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.
Find the sum of all three-digit numbers each of whose digits is
There are nasty versions of this dice game but we'll start with the nice ones...
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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?
Can you substitute numbers for the letters in these sums?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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.
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?
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 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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
There are six numbers written in five different scripts. Can you sort out which is which?
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?
Who said that adding, subtracting, multiplying and dividing
couldn't be fun?
What happens when you round these three-digit numbers to the nearest 100?
This activity involves rounding four-digit numbers to the nearest thousand.
Follow the clues to find the mystery number.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
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
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
What happens when you round these numbers to the nearest whole number?
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?
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?
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
Replace each letter with a digit to make this addition correct.
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?
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.
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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. . . .
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. . . .
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" .
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by