Use the clues to colour each square.
What happens when you try and fit the triomino pieces into these two grids?
How many different rhythms can you make by putting two drums on the wheel?
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?
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?
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?
Can you find all the different ways of lining up these Cuisenaire rods?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
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?
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....?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
What is the best way to shunt these carriages so that each train can continue its journey?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
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?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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?
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. . . .
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 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.
How many triangles can you make on the 3 by 3 pegboard?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
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?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
How many models can you find which obey these rules?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
This challenge extends the Plants investigation so now four or more children are involved.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.