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Constant vs. Varying Change. Consider the following…. Consider the following…. A new pencil is placed in an electric sharpener. Study the following chart. Does this chart show an increase or a decrease?. As time goes by, the length of the pencil is decreasing. Minus 2 inches.

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consider the following1
Consider the following…

A new pencil is placed in an electric sharpener.

as time goes by the length of the pencil is decreasing
As time goes by, the length of the pencil isdecreasing.

Minus 2 inches

Minus 2 inches

Minus 2 inches

this is a constant rate of decrease the pencil shrinks by 2 inches every minute
This is aconstantrate of decrease.The pencil shrinks by 2 inches every ½ minute.

Minus 2 inches

Minus 2 inches

Minus 2 inches

slide8

A Pencil’s 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)

slide9

A Pencil’s 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)

consider the following3
Consider the following…

Jack puts $5 into his piggy bank every week.

slide16

Jack’s 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

1

2

3

4

5

Time (in weeks)

slide17

Jack’s Savings

Numberofdollars

50

45

40

35

EXTEND THE GRAPH.

30

25

20

15

10

5

0

After 9 weeks, Jack will have $45.

0

1

2

3

4

5

6

7

8

9

Time (in weeks)

slide19

Consider the following…

John works the concession stand at football games

slide24

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

5:00

5:15

5:30

5:45

Time

slide26

Consider the following…

Jim is checking his heart rate every minute. He is in a relaxed state.

slide29

Jim’s 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

1:00

1:05

1:10

1:15

Time

slide35

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

slide36

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

Minus 5

Minus 5

Minus 5

slide37

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

slide38

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

slide39

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

slide40

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

slide41

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

slide42

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

slide43

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

slide44

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

slide45

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

Numberofbeats

Jim’s Heart Rate After Running 1 mile

120

115

110

105

100

95

90

85

80

1:00

1:01

1:02

1:03

1:04

1:05

1:06

1:07

1:08

Time

slide46

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

Numberofbeats

Jim’s Heart Rate After Running 1 mile

120

115

110

105

100

95

90

85

80

1:00

1:01

1:02

1:03

1:04

1:05

1:06

1:07

1:08

Time

slide47

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

NumberofStudents

Students in Period 1 Math Class

35

30

25

24

23

22

20

19

18

Aug

Sep

Oct

Nov

Dec

Jan

Feb

Mar

Apr

Month

slide48

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

NumberofStudents

Students in Period 1 Math Class

35

30

25

24

23

22

20

19

18

Aug

Sep

Oct

Nov

Dec

Jan

Feb

Mar

Apr

Month

slide49

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

NumberofDeer(in100s)

Deer Population

8

7

6

5

4

3

2

1

0

Aug

Sep

Oct

Nov

Dec

Jan

Feb

Mar

Apr

Month

slide50

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

NumberofDeer(in100s)

Deer Population

8

7

6

5

4

3

2

1

0

Aug

Sep

Oct

Nov

Dec

Jan

Feb

Mar

Apr

Month

slide51

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

Number of Books in the Library

200

NumberofBooks

175

150

125

100

75

50

25

0

1

2

3

4

5

6

7

8

9

Week Number

slide52

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

Number of Books in the Library

200

NumberofBooks

175

150

125

100

75

50

25

0

1

2

3

4

5

6

7

8

9

Week Number

slide53

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

PopsInTheFridge

Disappearing Cokes

16

14

12

10

8

6

4

2

0

Sat

Sun

Mon

Tue

Wed

Thu

Fri

Day of the Week

slide54

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

PopsInTheFridge

Disappearing Cokes

16

14

12

10

8

6

4

2

0

Sat

Sun

Mon

Tue

Wed

Thu

Fri

Day of the Week

slide61

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.

slide62

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.

slide63

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.

slide64

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.

slide65

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.

slide66

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.