Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
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?
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?
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?
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?
Sort the houses in my street into different groups. Can you do it in any other ways?
Investigate the different ways you could split up these rooms so that you have double the number.
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
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?
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?
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!
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 make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
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?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
In how many ways can you stack these rods, following the rules?
This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.
What do these two triangles have in common? How are they related?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
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?
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
How many models can you find which obey these rules?
This challenge extends the Plants investigation so now four or more children are involved.
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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.
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?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
Explore the triangles that can be made with seven sticks of the same length.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
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.
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?
Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.
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?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.