I love asking low-ability students or students whose first language is not English questions like this. Unpicking the etymology of words is something that can benefit all students but for low-ability or English as an additional language (EAL) groups this is of the utmost importance as they had anywhere near the same level of exposure to the subtleties, nuance and conventions of the English language. It is the job of educators to increase the level of exposure beyond what they would otherwise encounter.
For young students especially I really ham it up when I reveal that ‘percentage’ means ‘of 100’ and let them know that they are part of a small secretive club that will refuse to use the word ‘percentage’ willy-nilly but will stick to its strict definition.
I usually then go on to tell students that they would now be able to have an educated guess as to the meaning of any word with the word ‘cent’ in and I ask for a number of suggestions. Again for younger students a touch of the theatrics can be useful here (think Sherlock Holmes references).
When I asked this question last week it was with a Year 7 group, most of whom hadn’t encountered percentages yet but who were beginning to gain confidence with fractions of amounts and equivalent fractions. They quickly cottoned onto the idea that 25%=25/100=¼ and were then able to find percentages of amounts.
Focusing on the fact that percentages mean ‘out of 100’ and treating percentages as a special instance of the fractions work they had already encountered was something of a long way round. However, initially and in subsequent lessons students seemed to ‘get it’ and were far better able to explain some of the intuition behind percentages. Additionally, it made subsequent work on converting between fractions, decimals and percentages far easier.
Also posted @NWMaths