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

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?

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

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?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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?

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

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

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

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

You have 5 darts and your target score is 44. How many different ways could you score 44?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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!

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

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

This challenge is about finding the difference between numbers which have the same tens digit.

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

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

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

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

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

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?

This dice train has been made using specific rules. How many different trains can you make?

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

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?