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 make the birds from the egg tangram?
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?
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?
Here is a version of the game 'Happy Families' for you to make and play.
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?
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?
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?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
What is the greatest number of squares you can make by overlapping three squares?
How many triangles can you make on the 3 by 3 pegboard?
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.
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
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?
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 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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
A game in which players take it in turns to choose a number. Can you block your opponent?
How many models can you find which obey these rules?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
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?
How do you know if your set of dominoes is complete?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you deduce the pattern that has been used to lay out these bottle tops?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
Surprise your friends with this magic square trick.
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
What do these two triangles have in common? How are they related?
Exploring and predicting folding, cutting and punching holes and making spirals.
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
An activity making various patterns with 2 x 1 rectangular tiles.
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?