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?

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

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

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

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?

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

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

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

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.

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

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

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

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?

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

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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

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?

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?

A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

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?

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?

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?

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?

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?

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

A game for 2 players. Practises subtraction or other maths operations knowledge.

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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

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

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.

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?

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

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.

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.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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.

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.

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

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.