A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
How many different symmetrical shapes can you make by shading triangles or squares?
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
Try this interactive strategy game for 2
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
A triangle ABC resting on a horizontal line is "rolled" along the
line. Describe the paths of each of the vertices and the
relationships between them and the original triangle.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
I've made some cubes and some cubes with holes in. This challenge
invites you to explore the difference in the number of small cubes
I've used. Can you see any patterns?
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?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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!
Blue Flibbins are so jealous of their red partners that they will
not leave them on their own with any other bue Flibbin. What is the
quickest way of getting the five pairs of Flibbins safely to. . . .
Think of a number, square it and subtract your starting number. Is
the number you’re left with odd or even? How do the images
help to explain this?
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?
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?
When dice land edge-up, we usually roll again. But what if we
Reasoning about the number of matches needed to build squares that
share their sides.
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.
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.
Exploring and predicting folding, cutting and punching holes and
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Make a cube out of straws and have a go at this practical
Which of the following cubes can be made from these nets?
What shape has Harry drawn on this clock face? Can you find its
area? What is the largest number of square tiles that could cover
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of Little Fung at the table?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you find ways of joining cubes together so that 28 faces are
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of the child walking home from school?
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
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?
Can you fit the tangram pieces into the outlines of these clocks?