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 nasty versions of this dice game but we'll start with the nice ones...
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.
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
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?
Number problems for inquiring primary learners.
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?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Number problems at primary level that require careful consideration.
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?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
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?
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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.
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?
There are six numbers written in five different scripts. Can you sort out which is which?
Can you replace the letters with numbers? Is there only one solution in each case?
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?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
What is the sum of all the digits in all the integers from one to
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
Number problems at primary level to work on with others.
What happens when you round these numbers to the nearest whole number?
This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Four strategy dice games to consolidate pupils' understanding of rounding.
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?
Can you work out some different ways to balance this equation?
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. . . .
Number problems at primary level that may require determination.
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?
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?
Who said that adding couldn't be fun?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Find the sum of all three-digit numbers each of whose digits is
The number 3723(in base 10) is written as 123 in another base. What
is that base?
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!
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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
How many six digit numbers are there which DO NOT contain a 5?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Follow the clues to find the mystery number.