How many times in twelve hours do the hands of a clock form a right
angle? Use the interactivity to check your answers.
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.
A metal puzzle which led to some mathematical questions.
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?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you create a story that would describe the movement of the man
shown on these graphs? Use the interactivity to try out our ideas.
A game for two or more players that uses a knowledge of measuring
tools. Spin the spinner and identify which jobs can be done with
the measuring tool shown.
What shaped overlaps can you make with two circles which are the
same size? What shapes are 'left over'? What shapes can you make
when the circles are different sizes?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Use the interactivity to move Mr Pearson and his dog. Can you move
him so that the graph shows a curve?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Choose the size of your pegboard and the shapes you can make. Can
you work out the strategies needed to block your opponent?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
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
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.
Can you find all the different triangles on these peg boards, and
find their angles?
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?
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?
Investigate how logic gates work in circuits.
Explore this interactivity and see if you can work out what it
does. Could you use it to estimate the area of a shape?
If you have only four weights, where could you place them in order
to balance this equaliser?
A train building game for 2 players.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Experiment with the interactivity of "rolling" regular polygons,
and explore how the different positions of the red dot affects its
vertical and horizontal movement at each stage.
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!
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Can you find all the different ways of lining up these Cuisenaire
Can you work out what is wrong with the cogs on a UK 2 pound coin?
What is the relationship between the angle at the centre and the
angles at the circumference, for angles which stand on the same
arc? Can you prove it?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Do you know how to find the area of a triangle? You can count the
squares. What happens if we turn the triangle on end? Press the
button and see. Try counting the number of units in the triangle
now. . . .
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Use the interactivity or play this dice game yourself. How could
you make it fair?
How many different triangles can you make on a circular pegboard
that has nine pegs?
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of these clocks?
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?
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
Use the interactivity to make this Islamic star and cross design.
Can you produce a tessellation of regular octagons with two
different types of triangle?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?