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?
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?
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
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
These practical challenges are all about making a 'tray' and covering it with paper.
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
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?
How many triangles can you make on the 3 by 3 pegboard?
An activity making various patterns with 2 x 1 rectangular tiles.
What is the best way to shunt these carriages so that each train
can continue its journey?
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 models can you find which obey these rules?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
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.
On a digital 24 hour clock, at certain times, all the digits are
consecutive. How many times like this are there between midnight
and 7 a.m.?
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
In how many ways can you stack these rods, following the rules?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?