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

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

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.

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?

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

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Can you complete this jigsaw of the multiplication square?

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.

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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?

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!

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?

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

A game that tests your understanding of remainders.

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

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

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

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

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?"

An environment which simulates working with Cuisenaire rods.

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

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?

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

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.

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?

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 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.

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

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

An investigation that gives you the opportunity to make and justify predictions.

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

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?

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

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...

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

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Use the interactivities to complete these Venn diagrams.

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

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?

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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.

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