High School
Level Microworlds
(Arranged
alphabetically)
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3D
game of life
Author(s): james e. white
Topics: cellular automata, game of life, cartesian coordinates in 3 dimensions
(Level: High School)
Description: This playbook is about
the game of life. In this 3-dimensional version, cells are cubes in a 21x21x21
array. In each generation, a cell survives to the next by counting neighbors.
Empty cells are born if they have the right number of living neighbors.
Algebra
of work problems
Author(s): david dudley and anne dudley
Topics: algebra, equations (Level: High School)
Description: This microworld develops
strategies for analyzing and solving problems in which a number of workers with
different rates of work collaborate to finish a job. The reader is coaxed through
the solution of a complex problem of this type in gentle steps.
Best
linear fit
Author(s): ravinder kumar
Topics: linear interpolation, data fitting, linear regression, interpretation
of data (Level: High School)
Description: This microworld has tools
for solving discrete models that depend upon proportionality. What often happens
in such models is that some parameters or their powers are proportional. The problem
reduces to determining a line y = kx that fits the data best.
College
algebra set: quadratic functions
Author(s): samad mortabit
Topics: college algebra, graphing, relations, quadratic equations, quadratic
graphs, acceleration, gravity, growth models, parabolas, inequalities (Level:
High School)
Description: This microworld studies
quadratic equations and inequalities. It generates problems randomly or lets you
make them up. In either case, it draws the solution graphically then explains
step-by-step how to solve algebraically using completion of the square.
Duality
in the mirror game
Author(s): james white
Topics: logic (Level: High School)
Description: This workbook explores
the symmetry of a game often found in roadside restaurants. We call it the "mirror
game". There are 14 red pegs arranged in the playing board. After that, the moves
will be to "jump" one peg over another and to land in a hole.
Graphs
of functions and symmetry
Author(s): kanchan manaktala
Topics: symmetry of graphs of functions, reflection, translation, shifts (Level:
High School)
Description: This microworld is a gentle
introduction to the symmetries of a graph. It approaches this idea through the
metaphor of reflection, as in a mirror. The basic reflections that it considers
are: reflections across the x- and y-axis, and across the line y=x.
Graphs
of quadratic functions
Author(s): kwok-wai mok
Topics: quadratic functions, parabolas, guadratic graphs, quadratic equations
(Level: High School)
Description: This microworld explores
with animation and interactive algebra the properties of the graphs of quadratic
functions, and symbolic and graphical ways of understanding the solutions of quadratic
equations. It gives examples and step-by-step instructions.
How
to draw a star
Author(s): dan kalman and angela hare
Topics: geometry, logo graphics, line drawings (Level: High School)
Description: How do you draw a star?
The star playbook provides opportunities to explore the geometry of stars. There
are three activities pages. On the first you can explore the relationship between
the number of points in a star and the angle formed at each point.
Introduction
to mathwright32
Author(s): margie hale
Topics: this is the mathwright tutorial (Level: High School)
Description: This microworld discusses
the mechanics of reading and interacting in mathwright microworlds. It is a good
place to start.
Lines
and linear equations
Author(s): kanchan manaktala and ravinder kumar
Topics: college algebra, graphing (Level: High School)
Description: This microworld weaves
together themes from geometry and algebra as it exercises your skills in writing
and solving equations. It is designed for students who would like to understand
how to write equations of lines in various forms.
The
magical gravity tour
Author(s): james white
Topics: acceleration, vectors, conics ections, differential equations, equations,
extrema, mechanics, geometry, graphing, gravity, inflection points, momentum,
pendulum, plane curves, polar graphs (Level: High School)
Description: Gravitation is an interactive
microworld designed to be used by students for self-directed study and recreation.
It has playful explorations such as a lunar lander or a space shuttle launch that
also teach. Students may experiment with kepler's 3 laws.
Mastermind
Author(s): james white
Topics: logic, propositional calculus (Level: High School)
Description: Mastermind is a game of
deductive logic. Learn this intriguing game while playing it. The workbook teaches
you the rules of the game, then allows you to try out your deductive skills as
it creates codes for you to guess. Next, watch it guess your codes!
Periodic
functions
Author(s): jim swift
Topics: trigonometric functions, graphing, sine, cosine, amplitude, frequency
(Level: High School)
Description: This workbook aims to help
readers visualize the properties of trigonometric functions, beginning with the
wrapping functions through the exploration of the sine and cosine functions. Students
learn about amplitude, period and frequency, and phase shift.
Piecewise
defined functions
Author(s): ravinder kumar
Topics: piecewise function, graph, limit, continuity, derivative suggested use:
exploring the graph, continuity and derivability of functions (in particular
piecewise functions), and finding derivative algebraically. (Level: High
School)
Description: This microworld helps students
visualize the graphs of functions, piecewise continuous or not, and to explore
limits, continuity, and derivability. The book can be used to graph a function
and its derivative, create tables of values on an interval.
Playing
with points
Author(s): kanchan manaktala
Topics: plotting points, coordinate geometry (Level: High School)
Description: This microworld is an introduction
to points. The reader learns to plot a point if coordinates are given, to read
the coordinates if the point is given, to determine the distance between two points,
to determine collinearity of three points.
Points
and lines
Author(s): james white
Topics: college algebra, graphing (Level: High School)
Description: This microworld exercises
your skills in writing and solving equations. It is designed for students who
would like to understand how to write equations of lines in various forms, and
to determine the distance from a point to a line.
Rocket
science 101
Author(s): james white
Topics: acceleration, rocket equations, differential equations, equations, extrema,
mechanics, geometry,graphing, gravity, momentum, force (Level: High School)
Description: This microworld is an interactive
playbook that celebrates the role of mathematics in rocket science. It is designed
to be used by students ages 14 and older for self-directed study and play. The
player must dock the space shuttle with a space station.
SAT
math practice and tutorial 1
Author(s): james white
Topics: equations, graphing, factorization, tutorial, command line,differentiation,
symbolic algebra,function composition (Level: High School)
Description: This microworld will
give you unlimited opportunity to prepare for the mathematics section of the
scholastic aptitude test (sat). In its present form, it generates a new 25-question
diagnostic test each time you ask for one. Each test is unique.
A
story of light
Author(s): margie hale
Topics: refraction, reflection, snell's law, fermat's principle (Level:
High School)
Description: This microworld is about
the reflection and refraction of light rays. The material can be appreciated by
a wide range of students from high school through college. There is material on
conic sections, trigonometry, visualizing "virtual" images, etc.
Transformations
of a function
Author(s): mike pepe
Topics: graphs of functions, translations, shifts, contractions, expansions
(Level: High School)
Description: In mathematics, we often
use one function to define another. For example if we start with the function
f(x) = x^2 we can create a new function g by defining g(x) = f(x) +3, so g(x)
= x^2 +3. In words, f is the function that adds three to the output of f.
Trig
functions
Author(s): k.p. satagopan
Topics: amplitude, frequency, and phase in trigonometric functions (Level:
High School)
Description: This microworld illustrates
the effect of the parameters 'a' , 'b' , and 'c' on the graph of the function
f(x) = a*sin(b*x+c) which respectively represent the amplitude, period or frequency,
and phase shift of a trigonometric function.
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