An environment that enables you to investigate tessellations of regular polygons

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

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

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.

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?

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

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

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

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

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

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?

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

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

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

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

Week 2

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

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

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

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

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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

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

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

Board Block Challenge game for an adult and child. Can you prevent your partner from being able to make a shape?

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.

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

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

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?

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

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?

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

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

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

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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

What is the greatest number of squares you can make by overlapping three squares?

Can you find all the different triangles on these peg boards, and find their angles?

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?

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

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.

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.