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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you substitute numbers for the letters in these sums?
Can you work out some different ways to balance this equation?
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?
Find the sum of all three-digit numbers each of whose digits is
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
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?
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?
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.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
What happens when you round these numbers to the nearest whole number?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Follow the clues to find the mystery number.
What happens when you round these three-digit numbers to the nearest 100?
Have a go at balancing this equation. Can you find different ways of doing it?
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
What is the sum of all the digits in all the integers from one to
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
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.
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.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
This activity involves rounding four-digit numbers to the nearest thousand.
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
There are six numbers written in five different scripts. Can you sort out which is which?
How many six digit numbers are there which DO NOT contain a 5?
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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?
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. . . .
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Replace each letter with a digit to make this addition correct.
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
four strategy dice games to consolidate pupils' understanding of rounding.
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?
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. . . .
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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?
The number 3723(in base 10) is written as 123 in another base. What
is that base?
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!