Draw three straight lines to separate these shapes into four groups
- each group must contain one of each shape.
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?
A group activity using visualisation of squares and triangles.
In this problem, we have created a pattern from smaller and smaller
squares. If we carried on the pattern forever, what proportion of
the image would be coloured blue?
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
How many different triangles can you make on a circular pegboard
that has nine pegs?
How can you make an angle of 60 degrees by folding a sheet of paper
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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.
What is the greatest number of squares you can make by overlapping
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?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
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?
Anne completes a circuit around a circular track in 40 seconds.
Brenda runs in the opposite direction and meets Anne every 15
seconds. How long does it take Brenda to run around the track?
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP
: PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED.
What is the area of the triangle PQR?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
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.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
A game has a special dice with a colour spot on each face. These
three pictures show different views of the same dice. What colour
is opposite blue?
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.
Billy's class had a robot called Fred who could draw with chalk
held underneath him. What shapes did the pupils make Fred draw?
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?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
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?
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
These are pictures of the sea defences at New Brighton. Can you
work out what a basic shape might be in both images of the sea wall
and work out a way they might fit together?
Use the lines on this figure to show how the square can be divided
into 2 halves, 3 thirds, 6 sixths and 9 ninths.
It is possible to dissect any square into smaller squares. What is
the minimum number of squares a 13 by 13 square can be dissected
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .
Can you fit the tangram pieces into the outlines of the chairs?
See if you can anticipate successive 'generations' of the two
animals shown here.
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?
Can you fit the tangram pieces into the outline of the child walking home from school?
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
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. . . .
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Show that among the interior angles of a convex polygon there
cannot be more than three acute angles.
Can you fit the tangram pieces into the outlines of these clocks?
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?
This article for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
A package contains a set of resources designed to develop pupils'
mathematical thinking. This package places a particular emphasis on
“visualising” and is designed to meet the needs. . . .
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight