Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
Can you find all the different triangles on these peg boards, and find their angles?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
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....?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Try out the lottery that is played in a far-away land. What is the chance of winning?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
In this matching game, you have to decide how long different events take.
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?
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?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
These practical challenges are all about making a 'tray' and covering it with paper.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
Find out what a "fault-free" rectangle is and try to make some of your own.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you find all the different ways of lining up these Cuisenaire rods?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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?
If you had 36 cubes, what different cuboids could you make?
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.
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
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?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
A Sudoku that uses transformations as supporting clues.