How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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?
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?
What is the best way to shunt these carriages so that each train can continue its journey?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
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?
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?
A challenging activity focusing on finding all possible ways of stacking rods.
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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 different triangles can you make on a circular pegboard that has nine pegs?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
These practical challenges are all about making a 'tray' and covering it with paper.
An activity making various patterns with 2 x 1 rectangular tiles.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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 the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
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.
Can you find all the different ways of lining up these Cuisenaire rods?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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?
How many different rhythms can you make by putting two drums on the wheel?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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?
In how many ways can you stack these rods, following the rules?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
This challenge extends the Plants investigation so now four or more children are involved.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.