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

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

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

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?

Can you complete this jigsaw of the multiplication square?

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

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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?

Number problems at primary level that may require resilience.

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?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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.

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?

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

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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?

Number problems at primary level to work on with others.

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

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

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

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

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

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

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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

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

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

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?

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

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.

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?

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

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

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

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

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...

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?

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?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?