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.

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!

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?

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

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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

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

Investigate what happens when you add house numbers along a street in different ways.

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

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?

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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?

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

Fill in the numbers to make the sum of each row, column and diagonal equal to 15.

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?

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?

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

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

An environment which simulates working with Cuisenaire rods.

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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

Number problems at primary level that require careful consideration.

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?

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

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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

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

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

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

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

There were 22 legs creeping across the web. How many flies? How many spiders?

Can you find 2 butterflies to go on each flower so that the numbers on each pair of butterflies adds to the same number as the one on the flower?