Draw three straight lines to separate these shapes into four groups
- each group must contain one of each shape.
Try this interactive strategy game for 2
How many different triangles can you make on a circular pegboard
that has nine pegs?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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!
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
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.
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.
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
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?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Imagine a large cube made from small red cubes being dropped into a
pot of yellow paint. How many of the small cubes will have yellow
paint on their faces?
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?
Reasoning about the number of matches needed to build squares that
share their sides.
Can you fit the tangram pieces into the outlines of these clocks?
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?
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.
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?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outlines of these people?
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
Can you fit the tangram pieces into the outlines of the workmen?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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?
Which of these dice are right-handed and which are left-handed?
Can you maximise the area available to a grazing goat?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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 27 small cubes, 3 each of nine colours. Use the small
cubes to make a 3 by 3 by 3 cube so that each face of the bigger
cube contains one of every colour.
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
Imagine you have six different colours of paint. You paint a cube
using a different colour for each of the six faces. How many
different cubes can be painted using the same set of six colours?
Can you fit the tangram pieces into the outlines of the chairs?
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?
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?
Which of the following cubes can be made from these nets?
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!
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .
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. . . .
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?