The farmers want to redraw their field boundary but keep the area the same. Can you advise them?
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
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?
In how many ways can you fit all three pieces together to make shapes with line symmetry?
How much of the square is coloured blue? How will the pattern continue?
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?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
It would be nice to have a strategy for disentangling any tangled ropes...
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
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
What is the greatest number of squares you can make by overlapping three squares?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
Can you picture where this letter "F" will be on the grid if you flip it in these different ways?
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?
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?
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?
Join pentagons together edge to edge. Will they form a ring?
How good are you at estimating angles?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Use these four dominoes to make a square that has the same number of dots on each side.
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?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
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?
Move the corner of the rectangle. Can you work out what the purple number represents?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
How well can you estimate angles? Playing this game could improve your skills.
Board Block Challenge game for an adult and child. Can you prevent your partner from being able to make a shape?
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....?
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?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
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?
A generic circular pegboard resource.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
An environment that enables you to investigate tessellations of regular polygons
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Use the applet to make some squares. What patterns do you notice in the coordinates?
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.
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
A tool for generating random integers.