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 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?
An investigation that gives you the opportunity to make and justify
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
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?"
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...
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
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.
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
Given the products of adjacent cells, can you complete this Sudoku?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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. . . .
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Can you draw a square in which the perimeter is numerically equal
to the area?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
The clues for this Sudoku are the product of the numbers in adjacent 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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
A Sudoku with clues as ratios or fractions.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?