Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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?
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Can you explain the strategy for winning this game with any target?
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?
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you find all the different triangles on these peg boards, and find their angles?
Choose a symbol to put into the number sentence.
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
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!
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
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?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
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?
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
A card pairing game involving knowledge of simple ratio.
Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Try out the lottery that is played in a far-away land. What is the chance of winning?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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?
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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Work out how to light up the single light. What's the rule?
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
A train building game for 2 players.
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?
If you have only four weights, where could you place them in order to balance this equaliser?
Work out the fractions to match the cards with the same amount of money.
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...
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Find out what a "fault-free" rectangle is and try to make some of your own.
Use the interactivity or play this dice game yourself. How could you make it fair?
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you find all the different ways of lining up these Cuisenaire rods?