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?

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

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?

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!

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?

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?

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

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

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.

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

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

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?

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

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

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?

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?

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 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?

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

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?

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?

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

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?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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?

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?

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

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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

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?

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

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

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

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

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?

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?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

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?

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?

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

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?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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?