Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
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?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
A huge wheel is rolling past your window. What do you see?
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?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
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?
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
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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,. . . .
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
Blue Flibbins are so jealous of their red partners that they will
not leave them on their own with any other bue Flibbin. What is the
quickest way of getting the five pairs of Flibbins safely to. . . .
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?
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?
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!
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Exchange the positions of the two sets of counters in the least possible number of moves
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.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
A game for two players on a large squared space.
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?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
What happens when you turn these cogs? Investigate the differences
between turning two cogs of different sizes and two cogs which are
Can you work out what is wrong with the cogs on a UK 2 pound coin?
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?
An activity centred around observations of dots and how we visualise number arrangement patterns.
Can you mark 4 points on a flat surface so that there are only two
different distances between them?
How many different symmetrical shapes can you make by shading triangles or squares?
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
Seven small rectangular pictures have one inch wide frames. The
frames are removed and the pictures are fitted together like a
jigsaw to make a rectangle of length 12 inches. Find the dimensions
of. . . .