Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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?

Number problems at primary level to work on with others.

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. . . .

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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.

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

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?

Number problems at primary level that may require resilience.

By selecting digits for an addition grid, what targets can you make?

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?

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

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

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?

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

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

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

Use your knowledge of place value to try to win this game. How will you maximise your score?

Try out this number trick. What happens with different starting numbers? What do you notice?

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

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

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

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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. . . .

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

Where should you start, if you want to finish back where you started?

Number problems at primary level that require careful consideration.

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.

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

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Explore the relationship between simple linear functions and their graphs.

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

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

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

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

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

This article for primary teachers expands on the key ideas which underpin early number sense and place value, and suggests activities to support learners as they get to grips with these ideas.

In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.