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

These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.

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

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.

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

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

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.

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

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

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?

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?

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?

Number problems at primary level that require careful consideration.

Number problems for inquiring primary learners.

This is a game for two players. What must you subtract to remove the rolled digit from your number? The first to zero wins!

More upper primary number sense and place value tasks.

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.

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. . . .

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.

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

This feature aims to support you in developing children's early number sense and understanding of place value.

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

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.

What happens when you add a three digit number to its reverse?

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

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?

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

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

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. . . .

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

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

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?

Number problems at primary level that may require resilience.

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

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

Number problems at primary level to work on with others.

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

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

Explore the relationship between simple linear functions and their graphs.

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

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

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

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

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

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 substitute numbers for the letters in these sums?