# Resources tagged with: GeoGebra

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### There are 90 results

Broad Topics > Physical and Digital Manipulatives > GeoGebra

### Vanishing Point

##### Age 14 to 18Challenge Level

How can visual patterns be used to prove sums of series?

### Semi-regular Tessellations

##### Age 11 to 16Challenge Level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

### Rolling Around

##### Age 11 to 14Challenge Level

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

### Pythagoras Proofs

##### Age 14 to 16Challenge Level

Can you make sense of these three proofs of Pythagoras' Theorem?

##### Age 11 to 16Challenge Level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

### Subtended Angles

##### Age 11 to 14Challenge Level

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

### Tilting Triangles

##### Age 14 to 16Challenge Level

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

### Polygon Rings

##### Age 11 to 14Challenge Level

Join pentagons together edge to edge. Will they form a ring?

### Right Angles

##### Age 11 to 14Challenge Level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

### Triangles in Circles

##### Age 11 to 14Challenge Level

Can you find triangles on a 9-point circle? Can you work out their angles?

### Squaring the Circle and Circling the Square

##### Age 14 to 16Challenge Level

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

### Partitioning Revisited

##### Age 11 to 14Challenge Level

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

##### Age 14 to 16Challenge Level

Kyle and his teacher disagree about his test score - who is right?

### The Medieval Octagon

##### Age 14 to 16Challenge Level

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.

### A Tilted Square

##### Age 14 to 16Challenge Level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

### Where Is the Dot?

##### Age 14 to 16Challenge Level

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

### L-triominoes

##### Age 14 to 16Challenge Level

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

### Colour in the Square

##### Age 7 to 16Challenge Level

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

### Overlap

##### Age 11 to 14Challenge Level

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

### Angles Inside

##### Age 11 to 14Challenge Level

Draw some angles inside a rectangle. What do you notice? Can you prove it?

### Picturing Triangular Numbers

##### Age 11 to 14Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

### Beelines

##### Age 14 to 16Challenge Level

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

### More Twisting and Turning

##### Age 11 to 16Challenge Level

It would be nice to have a strategy for disentangling any tangled ropes...

### The Farmers' Field Boundary

##### Age 11 to 14Challenge Level

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

### Shear Magic

##### Age 11 to 14Challenge Level

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

### Nine Colours

##### Age 11 to 16Challenge Level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

### Same Length

##### Age 11 to 16Challenge Level

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

### Square Coordinates

##### Age 11 to 14Challenge Level

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

### Estimating Angles

##### Age 7 to 14Challenge Level

How good are you at estimating angles?

### Is There a Theorem?

##### Age 11 to 14Challenge Level

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

### Just Rolling Round

##### Age 14 to 16Challenge Level

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Bow Tie

##### Age 11 to 14Challenge Level

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

### Reflecting Squarely

##### Age 11 to 14Challenge Level

In how many ways can you fit all three pieces together to make shapes with line symmetry?

##### Age 14 to 16Challenge Level

The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?

### Tessellation Interactivity

##### Age 7 to 16Challenge Level

An environment that enables you to investigate tessellations of regular polygons

### Spinners Environment

##### Age 5 to 18Challenge Level

A tool for generating random integers.

##### Age 14 to 16Challenge Level

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?

### Diminishing Returns

##### Age 11 to 14Challenge Level

How much of the square is coloured blue? How will the pattern continue?

### Isosceles Triangles

##### Age 11 to 14Challenge Level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

### Magic Potting Sheds

##### Age 11 to 14Challenge Level

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

### How Far Does it Move?

##### Age 11 to 14Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

### Areas from Vectors

##### Age 11 to 16

Use the applet to explore the area of a parallelogram and how it relates to vectors.

### Coordinates of Corners

##### Age 11 to 16

Use the applet to make some squares. What patterns do you notice in the coordinates?

### Factor Lines

##### Age 7 to 14Challenge Level

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

### Translating Lines

##### Age 11 to 14Challenge Level

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

### Up and Across

##### Age 11 to 14Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

### Reflecting Lines

##### Age 11 to 14Challenge Level

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

### Exploring Diagonals

##### Age 11 to 16

Move the corner of the rectangle. Can you work out what the purple number represents?

### Triangle in a Triangle

##### Age 14 to 16Challenge Level

Can you work out the fraction of the original triangle that is covered by the inner triangle?