This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Bernard Bagnall looks at what 'problem solving' might really mean in the context of primary classrooms.
In my local town there are three supermarkets which each has a special deal on some products. If you bought all your shopping in one shop, where would be the cheapest?
Why does the tower look a different size in each of these pictures?
Bernard Bagnall describes how to get more out of some favourite NRICH investigations.
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
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?
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?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
Can you create more models that follow these rules?
How many triangles can you make on the 3 by 3 pegboard?
Explore one of these five pictures.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
Here are many ideas for you to investigate - all linked with the number 2000.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
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?
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.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?
Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.
We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
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?
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?
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?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
How many models can you find which obey these rules?
A follow-up activity to Tiles in the Garden.
How many tiles do we need to tile these patios?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
What do these two triangles have in common? How are they related?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Have a go at this 3D extension to the Pebbles problem.
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
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.
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?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?