Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
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?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
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?
What happens when you try and fit the triomino pieces into these
Explore the different snakes that can be made using 5 cubes.
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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?
How many models can you find which obey these rules?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Use the clues to colour each square.
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 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.
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?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Can you find out in which order the children are standing in this
My coat has three buttons. How many ways can you find to do up all
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you find all the different ways of lining up these Cuisenaire
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
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?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?