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

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.

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?

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. . . .

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.

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?

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?

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?

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?

Number problems for inquiring primary learners.

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?

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

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

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?

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.

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

How many six digit numbers are there which DO NOT contain a 5?

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

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?

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.

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

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

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?

Number problems at primary level that may require determination.

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

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

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

Explore the relationship between simple linear functions and their graphs.

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?

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

Number problems at primary level that require careful consideration.

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

Number problems at primary level to work on with others.

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

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

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?

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.

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, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions!

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?

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.