There are **81** NRICH Mathematical resources connected to **GeoGebra**, you may find related items under Physical and Digital Manipulatives.

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

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

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

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

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

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

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.

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

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

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

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

Can you complete this jigsaw of the multiplication square?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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?

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?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

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.

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

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.

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

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

How many different triangles can you make on a circular pegboard that has nine pegs?

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

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?

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

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

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?

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?

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

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?

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?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

How would you move the bands on the pegboard to alter these shapes?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

There are six numbers written in five different scripts. Can you sort out which is which?

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?

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?

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