This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you find all the different triangles on these peg boards, and find their angles?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
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?
How would you move the bands on the pegboard to alter these shapes?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
How many different triangles can you make on a circular pegboard that has nine pegs?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
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....?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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 lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Can you complete this jigsaw of the multiplication square?
What is the greatest number of squares you can make by overlapping three squares?
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?
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?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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?
There are six numbers written in five different scripts. Can you sort out which is which?
A generic circular pegboard resource.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
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?
Board Block Challenge game for an adult and child. Can you prevent your partner from being able to make a shape?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
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?
It would be nice to have a strategy for disentangling any tangled ropes...
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
How well can you estimate angles? Playing this game could improve your skills.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Can you find triangles on a 9-point circle? Can you work out their angles?
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?
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
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?
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?
The farmers want to redraw their field boundary but keep the area the same. Can you advise them?
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?
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