Math Activities NCTM

Illuminations  

Many, many, many worthwhile activities and explorations in the world of Math.    Activities are labeled with the suggested grade levels.  All the activities are interactive and require mathmatical reasoning.  Let the learning begin now at Illuminations!

Here is a list and a brief explanation of each activity.   

 

Teachers be sure to check out the Web Links on the orange border at the top of the page.

Illuminations has links to 724 math resources on the web. Click on a Standard to find the types of resources you’re looking for.

Numbers and OperationsAlgebraGeometry Measurement Data and Probability

	Fire		Simulate the spread of a wildfire using a probability applet.
	Light Bounce		Investigate rational functions and the “Light It Up” game with this interactive tool.
	Line of Best Fit		Use this applet to plot a set of data and determine a line of best fit.
	Mars Earth Orbit – Actual		Explore the path made by Mars in relation to the Earth.
	Mars Earth Orbit – Model		Explore the path made by Mars in relation to the Earth, when the ratio of their orbital radii is assumed to be 3:2, and when the ratio of their time to complete one revolution is assumed to be 2:1.
	Turtle Pond		Estimate length and angle measure while guiding a turtle to a pond using computer commands.

…as well as these additional 93 activities…

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	A Geometric Investigation of (a + b)2		Explore an interactive demonstration of why (a + b)2 = a2 +2ab + b2.
	Adjustable Spinner		Create a spinner and examine the experimental and theoretical outcomes for a specified number of spins.
	Affine Recurrence Plotter		Investigate affine recurrence relations of the form A(n) = b × A(n – 1) + c,   A(0) = a.
	Affine Recurrence Spreadsheet		Investigate affine recurrence relations with a pre‑loaded spreadsheet.
	Angle Sums		Explore the sum of the interior angle measures for various polygons.
	Area Tool		Investigate how changes in the base and height of trapezoids, parallelograms, and triangles affect their area.
	Bar Grapher		Create a customized bar graph with your own data, or display a bar graph from an included set of data.
	Box Plotter		Create a customized box plot with your own data, or display a box plot of an included set of data.
	Canada Data Map		Use color coding to represent data about the Canadian provinces and territories, including population, land area, and gas usage.
	Chairs		Explore the number of chairs needed when tables are arranged in a restaurant.
	Circle Grapher		Create a customized circle graph with your own data, or display a circle graph from an included set of data.
	Circle Tool		Compare the circumference and area of a circle to its radius and diameter.
	Codes		Explore substitution ciphers by encoding and decoding text messages.
	Compound Interest Simulator		This applet will allow you to investigate savings account earnings, credit card debt, and a stock market simulation.
	Computing Pi		Compare two methods for computing pi.
	Concentration		Play a matching game with different representations of equivalent items — match quantities to their numerals, shapes to their names, or fractions to decimals and percents.
	Congruence Theorems		Explore the conditions that guarantee uniqueness of a triangle, quadrilateral or pentagon, regardless of location or orientation.
	Cube Nets		Examine various two-dimensional figures to determine which ones can be folded into a cube.
	Cubes		Determine the volume of a box by filling it with cubes, rows of cubes, or layers of cubes.
	Cutting Corners		Divide a triangle, square, or trapezoid into smaller, less common shapes.
	Cyclic Figures		Students will recognize rotation symmetry in figures and examining various rotation symmetries.
	Diagonals to Quadrilaterals I		Investigate the quadrilaterals formed by various arrangements of diagonals.
	Diagonals to Quadrilaterals II		Investigate the types of quadrilaterals that can be formed when certain restrictions are placed on the diagonals.
	Dihedral Figures		Students will recognize dihedral symmetry and reflections in figures and examining various symmetries.
	Distance to Horizon		Investigate the relationship between your height above the Earth and the distance you can see to the horizon.
	Electronic Abacus		Explore an abacus model for representing numbers and performing addition.
	Equivalent Fractions		Create equivalent fractions by dividing and shading squares or circles, and match each fractions to its location on the number line.
	Factor Game		Play an interactive game that exercises your factoring ability. Test your skills against a human or the computer.
	Factorize		Divide numbers into two factors, and build arrays to represent each factorization.
	Five Frame		Practice counting and adding to 10, using frames to think of numbers in relation to 5.
	Flowing Through Mathematics		Simulate water exiting a tube through a hole in the bottom, and investigate the speed at which the water flows.
	Fractal Tool		Play with shapes to understand an iterative process.
	Fraction Game		Explore relationships among fractions while playing this interactive game.
	Fraction Model I		Explore different representations for fractions. (In this version, the numerator is restricted to values from 0 to 20, and the denominator is limited to benchmark values of 1, 2, 4, 5, 8, 10 and 20.)
	Fraction Model II		Explore different representations for fractions. (In this version, the numerator and denominator can both take values up to 20.)
	Fraction Model III		Explore different representations for fractions. (In this version, the numerator and denominator can take values up to 100.)
	Frieze Patterns		Experiment with the seven classes of Frieze patterns and explore the transformations that constitute each of the seven categories.
	Geometric Solids		Manipulate various geometric solids. Color the solid to investigate properties such as the number of faces, edges, and vertices.
	Graph Creator		Draw and manipulate vertex-edge graphs.
	Half Angle		Discover where the incenter of a triangle occurs.
	Hexagon Island		What point within a regular hexagon has the property that the sum of the distances to the sides is minimum?
