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

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

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

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

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?

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

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

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

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?

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

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 shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.

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?

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

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

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

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?

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

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?

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

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?

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

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?

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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?

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

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

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

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?

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

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

Week 2

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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

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?

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

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?

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

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.

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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