Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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 activity investigates how you might make squares and pentominoes from Polydron.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
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.
Investigate the different ways you could split up these rooms so
that you have double the number.
How many models can you find which obey these rules?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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....?
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?
Can you find all the different ways of lining up these Cuisenaire
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
How many different triangles can you make on a circular pegboard that has nine pegs?
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
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?
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or 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.
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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?
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
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.