This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
problem
A little light thinking
Age
14 to 16
Challenge level
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
problem
Steel cables
Age
14 to 16
Challenge level
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
problem
Double trouble
Age
14 to 16
Challenge level
Simple additions can lead to intriguing results...
problem
Picture story
Age
14 to 16
Challenge level
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
problem
Attractive tablecloths
Age
14 to 16
Challenge level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
problem
Painted cube
Age
14 to 16
Challenge level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
problem
Mystic rose
Age
14 to 16
Challenge level
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
problem
Partly painted cube
Age
14 to 16
Challenge level
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
Image
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.