Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on

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A Geometric Investigation of (a + b)2

This interactive demonstrates why (a + b)2 = a2 +2ab + b2.

Algebraic Transformations

6-8, 9-12
This applet allows you to explore commutativity and associativity within a geometric situation.
Data Analysis and Probability

Bar Grapher

3-5, 6-8
Graph data sets in bar graphs. The color, thickness and scale of the graph are adjustable. You can input your own data, or you can use or alter pre-made data sets.
Data Analysis and Probability

Circle Grapher

3-5, 6-8
Use this tool to graph data sets in a circle graph.  You can input your own data or alter a pre-made data set.
Cubes ICON


Use this applet to determine the volume of a box by filling it with cubes, rows of cubes, or layers of cubes. Determine the surface area as well by using the box's net.
Data Analysis and Probability

Data Grapher

3-5, 6-8
The Basic Data Grapher can be used to analyze data with bar graphs, line graphs, pie charts, and pictographs. You can enter multiple rows and columns of data, select which set(s) to display in a graph, and choose the type of representation.
Number and Operations

Electronic Abacus

Pre-K-2, 3-5
This applet explores the use of an abacus model for representing numbers and for performing addition.
Number and Operations

Factor Game

3-5, 6-8
Exercise your factoring ability against a human or the computer in this Calculation Nation game.
Data Analysis and Probability


3-5, 6-8, 9-12
This applet is designed to simulate the spread of a wildfire using probability.
Data Analysis and Probability

Fraction and Percent Tool

3-5, 6-8, 9-12
This tool allows you to explore fractions, decimals and percents by creating fractions with denominators up to 100.