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!
If you have only four weights, where could you place them in order
to balance this equaliser?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you complete this jigsaw of the multiplication square?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
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?
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
Given the products of adjacent cells, can you complete this Sudoku?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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 order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
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?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Can you make square numbers by adding two prime numbers together?
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?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Each light in this interactivity turns on according to a rule. What
happens when you enter different numbers? Can you find the smallest
number that lights up all four lights?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
A game that tests your understanding of remainders.
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?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
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?
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.
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?"
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?
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?
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.
An environment which simulates working with Cuisenaire rods.
Use the interactivities to complete these Venn diagrams.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you work out what a ziffle is on the planet Zargon?
56 406 is the product of two consecutive numbers. What are these
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.
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
An investigation that gives you the opportunity to make and justify