How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
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?
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
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?
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?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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.
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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.
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?
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.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many models can you find which obey these rules?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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 triangles can you make on the 3 by 3 pegboard?
What happens when you try and fit the triomino pieces into these
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you cover the camel with these pieces?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Use the clues to colour each square.
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
How many different rhythms can you make by putting two drums on the
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
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 merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Can you draw a square in which the perimeter is numerically equal
to the area?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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.
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.