Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .

Given the products of adjacent cells, can you complete this Sudoku?

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

Can you complete this jigsaw of the multiplication square?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

Given the products of diagonally opposite cells - can you complete this Sudoku?

A collection of resources to support work on Factors and Multiples at Secondary level.

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

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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

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

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

This article for teachers describes how number arrays can be a useful representation for many number concepts.

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Number problems at primary level that may require resilience.

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

An environment which simulates working with Cuisenaire rods.

How many different rectangles can you make using this set of rods?

Are these statements always true, sometimes true or never true?

Can you explain the strategy for winning this game with any target?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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.