Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
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?
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....?
What happens when you try and fit the triomino pieces into these two grids?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Use the clues to colour each square.
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
What is the best way to shunt these carriages so that each train can continue its journey?
How many different rhythms can you make by putting two drums on the wheel?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
These practical challenges are all about making a 'tray' and covering it with paper.
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
An activity making various patterns with 2 x 1 rectangular tiles.
Can you find all the different ways of lining up these Cuisenaire rods?
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
How many triangles can you make on the 3 by 3 pegboard?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you find the chosen number from the grid using the clues?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
Can you cover the camel with these pieces?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Investigate the different ways you could split up these rooms so that you have double the number.
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?