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.
In how many ways can you fit all three pieces together to make
shapes with line symmetry?
Draw three straight lines to separate these shapes into four groups
- each group must contain one of each shape.
Can you picture where this letter "F" will be on the grid if you
flip it in these different ways?
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 symmetrical shapes can you make by shading triangles or squares?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
Try this interactive strategy game for 2
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you explain why it is impossible to construct this triangle?
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.
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. . . .
Four rods, two of length a and two of length b, are linked to form
a kite. The linkage is moveable so that the angles change. What is
the maximum area of the kite?
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
A group activity using visualisation of squares and triangles.
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?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
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.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
What shape is the overlap when you slide one of these shapes half
way across another? Can you picture it in your head? Use the
interactivity to check your visualisation.
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?
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
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
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.
Can you maximise the area available to a grazing goat?
Which of these dice are right-handed and which are left-handed?
Each of the nets of nine solid shapes has been cut into two pieces.
Can you see which pieces go together?
Can you arrange the shapes in a chain so that each one shares a
face (or faces) that are the same shape as the one that follows it?
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.
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Reasoning about the number of matches needed to build squares that
share their sides.
You can move the 4 pieces of the jigsaw and fit them into both
outlines. Explain what has happened to the missing one unit of
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?
Mathematics is the study of patterns. Studying pattern is an
opportunity to observe, hypothesise, experiment, discover and
Which of the following cubes can be made from these nets?
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?
Can you fit the tangram pieces into the outlines of these people?
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?
Can you fit the tangram pieces into the outlines of these clocks?
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!
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?