Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
How many tiles do we need to tile these patios?
I cut this square into two different shapes. What can you say about the relationship between them?
These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
Investigate these hexagons drawn from different sized equilateral triangles.
Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?
Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?
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 are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
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?
Here are many ideas for you to investigate - all linked with the number 2000.
Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Bernard Bagnall describes how to get more out of some favourite NRICH investigations.
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.
If the answer's 2010, what could the question be?
Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.
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.
Bernard Bagnall looks at what 'problem solving' might really mean in the context of primary classrooms.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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?
This activity asks you to collect information about the birds you see in the garden. Are there patterns in the data or do the birds seem to visit randomly?
Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
This problem is intended to get children to look really hard at something they will see many times in the next few months.
Investigate what happens when you add house numbers along a street in different ways.
The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
What do these two triangles have in common? How are they related?
Why does the tower look a different size in each of these pictures?
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?
Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
How many different sets of numbers with at least four members can you find in the numbers in this box?
A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.
What is the largest cuboid you can wrap in an A3 sheet of paper?
Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?
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?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
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?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
Investigate the number of faces you can see when you arrange three cubes in different ways.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
A group of children are discussing the height of a tall tree. How would you go about finding out its height?