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.
This activity investigates how you might make squares and pentominoes from Polydron.
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?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
How many models can you find which obey these rules?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
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?
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....?
What is the best way to shunt these carriages so that each train
can continue its journey?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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?
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 put five cereal packets together to make different
shapes if you must put them face-to-face?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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 many different triangles can you make on a circular pegboard that has nine pegs?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
How many triangles can you make on the 3 by 3 pegboard?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
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.