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2002
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2003
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2004
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2004
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by Tim
Fahlberg, CoolSchoolTools.com, Tim.Fahlberg@CoolSchoolTools.com
Using
ExamView to Create Questions with Dynamic Graphs
ExamView’s algorithmic capabilities provide an easy way to create
an almost unlimited supply of math questions. In this article, you will
discover how easy it is to enhance those questions or build new ones
that include dynamic graphs.
The
first two examples are short answer questions that feature dynamic Cartesian
(x-y) graphs while the third is a bimodal question with a dynamic box-and-whisker
plot.
Getting
Started
If you are not familiar with the ExamView algorithmic capabilities,
I encourage you to review the ExamView
My Way article in the April 2003 newsletter. This article provides
a primer for understanding dynamic questions. If you want to learn how
to create dynamic math questions, check out the Dynamic
Corner article in the September 2003 newsletter. (See the newsletter
archives to access all of the previous articles.)
Before
you begin, download the following question bank (Dynamic
Corner-Part IV.bnk) Windows or (Dynamic
Corner-Part IV) Macintosh. The bank includes the sample
questions. (Remember that you will need ExamView 4.0 or a more recent
version.)
To
help you better understand how to create dynamic questions, use the
Question Bank Editor to open the question bank and review the algorithms
that make up each question.
Example
1: Parallel Line Segments
In this first example, a Cartesian graph shows a line segment. The problem
asks the student to sketch a parallel segment on the grid and prove
that the segments are parallel. Each time you recalculate the question,
the values and the graphs are automatically updated.
Parallel Line Segments (Question #1)
Parallel
Line Segments… Variables
Parallel Line Segments… Algorithm Definitions
A
Closer Look at the Algorithm Definitions
Below is an explanation of the algorithms used in this question. The
names you use for the algorithm definitions (or variables) are not critical
as long as you do not use function names. As for the functions (e.g.,
list, range, choose, etc.), you can get a detailed description by reviewing
the online help information in the program.
To
view the algorithms, open the question bank and choose to edit the question.
Then choose the Algorithm Definitions option from the
Edit menu. Double-click any variable to view the entire
description.
- x1,
y1, x2, y2 are variables used to generate random points.
These points are used in the dynamic graph. The definition for y1
is ((-1)^rand(2))*range(3,5). The first part of the
variable definition (-1)^rand(2) generates either
a +1 or a -1 so that when it is multiplied by range(3,5) it
yields integers in this set {-5, -4, -3, 3, 4, 5}.
- slope1
is a variable that uses the string function sfracs to generate
a string representing the slope as a fraction in lowest terms. It
is defined as the difference of y over the difference of
x. Note: String functions cannot be used
in other calculations. This kind of function is used for display purposes
only.
- shift
is a variable used to determine the distance that the parallel segment
will be drawn away from the original segment in the sample answer.
- x3,
y3, x4, y4 are variables used to generate the dynamic graph
in the answer. The points (x3,y3) and (x4,y4)
are endpoints of the new segment. The variables x3
and x4 are defined to have the same values as x1
and x2 respectively. A shift value (shift)
is added to both y1 and y2 to create
points (x3,y3) and (x4,y4) that
are the same distance from (x1,y1) and (x2,y2).
This creates a parallel line segment either above AB (if shift>
0) or below AB (if shift < 0).
- conditions
– abs(y3<8) and abs(y4<8) assure
that the y values remain between -8 and 8 so that the segments will
show on the graph.
Making
a Dynamic Graph
In this question, the Segment function is used as part
of a Cartesian graph. To view the Edit Segment window
shown below, double-click the graph and then double-click the segment
function definition.
In
the figure shown below, you can see that the variables x1, y1,
x2, and y2 are used to define the endpoints
for the segment. ExamView uses the current value of the variables to
draw the segment. (Variables defined as strings will not graph properly.)
If
you want to create your own graph, choose Graph from
the Insert menu and select a Cartesian, Polar, or Number
Line graph. Add new functions to create the graph. You can also change
attributes such as point style, label style, and label position for
the segment.
Check
out the solution to this problem. Double-click the graph to see that
there are two segments defined. Variables are used to draw the parallel
segment (MN) and to show the proof.
Example
2: Dynamic Lines
In this question, you can see a plot that models how much money two
students save over time. The question includes variables that change
the students’ names, how much they have already saved, and their
weekly savings rate.
Dynamic
Lines (Question #2)
Dynamic
Lines… Algorithm Definitions
A Closer Look at the Algorithm Definitions
-
Name1, Name2, WhichName1, WhichName2 are variables
used to generate two random student names from a list of names. These
variables simply add some variety to the problem.
- Week1,
Week2 are variables used to generate weekly savings rate
for the two students. The savings rate for the first student will
be an amount from $25 to $40 (at $5 increments). The savings rate
for the second student will be $5 to $20 more per week than the first
student’s rate.
- Diff
is a variable used to represent the difference between the
weekly savings.
- Num1,
Num2
are variables used to represent the initial amount of money each student
has saved. The amount for the second student ranges from $150 to $300.
The savings amount for the first student is based on the amount saved
by the second student plus an additional amount (difference between
the weekly savings rate multiplied by a random number from 5 to 10).
- Correct
is a variable used to calculate when the two students will have saved
the same amount of money towards their summer trip.
-
Correct2 is a variable that identifies how much money
both students will have saved when they reach the same total savings.
- condition
guarantees that the answer (total amount both have saved when their
savings are equal) is either an exact dollar amount or a dollar amount
+ $0.50. It prevents “ugly” answers like $1.3333….
These
variables are used as part of the problem and to draw the lines representing
the savings. Double-click the graph to see the functions included on
the graph. Double-click each function to see how the variables are used.
There are two f(x) functions to plot the savings over
time. Another function plots a point at which the savings are equal.
Finally, two functions display the student names on the graph.
Example
3: Box-and-Whisker Plot (Question #3)
The last question demonstrates how to create a different type of dynamic
graph. In this example, variables are used to create a dynamic box-and-whisker
plot that displays the number of students absent from school over several
months.
Check
out the algorithms and how they are used to make this graph dynamic.
Conclusion
Hopefully this article has provided some insight into how you can use
ExamView to create questions that include dynamic graphs. With just
a little extra effort you can enhance your math problems.
Reminder:
If you create some cool math problems, it’s easy to share those
questions with other educators from around the world. Click
here to access the Question Bank Exchange on the FSCreations Support
Forum. To date, educators from the United States to Macedonia to Australia
have contributed questions.
Tim Fahlberg (Tim.Fahlberg@CoolSchoolTools.com)
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