![Arithmagons](/sites/default/files/styles/medium/public/thumbnails/content-id-2670-icon.png?itok=QRL1B2me)
![Symmetricality](/sites/default/files/styles/medium/public/thumbnails/content-99-05-six1-icon.jpg?itok=Fer4KbI3)
problem
Symmetricality
Five equations and five unknowns. Is there an easy way to find the unknown values?
![Warmsnug Double Glazing](/sites/default/files/styles/medium/public/thumbnails/content-id-4889-icon.png?itok=pO_01kGN)
problem
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?](/sites/default/files/styles/medium/public/thumbnails/content-id-7342-icon.jpg?itok=sko93RPd)
problem
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?
![Mega Quadratic Equations](/sites/default/files/styles/medium/public/thumbnails/content-id-11009-icon.png?itok=S_bTzCPS)
problem
Mega Quadratic Equations
What do you get when you raise a quadratic to the power of a quadratic?
![How old am I?](/sites/default/files/styles/medium/public/thumbnails/content-99-03-six2-icon.png?itok=Y88RKpGX)
problem
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?
![Fair Shares?](/sites/default/files/styles/medium/public/thumbnails/content-00-05-six1-icon.png?itok=CBro7NhK)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-01-07-six5-icon.jpg?itok=_h3VHRnf)
problem
Iff
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
![CD Heaven](/sites/default/files/styles/medium/public/thumbnails/content-02-06-six4-icon.jpg?itok=fsB1RXyP)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-03-09-six9-icon.gif?itok=ei0Dje7n)
problem
Terminology
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
![Pick's Theorem](/sites/default/files/styles/medium/public/thumbnails/content-03-10-six4-icon.gif?itok=F-QyKCMj)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-id-5674-icon.jpg?itok=SdoykSTs)
problem
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 ?
![Which is bigger?](/sites/default/files/styles/medium/public/thumbnails/content-id-7344-icon.png?itok=Dq9q7UTS)
problem
Which is bigger?
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
![Training schedule](/sites/default/files/styles/medium/public/thumbnails/content-id-7366-icon.png?itok=MC5E5KIZ)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-id-7447-icon.jpg?itok=Tu0QuZpK)
problem
Multiplication arithmagons
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
![How old am I? Poster](/sites/default/files/styles/medium/public/thumbnails/content-id-8007-icon.png?itok=8zT5tg2l)
![Which is Bigger? Poster](/sites/default/files/styles/medium/public/thumbnails/content-id-8017-icon.png?itok=7hoiJV6c)
Image
![Equations and Formulae - Stage 4 STEM footer Equations and Formulae - Stage 4 STEM footer](/sites/default/files/styles/large/public/thumbnails/content-id-13485-STEMlogo.png?itok=AIp6YkH9)
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.