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?

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.

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?

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?

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

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

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?

How many different sets of numbers with at least four members can you find in the numbers in this box?

How many trains can you make which are the same length as Matt's, using rods that are identical?

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?

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!

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

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?

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

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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

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?

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?

"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 ...?

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.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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

56 406 is the product of two consecutive numbers. What are these two numbers?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

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

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

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

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

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

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

Can you find any perfect numbers? Read this article to find out more...

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

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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?

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

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

A game that tests your understanding of remainders.

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