# Why do so many students work out 33% off when the question asks for 1/3 off?

Discussion in 'Mathematics' started by waikatoriv, Jul 10, 2011.

1. ### waikatorivNew commenter

Marking GCSE HIGHER (non-calculator) online. The question is to work out a sale price with a 1/3 off. A simple division by 3 and then either multiply by 2 or subtract off. You would think it was easy (original price is a multiple of 3) but <u>so many</u> candidates are working out 33% (even some are working out 30%) and making it so very much harder for themselves with decimals involved. Invariably they are getting it wrong and worse spending ages on it judging by the screeds of workings out that you have to trawl through. This is happening OFTEN,not just an occasional student. Why do students immediately go for the percentage method? It would not have been the case when I did my O' levels!

2. ### Betamale

Same reasons so many think 5 squared is 10
(i) They have never really grasped the basics of number
(ii) They panic in exams and forget things
(iii) They spend 11 years never really fully taking responsibility for their learning
(iv) They quick split 100 into 3 and dont bother with the .3 recurring....perhaps.....

3. ### waikatorivNew commenter

I agree with you Betamale. I think the main problem is they haven't grasped the basics of number. Working out 33% (rounded I know) and then subtracting off is given full marks if they do it correctly(although it isn't actually the correct answer but an approximation) but the students who use this method are often getting it wrong and spending ages doing it as well. The ones that divide by 3 (simple "bus shelter" method) and subtract off are getting it correct far more often and spending less time on the question as well. Oh well!

4. ### PaulDGOccasional commenter

My experience of teaching percentages to secondary school children is that the notion of "take a tenth, then another (or halve it)" is so drilled into them that it's near impossible to get them to even consider percentages any other way.
Many simply refuse to engage with reverse percentages, ignoring any feedback pointing out why their "take a tenth" method has given them the "wrong" answer, or perhaps shrugging it off with a decision that as this will only be a couple of marks at the end of a percentages question, they're not bothered.

So, IMHO, this is another aspect of "teaching to the test". The test in question being the KS2 SAT.

5. ### AnonymousNew commenter

You are looking at it through the eyes of someone who is good at maths and likes maths. I remember going on a primary school course using Excel in maths. The course leader wanted us to come up with a formula to add 10% to a number. I simply put in the number times 1.1
She did not understand what I meant. She had never used this simple method (and granted primary school children would find it hard to grasp). So yes - we had the divide a number by 10 and add that to the original number. Yes - I was very bored on that course.
What got me was this so called maths leader did not understand that multiplying a number by 1.1 adds 10%.
Yes - primary schools do teach divide by 10 to find 10%. Double, half etc to find 20%, 5%. I also teach divide by 100 to get 1%. Why - it's a quick method to get relatively simple percentages. But then you are right - it is a lot easier to find 80% of a number rather than subtract 20%. That still requires "maths thinking" which is what needs teaching.

6. ### waikatorivNew commenter

The issue that really bothers me is the fact that they used a percentage method in the first place. Why didn't they just divide by 3 rather than going through the rigmarole of 10% = etc etc etc and then getting it wrong becaue of all the decimal points involved. I am talking about a sizeable minority, possibly even a majority, who used this method. I wish the exam board would state that in future years no credit will be given for this method what is in effect leads to a wrong answer, unless 33.33333333..% is used, which in not going to happen on a non-calculator question.

7. ### AnonymousNew commenter

You mean that little link between decimals, fractions and percentages. 1/3 = 33.3333% = 0.33 recurring, 1/4 = 25% = 0.25 etc.
I would suggest that it's the kind of thing that needs to be explicitly shown regularly in lessons and reinforced as percentages are ingrained as divide by 10.
I work as a tutor so have the advantage of being able to reinforce that link on a 1-1 basis - but it takes a long time to ingrain what people who are "experienced in maths" would see as a quick method.

8. ### ResourceFinder

What were the numbers involved in this question?

9. ### waikatorivNew commenter

1/3 off &pound;192

10. ### ResourceFinder

hmmmmm

Something that confuses me about your posts is that you seem to suggest that the board are awarding marks for anything other than £128 and I am not sure why?

