Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
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.
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?
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?
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.
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
There are nasty versions of this dice game but we'll start with the nice ones...
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Who said that adding, subtracting, multiplying and dividing
couldn't be fun?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Can you work out some different ways to balance this equation?
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you replace the letters with numbers? Is there only one
solution in each case?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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
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?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
What is the sum of all the digits in all the integers from one to
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.
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
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
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.
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!
Follow the clues to find the mystery number.
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?
Find the sum of all three-digit numbers each of whose digits is
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?
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 is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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 six numbers written in five different scripts. Can you sort out which is which?
Explore the relationship between simple linear functions and their
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
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...
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these three-digit numbers to the nearest 100?
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?
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. . . .