Negative numbers
I've adopted two approaches for the negative numbers problem - thanks for all the helpful comments.
I've presented the number line in the form of an elevator going up and down and explained (truthfully) that my old university was built on a slope, and floor 0 was street level.
The lift had -ve numbers for floors below street level and +ve for above.
Thus, the answer to any problem with negative numbers is a floor level - which hopefully gives it a concrete meaning.
Secondly, I have forbidden her from using any 'methods' for solving this kind of problem. (She's not at an age where she's expected to be able to do anything complicated with negative numbers, so rules on how to resolve them are not necessary. She just needs to understand that they go in opposite directions on the number line.
It worked in the lesson - let's see how she fares with her homework.
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