Can you make a 3x3 cube with these shapes made from small cubes?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
A toy has a regular tetrahedron, a cube and a base with triangular
and square hollows. If you fit a shape into the correct hollow a
bell rings. How many times does the bell ring in a complete game?
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?
Exchange the positions of the two sets of counters in the least possible number of moves
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!
An activity centred around observations of dots and how we visualise number arrangement patterns.
Which of these dice are right-handed and which are left-handed?
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
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Can you find ways of joining cubes together so that 28 faces are
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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 shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
A game for two players on a large squared space.
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
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?
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?
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?
One face of a regular tetrahedron is painted blue and each of the
remaining faces are painted using one of the colours red, green or
yellow. How many different possibilities are there?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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.
What shape is made when you fold using this crease pattern? Can you make a ring design?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Looking at the picture of this Jomista Mat, can you decribe what
you see? Why not try and make one yourself?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Make a cube out of straws and have a go at this practical
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
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 work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
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?
Try this interactive strategy game for 2
Can you fit the tangram pieces into the outline of this plaque design?
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
Can you cut up a square in the way shown and make the pieces into a
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
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?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
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,. . . .
Which of the following cubes can be made from these nets?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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 these rabbits?
On which of these shapes can you trace a path along all of its
edges, without going over any edge twice?