Challenge Level

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?

Challenge Level

Can you make the birds from the egg tangram?

Challenge Level

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?

Challenge Level

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?

Challenge Level

Here is a version of the game 'Happy Families' for you to make and play.

Challenge Level

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

Challenge Level

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?

Challenge Level

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Challenge Level

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

Challenge Level

What is the greatest number of squares you can make by overlapping three squares?

Challenge Level

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.

Challenge Level

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Challenge Level

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Challenge Level

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Challenge Level

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.

Challenge Level

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Challenge Level

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?

Challenge Level

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?

Challenge Level

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?

Challenge Level

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?

Challenge Level

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Challenge Level

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Challenge Level

You have a set of the digits from 0 â€“ 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

Challenge Level

These practical challenges are all about making a 'tray' and covering it with paper.

Challenge Level

A game in which players take it in turns to choose a number. Can you block your opponent?

Challenge Level

How many models can you find which obey these rules?

Challenge Level

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Challenge Level

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

Challenge Level

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Challenge Level

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?

Challenge Level

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Challenge Level

Can you deduce the pattern that has been used to lay out these bottle tops?

Challenge Level

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Challenge Level

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Challenge Level

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

Challenge Level

Surprise your friends with this magic square trick.

Challenge Level

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Challenge Level

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Challenge Level

What do these two triangles have in common? How are they related?

Challenge Level

Exploring and predicting folding, cutting and punching holes and making spirals.

Challenge Level

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Challenge Level

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Challenge Level

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

Challenge Level

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Challenge Level

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Challenge Level

An activity making various patterns with 2 x 1 rectangular tiles.

Challenge Level

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Challenge Level

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?