Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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?
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?
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?
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
How many different triangles can you make on a circular pegboard that has nine pegs?
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 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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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 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.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
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?
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?
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?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you fit the tangram pieces into the outline of these convex shapes?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Can you fit the tangram pieces into the outline of Mai Ling?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Can you find ways of joining cubes together so that 28 faces are
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outline of the telescope and microscope?
An extension of noughts and crosses in which the grid is enlarged
and the length of the winning line can to altered to 3, 4 or 5.
Can you fit the tangram pieces into the outline of this junk?
Can you fit the tangram pieces into the outline of this sports car?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you fit the tangram pieces into the outline of this plaque design?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outline of these rabbits?
Can you fit the tangram pieces into the outline of Granma T?
Can you cut up a square in the way shown and make the pieces into a
Exchange the positions of the two sets of counters in the least possible number of moves
Can you fit the tangram pieces into the outlines of the workmen?
Seven small rectangular pictures have one inch wide frames. The
frames are removed and the pictures are fitted together like a
jigsaw to make a rectangle of length 12 inches. Find the dimensions
of. . . .