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?

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

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

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?

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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?

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 hang weights in the right place to make the equaliser balance?

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

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?

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

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

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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?

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

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.

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

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

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!

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?

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?

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?

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

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

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

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

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?

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

Use the number weights to find different ways of balancing the equaliser.

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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.

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

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

Use the interactivities to complete these Venn diagrams.

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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 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?