Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . .

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

This article for the young and old talks about the origins of our number system and the important role zero has to play in it.

There are six numbers written in five different scripts. Can you sort out which is which?

Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.

The number 3723(in base 10) is written as 123 in another base. What is that base?

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

This article, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions!

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

four strategy dice games to consolidate pupils' understanding of rounding.

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

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

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

Dicey Operations for an adult and child. Can you get close to 1000 than your partner?

Can you replace the letters with numbers? Is there only one solution in each case?

What happens when you round these numbers to the nearest whole number?

This activity involves rounding four-digit numbers to the nearest thousand.

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

What is the sum of all the digits in all the integers from one to one million?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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?

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

What happens when you round these three-digit numbers to the nearest 100?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

There are nasty versions of this dice game but we'll start with the nice ones...

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

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?