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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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?
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
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?
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.
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 work out how to balance this equaliser? You can put more
than one weight on a hook.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many models can you find which obey these rules?
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?
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?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
How many triangles can you make on the 3 by 3 pegboard?
What happens when you try and fit the triomino pieces into these
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 different triangles can you make on a circular pegboard that has nine pegs?
Use the clues to colour each square.
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
How many different rhythms can you make by putting two drums on the
These practical challenges are all about making a 'tray' and covering it with paper.
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?
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?
Can you find all the different triangles on these peg boards, and
find their angles?
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you find all the different ways of lining up these Cuisenaire
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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.
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.
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
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?