Once a basic number sense has developed for numbers up to ten, a strong 'sense of ten' needs to be developed as a foundation for both place value and mental calculations.

Marion Bond recommends that children should be allowed to use 'apparatus', so that they can physically handle the numbers involved in their calculations, for longer, or across a wider ability band,. . . .

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

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

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

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?

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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

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?

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

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

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

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?

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

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

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

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

What two-digit numbers can you make with these two dice? What can't you make?

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

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

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?

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

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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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

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

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

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.

A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

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

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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?

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

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

Can you find the chosen number from the grid using the clues?

I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.

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.

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?