It starts quite simple but great opportunities for number discoveries and patterns!
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
This challenge extends the Plants investigation so now four or more children are involved.
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.
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
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.
Have a go at this 3D extension to the Pebbles problem.
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?
A challenging activity focusing on finding all possible ways of stacking rods.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
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?
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?
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?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
A follow-up activity to Tiles in the Garden.
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.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?
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.
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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!
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?
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?
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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.
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?
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Can you find ways of joining cubes together so that 28 faces are visible?
How many models can you find which obey these rules?
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.
Explore one of these five pictures.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .
In how many ways can you stack these rods, following the rules?