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 many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many different triangles can you make on a circular pegboard that has nine pegs?
Use the clues to colour each square.
Sort the houses in my street into different groups. Can you do it in any other ways?
Find out what a "fault-free" rectangle is and try to make some of your own.
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
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 ways of lining up these Cuisenaire rods?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Can you find all the different triangles on these peg boards, and find their angles?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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....?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Can you sort these triangles into three different families and explain how you did it?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Choose a symbol to put into the number sentence.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put these shapes in order of size? Start with the smallest.
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?