What to do about all that algebra
Physics Narrative for 14-16
Keeping the algebra under control
There are two relationships for any given lamp or resistor: V1 = R1 × I, the constraint relationship that links the potential difference, voltage and current; and P1 = I × V1, which relates the power in the electrical pathway to the potential difference and current.
You might be tempted to combine these, in all kinds of ways. And doing so could be correct, as it is the same potential difference, and the same current.
Such algebraic manipulations could give you:
P = I 2 × R and P = V 2R.
Keeping the physical relationships to the fore
However, although you might derive pleasure from such manipulations, we don't recommend using such complicated short cuts with all children. Such short cuts are for the confident who are already familiar with the countryside, but may often turn into
long cuts for those who are not so certain in their navigational abilities. Such manipulations would earn their place in teaching at this level if they helped to focus attention on the physical situation and the fundamental relationships, but we think their purpose is rather to avoid such a focus, jumping to a solution instead.
So these may be best avoided for now, being left for later study, when the fundamentals are much more secure. We suggest that you exploit the opportunity to work and talk through the fundamental relationships in making sense of a circuit. Once your students are comfortable with these, they may then benefit from suitable exposure to the elegance afforded by algebraic manipulations.
Teach the physics first.