Something in Common: Algebra

This sub-collection of resources from the ‘Something in Common’ collection contains three resources designed to bring a problem solving approach to the teaching of algebra in Key Stages 3 and 4. Each problem comes with several different versions of a problem that have ‘something in common’. Having discovered the ‘something in common’ the challenge is to understand the underlying mathematics that gives these results.


Think of a Number

After thinking of a number, a series of steps is given that result in an answer that is independent of the initial number. There is scope to use fractions and directed numbers in the problem....

Leonardo of Pisa

This is an investigation into how the Fibonacci sequence gives rise to the Golden Ratio. The supporting spreadsheet allows the initial values of the sequence to be changed and an interactive...


A series of eight simultaneous equations are given and the initial challenge is to discover the single point of intersection of the lines. On each of the examples given the intersection takes as...

Partial mean

In this resource the mass of a group of objects is given, with the mean matching the number of objects. The mass of a subset of the objects is given, again with the mean mass matching the number of objects. The challenge is to calculate the mean mass of the remaining objects.

Solving the problem requires the...


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