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?
Can you complete this jigsaw of the multiplication square?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Got It game for an adult and child. How can you play so that you know you will always win?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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 interactivities to complete these Venn diagrams.
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?"
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.
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?
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?
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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. . . .
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?
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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.
A game that tests your understanding of remainders.
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?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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?
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Given the products of adjacent cells, can you complete this Sudoku?
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?
An environment which simulates working with Cuisenaire rods.
Can you work out what a ziffle is on the planet Zargon?
56 406 is the product of two consecutive numbers. What are these
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?
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?
Follow the clues to find the mystery number.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
An investigation that gives you the opportunity to make and justify