Visual Calculus

1
Visual Calculus
Ana Franco Amra Kanlic Gabriel Mendoza Alister
Ng Alfredo Rodriguez Lina Yick

• University of Texas at El Paso
• April 6,2002

2
Introduction

• Intervention - Cone problem
• Video- Classroom activity
• Pretest
• Posttest
• Results
• Acknowledgements
• Discussion

3
Intervention
On a hot, sunny El Paso day, you and your
buddies decide to buy some ice cream. When you
get to the ice cream shop, theres a sign that
reads, "SALE! Eat ice cream by making your own
waffle cone for only 1.00!" . The store sells
you a circular waffle and allows you to roll it
up into a cone, which will be filled with ice
cream for a 1. Of course you want the most
amount of ice cream in your waffle cone.
4
Finding Equation
(1)
(2)
(3)
Substitute the value of h into equation (3).
(4)
5
Graph of diameter v.s volume
V (ml)
250
225
200
175
150
125
100
75
50
25
d (cm)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
6
Students Data
D (cm)
V (ml)
S
14
265
1
14
250
2
14
205
3
V (ml)
13.9
265
4
15
235
5
1
12.25
205
6
260
4
12
215
7
2
25
14
242
8
20
240
13
22
24
8
19
10
180
9
5
11
12
14
17
15.5
157.5
10
220
26
12
235
11
18
7
16
12.5
235
12
15
23
3
6
21
200
12
235
13
14
235
14
180
13.5
210
15
9
14.5
215
16
12.5
235
17
160
10
14.5
215
18
11.5
240
19
11.5
240
20
11
12
13
14
15
16
17
11
205
21
d (cm)
13.5
243
22
11
205
23
12.5
235
24
14
250
25
12
220
26
7
Students graph
V (ml)
4
1
22
250
2
25
19
20
8
5
12
14
17
13
225
11
24
26
15
18
7
16
23
3
21
200
6
9
175
10
150
125
100
75
50
25
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
d (cm)
8
Calculus Solution
Take the derivative with the respect to r.
To solve
Thus,
9
Pretest
Three firefighters are called about a fire at a
house (H), figure 1. The fire station is located
at F. Each firefighter Ana, Bobby, and Roberto
leave the fire station with an empty bucket. They
each pick a path to the ocean to fill their
bucket with water. Then they proceed to the
burning house.

• Figure 1. Three firefighters, at station F,
  first run to ocean for water and then run to the
  burning house. Notice that the first letter in
  their name marks the path to the ocean of each
  firefighter.

10
Pretest Graph

• Figure 2. The distance of each firefighter is
  marked on the graph by the first letter of their
  name.

11
Questions

• a) Who ran the shortest distance to the ocean?
• b) By person, rank the distance they had to run
  to the ocean (from shortest to longest).
• 1.
• 2.
• 3.
• c) Who ran the shortest total distance to the
  house?
• d) By person, rank the total distance they ran
  from the fire station to the burning house (from
  shortest to longest).
• 1.
• 2.
• 3.
• e) Is there an optimal way to run to shorten your
  distance from the station to the house? Explain.
   
• f) Which way would you run to the ocean to create
  the shortest path from the station to the burning
  house (create your own path)? Label your path on
  figure 1 and also on figure 2. Explain.

12
Posttest

• Four fighter fighters Ana(A), Bobby(B),
  Edith(E) and Roberto (R) are called about a fire
  at a house (H), figure 1. The fire station is
  located at F. Each firefighter leaves the fire
  station with an empty bucket.

13

• Figure 2. The distance of each firefighter is
  marked on graph by their first letter of their
  name.

14
Questions

• a) By using figure 2, who ran the best way to the
  house? Why?
•  
•  
• b) To save the house from the fire, which way
  would you run? If there is not a point on the
  graph, then mark your own point and explain this
  path on figures 1 and 2.

15
Pretest Solution
16
Posttest Solution
17
Results
18
Acknowledgements

• Alisters 8th grade classes at St. Joseph
• Erandi Perez and O. Perez
• Veronica Herrera

19
References

• Lott, W. Johnny and Smith, Paul. (1979).
  Reflections on putting out a fire. School Science
  and Mathematics, 79 (5), 434-38.
• Sobel A. Max and Maletsky M. Evan. (1999).
  Teaching mathematics a sourcebook of aids,
  activities, and strategies. Boston, MA Allyn
  and Bacon.

http//www.math.utep.edu/Student/alfredo/opt/optim
ization.html
20
Discussion

• Any questions?
• Thank you.

http//www.math.utep.edu/Student/alfredo/opt/optim
ization.html