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. . . .
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)?
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?
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
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
This activity involves rounding four-digit numbers to the nearest thousand.
Replace each letter with a digit to make this addition correct.
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
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. . . .
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
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?
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.
Find the sum of all three-digit numbers each of whose digits is
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 letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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!
There are nasty versions of this dice game but we'll start with the nice ones...
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
What is the sum of all the digits in all the integers from one to
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?
When asked how old she was, the teacher replied: My age in years is
not prime but odd and when reversed and added to my age you have a
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
The number 3723(in base 10) is written as 123 in another base. What
is that base?
Who said that adding couldn't be fun?
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?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
Can you work out some different ways to balance this equation?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Number problems at primary level that require careful consideration.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Who said that adding, subtracting, multiplying and dividing
couldn't be fun?
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?
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" .
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?
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?
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?
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. . . .