# Geometry Virtual Manipulatives

#### Sound WaveNew!

This clever applet from Illuminations should help you understand the dynamics of sound.  You can hear the sound then see the animated sound wave, which has been slowed down so that you can see it.  You can then see how changing the string’s tension and initial displacement changes this wave.  This applet can provide a starter to an activity on Modelling Sound which will help you discover the underlying mathematics behind music.

## Geometry Virtual Manipulatives

'Great tools, freely available on the web for teaching Geometry and Measurement!'

The following page lists some examples of some of the best freely available virtual manipulatives on the web for teaching Geometry and Measurement. Where possible they will link to an example of how they can be used in the classroom. Entries are listed by topic subheading, although its not always easy to separate so its worth looking through the lists!

### Properties of Shapes

#### Geoboard

Anyone who has enjoyed playing with geoboards (nails half driven into a wooden board with elastic bands to investigate geometric properties) will love this virtual version.  Five accompanying investigations to go with it give you some ideas how to use it: find shapes with perimeter 16, maximize area, finding area of a triangle, … Simple but with oodles of possiblities.

#### Logo The Turtle

A free online Microworld from mathsnet .  Enter commands to move an arrow around the screen.  A ready to go activity to discover the rules for a) the sum of exterior angles of a regular polygon and b) the exterior angle of any regular polygon or star can be found at  Polygons and Stars.  Those not familiar with programming should take care to use the right syntax.  A missing space, for example, will cause an error.

#### 3D Shapes

Explore the properties of 3D shapes with a series of lessons using various virtual manipulatives.  Nets are explored, surface areas and volumes investigated, Euler’s Theorem explained and we discover the Platonic solids.  There are 15 accompanying questions will check up knowledge.  Very thorough!

### Plans and Elevations

#### Building Blocks

The Freudenthal Institute's excellent wisweb (http://www.fi.uu.nl/wisweb/) offers two resources for exploring front, side and plan elevation 2D representations of 3D objectsLots of interactivity and a superb medium by which students can acquire the necessary experiences for developing their visual awareness. A ready made lesson resource integrating the best of this website is available from the  Plans and Elevations.

#### Draw and Name the 3D shape given its Elevations

Harcourt School publishers (www.harcourtschool.com) have a very useful "Learning Site" with some virtual manipulatives available. Here is one that makes a good introduction to 2D representations of 3D shapesA ready made lesson resource that links to this activity is available from the  Plans and Elevations.

### Symmetry and Transformations

#### Art using Reflections

In this simple applet from the University of Tennessee you can use the mouse as a paintbrush to draw a picture and watch its reflection appear.  Let students play with it for a while then ask them to draw some specific shapes.  I like asking them to write the reflection of their name and watching the applet write it the correct way around.  A great introduction to line symmetry.

### Trigonometry

#### Ferris Wheel Unit Circle

This is an outstanding Geogebra applet for introducing the Unit Circle from EDC in Maine.  Students create a graph of the height of a seat on a Ferris wheel to explore the sine function and characteristics of the unit circle.

#### Sound Wave

This clever applet from Illuminations should help you understand the dynamics of sound.  You can hear the sound then see the animated sound wave, which has been slowed down so that you can see it.  You can then see how changing the string’s tension and initial displacement changes this wave.  This applet can provide a starter to an activity on Modelling Sound which will help you discover the underlying mathematics behind music.

#### Fourier: Making Waves

This lovely VM from PHET helps you learn how to make waves of all different shapes by adding up sines or cosines. Make waves in space and time and measure their wavelengths and periods. See how changing the amplitudes of different harmonics changes the waves. Compare different mathematical expressions for your waves.  This virtual manipulative is best used after you have tried our activity  Modelling Music

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