2. We see change all around us. In many
instances, change is related to the
passage of time.
Take a look at the following video. You
can see that the height of the plant
changes over the course of 5 days.
3.
4. Today we will identify the
change in value over time and
make simple predictions.
We will use a series of steps to help us identify
the change over time shown on both tables
and graphs.
5. The Steps:
1. What is the variable? (In other words, what
is changing with the passage of time?)
2. How is the variable changing?
(Do you see an increase, decrease, or does the
data remain constant?)
3. By how much does the data change?
4. Apply the rule to the pattern to make a
prediction.
6. Change in data can be displayed in graphs and tables.
Do you remember what type of graph shows change
over time?
**************************************
That’s right! A line graph. Let’s look
at our first example.
7. This line graph shows the height of a
plant over five days.
10
9
8
Height (cm)
7
6
5
4
3
2
1
0
1 2 3 4 5
Days
Let’s use the steps to determine how the height
of a plant changes over the course of 5 days.
8. STEP ONE: What is the variable? (In other
words, what is changing?)
10
9
Height (cm) 8
7
6
5
4
3
2
1
0
1 2 3 4 5
Days
The height of the plant is changing. Height is our
variable.
9. STEP TWO: How is the variable changing?
(Do you see an increase, decrease, or does the data remain constant?)
10
9
8
7
Height (cm)
6
5
4
3
2
1
0
1 2 3 4 5
Days
The line slopes upwards. This means the height is
increasing. Write a “plus” sign +
10. STEP THREE: By how much does the data
change?
+2
10 +2 10
9 8
8
+2 The change
6
Height (cm)
7 follows a pattern. This
+2
6 will help us make a
5 4 prediction.
4
3 2
2
1
0
1 2 3 4 5
Days
* The height increases by 2 centimeters each day. *
11. STEP FOUR: Apply the rule to the pattern to
make a prediction.
+2
12
+2 If the pattern
10
10 +2 continues, we
9 8 can add 2 to predict
8
+2 6 the height of the
Height (cm)
7
6 +2 plant on day 6.
5 4
4
3 2 On day 6, it is likely
2
the height of the
1
0 plant will be 12
1 2 3 4 5 6 centimeters.
Days
12. Change in time can also be seen on a bar graph.
Let’s take a look at an example.
Paintings Sold by James
40
Number of Paintings
30
20
10
0
January February March April
This bar graph shows the number of paintings John sold for 4
months. Let’s use those steps again to determine the change
in value over time!
13. STEP ONE: What is the variable? (In other
words, what is changing?)
Painting Sold by James
40
Number of Paintings
30
20
10
0
January February March April
The number of paintings is changing.
14. STEP TWO: How is the variable changing?
(Do you see an increase, decrease, or does the data remain constant?)
Painting Sold by James
Number of Paintings
40
30
20
10
0
January February March April
The height of the bars is getting smaller and smaller.
The number of paintings is decreasing. -
15. STEP THREE: By how much does the data
change?
Painting Sold by James
40 -5 -5
40 35
Number of Paintings
30 -5
30 25
20
10
0
January February March April
* The number of paintings decreases by 5 each month. *
16. STEP FOUR: Apply the rule to the pattern to
make a prediction.
Painting Sold by James
40 -5 -5
40 35
Number of Paintings
30 -5
30 25 -5
20
20
10
0
January February March April May
If we continue to follow the pattern by subtracting 5, we
can predict the number of paintings sold in May.
17. √ Check for Understanding
Can you list the steps that will
help you determine change over time?
Did you say:
1. What is the variable?
2. How does variable change?
3. By how much does the variable change?
4. Apply the rule to the pattern to make a prediction.
18. Now let’s try using these steps to
find change in time using a chart.
19. Janice is starting a cooking club. The following
chart shows the number of people who joined
her club over a 4 month period.
Month 1 30
Month 2 60
Month 3 90
Month 4 120
20. STEP ONE: What is the variable? (In other
words, what is changing?)
Month 1 30
Month 2 60
Month 3 90
Month 4 120
The number of people joining the club is the
variable.
21. STEP TWO: How is the variable changing?
(Do you see an increase, decrease, or does the data remain constant?)
Month 1 30
Month 2 60
Month 3 90
Month 4 120
The variable is increasing. +
22. STEP THREE: By how much does the data
change?
The value of change can
be found by looking at the
Month 1 30
Month 2 60
} + 30 first two numbers.
Subtract the smaller
number from the larger
Month 3 90
} + 30 number.
Month 4 120
} + 30 60
-30
30
* The number of people joining the club increases by 30
each month. *
23. STEP FOUR: Apply the rule to the pattern to
make a prediction.
Month 1 30
Month 2 60
Month 3 90
Month 4 120
Month 5 150 } + 30
Since the variable is increasing, add 30 to the last
number to predict the number of people for month 5.
24. Let’s look at another chart.
The following table shows Sam’s weight
over a 5 month period.
July August September October November
230 222.5 215 207.5 200
25. STEP ONE: What is the variable? (In other
words, what is changing?)
July August September October November
230 222.5 215 207.5 200
Sam’s weight (in pounds) is the variable.
26. STEP TWO: How is the variable changing?
(Do you see an increase, decrease, or does the data remain constant?)
July August September October November
230 222.5 215 207.5 200
The variable is decreasing. -
27. STEP THREE: By how much does the data
change?
July August September October November
230 222.5 215 207.5 200
}
}
}
}
-7.5 -7.5 -7.5 -7.5
230.0
-222.5 * Sam’s weight decreases by 7.5 lbs. each
7.5 month. *
28. STEP FOUR: Apply the rule to the pattern to
make a prediction.
July August Sept. October November December
230 222.5 215 207.5 200 192.5
}
-7.5
To predict Sam’s weight in December, subtract 7.5 lbs
from 200 to get 192.5 pounds.
29. Closure
Let’s review those steps one more
time!
Turn to your neighbor and tell them
the steps that will help you identify
the change in value over time and
make simple predictions.
