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.
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?
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?
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!
Can you make square numbers by adding two prime numbers together?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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?
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.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Follow the clues to find the mystery number.
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.
An investigation that gives you the opportunity to make and justify
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?
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?
Can you complete this jigsaw of the multiplication square?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
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?
An environment which simulates working with Cuisenaire rods.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
A game in which players take it in turns to choose a number. Can you block your opponent?
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 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. . . .
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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 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.
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...
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.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Given the products of adjacent cells, can you complete this Sudoku?
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
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Given the products of diagonally opposite cells - can you complete
How many different sets of numbers with at least four members can
you find in the numbers in this box?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
A game that tests your understanding of remainders.
Use the interactivities to complete these Venn diagrams.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
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 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?
"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
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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?"
56 406 is the product of two consecutive numbers. What are these