Resources tagged with: GeoGebra

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There are 90 results

Broad Topics > Physical and Digital Manipulatives > GeoGebra

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?

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?

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?

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?

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?

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?

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

More Twisting and Turning

Age 11 to 16Challenge Level

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

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?

Diminishing Returns

Age 11 to 14Challenge Level

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

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?

Reflecting Squarely

Age 11 to 14Challenge Level

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

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?

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?

Guesswork

Age 14 to 16Challenge Level

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

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. . . .

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?

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?

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?

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?

Age 14 to 16Challenge Level

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

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?

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.

4 Dom

Age 5 to 16Challenge Level

Use these four dominoes to make a square that has the same number of dots on each side.

Polygon Rings

Age 11 to 14Challenge Level

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

More Magic Potting Sheds

Age 11 to 14Challenge Level

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Estimating Angles

Age 7 to 14Challenge Level

How good are you at estimating angles?

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.

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?

Teddy Town

Age 5 to 14Challenge Level

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Farey Sequences

Age 11 to 14Challenge Level

There are lots of ideas to explore in these sequences of ordered fractions.

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.

Triangles in Circles

Age 11 to 14Challenge Level

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

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?

Squirty

Age 14 to 16Challenge Level

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

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?

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?

Solving Together - Estimating Angles

Age 11 to 14

Week 2
How well can you estimate angles? Playing this game could improve your skills.

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?

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?

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?

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?

Exploring Diagonals

Age 11 to 16

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

Tessellation Interactivity

Age 7 to 16Challenge Level

An environment that enables you to investigate tessellations of regular polygons

Speeding Up, Slowing Down

Age 11 to 14Challenge Level

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

Rollin' Rollin' Rollin'

Age 11 to 14Challenge Level

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

Spinners Environment

Age 5 to 18Challenge Level

A tool for generating random integers.