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 z-function 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

Pattern-Building 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