How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
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?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you find ways of joining cubes together so that 28 faces are
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?
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?
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?
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,. . . .
Can you visualise what shape this piece of paper will make when it is folded?
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
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 make a 3x3 cube with these shapes made from small cubes?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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 Little Ming and Little Fung dancing?
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?
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 Granma T?
Exchange the positions of the two sets of counters in the least possible number of moves
What shape is made when you fold using this crease pattern? Can you make a ring design?
This problem invites you to build 3D shapes using two different
triangles. Can you make the shapes from the pictures?
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 fit the tangram pieces into the outlines of the watering can and man in a boat?