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Knex 78890 - Education Amusement Park Experience Teachers Guide Manual

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LESSON 7
7: E
7: E
XAMINING
XAMINING
S
S
LOPE
LOPE
AS
AS
A
A
R
R
ATE
ATE
OF
OF
C
C
HANGE
HANGE
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In Groups
1. Ask the students to use the data from the tables completed in Activity #1, step 13, to construct
two sets of line graphs, side-by-side, and drawn as follows:
G
raph 1:
(1) x-axis = time
(2) y-axis = distance traveled by the inner circle horses
Graph 2:
(3) x-axis = time
(4) y-axis = distance traveled by the outer circle horses
Each graph will include five data points (ordered pairs) from their data chart.
2. Once plotted they should draw a line of best fit through the points. Students should be reminded
that a line of best fit may not necessarily pass through any of the ordered pairs but represents the
best linear relationship between the points.
Teacher’s Notes
• The idea of a “line of best fit” may need to be reviewed with the students. There is an opportunity for
the teacher to discuss why data isn’t perfect and why a line of best fit is used.
3. Students should now calculate the slope of the lines of best fit on the distance-time graphs. They
will compute one value for each graph. Students should do this by identifying two ordered pairs
the line passes through. One of the ordered pairs should be identified as (x
1
, y
1
) and the other as
(x
2
, y
2
).
y
2
- y
1
x
2
- x
1
Students should then compute the following , which is the slope of the line.
4. Students should compare the slope they have computed to the speed values they determined
experimentally for the two sets of horses.
5. Students should report their findings in their notebooks/journals and describe any relationship they
discovered when they compared the slopes of the two lines to the speeds they computed.
Whole Class
6. This lesson covers concepts drawn from both mathematics and science. It is important to review
both the terminology presented, as well as the concepts developed.
7. Have students describe the relationships they discovered when they compared the slopes of the
lines and the speeds they had calculated.
8. Can students offer any suggestions as to the benefits of the relationship they determined?
(Students may suggest that they would not have had to compute all of the speed data since the
slope of the graph would have provided them with the same information. They should realize that
the slope of a straight line comparing distance traveled versus time provides the speed of the
object measured.)
… 50 …


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