Arrange the shapes in a line so that you change either colour or
shape in the next piece along. Can you find several ways to start
with a blue triangle and end with a red circle?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
Can you find six numbers to go in the Daisy from which you can make
all the numbers from 1 to a number bigger than 25?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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.
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?
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 all the different shapes that can be made by joining five
equilateral triangles edge to edge.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
A Sudoku with clues given as sums of entries.
An activity making various patterns with 2 x 1 rectangular tiles.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
This activity investigates how you might make squares and pentominoes from Polydron.
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
An investigation that gives you the opportunity to make and justify
Can you draw a square in which the perimeter is numerically equal
to the area?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
Find out what a "fault-free" rectangle is and try to make some of
Place the 16 different combinations of cup/saucer in this 4 by 4
arrangement so that no row or column contains more than one cup or
saucer of the same colour.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
How many different triangles can you make on a circular pegboard
that has nine pegs?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
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?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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....?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?