I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Investigate the different ways you could split up these rooms so
that you have double the number.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
In how many ways can you stack these rods, following the rules?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
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
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 are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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
How many trains can you make which are the same length as Matt's, using rods that are identical?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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?
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.
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?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
An activity making various patterns with 2 x 1 rectangular tiles.
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
How many different triangles can you make on a circular pegboard that has nine pegs?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
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?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
This activity investigates how you might make squares and pentominoes from Polydron.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them