Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
How many different triangles can you make on a circular pegboard that has nine pegs?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Choose a symbol to put into the number sentence.
Here is a chance to play a version of the classic Countdown Game.
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....?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you find all the different triangles on these peg boards, and find their angles?
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?
Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway 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?
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 find all the different ways of lining up these Cuisenaire rods?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Can you fit the tangram pieces into the outline of Granma T?
Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?
Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outlines of the chairs?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.
If you have only four weights, where could you place them in order to balance this equaliser?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
An interactive activity for one to experiment with a tricky tessellation
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.