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

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

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

Number problems for inquiring primary learners.

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

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

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. . . .

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.

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

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

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

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.

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?

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?

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

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?

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

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. . . .

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

Number problems at primary level that require careful consideration.

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

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

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

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?

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?

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

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?

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

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

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit 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)?

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.

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

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.

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

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

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

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?

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

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

Number problems at primary level that may require determination.

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

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

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