11. ### AnonymousNew commenter

You're telling me they do a percentage method for this???
Divide by 3. Subtract from &pound;192
What could be easier - or divide by 3 and times by 2
I am really surprised they are doing a percentage method - it's not the first thing that jumps to mind.

12. ### PaulDGOccasional commenter

It is if you've been conditioned to "spot the method" when dealing with maths exams - and most kids these days have been taught to do exactly that.

"something off" is therefore recognised as a "percentage question" and "percentage questions" are always answered by "taking a tenth and then halving".

This is one reason why GCSE results have improved over the years - we are all much better at teaching the kids to spot the question types, the examiners are much better at setting questions that conform to a strict type and the kids are much better at remembering which method to apply to which type of question.

It's also a reason why employers comment that kids come to them with long lists of qualifications but can't do the simplest tasks.

13. ### Betamale

I am looking at it through the eyes of a someone who is teaching kids who have been in formal education for 11 years and deemed capable enough of doing a Higher GCSE exam, ergo they should be able to master this.
Beyond exam nerves is its little more than an inability to take responsibility for their own learning.
IMO knowing 1/3 = 33. 3 recurring is little more than a fact they should have learned.

14. ### ResourceFinder

I can not imagine any of my students doing this (unless a serious mis-read)

But students do make errors on exams

I am still unsure why the exam board is awarding marks for the incorrect answer

Was the question one of those that asked "which is a better deal" with one giving a fraction off and the other using a percentage ... ... if so were marks given because the conclusion was correct in spite of the fact that the working out was wrong?

15. ### mevdog1971New commenter

Agree with Piranha - surely we are here to teach students not to make these mistakes. It is a common misconception and hence should be addressed as such.
Ask students to work out 1/3 of 99 and 33% of 100 mentally and see if they can understand why they can do this and get integer answers; then compare to 1/3 of 100 and 33% of 99.

16. ### NazardNew commenter

Another thought: there are times when we want pupils to round off answers in only one way, time when we are happy with any sensible level of rounding and times when rounding is absolutely unacceptable. Are our pupils clear when each of these are required?
Examples:
Money questions - will almost always need to be rounded to 2dp
Trig questions - depending on the numbers in the question the answers may be rounded off to different sig figs/dps without being incorrect
Converting fractions to decimals - we usually want to know if it is a recurring answer.

17. ### Betamale

We do, in years 1-6 as primary teachers and 7-11 in secondary. The suggestion we dont is somewhat strange.
% is taught every year, misconceptions addressed but at the end of the day if a kid doing their final GCSE <u>higher</u> exam makes this mistake then TBH (other than it being as a result of exam nerves) is merely a case of them not taking responsibility for a simple skill.
Its not the teachers 'fault' as this is covered time and time again. Its the pupils for either (i) being lazy or (ii) the pupils being very lazy in developing such a basic skill.
If the kid gets the last question on some hard trig then thats fine, but basic skills? no, purely down to the pupils desire to further themselves.

18. ### cyolba

It is a skill that it at level 5 of the NC, so many year 6 kids will be able to do it (mayber heading for level 6 as it's a fairly large number to start with). As far as GCSE questions are concerned, I would consider this to be one of the easiest on a Higher tier paper, basically a D/C (at best) question. This begs the questions:
1) If they can't do this, why the heck are they doing Higher at all?
2) Is it a case of a skill once covered, but not embedded sufficiently well, so that the last two years of romping through surds, 3-D trig, volumes of pyramids, factorising quadratics etc have meant that it has been forgotten and that the kids will end up with B grades because they can do thr hard stuff, but haven't understood the more basic stuff well enough?
To be honest, I don't think such a straightforward question should even be on a Higher tier paper...

cyolba, feeling sorry for these kids' prospective A-level Maths teachers

19. ### Betamale

Good post.
On part 2 though I think the skill gets hammered every year explicity or implicitly in maths and TBH used throughout real life.
RE the A level part. I had one who refused to use fractions and said they would work in decimals throughout as it was easier..........................