Design an arrangement of display boards in the school hall which fits the requirements of different people.
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
These practical challenges are all about making a 'tray' and covering it with paper.
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many models can you find which obey these rules?
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
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
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
An activity making various patterns with 2 x 1 rectangular tiles.
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.
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
How many triangles can you make on the 3 by 3 pegboard?
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 different triangles can you make on a circular pegboard that has nine pegs?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
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?
Can you find all the different ways of lining up these Cuisenaire
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
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
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?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.