Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
A challenging activity focusing on finding all possible ways of stacking rods.
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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?
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?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
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?
We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
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?
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?
If we had 16 light bars which digital numbers could we make? How will you know you've found 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?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
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?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
In how many ways can you stack these rods, following the rules?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
An activity making various patterns with 2 x 1 rectangular tiles.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
An investigation that gives you the opportunity to make and justify predictions.
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
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?
Investigate the different ways you could split up these rooms so that you have double the number.
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?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
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.
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?
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.
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.