a decrease?
21
As time goes by, the number of hotdogs sold is
increasing.
Plus 7
Plus 18
Plus 5
22
Is the rate of increase constant or does the rate
vary?
23
This is a varying rate of increase.Plus 7/Plus
18/Plus 5
Plus 7
Plus 18
Plus 5
24
Hot Dog Sales
Numberofhotdogs
50
Notice how the graph does NOT make a straight
line. This is an example of change that is NOT
constant.
45
40
35
30
25
20
15
10
5
0
500
530
545
515
Time
25
Consider the following
26
Consider the following
Jim is checking his heart rate every minute. He
is in a relaxed state.
27
Study the following chart. Does this chart show
an increase or a decrease?
28
There is neither an increase nor a decrease.
There is NO change.
Plus 0
Plus 0
Plus 0
29
Jims Resting Heart Rate
Numberofbeatspermin.
100
This is an example of a graph that shows NO
CHANGE.
90
80
70
60
50
40
30
20
10
0
100
110
115
105
Time
30
This graph shows a constant increase.
31
This graph shows a constant decrease.
32
This graph shows no change.
33
This graph shows an increase and a decrease.
34
Practice Time!
35
1) Determine the kind of change represented by
the chart. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

36
1) Determine the kind of change represented by
the chart. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

Minus 5
Minus 5
Minus 5
37
2) Determine the kind of change represented by
the chart. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

38
2) Determine the kind of change represented by
the chart. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

Plus 8
Plus 16
Plus 32
39
3) Determine the kind of change represented by
the chart. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

40
3) Determine the kind of change represented by
the chart. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

Plus 25
Plus 25
Plus 25
41
4) Determine the kind of change represented by
the chart. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

42
4) Determine the kind of change represented by
the chart. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

Minus 15
Minus 10
Minus 5
43
5) Determine the kind of change represented by
the chart. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

44
5) Determine the kind of change represented by
the chart. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

45
6) Determine the kind of change represented by
the graph. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

Numberofbeats
Jims Heart Rate After Running 1 mile
120
115
110
105
100
95
90
85
80
100
102
103
101
104
105
106
107
108
Time
46
6) Determine the kind of change represented by
the graph. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

Numberofbeats
Jims Heart Rate After Running 1 mile
120
115
110
105
100
95
90
85
80
100
102
103
101
104
105
106
107
108
Time
47
7) Determine the kind of change represented by
the graph. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

NumberofStudents
Students in Period 1 Math Class
35
30
25
24
23
22
20
19
18
Aug
Oct
Nov
Sep
Dec
Jan
Feb
Mar
Apr
Month
48
7) Determine the kind of change represented by
the graph. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

NumberofStudents
Students in Period 1 Math Class
35
30
25
24
23
22
20
19
18
Aug
Oct
Nov
Sep
Dec
Jan
Feb
Mar
Apr
Month
49
8) Determine the kind of change represented by
the graph. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

NumberofDeer(in100s)
Deer Population
8
7
6
5
4
3
2
1
0
Aug
Oct
Nov
Sep
Dec
Jan
Feb
Mar
Apr
Month
50
8) Determine the kind of change represented by
the graph. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

NumberofDeer(in100s)
Deer Population
8
7
6
5
4
3
2
1
0
Aug
Oct
Nov
Sep
Dec
Jan
Feb
Mar
Apr
Month
51
9) Determine the kind of change represented by
the graph. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

Number of Books in the Library
200
NumberofBooks
175
150
125
100
75
50
25
0
1
3
4
2
5
6
7
8
9
Week Number
52
9) Determine the kind of change represented by
the graph. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

Number of Books in the Library
200
NumberofBooks
175
150
125
100
75
50
25
0
1
3
4
2
5
6
7
8
9
Week Number
53
10) Determine the kind of change represented by
the graph. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

PopsInTheFridge
Disappearing Cokes
16
14
12
10
8
6
4
2
0
Sat
Mon
Tue
Sun
Wed
Thu
Fri
Day of the Week
54
10) Determine the kind of change represented by
the graph. A) Constant Increase D) Varying
Increase B) Constant Decrease E) Varying
Decrease C) No Change F) None of the above

PopsInTheFridge
Disappearing Cokes
16
14
12
10
8
6
4
2
0
Sat
Mon
Tue
Sun
Wed
Thu
Fri
Day of the Week
55
11) Which graph shows a constant increase?
A)
B)
C)
D)
56
11) Which graph shows a constant increase?
A)
B)
C)
D)
57
12) Which graph shows a constant decrease?
A)
B)
C)
D)
58
12) Which graph shows a constant decrease?
A)
B)
C)
D)
59
13) Which graph shows no change?
A)
B)
C)
D)
60
13) Which graph shows no change?
A)
B)
C)
D)
61
14) Imagine that you are riding in a car. When
might you experience a constant increase in speed?
A) You are 25 yards away from a stop sign.
B) A traffic light just turned from red to green.
C) You are on interstate 71, and there is no
traffic.
62
14) Imagine that you are riding in a car. When
might you experience a constant increase in speed?
A) You are 25 yards away from a stop sign.
B) A traffic light just turned from red to green.
C) You are on interstate 71, and there is no
traffic.
63
15) Imagine that you are riding in a car. When
might you experience a constant decrease in speed?
A) You are 25 yards away from a stop sign.
B) A traffic light just turned from red to green.
C) You are on interstate 71, and there is no
traffic.
64
15) Imagine that you are riding in a car. When
might you experience a constant decrease in speed?
A) You are 25 yards away from a stop sign.
B) A traffic light just turned from red to green.
C) You are on interstate 71, and there is no
traffic.
65
16) Imagine that you are riding in a car. When
might you experience no change in speed?
A) You are 25 yards away from a stop sign.
B) A traffic light just turned from red to green.
C) You are on interstate 71, and there is no
traffic.
66
16) Imagine that you are riding in a car. When
might you experience no change in speed?
A) You are 25 yards away from a stop sign.
B) A traffic light just turned from red to green.
C) You are on interstate 71, and there is no
traffic.
67
The End