COMPUTATIONAL TOOLS
Introduction: Software like Mathematica® and Math CAD® are powerful
computational and programming tools. In this assignment you will become familiar with
the basic features of Math CAD®, a program that is particularly attractive to secondary
school mathematics teachers because the text editing features resemble standard
mathematical form rather than standard computer form.
Before you get started:
• Review Getting Started Under the Help Menu from within Mathcad
• Review the Topics Under the Help Menu
• Use Balloon Help to Identify all icons on the screen. Click on the top icon to get
additional palates.
Assignment: Demonstrate competence using MathCAD and Geometer's Sketchpad by
providing a printout of the following. Use the text tool to identify your work
MATHCAD
(1) Calculations: Five different calculations using a variety of functions.
(2) Variables: Write three or more different equations relevant to your subject such as
those shown below. Solve each equation for one or more specific situation.
Biology
Chemistry
Physics
Logistic Growth Curve
K  N 
Ir
N
 K 
Where I= rate of increase
K=carrying capacity
r=intrinsic rate of
increase=(b-d)=birthsdeaths
N=number of individuals in
the population
Force between charges
QQ
F  k 12 2
d
F=Force between two point
charges
k=constant of
proportionality
Q1 and Q2 =charges
V=potential difference
Relativity
2
E  mc
E=energy
m=mass
c=speed of light
(3) Iterative Calculations: Solve an equation for a range of variables.
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(4) Graphs: Create a graph of a function relative to the subject you teach.
(5) Integration/Summation: Use the integral and summation functions to solve problems
of your choice.
(6) Implications for Teaching:
(a) What are the implications of tools such as Mathematica and MathCAD for the
teaching and learning of mathematics? What are the issues, problems, benefits,
challenges, and dangers?
(b) Should mathematics teachers be required to have mastery of such programs? Why or
why not?
(c) How should such software be incorporated into the mathematics or science
curriculum?
GEOMETER'S SKETCHPAD
(a) Illustrate the concept of Pi using Geometer's sketchpad.
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(b) Solving real-life problems:
(a) Knowing that P waves travel approximately 740 km/minute faster than S waves,
determine the epicenter of an earthquake that produced the seismograms shown. Copy a
map of showing three of the cities into Geometer's Sketchpad, and use the circle tool to
draw circles around each with a radius equivalent to the distance to the epicenter. The
location where all three circles meet is the epicenter. Include a screen shot showing how
you determined the epicenter using Geometer's Sketchpad.
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(c) Using Geopeter's sketchpad develop a lesson to show how to calculate the height of a
building or the diameter of the moon. The average distance to the moon is 384,402 km.
Include graphics in your drawing.
(d) Using the Sketchpad, develop a lesson to illustrate one or more theorems.
Pythagorean Theorem
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