How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
A challenging activity focusing on finding all possible ways of stacking rods.
How many different symmetrical shapes can you make by shading triangles or squares?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
In how many ways can you stack these rods, following the rules?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
Use the clues about the symmetrical properties of these letters to
place them on the grid.
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 many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
This activity investigates how you might make squares and pentominoes from Polydron.
An activity making various patterns with 2 x 1 rectangular tiles.
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
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
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.
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you find all the different triangles on these peg boards, and
find their angles?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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 shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
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
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?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
Can you draw a square in which the perimeter is numerically equal
to the area?
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....?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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.
Investigate the different ways you could split up these rooms so
that you have double the number.
Can you find all the different ways of lining up these Cuisenaire
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?