Resources tagged with: GeoGebra

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There are 90 results

Broad Topics > Physical and Digital Manipulatives > GeoGebra

Tessellation Interactivity

Age 7 to 16
Challenge Level

An environment that enables you to investigate tessellations of regular polygons

Pegboard Quads

Age 14 to 16
Challenge 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?

Rolling Around

Age 11 to 14
Challenge 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?

Angles Inside

Age 11 to 14
Challenge Level

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

Using Geogebra

Age 11 to 18

Never used GeoGebra before? This article for complete beginners will help you to get started with this free dynamic geometry software.

Bow Tie

Age 11 to 14
Challenge 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.

Rollin' Rollin' Rollin'

Age 11 to 14
Challenge 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?

The Medieval Octagon

Age 14 to 16
Challenge Level

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

Same Length

Age 11 to 16
Challenge Level

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

Cyclic Quadrilaterals

Age 11 to 16
Challenge Level

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

Polygon Rings

Age 11 to 14
Challenge Level

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

Where Is the Dot?

Age 14 to 16
Challenge 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?

Impossible Picture?

Age 14 to 16
Challenge Level

Under what circumstances can you rearrange a big square to make three smaller squares?

Points in Pairs

Age 14 to 16
Challenge Level

Move the point P to see how P' moves. Then use your insights to calculate a missing length.

Right Angles

Age 11 to 14
Challenge Level

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

Squaring the Circle and Circling the Square

Age 14 to 16
Challenge Level

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

Subtended Angles

Age 11 to 14
Challenge 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?

Semi-regular Tessellations

Age 11 to 16
Challenge Level

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

Triangles in Circles

Age 11 to 14
Challenge Level

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

Solving Together - Estimating Angles

Age 11 to 14

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

Exploring Diagonals

Age 11 to 16

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

Arrowhead

Age 14 to 16
Challenge 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?

Just Rolling Round

Age 14 to 16
Challenge 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?

Tilting Triangles

Age 14 to 16
Challenge 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?

At Right Angles

Age 14 to 16
Challenge Level

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

Squirty

Age 14 to 16
Challenge 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.

Sine and Cosine for Connected Angles

Age 14 to 16
Challenge Level

The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.

Areas from Vectors

Age 11 to 16

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

Pythagoras Proofs

Age 14 to 16
Challenge Level

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

Mixing Paints

Age 11 to 14
Challenge Level

Can you work out how to produce different shades of pink paint?

Mixing More Paints

Age 14 to 16
Challenge Level

Can you find an efficent way to mix paints in any ratio?

Coordinates of Corners

Age 11 to 16

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

Speeding Up, Slowing Down

Age 11 to 14
Challenge 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.

A Brief Introduction to the Argand Diagram

Age 14 to 18
Challenge Level

Complex numbers can be represented graphically using an Argand diagram. This problem explains more...

Sine and Cosine

Age 14 to 16
Challenge Level

The sine of an angle is equal to the cosine of its complement. Can you explain why and does this rule extend beyond angles of 90 degrees?

Strolling Along

Age 14 to 18
Challenge Level

What happens when we multiply a complex number by a real or an imaginary number?

Opening the Door

Age 14 to 18
Challenge Level

What happens when we add together two complex numbers?

Into the Wilderness

Age 14 to 18
Challenge Level

Let's go further and see what happens when we multiply two complex numbers together!

Mapping the Territory

Age 14 to 18
Challenge Level

Can you devise a system for making sense of complex multiplication?

Parallel Lines

Age 11 to 14
Challenge Level

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

Perpendicular Lines

Age 14 to 16
Challenge Level

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

Estimating Angles

Age 7 to 14
Challenge Level

How good are you at estimating angles?

Dice/spinner Interactives

Age 11 to 14
Challenge Level

Surprising Equalities

Age 14 to 18
Challenge Level

Take any triangle, and construct squares on each of its sides. What do you notice about the areas of the new triangles formed?

Round and Round a Circle

Age 14 to 16
Challenge Level

Can you explain what is happening and account for the values being displayed?

Polar Coordinates

Age 14 to 18

Cartesian Coordinates are not the only way!

Quad in Quad

Age 14 to 16
Challenge Level

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

Up and Across

Age 11 to 14
Challenge 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.

Vanishing Point

Age 14 to 18
Challenge Level

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

Reflecting Lines

Age 11 to 14
Challenge 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.