Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
What does the overlap of these two shapes look like? Try picturing
it in your head and then use the interactivity to test your
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!
This second article in the series refers to research about levels
of development of spatial thinking and the possible influence of
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 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.
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?
This article looks at levels of geometric thinking and the types of
activities required to develop this thinking.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
What is the best way to shunt these carriages so that each train
can continue its journey?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
What can you see? What do you notice? What questions can you ask?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Move just three of the circles so that the triangle faces in the
A game for two players. You'll need some counters.
Exchange the positions of the two sets of counters in the least possible number of moves
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 many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
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
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
Can you make a 3x3 cube with these shapes made from small cubes?
Try this interactive strategy game for 2
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 each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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?
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?
This challenge involves eight three-cube models made from
interlocking cubes. Investigate different ways of putting the
models together then compare your constructions.
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
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?
Exploring and predicting folding, cutting and punching holes and
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
What is the least number of moves you can take to rearrange the
bears so that no bear is next to a bear of the same colour?
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 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?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you find ways of joining cubes together so that 28 faces are
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?
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,. . . .