Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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?

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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....?

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

Can you complete this jigsaw of the multiplication square?

Challenge Level

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

Challenge Level

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?

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

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?

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

Challenge Level

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

Challenge Level

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

Week 2

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

Challenge Level

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

Challenge Level

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

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?

Challenge Level

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

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?

Challenge Level

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?

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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