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?

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

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?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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!

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?

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

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?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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?

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

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

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

This challenge combines addition, multiplication, perseverance and even proof.

This task combines spatial awareness with addition and multiplication.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

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!

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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?

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

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

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.

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

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?

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

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Number problems at primary level that require careful consideration.

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

Number problems at primary level that may require resilience.

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.