Algebra - demystifying formulas

Demystifying formulas in algebra – a journey into a bright forest.

Algebra may be seen as a universal language that is found all over the globe and is applied in a myriad of different contexts.

Perhaps the reason algebra may seem so challenging for so many is that the letters used need to be placed in context so that students can see that each letter stands for something in everyday life.   X could represent the blood sugar level in a diabetic patient and Y could represent the heart-beat of a patient receiving specialist care.


Algebra and Taxi Fares

I have found that algebra can be demystified for students in the years leading up to GCSE exams by considering a taxi metre as a starting point.  Therefore, I set the scene by imaging a taxi journey from Paddington Station to a location in the city of London:


C  =  380  +   70n


C represents the cost of the journey in pence and n represents the number of miles.  Before the journey even begins, there is a fixed charge of 380 pence.

The layout of clear, concise method work is immensely helpful with ‘flushed’ equals signs and sequential working:

Algebra - taxi example

For a journey of five miles:

C  =  380  +  (70×5)

So, C  =  380 +  350

Add the sum to get:

C =   730 pence

C  =  £7.30


It is also very helpful to gain experience with ‘working backwards’ with a taxi meter formula, for instance, finding the number of miles given the total cost:


Cost =  £8.70

870    =    380  +  70n

Subtracting 380 from each side:

490  =   70n

Dividing each side by 70:

7  =  n

Hence the taxi journey costing £8.70  is seven miles.


Algebra and Temperature

Another very helpful formula to bring a clear context to formulae in algebra is the relationship between degrees Fahrenheit and degrees Centigrade:


C   =   5/9 (F  –  32)


I have found that I can achieve great breakthroughs have been made when we post the question, what is the temperature in Centigrade when the temperature in Fahrenheit is 32 degrees.  Students quickly realise that 5/9 times zero is zero and future calculations are easily made.


I also find that this formula is very helpful for teaching rearranging of formula to make F ‘the subject’


C   =  5/9 (F  –  32)

Multiplying each side by 9 gives:

9C   =  5(F – 32)

Dividing each side by 5 gives:

1.8 C  =  F  –  32

Adding 32 to each side gives:

F  =  1.8 C  +  32


I build confidence with algebra, immeasurably, by asking students to reflect for a moment on the huge number of words that they have learned in the thousand weeks or so that they have been alive on the planet; the universal language of algebra is just a small addition to our amazingly successful brain processing skills.


Want your child to succeed? Why not try one of our expert tutors. You can read why this helps here: Why Should I book a Maths Tutor


A bit about the author of this article, Chris C:

Chris is a freelance tutor who has 28 years of full-time teaching experience. He was Head of Department in a large Somerset college from 1992 to 2014.

He holds a B.Sc. in Maths & Science and a B.Ed. in Mathematics.

With an enthusiasm and interest in mathematics, Chris can raise self-confidence and belief by making maths fun. He concentrates on setting the language in context and building clear scaffolding in topics based on his insight and understanding of the subject.

You can enquire about tutoring with Chris here

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