Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
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?
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.
These practical challenges are all about making a 'tray' and covering it with paper.
How many models can you find which obey these rules?
How many triangles can you make on the 3 by 3 pegboard?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Here is a version of the game 'Happy Families' for you to make and play.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
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?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
Can you make the birds from the egg tangram?
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
What is the greatest number of squares you can make by overlapping three squares?
Delight your friends with this cunning trick! Can you explain how it works?
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
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?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
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?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Here are some ideas to try in the classroom for using counters to investigate number patterns.
We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.
How is it possible to predict the card?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Exploring and predicting folding, cutting and punching holes and making spirals.
What do these two triangles have in common? How are they related?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Can you deduce the pattern that has been used to lay out these bottle tops?
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 ...
Make a flower design using the same shape made out of different sizes of paper.
Can you visualise what shape this piece of paper will make when it is folded?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
Use the tangram pieces to make our pictures, or to design some of your own!