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. . . .

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?

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

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.

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.

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?

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!

Can you substitute numbers for the letters in these sums?

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

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?

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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. . . .

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?

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.

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

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

Number problems at primary level that require careful consideration.

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

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?

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

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

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.

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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

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

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?

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

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.

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

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

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

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 numbers to the nearest whole number?

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?

Find the sum of all three-digit numbers each of whose digits is odd.

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?

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?

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

Try out some calculations. Are you surprised by the results?

Number problems for inquiring primary learners.

Number problems at primary level to work on with others.

Number problems at primary level that may require resilience.

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

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