What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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!

An environment which simulates working with Cuisenaire rods.

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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?

Here is a chance to play a version of the classic Countdown Game.

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Can you complete this jigsaw of the multiplication square?

If you have only four weights, where could you place them in order to balance this equaliser?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each 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 sort these numbers into sets. Can you give each set a name?

How many trains can you make which are the same length as Matt's, using rods that are identical?

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 work out how to balance this equaliser? You can put more than one weight on a hook.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Can you find all the different ways of lining up these Cuisenaire rods?

Complete the squares - but be warned some are trickier than they look!

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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?

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?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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?

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?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Can you find all the different triangles on these peg boards, and find their angles?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?