Geometry Online Demonstration/Exploration Tools

 
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Explanation of Column Headings
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  Page Contents:

Number and Operations
Algebra
Geometry
Measurement
Data Analysis and Probability

Number and Operations

Broad Expectation* Topic
Link to Applet and Description
How good for teacher demos (1-3)?
How easy for students (1-3)?
How good for exploration (1-3)?
Available activities
Understand numbers, ways of representing numbers, relationships among numbers, and number systems            
             
Understand meanings of operations and how they relate to one another            
             
Compute fluently and make reasonable estimate            
             

Algebra

Broad Expectation* Topic
Link to Applet and Description
How good for teacher demos (1-3)?
How easy for students (1-3)?
How good for exploration (1-3)?
Available activities
Understand patterns, relations, and functions Slope Slope Comparison - Manipulate two segments. Slopes shown in decimal and fraction form. Can study parallel and perpendicular lines.
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 Quickie
  Function (general) Function Flyer - one of the best applets on the web. Allows user to input function, manipulate x, and manipulate coefficients.
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Represent and analyze mathematical situations and structures using algebraic symbols            
             
Use mathematical models to represent and understand quantitative relationships            
             
Analyze change in various contexts            
             
             

Geometry

Broad Expectation* Topic
Link to Applet and Description
How good for teacher demos (1-3)?
How easy for students (1-3)?
How good for exploration (1-3)?
Available activities
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Exterior Angles The Sum of Exterior Angles of a Polygon - This shows the sum of the exterior angles of any (user-defined) polygon.
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  Inscribed and Central angles

Inscribed and Central Angles - One inscribed angle and central angle. Use this first.
Circle Geometry - Inscribed and central angles again, but two inscribed angles.

In both cases, manipulate points on the circle. See the angles.

Soccer Problem - Figure out when to shoot.

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  Pythagorean Theorem Pythagorean Theorem (1) (2) and (5) - Visual (geometric) demonstrations of the Pythagorean Theorem.
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  Shapes Geoboard – Use geoboards (virtual rubber bands) to illustrate area, perimeter, and more.
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built in
  Congruent Triangles Congruent Triangles – Build triangles by combining sides and angles.
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  Tessellations Polygons Around a Point - Use regular polygons to surround a point in a plane. See if it tessellates.
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 Polygons Around a Point
  Similarity Similar Triangles - Drag any orange dot at either triangle's vertex. Both triangles will change shape and remain similar to each other.
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Specify locations and describe spatial relationships using coordinate geometry and other representational systems          
             
Apply transformations and use symmetry to analyze mathematical situations Transformations Transmographer 2 - Translate, reflect, or rotate point in the coordinate plane.
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    Transformations - Composition – Explore the effect of applying two of the following: translation, rotation, and reflection.
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    Transformations - Dilation – Dynamic dilation transformation.
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  Tessellations Tessellations – Tile the plane.
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    Tessellate! - This tool allows you to make your own shape to tessellate the plane. (Shodor)
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Use visualization, spatial reasoning, and geometric modeling to solve problems Polyhedra Platonic Solids - Investigate the solids (cube, tetrahedron, ...). Rotate the shape. Shift-click the edges, vertices, and the faces to color (and count them). V - E + F =   ?
Platonic Solid Duals - Investigate the solids and their duals.
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 Platonic Solids
    3D Shapes-Platonic Solids - Part of the Interactives site at Annenberg.       Test your skills (online)
    Euler's Theorem - Part of the Interactives site at Annenberg.       Test your skills (online)
   
Truncate, Expand, Snubify - From the five platonic solids, you can get other solids using these three processes.
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    Drawing in Polyhedra - Draw segments on (or in) a polyhedron. Draw planes on (or in) a polyhedron. To draw a line, click on two (corner) points in the polyhedron. To draw a plane, click on a number of points then click on the first point again to draw the plane. Click and drag to rotate the polyhedron.
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  Nets Cut-outs, Nets - This applet folds a 2D net into a 3D object. Click and drag to manipulate the object/net.
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    3D Shapes - Part of the Interactives site at Annenberg. A couple pages of information then some interactive demos. Prisms, Pyramiods,       Test your skills (online)
  Solids of Revolution Lathe - Click a line in the white area in the lower left corner to create a "curve." This curve is rotated around the axis to create a 3D shape. Manipulate the object with the mouse.
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  3D Visualization (Views) Building Houses - Good Starter 3D visualization tool. Build with blocks and see the views. Click and drag to manipulate the object.
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    Houses with Height Numbers - Also a good beginner 3D visualization tool. Build with blocks. Click and drag to manipulate the object.        
  Spheres Great Circle – Use a 3D globe to visualize and measure the shortest path between cities. Spherical geometry.
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  Isometric Drawing Isometric Drawing Tool - from NCTM.
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Measurement

Broad Expectation* Topic
Link to Applet and Description
How good for teacher demos (1-3)?
How easy for students (1-3)?
How good for exploration (1-3)?
Available activities
Understand measurable attributes of objects and the units, systems, and processes of measurement Rates Understanding Distance, Speed, and Time Relationships - Simulation of two runners along a track. Explore slope and starting points.
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Apply appropriate techniques, tools, and formulas to determine measurements Angle Measure Protractor applet - Very nice. Has an introduction (which can be skipped). Various interactive activities with and without a virtual protractor.
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included
online

  Area and Perimeter Shape Builder - Draw your own, or computer generate, shapes and investigate area and perimeter. Shodor
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Keep Score is build in
  Surface Area & Volume Surface Area and Volume - Manipulate dimensions of polyhedra, and watch how the surface area and volume change. Also manipulate the solid.
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use compute mode
    Three Dimensional Box Applet: Working With Volume - Cut (equal) corners from a rectangular piece of cardboard and fold into a box.
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Find the maximum volume
  Convert Units Converting Units - Interactive. "Multiply by a form of 1" to convert.
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built in

Data Analysis and Probability

Broad Expectation* Topic
Link to Applet and Description
How good for teacher demos (1-3)?
How easy for students (1-3)?
How good for exploration (1-3)?
Available activities
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them            
             
Select and use appropriate statistical methods to analyze data            
             
Develop and evaluate inferences and predictions that are based on data            
             
Understand and apply basic concepts of probability            
             
 
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Explanation of Column Headings

(This page is organized using the five content areas in school mathematics, as articulated in the NCTM Principles and Standards, 2000.)

by: James R. Olsen, Western Illinois University
updated: December 14, 2011