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 make dice stairs using the rules stated? How do you know you have all the possible stairs?
Surprise your friends with this magic square trick.
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?
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.
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?
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.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
How many triangles can you make on the 3 by 3 pegboard?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Here is a version of the game 'Happy Families' for you to make and play.
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
How many models can you find which obey these rules?
These practical challenges are all about making a 'tray' and covering it with paper.
Delight your friends with this cunning trick! Can you explain how it works?
Here are some ideas to try in the classroom for using counters to investigate number patterns.
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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?
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?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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 new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
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.
An activity making various patterns with 2 x 1 rectangular tiles.
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
How do you know if your set of dominoes is complete?
Can you deduce the pattern that has been used to lay out these bottle tops?
What do these two triangles have in common? How are they related?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
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?
How is it possible to predict the card?
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?
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
A game to make and play based on the number line.
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
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?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Use the tangram pieces to make our pictures, or to design some of your own!