During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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

This article for teachers suggests ideas for activities built around 10 and 2010.

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

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

There are nasty versions of this dice game but we'll start with the nice ones...

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

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?

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

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

Investigate the different distances of these car journeys and find out how long they take.

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?

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?

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?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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

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?

On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

In this game for two players, the aim is to make a row of four coins which total one dollar.

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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.

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

Got It game for an adult and child. How can you play so that you know you will always win?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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

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

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.