The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Delight your friends with this cunning trick! Can you explain how it works?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Here is a version of the game 'Happy Families' for you to make and play.
Which of the following cubes can be made from these nets?
How can you make an angle of 60 degrees by folding a sheet of paper twice?
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
Surprise your friends with this magic square trick.
I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?
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?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.
I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?
How is it possible to predict the card?
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Can you make the birds from the egg tangram?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Here are some ideas to try in the classroom for using counters to investigate number patterns.
How do you know if your set of dominoes is complete?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
What do these two triangles have in common? How are they related?
Exploring and predicting folding, cutting and punching holes and making spirals.
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?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
These practical challenges are all about making a 'tray' and covering it with paper.
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?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
Can you create more models that follow these rules?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
A game to make and play based on the number line.
How many triangles can you make on the 3 by 3 pegboard?
What is the greatest number of squares you can make by overlapping three squares?
Use the tangram pieces to make our pictures, or to design some of your own!