Can you draw a square in which the perimeter is numerically equal
to the area?
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.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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?
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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?
This activity investigates how you might make squares and pentominoes from Polydron.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Find out what a "fault-free" rectangle is and try to make some of
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
An activity making various patterns with 2 x 1 rectangular tiles.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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?
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
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.
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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?
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?
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
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?
How many triangles can you make on the 3 by 3 pegboard?
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.
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 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.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?