Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
There are a number of coins on a table.
One quarter of the coins show heads.
If I turn over 2 coins, then one third show heads. How many coins are there altogether?
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
56 406 is the product of two consecutive numbers. What are these
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Nearly all of us have made table patterns on hundred squares, that
is 10 by 10 grids. This problem looks at the patterns on
differently sized square grids.
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Norrie sees two lights flash at the same time, then one of them
flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
I am thinking of three sets of numbers less than 101. They are the
red set, the green set and the blue set. Can you find all the
numbers in the sets from these clues?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Got It game for an adult and child. How can you play so that you know you will always win?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Can you find any perfect numbers? Read this article to find out more...
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
Can you work out what a ziffle is on the planet Zargon?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
A game that tests your understanding of remainders.
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
Find the highest power of 11 that will divide into 1000! exactly.
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some. . . .
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
What is the smallest number with exactly 14 divisors?
Can you find a way to identify times tables after they have been shifted up?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Can you complete this jigsaw of the multiplication square?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?