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.
Arithmagons
Can you find the values at the vertices when you know the values on the edges?
Mega quadratic equations
What do you get when you raise a quadratic to the power of a quadratic?
How old am I?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Symmetricality
Five equations and five unknowns. Is there an easy way to find the unknown values?
Warmsnug double glazing
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Which is cheaper?
When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
Which is bigger?
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
Training schedule
The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
Multiplication arithmagons
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Fair shares?
A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?
Iff
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
CD Heaven
All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?
Terminology
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
Pick's theorem
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Matchless
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.