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?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
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.
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?
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?
What is the sum of all the digits in all the integers from one to
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
Can you substitute numbers for the letters in these sums?
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.
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. . . .
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
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?
There are six numbers written in five different scripts. Can you sort out which is which?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
There are nasty versions of this dice game but we'll start with the nice ones...
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?
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!
Can you replace the letters with numbers? Is there only one
solution in each case?
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"?
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?
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Follow the clues to find the mystery number.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
The number 3723(in base 10) is written as 123 in another base. What
is that base?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
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?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
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?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
This activity involves rounding four-digit numbers to the nearest thousand.
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?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
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
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?
Explore the relationship between simple linear functions and their
Who said that adding, subtracting, multiplying and dividing
couldn't be fun?
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
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. . . .
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.