Number problems at primary level that may require resilience.

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.

Number problems at primary level to work on with others.

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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 primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

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?

Number problems at primary level that require careful consideration.

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

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?

Can you substitute numbers for the letters in these sums?

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

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

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

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

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

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

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.

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

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

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

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

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

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

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.

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?

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

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?

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?

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

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.

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

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

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

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?

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?

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?

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?

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

More upper primary number sense and place value tasks.

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.

This article develops the idea of 'ten-ness' as an important element of place value.

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.

One of the key ideas associated with place value is that the position of a digit affects its value. These activities support children in understanding this idea.

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. . . .