48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
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?
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?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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?
A game in which players take it in turns to choose a number. Can you block your opponent?
Factor track is not a race but a game of skill. The idea is to go
round the track in as few moves as possible, keeping to the rules.
Can you work out what a ziffle is on the planet Zargon?
Follow the clues to find the mystery number.
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position
yourself so that you are 'it' if there are two players? Three
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?
56 406 is the product of two consecutive numbers. What are these
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
This activity focuses on doubling multiples of five.
Can you find any perfect numbers? Read this article to find out more...
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Can you work out some different ways to balance this equation?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
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.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Have a go at balancing this equation. Can you find different ways of doing it?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Help share out the biscuits the children have made.
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
A game that tests your understanding of remainders.
An investigation that gives you the opportunity to make and justify
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?
Can you place the numbers from 1 to 10 in the grid?
Are these domino games fair? Can you explain why or why not?