Does anyone know of links to resources to explain why basic algebra rearrangement operations take place in a certain order?
A simple, seemingly absurd example, but not uncommon follows.
Say the student is tasked to make "y" the subject of:
x = 3y - 7
Now "obviously" the first step is to add 7 to both sides. But I see students whose first step is to try to divide by 3 - maybe because that's what they need to do to "get y on its own".
Or teaching a rearrangement of, say
3xy = 7x - 4y
to make "x" (or "y") the subject.
Weaker students find it difficult to know where to start and often try actions like "divide by y" rather than rearrange and apply linear factorisation (a very challenging step for weaker students).
Now, I'm not thinking the process of rearrangement can be reduced to a simple algorithm but are there any resources that can help the student to think "well, first I do this, then I do that, then I do that"? All the examples I can find example what to do in a particular situation but don't go into the why.