Interactive applets for mathematics

Most are in GeoGebra, which should run on any computer. We are in the process of updating these to run withough java; updated applets have a *.

Most coordinate with the curriculum Measuring the World: Mathematics for Elementary and Middle School Teachers.

Elementary mathematics

Arithmetic

Place value

Base blocks (any base up to 10) with 6 place values *

Addition and subtraction

A slide rule for adding and subtracting

Multiplication

The Frog Stretcher: multiplication as scaling

The Frog Stretcher for fractions: multiplication as scaling

The Stack Stretcher for integers: multiplication as scaling

The area model for multiplying whole numbers

The area model for multiplying fractions

Multiplication and division

Daisy chains: arrow diagrams for multiplying and dividing fractions

A slide rule for multiplying and divding

Ratio, proportion, percent

Strip diagrams for percent

Geometry

Polygons

What is a rectangle?

What is a parallelogram?

What is a rhombus?

What is a trapezoid?

What is a kite?

The height of a parallelogram with fixed side lengths

The side lengths of a parallelogram with fixed height

The area of a parallelogram (dissection to a rectangle)

The area of a triangle (dissection to a rectangle)

The area of a trapezoid (dissection to a rectangle)

Circles

The circumference and area of a circle

Angles

Angles as rotations versus angles as wedges

Making a rotation into a wedge angle

Exterior angles as turns while walking

Regular polygon and regular star polygons

Scaling and similarity

Dilating a triangle: scaling and similarity

Dilating a quadrilateral: scaling and similarity

Dilating a pentagon: scaling and similarity

Dilating a fish: scaling and similarity

Making base 10 blocks by scaling. Nonuniform scaling in 3 directions. Also allows nonuniform scaling of a rectangular prism.

Geometry in 3 dimensions

Makinga cone from a circle sector

Transformations and symmetry

Vectors and translations (Created in Java Sketchpad)

Checking a figure for reflection and rotation symmetry

Secondary mathematics

Geometry

(Most of the elementary geometry applets are valuable for secondary students, too. In U.S. schools, students get very few chances to explore geometry before being expected to do proofs in high school.)

Triangle inscribed in a circle

A geometric construction of square roots

Algebra

Solving quadratic equations with algebra tiles

Trigonometry

Radian measure: unrolling a circle

Trig functions as lengths

Sine wave controlled by sliders

Sine wave controlled by dragging

Logarithms

(These are all from Mathematical Intentions. There are more specialized applets there, as well as the connection between square roots and logarithms.)

An ancient Babylonian square root algorithm

An ancient Hindu square root algorithm

A medieval European square root algorithm

A slide rule for multiplying and dividing

A slide rule that also does roots, exponents, and logarithms

A circular slide rule

History of mathematics: applets for Mathematical Intentions