The following question is taken from my website Diagnostic Questions. Here you will find 1000s of high quality maths questions, ideal for assessment for learning, which have been created and shared by maths teachers all over the world.

A nice little algebra question for you to try out on your students this week.

I find that rearranging formula is one area that quite a few students find difficulty. Algebra as a whole is a minefield of misconceptions, and rearranging formula tends to expose any errors in thinking and understanding that a student might have.

Let’s have a look at what we might learn from student responses to this question:

Answer a) suggests students have divided by two (incorrectly!) first. Perhaps they need to work on their order of operations, and their reading  of algebraic expressions

Answer b) implies that students have simply switched the two letters’ positions and don’t really understand what making the subject of a formula actually means

Answer c) is the correct answer

Answer d) may suggest that students have the right idea, but have subtracted the 5 to from sides instead of adding.

On a related matter, I am currently teaching the delights of algebra to my lovely Year 7 class, and I have found the approach advocated by one of my all time favourite maths bloggers, Don Steward, to be particularly useful.

As can be seen from the worksheets below, Don advises students to get to grips manipulating numbers first – with the obvious advantage being that students can check each line of their working by calculating the left hand side of the equation and ensuring it matches with the right hand side. With algebra, this is often not possible, and hence students can get several lines through a problem without realising they have made an early mistake. As I say to my students – if it works with numbers, it works with algebra, and vice versa.

I would hope that if rearranging formulae was introduced this way, then perhaps not as many students would have the misconceptions revealed by the question above.

Incidentally, if I had my way, I would have Don Steward knighted. His Median Maths Blog is one of the best things I have ever seen and a constant source of inspiration.

And if you have used the question, or have any thoughts or comments about it – perhaps you would include a different incorrect answer – then please share your comments below. And please consider creating a question yourself on the website!