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?

Can you complete this jigsaw of the multiplication square?

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

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

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?

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

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

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

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....?

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

An environment which simulates working with Cuisenaire rods.

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?

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

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.

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

Use the interactivities to complete these Venn diagrams.

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!

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?

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

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

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?

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

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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

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

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

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

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?

An interactive activity for one to experiment with a tricky tessellation

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

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?

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?

How many different rhythms can you make by putting two drums on the wheel?

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?

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.

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 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?

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

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?

Work out how to light up the single light. What's the rule?