What happens when you try and fit the triomino pieces into these two grids?
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?
Can you cover the camel with these pieces?
Use the clues to colour each square.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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?
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 find all the different ways of lining up these Cuisenaire rods?
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
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....?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
What is the best way to shunt these carriages so that each train can continue its journey?
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
How many different rhythms can you make by putting two drums on the wheel?
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?
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?
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?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
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 clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Can you find out in which order the children are standing in this line?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
This challenge is about finding the difference between numbers which have the same tens digit.
How many trains can you make which are the same length as Matt's, using rods that are identical?