Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
How many triangles can you make on the 3 by 3 pegboard?
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?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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?
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?
Have a go at this 3D extension to the Pebbles problem.
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
In how many ways can you stack these rods, following the rules?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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.
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 a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
A challenging activity focusing on finding all possible ways of stacking rods.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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 extends the Plants investigation so now four or more children are involved.
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
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?
Can you create more models that follow these rules?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Can you find ways of joining cubes together so that 28 faces are visible?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
How many models can you find which obey these rules?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
What do these two triangles have in common? How are they related?
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?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Investigate the different ways you could split up these rooms so that you have double the number.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
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.
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?
The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.