
Kids and Cookies
This game, designed for preschool and elementary students, introduces
concepts of rational number and division through the simulation of sharing
cookies with friends. The online version has no sound; downloadable versions
have additional (and optional) voiceover and music.
Go to Kids and Cookies


Integral Machine
This file allows the student to change the width dx of rectangles under the
curve. The student can
see sums of rectangles under a curve, rectangles over a curve, rectangles
reaching to f(xmidpoint),
and to see rectangles of measurements dx*dy. Go to Integral Machine


Derivative Machine
This machine allows the student to see how the secant line defined by (x,
f(x)) and (x+h, f(x+h)) approaches the slope of the line tangent to a
function at (x, f(x)). The user can switch between
algebra (delta) notation and precalculus (f(x)) notation. Go to Derivative Machine


The Mean Value Theorem
Modeled on the derivative machine, this machine shows how, on the interval
(a, b), there is a point c such that the slope of f(c) is equal to the slope
of the secant line from (a, f(a)) and (b, f(b)). Go
to Mean Value Theorem Applicino


Taylor Series Expansions
This machine shows how successive polynomial expansions approach the
functions from which they are derived. The student can show up to ten
expansions at the same time, either in a table or as a graph. Go to Taylor Series Expansions


Sampling Distribution of the Mean
This machine shows the consistency of sampling means in variously shaped
populations. A student can change sample sizes, view raw data, choose samples
singly or by the thousands, and observe changes as the sample numbers and
populations change. Go to Sampling Mean
Machine


Calculating Margin of Error for a Population Sample
This machine shows the margin of error for a population sample, given a
certain level of confidence, sample size, and proportion of yes/no answers.
The sample size can be set to values between 25 and 2000, the proportion
value to values between .01 and .99, and the confidence level at 95 or 99
percent. Go to Margin of Error
Machine


Linear Programming  A 3D Model
A model of everyday linear programming problems, which explains why maxima
and minima are at the corner points of the area satisfying the constraints.
The constraints and zfunction are manipulable, to fit many types of
problems. Go to Linear
Programming


Compound Interest Calculator
Calculation and graphic model of compound interest on a loan. Students can
choose the amount of principal, the rate, the pay period, and the duration of
a loan, and see how the structure of a loan changes with different
parameters. Go to Compound
Interest Calculator


Quincunx/Random Walk
This strange machine (highly idealized) produces a roughly normal
distribution by dropping dots through a triangular arrangement of obstacles.
Probability and organized randomness at work.
Go to Quincunx


Rhythm Player
This tool shows the fractional relationships of simple rhythms. The pitches
at which the rhythms play are based on the harmonic series, with an octave
below middle C as the fundamental. Students can listen to up to four or more
rhythms at a time, depending on the capacity of their workstations. Students
can also choose different number sequences to investigate: primes, evens,
odds, and fibonacci numbers.
Go to Rhythm Player


Continued Fraction Machine
This tool shows rational numbers as areas made up of squares, and a
corresponding continued fraction. Each step in the division is equivalent to
an iteration of Euclid's
algorithm.
Go to Continued Fraction
Machine


PatternBuilding with Cellular Automata
This tool shows the beginnings of 256 possibilities of a simple cellular
automaton. See how simple rules can yield complex results.
Go to Pattern Builder


Slide Rule
This circular slide rule shows spiraling logarithms, and can be used to do
multiplication and find roots.
Go to Slide Rule


Eggs
This tool, designed for
elementary school students, is a fun way to investigate the discrete model of
rational numbers using eggs and egg cartons. The cartons can be partitioned in a
variety of ways to represent fractions and their equivalents.
Go to Eggs


Fraction Rods
Go to Fraction Rods


Integer Cars
Go to Integer Cars
