This activity investigates how you might make squares and pentominoes from Polydron.
Can you draw a square in which the perimeter is numerically equal
to the area?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
Use the clues about the symmetrical properties of these letters to
place them on the grid.
A challenging activity focusing on finding all possible ways of stacking rods.
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
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
These practical challenges are all about making a 'tray' and covering it with paper.
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
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?
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?
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?
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?
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.
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
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.
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?
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 largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
How many different symmetrical shapes can you make by shading triangles or squares?
An investigation that gives you the opportunity to make and justify
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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.
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?
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?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
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?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?