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. . . .

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

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.

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

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

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?

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

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.

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?

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.

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.

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?

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

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

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

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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?

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

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

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. . . .

Number problems at primary level that may require determination.

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?

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

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

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

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. . . .

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

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

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?

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?

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

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

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

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?

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

Number problems at primary level that require careful consideration.

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

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

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

Number problems at primary level to work on with others.

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

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