How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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?
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?
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?
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?
A challenging activity focusing on finding all possible ways of stacking rods.
What is the best way to shunt these carriages so that each train can continue its journey?
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 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.
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
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 the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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....?
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
In how many ways can you stack these rods, following the rules?
How many different triangles can you make on a circular pegboard that has nine pegs?
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 symmetrical shapes can you make by shading triangles or squares?
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. . . .
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.
These practical challenges are all about making a 'tray' and covering it with paper.
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.
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
Can you find all the different ways of lining up these Cuisenaire rods?
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.
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Find out what a "fault-free" rectangle is and try to make some of your own.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Can you find all the different triangles on these peg boards, and find their angles?