	Histogram Tool		Create a customized histogram with your own data, or display a histogram from an included set of data.
	Hospital Locator		Investigate the placement of a new medical center so it is mutually convenient to three cities.
	Interactive Geometry Dictionary: Areas in Geometry		Understand and investigate the area of the rectangle, parallelogram and triangle.
	Interactive Geometry Dictionary: Lines in Geometry		Understand and investigate lines, segments, and rays.
	Isometric Drawing Tool		Create dynamic drawings on isometric dot paper. Draw figures using edges, faces, or cubes, and then shift, rotate, color, decompose, or view them in 2‑D or 3‑D.
	Isosceles Triangle Investigation		Investigate the relationship between the area of an isosceles triangle and the length of its base.
	Limits		Explore visual representations of geometric and harmonic series.
	Linear Regression I		Investigate a regression line and determine the effects of adding points to a scatterplot.
	Mean and Median		Investigate the mean, median, and box-and-whisker plot for sets of data that you create.
	Mirror Tool		Create reflection symmetry with a mirror.
	Mixtures		Explore mixture problems using colored circles from two different piles.
	Nim Games		Play several different versions of Nim against the computer.
	Octagon Island		What point within a regular octagon has the property that the sum of the distances to the sides is minimum?
	Pan Balance – Expressions		Investigate the concept of equivalence by “weighing” numeric and algebraic expressions.
	Pan Balance – Numbers		Find equivalent numerical expressions using a balance scale.
	Pan Balance – Shapes (Fixed Values)		Explore relationships among the weights of various objects by placing them on either side of a balance scale. (This activity is a special version of the Pan Balance – Shapes applet. It uses numbers that are friendly for primary classrooms.)
	Pan Balance – Shapes		Explore relationships among the weights of various objects by placing them on either side of a balance scale.
	Paper Pool		Shoot a pool ball so that it continually bounces off the sides of a pool table at a 45° angle until it lands in a corner.
	Parallelogram Exploration Tool		Investigate the resulting areas when two parallel segments are constructed through a point on the diagonal of a parallelogram.
	Patch Tool		Design a pattern using geometric shapes.
	Power of a Point		The point of intersection of chords, secants, and tangents allows for some interesting investigations. The Power of a Point tool allows for the exploration of various relationships that occur because of this point.
	Primary Krypto		Use five number cards and arithmetic operations to create the “target” number in this fun math game.
	Product Game		Exercise your skill with factors and multiples.
	Proof Without Words: Completing the Square		Carry out an interactive, geometric “proof without words” for the algebraic technique of completing the square.
	Proof Without Words: Pythagorean Theorem		Watch a dynamic, geometric “proof without words” of the Pythagorean Theorem.
	Random Drawing Tool – Individual Trials		Explore the relationship between theoretical and experimental probabilities.
	Random Drawing Tool – Sampling Distribution		Explore sampling distributions by drawing multiple numbers many times.
	Robot Sketcher		Explore various robot arm constructions, using one, two or three arms that rotate (like a rotary motor) or slide (like a hydraulic lift).
	Scale Factor		A common misconception is that when the dimensions of an object are doubled, the area is doubled, too. But this is not true! Use this applet to investigate how changes in the scale factor influence the ratio of perimeters and the ratio of areas between two figures.
	Shape Cutter		Draw and cut shapes, then use slides, turns, and flips to move the cut pieces around.
	Shape Sorter		Sort shapes according to their properties using Venn diagrams.
	Shape Tool		Draw, color, paste, slice, rotate, reflect, expand, and contract various shapes.
	Soccer Problem		Explore a soccer’s players angles when kicking a ball at the goal.
	Soda Cans		Examine an interesting result when circular cans are arranged in a rectangular container.
	Sound Sketch Tool		Sketch and quantify sound using two different representations.
	Sound Wave		Explore the dynamics of a sound wave, including pitch, tone, frequency, intensity and loudness.
	Spreadsheet and Graphing Calculator		Use the combined features of a spreadsheet and a graphing calculator.
	Square Graphs		Explore the graphs that result when two characteristics of a square (side length, diagonal length, perimeter, area) are plotted.
	Squares on a Triangle		Explore a geometric interpretation of the Law of Cosines.
	State Data Map		Use color-coding to represent state information, such as population, area, and gasoline usage.
	Ten Frame		Practice counting and adding to 20, using frames to think of numbers in relation to 10.
	Times Table		Practice multiplying single-digit numbers with this interactive multiplication table.
	Tower of Hanoi		Solve the Tower of Hanoi puzzle by moving all of the disks from one peg to another.
	Triangle Classification		Classify triangles in the plane by their sides and their angles.
	Triangle Island		What point within an equilateral triangle, a square, or another regular polygon has the property that the sum of the distances to the sides is minimum?
	Trigonometric Graphing		Explore the amplitude, period, and phase shift of various trigonometric functions.
	Trout Population Calculator		Explore the growth or decline of a trout population in a restocked pond.
	Tube Viewer Simulation		Simulate the effect of viewing an image through a tube.
	Two Terrains		Determine the best path for a vehicle that can’t go as fast when it travels off‑road.
	Vector Investigation: Car Storm Chaser		Adjust the magnitude and direction of a velocity vector to “drive” a car.
	Vector Investigation: Dual Vector, Airplane Storm Chaser		Adjust the magnitude and direction of a velocity vector and a wind vector to “fly” a plane.
	Volt Meter		Use the voltage of batteries to explore