Real Numbers
MathSteps - lesson ideas for teaching real number classifications
Purplemath - a nice lesson on number types
Multiple
Choice Test of Number Sets - a nice interactive
test over number sets definitions and closure under the various
sets - would make a great review or extra credit
Types
of Numbers - a great 3D Venn of the number
sets - you will have to download a plug-in to see it
Relations & Functions
Vertical
Line Test - a Project Interactive applet allowing
students to investigate the vertical line test
Possible
or Not? - a Project Interactive
applet - students decide if a given graph is a function and if
it represents a possible situation in the real world
Purplemath - a wealth of lessons including function definition, function notation,
function transformations, direct and inverse variation, etc.
Moving
Man - a great applet by Lisa Denise Murphy -
drag the "moving man" and the applet generates distance, velocity,
and acceleration graphs
Operations on Functions
- a graphing applet that will graph f(x), g(x),
and the sum, difference, product, quotient, inverse, and composite
functions - a little slow to load, but worth it - includes linear
and trig functions
Graph
or Not a Graph? - an interactive test
- for each graph click "function" or "not a function" then
check out your score - a great review or extra credit activity
Function
Transformation Applets - separate applets for
vertical translations, horizontal translations, vertical stretch,
and horizontal stretch
Function
Composition Applet - input f(x) and g(x)
then drag a point to vary the input - watch the composition change
accordingly
Inverse
Functions - an explanation of inverse functions
with very nice visuals
Exploring
Inverse Functions - a very nice treatment of
inverse functions including Java applets and a QuickTime movie
TOP
Linear
Functions
Function
Toolkit - A JavaSketchpad Interactive - drag
a point along the x-axis and generate a linear function - see
effects of parameter changes
Modeling
Orbital Debris Problems - uses the orbital debris
problem to investigate linear and quadratic functions - with printable
student activity sheets
Linear
Regression & Correlation - i-Maths Investigation
- investigate best fit line with an interactive online applet,
online and downloadable student questions
Exploring
Linear Functions - a nice applet showing the
effect of changes to m and b on the graph of y
= mx + b
Exploring
Linear Data - printable student pages investigating
four different situations modeled by linear functions - high student
interest topics
Fun and Sun Rent-a-Car
- an exploration by Cynthia Lanius modeling various
rate plans using a Java based grapher - also available as a print
version
Function Machine
- from Utah State University - a very nice animated
function machine - students look for patterns and predict results
Slope
Slider and Function
Flyer - Project Interactive applets designed
for student exploration - very nice
Function Machines
from Project Interactive - several to choose
from
MathSteps -
lesson ideas for teaching linear equations
Purplemath - a wealth of lessons including all aspects of linear functions
The
Big Function Graph Puzzle - earn points by correctly
matching the equation to the graph - a great way to review transformations
- combination of linear and quadratic functions
Linear
Functions Applets - Java applets for slope-intercept,
point-slope, and standard form - change the values of the coefficients
and watch the resulting change in the graph TOP
Systems
Systems of Equations
in Electronics - applications of systems to
electronics, several solving methods with interactive "solvers",
includes matrices
Supply
and Demand - An Application of Linear Systems
- three printable student activity sheets with internet extensions
Purplemath - a wealth of lessons including systems of equations and inequalities
- includes solving by Gaussian elimination and systems word problems
Solving Two Equations - from Webmath - the users inputs two equations - the applet solves the
system and walks the user step by step through the process
Intersection
Calculator - input the slope and y-intercept
of two lines and the calculator finds the intersection
TOP
Quadratic Functions
Exploring Parabolas
- a JavaSketchpad interactive
Function
Toolkit - A JavaSketchpad Interactive - drag
a point along the x-axis and generate a linear function - see
effects of parameter changes
Completing
the Square Applet - students change the parameters
and the calculator completes the square
Purplemath - a wealth of lessons including quadratic formula, completing the square,
etc.
The
Big Function Graph Puzzle - earn points by correctly
matching the equation to the graph - a great way to review transformations
- combination of linear and quadratic functions
Where
does the quadratic formula come from? - a nice
derivation of the quadratic formula that would be good for extra
credit or inclusion in a webquest
Quadratic
Solver - input the values of the coefficients
and the solver gives the discriminant and the roots (including
complex roots)
TOP
Polynomial Functions
Function
Toolkit - A JavaSketchpad Interactive - drag
a point along the x-axis and generate a linear function - see
effects of parameter changes
Polynomial
Roots Calculator - calculates the roots of a
polynomial function up to degree 5 (real roots only)
Polynomial
Function Graphs - Java applets for graphing
polynomial functions up to the fifth degree - change the values
of the coefficients and watch the resulting change in the graph
TOP
Radicals
and Roots and Square Root Functions
Function
Toolkit - A JavaSketchpad Interactive - drag
a point along the x-axis and generate a linear function - see
effects of parameter changes
Purplemath - a wealth of lessons including radicals
Radical
Equations - a nice step by step tutorial - would
be great for the student who was absent the day you taught this!
