Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity to sort these numbers into sets. Can you give each set a name?
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
This activity challenges you to make collections of shapes. Can you give your collection a name?
Sort the houses in my street into different groups. Can you do it in any other ways?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
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?
Take it in turns to make a triangle on the pegboard. Can you block your opponent?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Can you find all the different triangles on these peg boards, and find their angles?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
An odd version of tic tac toe
If you have only four weights, where could you place them in order to balance this equaliser?
Twenty four games for the run-up to Christmas.
Can you find all the different ways of lining up these Cuisenaire rods?
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?
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
An environment that enables you to investigate tessellations of regular polygons
How many different triangles can you make on a circular pegboard that has nine pegs?
Complete the squares - but be warned some are trickier than they look!
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
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....?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
A variant on the game Alquerque
Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?
Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
How many different rhythms can you make by putting two drums on the wheel?
Can you find just the right bubbles to hold your number?
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?
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?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
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!