We did look at that, which led to us looking at the question “When does green become red?”

Ah, we allowed ourselves the use of the plus/minus symbol and defined more of a mapping than a function.

I agree that it’s demanding. The list of 3 things I wrote earlier is actually a list of the things I had to do to complete the rearrangement. TheMathsBazaar is right that the context was iterative methods.

We had, in no particular order…
1) Remove decimal coefficients.
2) Identify what the last few steps in the rearrangement must be.
3) Work towards a middle with both forms then rewrite the process start to finish afterwards.

Answers below.

Recently I’ve been going with “Two sinh sinh, hush hush, minus sign” to the tune of Kajagoogoo’s Too Shy.

This led to good discussion, partly because, with v = 0 there is no way to reverse engineer the right numerator. I think v has to be v or -v throughout. Ordinarily I’d take my own advice and have the “after” arrows pointing in the same direction. I find pupils make sign errors less often that way.

I also showed them the classic puzzle, “how do you slice a cake into 8 equal pieces with only 3 cuts?” Here the natural model for the cake, a circle, makes the problem impossible.

One student did ask about the reason for taking the +ve square root. We looked at the graphs below to help us decide.