My starting point is that generally we spend too long ‘starting off with 100%’ and this becomes ‘what you do with percentages’ (see also Engelmann’s idea of ‘stipulation’). This leads to problems further down the line when students default to doing this irrespective of problem type.
Related point is stipulating that 100% is the most you can ever have and students getting a bit stuck when starting percent increases. I try to hammer this out early by including lots of incidental percentage questions where it's greater (both in the 100%–200% range and beyond, often 1000%).
Step 1 would be to mix percentage calculations from the start. Eg, given a % to get to 100%, given a % to get to another %, alongside some where you are actually given 100% to find another %.
Totally. I think this occurs more often at primary when accompanying a visual approach (shouldn’t be the case). Fractions of amounts should be part of that percentage sequence somewhere too.
Once competent here, step 2 would be a lot of practice of reading contexts and answering the question ‘what percentage do we know?’. This would include reverse percentages from the very start.
I get that there are quite a few other sub-steps in there, but my gut says it would lead to more success and understanding, plus it would be more efficient.
Comments
If 1/4 is 36, what is 1? 2/4? 3/4? 5/4? 10/4? 100/4?
If 3/4 is 36, what is 3? 6/4? 3/2? 9/4? 1.5/4? 1?
As above, but with the question ‘what percentage do we need to know’.
Step 4
Combine all previous steps.