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 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?
Can you replace the letters with numbers? Is there only one
solution in each case?
Find the sum of all three-digit numbers each of whose digits is
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 substitute numbers for the letters in these sums?
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?
Who said that adding couldn't be fun?
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.
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?
What happens when you round these numbers to the nearest whole number?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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?
Have a go at balancing this equation. Can you find different ways of doing it?
Follow the clues to find the mystery 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?
What happens when you round these three-digit numbers to the nearest 100?
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?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
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?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
What is the sum of all the digits in all the integers from one to
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 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.
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?
There are nasty versions of this dice game but we'll start with the nice ones...
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?
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?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
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 letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
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. . . .
Four strategy dice games to consolidate pupils' understanding of rounding.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
This activity involves rounding four-digit numbers to the nearest thousand.
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 oponent.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
How many six digit numbers are there which DO NOT contain a 5?
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
The number 3723(in base 10) is written as 123 in another base. What
is that base?
Replace each letter with a digit to make this addition correct.
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?