Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Find the sum of all three-digit numbers each of whose digits is
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
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. . . .
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)?
Carry out cyclic permutations of nine digit numbers containing the
digits from 1 to 9 (until you get back to the first number). Prove
that whatever number you choose, they will add to the same total.
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.
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
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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. . . .
Replace each letter with a digit to make this addition correct.
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?
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.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The number 3723(in base 10) is written as 123 in another base. What
is that base?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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?
What happens when you round these three-digit numbers to the nearest 100?
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?
What happens when you round these numbers to the nearest whole number?
Can you replace the letters with numbers? Is there only one solution in each case?
Who said that adding couldn't be fun?
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
Four strategy dice games to consolidate pupils' understanding of rounding.
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
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.
Can you work out some different ways to balance this equation?
Number problems at primary level that require careful consideration.
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Number problems at primary level that may require determination.
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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.
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?
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
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!
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?
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.
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?