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.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Number problems at primary level that may require determination.
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?
Number problems at primary level to work on with others.
Number problems at primary level that require careful consideration.
Can you work out some different ways to balance this equation?
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?
Find the sum of all three-digit numbers each of whose digits is
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
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?
Who said that adding couldn't be fun?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
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.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole 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?
Can you replace the letters with numbers? Is there only one
solution in each case?
What happens when you round these three-digit numbers to the nearest 100?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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 is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
There are six numbers written in five different scripts. Can you sort out which is which?
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?
What is the sum of all the digits in all the integers from one to
Follow the clues to find the mystery number.
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" .
Number problems for inquiring primary learners.
This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these numbers to the nearest whole number?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Explore the relationship between simple linear functions and their
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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. . . .
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
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.
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
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?
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 solutions can you find to this sum? Each of the different letters stands for a different number.
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?