Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
What happens when you try and fit the triomino pieces into these
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?
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?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you fit the tangram pieces into the outlines of the candle and sundial?
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 workmen?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Can you cut up a square in the way shown and make the pieces into a
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?
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?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Can you fit the tangram pieces into the outline of this telephone?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Exchange the positions of the two sets of counters in the least possible number of moves
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 outlines of these people?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
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 Ming playing the board game?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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!