Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

A game that tests your understanding of remainders.

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

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

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?"

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.

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...

Can you complete this jigsaw of the multiplication square?

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

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

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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.

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

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Use the interactivities to complete these Venn diagrams.

Can you find a way to identify times tables after they have been shifted up?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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

Is there an efficient way to work out how many factors a large number has?

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

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

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

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

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?

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.

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

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

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?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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

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

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

A game in which players take it in turns to choose a number. Can you block your opponent?

I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?