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" .
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?
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?
What is the sum of all the digits in all the integers from one to
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?
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.
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?
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
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
Number problems at primary level that require careful consideration.
Number problems at primary level that may require determination.
Number problems at primary level to work on with others.
Can you replace the letters with numbers? Is there only one solution in each case?
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. . . .
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
There are six numbers written in five different scripts. Can you sort out which is which?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
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.
Can you create a Latin Square from multiples of a six digit number?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
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?
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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
How many six digit numbers are there which DO NOT contain a 5?
Find the sum of all three-digit numbers each of whose digits is
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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.
Explore the relationship between simple linear functions and their
Four strategy dice games to consolidate pupils' understanding of rounding.
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 three-digit numbers to the nearest 100?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even 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?
Who said that adding couldn't be fun?
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?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Number problems for inquiring primary learners.
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
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?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
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?
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 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