Resources tagged with: GeoGebra

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There are 90 results

Broad Topics > Physical and Digital Manipulatives > GeoGebra

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?

Angles Inside

Age 11 to 14 Challenge Level:

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

Tessellation Interactivity

Age 7 to 16 Challenge Level:

An environment that enables you to investigate tessellations of regular polygons

Triangles in Circles

Age 11 to 14 Challenge Level:

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

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?

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?

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.

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?

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?

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.

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?

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?

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?

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?

Polygon Rings

Age 11 to 14 Challenge Level:

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

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.

Pythagoras Proofs

Age 14 to 16 Challenge Level:

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

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.

L-triominoes

Age 14 to 16 Challenge Level:

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

Estimating Angles

Age 7 to 14 Challenge Level:

How good are you at estimating angles?

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.

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.

Mixing Paints

Age 11 to 14 Challenge Level:

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

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...

Mixing More Paints

Age 14 to 16 Challenge Level:

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

Colour in the Square

Age 7 to 16 Challenge 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?

A Tilted Square

Age 14 to 16 Challenge Level:

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

Shear Magic

Age 11 to 14 Challenge Level:

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

The Farmers' Field Boundary

Age 11 to 14 Challenge Level:

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

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.

Triangle in a Triangle

Age 14 to 16 Challenge Level:

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

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?

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?

Polar Coordinates

Age 14 to 18

Cartesian Coordinates are not the only way!

Round and Round a Circle

Age 14 to 16 Challenge Level:

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

Vanishing Point

Age 14 to 18 Challenge Level:

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

Spinners Environment

Age 5 to 18 Challenge Level:

A tool for generating random integers.

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?

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?

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?

Coordinates of Corners

Age 11 to 16

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

Beelines

Age 14 to 16 Challenge Level:

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

Areas from Vectors

Age 11 to 16

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

Exploring Diagonals

Age 11 to 16

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

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.

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?

Solving Together - Estimating Angles

Age 11 to 14

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