Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
What is the best way to shunt these carriages so that each train
can continue its journey?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
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 fit the tangram pieces into the outlines of these people?
This article for teachers describes a project which explores
thepower of storytelling to convey concepts and ideas to children.
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the chairs?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Can you fit the tangram pieces into the outlines of the workmen?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Can you make a 3x3 cube with these shapes made from small cubes?
Try this interactive strategy game for 2
Exchange the positions of the two sets of counters in the least possible number of moves
Can you visualise what shape this piece of paper will make when it is folded?
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 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?
Make a flower design using the same shape made out of different sizes of paper.
Can you fit the tangram pieces into the outline of Little Ming?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you fit the tangram pieces into the outline of Granma T?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Here's a simple way to make a Tangram without any measuring or
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?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
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.
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Reasoning about the number of matches needed to build squares that
share their sides.
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
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.