These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Can you draw a square in which the perimeter is numerically equal
to the area?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Find out what a "fault-free" rectangle is and try to make some of
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?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
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 can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
An activity making various patterns with 2 x 1 rectangular tiles.
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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.
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?
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?
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.
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
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
This activity investigates how you might make squares and pentominoes from Polydron.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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.
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.
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
How many triangles can you make on the 3 by 3 pegboard?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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 these head, body and leg pieces to make Robot Monsters which
are different heights.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?