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?

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.

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

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.

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

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?

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!

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

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

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

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

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

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?

An environment which simulates working with Cuisenaire rods.

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?

Use the interactivities to complete these Venn diagrams.

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?

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

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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?

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....?

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

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

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?

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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

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

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

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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?

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?

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

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

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

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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?

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?

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?

Move just three of the circles so that the triangle faces in the opposite direction.

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

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?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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?