# Ratio and proportion made simple?!

Discussion in 'Primary' started by hammie, Mar 10, 2012.

bear in mind that most entrants at GCSE would miss this question out, so don't give yourself too hard a time of it!
I have tried using envelopes to share things into equla shares etc.
Funny when i trained as a Maths teacher, it was educational theory that children under the age of approx 13 were generally unable to imagine most problems invilving algebra etc. ie brain development tests had shown that abstract thought was beyond most preadolescent brains.
I suppose they could use their chunking method approach to division
i would draw a cross for each boy, then a circle for each girl:
xoo xoo xoo xoo xoo
and keep going til they have the correct amount
then add up the o and x
worth a try
but remember that the best way to get top grades is to do all the things you can perfectly and spend as little time as possible on the very difficult bits. then go back and have a go at the end.
incidentally do you get them to add yp the points lost to silly mistakes, and give them their level AND crucially "marks needed to get the next level" very often they are 1 or 2 marks away and blew more than that on page one!

2. ### milliebear1

Yes, it was a level 5 question certainly, but I have a few children whom I want to leave me at that level, who 'should' be able to get this. I agree, to a point, about the unfair requirement for abstract thinking upon immature brains though!
Loving the suggestion about adding up marks lost to silly errors. I always give mine the 'cut-off' and many are gutted to realise they are a single mark from the next level! Never thought of actually adding up the daft mistake ones though - might try this next time!
I will go back to the original question with them and try the symbols idea for girls and boys. Maybe I'll make it a bit more primary friendly by invoking a gender stereotyped picture - no doubt they'll love that!

3. ### tafkamOccasional commenter

Have a look at Singapore math bar representations. They might help.

good luck with it
re x marks to the next grade, the best bit of inset i ever received yet hardly known about or used. I have used it from ks2 to A level and it always motivates especially thoses pupils who are gutted becaues they feel that they cannot succeed

5. ### thumbshrew

Well it's a bit of a red herring question as you don't need to know how many boys there are, knowing there are twice as many girls gives you the answer of 2:1. A lot of children would be put off by being told how many boys there are, x or otherwise, it seems a bit unfair. Perhaps that is why so many struggled with the question, and they need to learn to read the question carefully and decide which information is important and which extraneous.

As thumbie said, they actually tell you the answer. What's to work out?

7. ### milliebear1

Sorry for the confusion. The question actually gives the total number of pupils, not the number of boys. I think part of the issue is with the language of 'twice as many', which a lot of them didn't fully understand.

8. ### thumbshrew

In being told there were twice as many girls as boys the pupils were being given the ratio. All other information is extraneous. You do not need to know the total number of children, boys or girls. It may have been that the problem was with the phrase "Twice as many", or with reading the problem, or with understanding how to express 'Twice as many' as a ratio, or with getting confused because they were told total amounts they didn't actually need. It would be interesting to know exactly what they wrote for their answers. Could it be that, in concentrating on practical work when tackling ratios, the childn have nt become acquainted with how ratios are expressed in language and how to interpret written questions. Ie that they've got a grasp of the Maths but not of the English?

9. ### milliebear1

Yes, I think there may be a language issue. Many do generally struggle with word problems as well (although not usually the very top ability children). This question in particular caught them out. They seemed to want to halve the total they were given, or some divided it by four then multiplied by three. Others simply left it blank and had no clue what to do.

10. ### thumbshrew

Can I just check millibear - were the children asked to provide a ratio for their answer or did they in fact have to calculate how many boys or girls, or how many children altogether?

11. ### milliebear1

They had to calculate how many girls to boys. Sorry - I wasn't very clear.

12. ### thumbshrew

So the correct answer was 2:1? (sorry, I think I might be misunderstanding).

13. ### milliebear1

LOL. No, the answer was a numerical one. I think the actual figures were something like 20 girls to 40 boys (but with less obvious numbers!) They needed to know to divide the total number by three, then multiply by two (off the top of my head, but I think that was right).
They are given the ratio, as you say, by the information 'twice as many boys'. They then needed to know what that actually means in terms of calculating the real numbers of each gender.

14. ### thumbshrew

Ah. I thought I might have misunderstood. However, you need to say 20 girls and 40 boys. When you use the term 'to' you are suggesting the ratio. It's sort of short for 'to every' - to every girl there are 2 boys, 1:2 girls to boys. When you are talking about the total numbers 'to' doesn't come into it because you can't extrapolate anything from it, whereas from 1:2 you can assume 4:8, 10:20 etc, and once you know any of the actual numerical values you can calculate the total number of boys/girls/children. I hope you don't mind me pointing this out, but it was what caused my misunderstanding and that of someone else who posted further up.

15. ### AnonymousNew commenter

I teach ratio as a tutor to secondary pupils. Always introduce it on a 2 for you, 1 for me basis. Cards, money, smarties etc.
It is a very hard concept but it does build up logically when presented using concrete practical apparatus. The hardest thing is getting them to understand the relationship between ratio and proportion.
Some of my older tutees have been told the link between horse betting and ratio!

16. ### thumbshrew

I suppose the simplest method they can use, although laborious, is to draw a line, tally one (girl) on one side and 2(boys) on the other. Continue to do this, 1 girl then 2 boys, until they have reached the numerical value they have been given, whether that is total girls, total boys or total children. This should give them the data they need to answer the question. They would have to make sure they do it carefully and methodically. After doing this a few times, and with some guidance, they would probably start to predict what the totals would be and identify some shortcuts they could use. The word 'every' is a key word. "Every time you tally a girl tally 2 boys".

17. ### milliebear1

Thanks for all advice. I have a few suggestions that I will definitely try with them.
Thanks also for the heads up on my own use of language Thumbie - much appreciated.