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?
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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?
56 406 is the product of two consecutive numbers. What are these
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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. . . .
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
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?
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.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Can you work out what a ziffle is on the planet Zargon?
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?
Can you find any perfect numbers? Read this article to find out more...
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
What is the smallest number with exactly 14 divisors?
Can you find a way to identify times tables after they have been shifted up?
A game that tests your understanding of remainders.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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.
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?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
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 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?"
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Got It game for an adult and child. How can you play so that you know you will always win?
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.
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
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?
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?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you complete this jigsaw of the multiplication square?
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 predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
Find the highest power of 11 that will divide into 1000! exactly.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?