# 45 divided by 3

Discussion in 'Private tutors' started by stevencarrwork, Nov 4, 2011.

1. ### stevencarrwork

This division comes up quite often, and I dread questions where it is going to appear.
I have many 'GCSE borderline C-D ' students who are simply stopped in their tracks by this question. Surprisingly many.

They can no more begin to produce an answer than if I had asked them to work out a Fourier transform of x cubed.

I am not a numeracy teacher. I am no good at that. I need to be able to take for granted that my students can work with basic numbers.

But why am I trying to teach grouped frequency tables to students who have no idea how to approach a question like 45 / 3?

2. ### stevencarrwork

This division comes up quite often, and I dread questions where it is going to appear.
I have many 'GCSE borderline C-D ' students who are simply stopped in their tracks by this question. Surprisingly many.

They can no more begin to produce an answer than if I had asked them to work out a Fourier transform of x cubed.

I am not a numeracy teacher. I am no good at that. I need to be able to take for granted that my students can work with basic numbers.

But why am I trying to teach grouped frequency tables to students who have no idea how to approach a question like 45 / 3?

3. ### AnonymousNew commenter

I wouldn't take that for granted. Unfortunately many children still struggle with basic number work. Have you tried rephrasing it or putting it in context?
Share &pound;45 between 3 people. &pound;45 into groups of 3.

4. ### DeborahCarolNew commenter

Hi Steven
If you are a maths tutor, you must teach your students whatever is necessary for them to progress. Sure, they may be C/D borderline candidates, but if they can't handle a simple division...you'll have to teach them division!
I've met many 14-16 yr olds (even those doing Higher GCSE), who have no written method for division, eg have never been taught 'bus-stop' division, but can learn it pretty quickly when shown. They have indeed 'slipped through the net'...
Bit puzzled to hear you saying you are not a 'numeracy' teacher and that you are 'no good' at that. If you are tutoring maths, you need to be good at tutoring all areas of maths. Whenever you come across 'gaps', whether they are conceptual, high-level, low-level, or basic arithmetic, you must fill them.
I recommend giving all your borderline C/D students a test at first session, of tables, and written addition/subtraction/multiplication/division methods. Whatever they can't do, note, then spend the first ten minutes of each of the next few sessions working on those areas.
Apologies if I've got the wrong end of the stick.

5. ### DeborahCarolNew commenter

To stephencarrwork
(Sorry, still haven't got the hang of this 'quotes' thing - must revise!)
Coincidentally, I've just done a one-off intensive revision session for a C/D borderline candidate taking the exam this Wednesday.
Sure, if you were only tutoring the student for ONE session prior to the exam, it wouldn't be so easy. Although, my student yesterday also drew a blank on a simple division. I had to remind him how to do it, and I do think he'll be fine for the exam on Wednesday. When your students say they 'can't do' 45 divided by 3', it's more likely that they've been taught a written method in the past, but have forgotten it. You just have to bring it to front of mind. (Students will often maintain 'I've never been taught that....' - but that's not usually actually the case.)
If, however, you've had your student for several sessions prior to the exam, you would have had time to teach the VERY basic division needed for 45 divided by 3 and cover lots of the syllabus as well.
(Also, as others say, depending on board, this sort of problem might be on the calculator paper anyway.)
When the parent looks at the topics covered, you tell them what you've covered and say 'And we did have to recap basic division too'. I wouldn't have a problem telling the parent that, as a) it's the truth and b) it would at least have the effect of making their expectations for their precious a little more realistic.

6. ### AnonymousNew commenter

Mine frequently "forget" division or multiplication, Just takes a reminder - often linked into the question we are working on.
Same with fractions and percentages!! Regular practise. Parents need to know where their children are instead of being fobbed off.

7. ### CathySupplyNew commenter

I think if you're going to take on a student you should be able and willing to give them whatever they need, regardless of your own preferences - or you should just say no. I myself advertise my services for English up to GCSE and maths to Year 6 level (not necessarily Y6 age). I wouldn't touch anything else. I think it's easier to work 'bottom-up' as I do; having taught primary (mostly Infants) for nearly 30 years I find it relatively easy to adjust to secondary-age children - although I would pass high-achieving older ones to a secondary teacher. I expect to have to fill gaps in knowledge from primary school. What I think a lot of secondary colleagues find hard is that younger/less able children do think and learn differently from older ones ... so a degree in child psychology would actually be very useful! Back in the day (1983) we post-grad primary students had to do a sizeable Child Development module and it's scandalous (IMHO) that this seems to have disappeared. All teachers and tutors should know how to teach basic skills (again IMO).

8. ### AnonymousNew commenter

I've taught primary for 10 years in both Key Stages and my PGCE had a module in child development. I'm comfortable doing KS1 and KS2 (although I don't think KS1 should have tuition) and I do upto GCSE as I've a very good maths background. I've only stopped doing 1 child as he had ADHD and found it very difficult to focus in lessons.
It still surprises me the thought processes and insecurities of teenagers. How they "forget" or "don't know" - yet when pushed they do. How they lack an ability to work through a problem. How they don't know how to apply themselves to a problem. How they seem to forget the basics.
Still - keeps me busy.

9. ### ic3g1rl

I'm a bit confused are you saying that in the subtraction 7002 - 1873 you would say something like borrow from the 700. What do you get them to borrow? Strictly you're changing the 7000 into a 6000 and a 1000, then you're changing this 1000 into 990 and 10 so you end up with 6000 and 990 and 12 (6000+990+12=7002) . How much of that do you actually explain?

