Can you make a 3x3 cube with these shapes made from small cubes?
An activity centred around observations of dots and how we visualise number arrangement patterns.
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?
A game for two players on a large squared space.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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.
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!
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?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Exchange the positions of the two sets of counters in the least possible number of moves
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.
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 each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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?
Which of these dice are right-handed and which are left-handed?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you cut up a square in the way shown and make the pieces into a
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 this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of Little Ming?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
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?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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
Can you visualise what shape this piece of paper will make when it is folded?
Can you fit the tangram pieces into the outline of Granma T?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
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?
Can you fit the tangram pieces into the outline of this telephone?
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?
Can you fit the tangram pieces into the outline of this goat and giraffe?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
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?
Reasoning about the number of matches needed to build squares that
share their sides.
Can you fit the tangram pieces into the outline of this sports car?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are