Here is a version of the game 'Happy Families' for you to make and play.
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?
Use the tangram pieces to make our pictures, or to design some of your own!
A game to make and play based on the number line.
What is the greatest number of squares you can make by overlapping three squares?
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.
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?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
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?
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
Can you make the birds from the egg tangram?
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 your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
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?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
How do you know if your set of dominoes is complete?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
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?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
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?
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?
How many models can you find which obey these rules?
An activity making various patterns with 2 x 1 rectangular tiles.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
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 ...
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
Can you split each of the shapes below in half so that the two parts are exactly the same?
Make a flower design using the same shape made out of different sizes of paper.
These pictures show squares split into halves. Can you find other ways?
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?
This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?