10. ### langteacherOccasional commenter

for a first lesson, iwould go armed with a list from the syllabus for an exam student or nc level descriptors / topics etc for ks3 student. I then ask the student to give themselves a score out of 10 for how much they know / can remember for each one. I find that students are very honest about what they know / don't know and it then gives us something to revisit so they can score themselves again a feww lessons later. it also gives you a list that you can put in order of priority

11. ### AMathsTutor

They are borrowing 10 from 7000 leaving 6990 but I tell them to cross out the "700" and above it write "699" and write a little "1" to the left of the 2.

It works nicely in that struggling students suddenly find they can do these questions and they seem to retain it quite well too.

12. ### ic3g1rl

I'm amazed they understand this and not the original algorithm but that's students for you!

13. ### ic3g1rl

Picking up this point Steven, doesn't it depend what you mean by numeracy. Whereas literacy is fairly clearly defined there is quite a grey area surrounding being numerate. What special skills do you think are required to teach numeracy?
On a related idea I find that my students struggle with the arithmetic of algebra. To work on this I find I have to cover the arithmetic of numbers. This is mainly because once I remove letters the students brain becomes engaged again and, also, they are resonably familiar with arithmetic operations they just don't necessarily use them in a manner which helps them with algebra.
How do you manage with foundation GCSE students? Most of their exam is numeracy based. Also, if you ever tutor students doing Mathematical Studies as part of their IB course then you would be tackling numeracy ideas. How do you manage then?

14. ### stevencarrwork

I give them computer programs to practice their addition, subtraction and tables, and division.

The trouble with teaching subtraction is that schools seem to have about 8 ways of doing the algorithims, and I never know which one of those my student has failed to grasp.

They can get very confused, if you try to teach another method for subtraction.

How do you teach numeracy? 12 take away 7 is 5. That is just a fact to be learned. I can give them counters so they can convince themselves it is true. But they have to learn all these number facts themselves. I can't really spend a huge amount of time teaching them 12 take way 7, 13 take away 7, 14 take away 7 etc etc.

Hence I now give them computer programs, so they can practice and learn these number facts in their own time.

15. ### stevencarrwork

Agreed

I have a lot of A-level students who are happy with the idea that a -b = a.

3 square roots of 6 minus square root of 6 is 3 square roots of 6. They see nothing wrong with that statement.

As there is no number written in front of the second square root of 6, it can be difficult to convince them that the answer is 2 square roots of 6.

Now if I can also get them to not automatically cancel out any x which appears on the top and bottom of a fraction like (3x+1/(x-6)

It can be hard teaching basic numeracy.

What is 1/3 of x^3 when x is 3?

FIrst, many students say that 3 cubed is 9. I pointed out to my student yesterday that 3 cubed was 27, not 9. 'That was a bad mistake by me', he said.

OK, I said , so it is one third of 27. What is that?

'Three - he replied.

16. ### AMathsTutor

Rather than finding this method easier to understand it might just be the fact that they're getting this method one-to-one whereas the other method that they learned in school was probably explained to the whole class.

I could experiment by teaching the usual school method to see if they pick it up one-to-one but to be honest I prefer my method anyway. I really do think it's easier.

17. ### AnonymousNew commenter

Get that a lot. 5 x 5 = 10!!
You should try working in primary schools - at the end of the day, your job is to help them improve their maths and fundamental numeracy work is a key part of that. Then again - basic numeracy does crop up in most foundation questions - fractions, algebra, ratio, addition, etc - it's all numeracy.
What's your experience in education as a teacher?

18. ### stevencarrwork

I couldn't work in primary schools.

My biggest problem teaching numeracy is that I don't know what is the ground level to build on.

I have a year 11 doing GCSE. One topic for revision was finding fractions of a quantity. I asked what was one-third of 60. He looked blank. I explained that you had to divide the 60 by 3. He looked blank.

I asked him if he had been taught any methods for division. How would he set about dividing 60 by 3? He responded, 'well, a half of 60 is about 30' and tried to work from that starting point.

Where do I start?

19. ### AnonymousNew commenter

Ask him what a 1/3 means. If he's not sure, your job is to explain to him. Visually, numerically.
Sorry - but that's what a good tutor should do.

20. ### rohirrim

By the time kids are 15ish, alot of their methods have become almost imprinted upon their brains because they have used them so often. Great if they are good methods but obviously not when bad. And it does go back to Primary. Many kids at that age (Y3 and 4) often have semi-understood methods and often poor basic number facts. New methods are piled on top of these and the kids pick things they think work or find help them sort of get by. As a former Primary teacher I used to tie myself up in knots trying to help these kids because those who had problems had individual problems that needed solving on a one to one basis preferably but in max 2s/3s.But they are usually covered in larger groups with several different methods being offered which just thoroughly confuses them, ending up in a these methods being conflated in the kids minds. and these methods frequently let the kids down - so they try to avoid/plead lack of knowledge. When I started doing one to one with KS3 students, all of this really came home to me -times tables, +/- facts, subtraction, division, x/ by 10etc, x of decimals (they generally used the grid method of x so couldn't see how to x decs linked to previous point), fractions - and i find this with C/D GCSE students as well.
Maths needs more input at Primary - but emphasis on number facts, 4 ops, x/10 etc. but needs of SATs ie league tables, beats all. The number of times I was told that the kids must go through more advanced maths because they need for SATs even tho knowledge and understanding of more basic stuff was shaky. And i hate to say it, the K and U of too many Primary teachers lets them down when trying to help kids.