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

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

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

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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

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?

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?

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

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

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

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?

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.

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?

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.

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

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

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

Have a go at balancing this equation. Can you find different ways of doing it?

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?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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 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?

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!

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?

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.

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

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

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?

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

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

Can you work out some different ways to balance this equation?

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?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

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

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.

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

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

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?

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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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

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

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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?

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

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?