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.

Number problems for inquiring primary learners.

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?

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

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. . . .

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. . . .

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

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

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

We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.

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

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.

Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total.

Can you create a Latin Square from multiples of a six digit number?

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?

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

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?

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

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?

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?

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

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

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

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

Number problems at primary level that may require determination.

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

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

Number problems at primary level to work on with others.

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

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

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?

Explore the relationship between simple linear functions and their graphs.

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

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

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

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

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

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

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

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

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

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Number problems at primary level that require careful consideration.

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?

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

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

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. . . .