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
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.
Choose two digits and arrange them to make two double-digit
numbers. Now add your double-digit numbers. Now add your single
digit numbers. Divide your double-digit answer by your single-digit
answer. . . .
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. . . .
Can you create a Latin Square from multiples of a six digit 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
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
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.
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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?
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?
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)?
The number 3723(in base 10) is written as 123 in another base. What
is that base?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
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?
Four strategy dice games to consolidate pupils' understanding of rounding.
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.
How many six digit numbers are there which DO NOT contain a 5?
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
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
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. . . .
This activity involves rounding four-digit numbers to the nearest thousand.
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.
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
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 is the sum of all the digits in all the integers from one to
There are six numbers written in five different scripts. Can you sort out which is which?
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?
Who said that adding couldn't be fun?
Number problems for inquiring primary learners.
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?
A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?
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?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Can you replace the letters with numbers? Is there only one
solution in each case?
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 substitute numbers for the letters in these sums?
We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
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!
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?
Find the sum of all three-digit numbers each of whose digits is
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
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?