Trying to use variation theory
A question to start
Reversing the terms. Does balancing still work?
A subtraction. How does this effect our balance.
Does reversing the terms still lead us to the same answer
Increasing the constant by one. What happens? Also: a decimal answer.
We can have a negative answer
Divide x, instead of multiplying it.
Increasing co-efficient of x by one. What happens to our answer?
Doubling co-efficient of x. Not sure about these last two. I think they may be a step back from question 7. This is the problem with presenting these in a linear format. These questions are variations on question 1, not question 7. I might experiment with some kind of spider diagram.
Doubling the divisor from 7. Again, maybe the linear way these are written is a bit rubbish.
Don’t know how I like the order of these questions, but there’s lots to think about and something to tweak.
I have found the transition to asking ‘why have they asked you that question? What are they trying to tell you?’ has been difficult for some students, but I think it’s worth devoting time to it. If students are inspecting questions for things like this, maybe they’re more likely to read the question thoroughly and pick out it’s mathematics. Big hope, I know.