NumberGym Geometry

(KS3,4: age 11-16)

NumberGym Geometry comprises a set of clear, easy-to-use interactive explorations and challenges to assist in the teaching of mathematics at ages 12 to 16. These activities are brilliant on interactive whiteboards for whole-class or group participation. Topics include the the four transformations (animated explorations and challenges), interactive circle geometry, understanding basic trigonometry using an interactive triangle and powerful yet easy-to-use graphing tools allowing pupils to create and compare all major graph types.

Drag the triangle to different sizes and watch the trig functions recalculate in an easy-to-understand way. Why is the Cosine of angle A equal to the Sine of angle B? Can you make a triangle with a Tangent of 1? Why is it easier to calculate Sine and Cosine when the Hypotenuse is length 10 or 100? Each trig line has its own 'hide' button so you can keep it simple to begin with.

Use the mouse to draw your original shape. Then set the vector of translation, click the translate button and watch your shape be transformed. Once you are confident try the challenge by clicking the Set Challenge button. If a transformation moves off the grid, use the 'Zoom' controls to adjust the visible grid.

Use the mouse to draw your shape. Optional guidelines available. Amend the scale factor and centre of enlargment as required. Then click the 'enlarge' button and watch your shape be transformed. Set challenge feature available. Scale factors can be less than one or negative, which creates a new set of guidelines. To create a challenge with a negative enlargement, set the Scale Factor to a negative value before pressing the 'Set Challenge' button. Zoom available.

Start by drawing a shape for reflection. Simply hold down the left mouse button and drag a line out before releasing the button. All lines automatically click to the grid.
If required, you may then click the 'Set Challenge' button to generate a target image.
Select the required line of reflection using the radio buttons and, optionally, adjust further using the blue triangular controls to the left of the x axis or below the y axis.
Click the 'Reflect' button to view the animated reflection.

Use the mouse to draw some shapes. Optionally use the Set Challenge button. Change the centre of rotation if required. Set the degrees and direction of rotation. Then press the 'rotate' button and watch the transformation The 'Clear Images' button deletes the transformed images but keeps the original drawing and any target image.

This activity follows on from the four separate activities above. As before start by drawing your shape. Then select the type of transformation required and click the transform button. A second transformation will be applied to the new image and so on.

The Set Challenge button will generate a target that can be reached in not more than two transformations.

Choose the setting from the drop-down combo box. Then drag the blue handles to change the triangles. Each angle can be hidden or shown separately to encourage the setting of challenges.

Use the drop-down box to select the required graph type. Then use the blue up/down buttons to set your required equation or just experiment and observe the effects of adjusting each component. By default, each change to the equation replaces the old graph with the latest. To overlay graphs just click on the Keep Previous check-box (bottom right). The Draw on Change check-box causes a new graph to be drawn each time the equation is modified. Click on this check-box to turn off this feature and just use the Draw Graph button when required.

This activity uses similar buttons and check-boxes to graphing tool above. The available functions are:
y= aSin(bx +c),
y= aCos(bx +c)
y= aTan(bx +c), where c will increment/decrement in multiples of 15 degrees.

This activity is ideal for demonstrating the effects of changing each component of the trig functions eg the difference between y= 2Sin(x) and y Sin(2x)

This is essentially a novel way of demonstrating visually Pythagoras' theorem. You may want to show it first without the algebra. Then use the 'restart' button and tick the 'show algebra' box. With this option on there's an extra few frames at the end working out the algebra - don't miss them!