Teaching in a Queensland high school, with year levels from 8 to 12, has some interesting moments. A teacher may finish a lesson on differential equations with the year 12s, and immediately start a lesson on percent with the year 8s or year 9s. Even more interesting, I find teaching percent to the year 8s and year 9s to be a much more difficult task.
I find that all students initially have difficulty with distinguishing the different 'types' of percent problems, eg 'find 15% of 40', '15 is what percent of 40' and '40 is 15% of what amount'. Some students get a feel for these questions quite quickly, others after a fair bit of practice. Still others manage reasonable success by learning little tricks and algorithms, but if the 'type' is disguised somewhat in a word problem, a lack of understanding becomes evident.
And some students never seem to catch on. I remember once teaching a whole semester of 'Maths of Money' in our old Maths in Society course in year 11, and having a few students still getting the easy percent questions at the start of the test incorrect.
In year 8, we have adopted a mental maths approach to the 'find 15% of 40' type of questions, very successfully, thanks to 'Mental Maths for Junior High' from Creative Publications. We only teach this one type of question in year 8.
In year 9 (starting on Monday, in fact), we add the other two types. This is where the problem begins. Could those of you who have found successful strategies for teaching understanding on this topic please share them with the rest of us?
I manage a website that contains resources for teaching mathematics at the secondary level. I would like to monitor any ensuing discussion and summarise the results in a brief paper that will be stored on the website. If you wish to participate but don't wish your comments to be included in such a document, could you please email me and let me know.