TOP
Matrices
Purplemath - a wealth of lessons including lots of matrices
Stepwise
Matrix Multiplier - an interactive applet showing
step by step how to multiply matrices - very nice
Matrix
Multiplier - the next step from the previous
source - students must perform the calculation and the applet
checks their work
TOP
Virtual Manipulatives
Virtual
Algebra Tiles - from Utah State University -
my favorite web-based tiles - easy to manipulate - includes activities
Algebra
Balance Scales - from Utah State University
- place x and units blocks on a scale and keep it balanced
while solving for x - very nice - includes lots of problems
to solve
Expression
Balance - interactive pan balance allows numeric
or algebraic expressions to be entered and compared - great for
deciding if expressions are equal TOP
Trigonometric Functions
Function
Toolkit - A JavaSketchpad Interactive - drag
a point along the x-axis and generate a linear function - see
effects of parameter changes
Sine
and Tangent
Curve Animations - QuickTime movies - very good
Trigonometric
Functions Resources from Charles Sturt University - includes
slide shows, teaching ideas, tutorials, applications, assessments
Operations on Functions
- a graphing applet that will graph f(x), g(x),
and the sum, difference, product, quotient, inverse, and composite
functions - a little slow to load, but worth it - includes linear
and trig functions
Trig
Graphs from the Unit Circle - a Java applet
that shows how the sine, cosine, and tangent graphs are generated
from the unit circle
Trig
Graphs Match-up Puzzles - two interactive puzzles
matching graphs of rational funcitons to their equations - fun
- from the same source as the link above
Sound
Sketch - see how sine waves convert to sound
- sketch and sound and then listen to see how varying the wave
varies pitch and intensity - fun!
Sine Wave Applet
- set the frequency and amplitude of two sine waves then watch
the applet graph both waves and their sum
Superposition
Applet - type in any functions f(x,t) and g(x,t)
and see their sum - really a Physics site with great flexibility
Common
Angles Around a Circle - shows all the common
angles in the unit circle and gives their measure in degrees and
radians
Trig
Functions Point Definitions - a really nice
applet that shows a point on the x-y plane with its accompanying
reference triangle and the point's corresponding position on the
graph of the trig function - all six trig functions available
- one of my favorites!
The
Radian - a great definition of the radian with
a Java animation showing the radius equal to the arc length
TOP
Trigonometric Identities
Identities
Applets - four Java applet quizzes over identities
and a true/false quiz
TOP
Continuity, Limits, and Tangents
Stressed Out: Slope
as a Rate of Change - Cynthia Lanius investigates
the slope of a tangent to a parabola
Moving
Man - a great applet by Lisa Denise Murphy -
drag the "moving man" and the applet generates distance, velocity,
and acceleration graphs - could be used to introduce derivatives
Numerical
Computation Tools for Sequence and Series - input
the formula for the nth term and quickly computer terms in the
sequence or partial sums - quick and easy to see terms and sums
approaching a limit
Continuous
or Discontinuous? - an interactive quiz - label
each sequence as continuous or discontinuous then check out your
score - would make a great review or extra credit
TOP
Graphing Calculators
Virtual
Grapher - from Utah State University - a very
user friendly interface - graph up to 3 functions in 3 colors,
change parameters with sliders
Graph
Sketcher - a Project Interactive applet - type
in your function, set your view window and click graph - a nice
source for printing graphs
SimCalc - software
for the TI-83 plus allowing it to run simulations - sample available
for download
Simple
Data Grapher - input the legend and scale for
your graph then input the data - the grapher creates a nice printable
graph
EZ Graph - a fully functional online grapher
TI Tutorials
- how to documents for the TI-82 and TI-83
Casio Programs
- downloadable programs for the Casio 9850+
Casio Programs
- more downloadable programs for the Casio 9850+ and 7400G
Casio
Programs - more downloadable programs for the
Casio 9850+
Casio
Programs - downloadable programs for the Casio
FX 2.0
Casio
Programs - downloadable programs for the Casio
EA100 Data Collector
ticalc.org - TI calculator help,
downloadable programs, programming contests, etc.
TI Program Archives - downloadable programs for all TI graphing calculators
TI Programs - downloadable programs for the TI CBL Data Collector
TOP
Lists
of Famous Curves
Famous Curves
Index - from the University of St. Andrews,
Scotland - everything from lines to conics and polars to curves
you may never have heard of before!
2dcurves - A collection of
674 mathematical curves by Jan Wassenaar with Java interactives
- a great site
Visual
Dictionary of Famous Plane Curves- by Xah Lee
- galleries of curve families -nicely done
TOP
General Sites
WebMath - a good student tutorial from basic
Algebra to Calculus
Purplemath - extensive lessons covering
all of High School Math
Illuminations - a
collaboration between NCTM and MarcoPolo Education - a great collection
of lesson plans and interactives
Zona Land - lots
of great explanations and interactives for Math and Science
TOP
compiled
by De-Vonna Clark
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supported
by the THECB and TEA