Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Can you cover the camel with these pieces?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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 happens when you try and fit the triomino pieces into these
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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 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?
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
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 triangles can you make on a circular pegboard that has nine pegs?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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 fit the tangram pieces into the outlines of the watering can and man in a boat?
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?
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 fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outline of the telescope and microscope?
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?
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 fit the tangram pieces into the outlines of the candle and sundial?
Can you cut up a square in the way shown and make the pieces into a
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
Can you fit the tangram pieces into the outline of Little Fung at the table?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
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 ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Can you fit the tangram pieces into the outline of this telephone?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
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 the workmen?
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!
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outline of this goat and giraffe?
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?