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Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?
Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
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?
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
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.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
What could the half time scores have been in these Olympic hockey matches?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
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?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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 models can you find which obey these rules?
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
Can you find all the different triangles on these peg boards, and find their angles?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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?
When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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 it up?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
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?
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?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
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.