How would you find out how many football cards Catrina has collected?

It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?

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

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!

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

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!

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.

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?

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?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Number problems at primary level that require careful consideration.

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

Can you find different ways of creating paths using these paving slabs?

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

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.

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

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?

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

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

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?

56 406 is the product of two consecutive numbers. What are these two numbers?

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

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.

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?

Number problems at primary level that may require resilience.

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?

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Play this game and see if you can figure out the computer's chosen number.

This number has 903 digits. What is the sum of all 903 digits?

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

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

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 score 100 by throwing rings on this board? Is there more than way to do it?

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

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?

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?

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