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 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?
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?
Here are the six faces of a cube - in no particular order. Here are
three views of the cube. Can you deduce where the faces are in
relation to each other and record them on the net of this cube?
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?
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
How can you paint the faces of these eight cubes so they can be put
together to make a 2 x 2 cube that is green all over AND a 2 x 2
cube that is yellow all over?
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
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 ...
Can you fit the tangram pieces into the outline of Mai Ling?
What is the greatest number of squares you can make by overlapping
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
Make a cube out of straws and have a go at this practical
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.
Can you fit the tangram pieces into the outline of this telephone?
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.
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 Granma T?
Can you cut up a square in the way shown and make the pieces into a
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Can you visualise what shape this piece of paper will make when it is folded?
Can you work out what kind of rotation produced this pattern of
pegs in our pegboard?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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
Exchange the positions of the two sets of counters in the least possible number of moves
Can you fit the tangram pieces into the outlines of these people?
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 fit the tangram pieces into the outline of this brazier for roasting chestnuts?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
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 clocks?
Can you fit the tangram pieces into the outline of the child walking home from school?
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?
Can you cut a regular hexagon into two pieces to make a
parallelogram? Try cutting it into three pieces to make a rhombus!
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Exploring and predicting folding, cutting and punching holes and
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?
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!
Can you fit the tangram pieces into the outline of Little Ming?
A game for two players on a large squared space.
These points all mark the vertices (corners) of ten hidden squares.
Can you find the 10 hidden squares?
What are the next three numbers in this sequence? Can you explain
why are they called pyramid numbers?