How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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 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.
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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 triangles can you make on the 3 by 3 pegboard?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
These pictures show squares split into halves. Can you find other ways?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
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?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
How many models can you find which obey these rules?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
In how many ways can you stack these rods, following the rules?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
A challenging activity focusing on finding all possible ways of stacking rods.
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?
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?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Investigate the different ways you could split up these rooms so that you have double the number.
Can you create more models that follow these rules?
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.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
Explore the triangles that can be made with seven sticks of the same length.
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?