# how do you teach ratio?

Discussion in 'Mathematics' started by moved, Mar 26, 2008.

1. ### moved

I spent the last 3 lessons of the Spring term teaching ratio and proportion to my year 7's.

I have two groups - one made up of pupils at the top of level 3/bottom of level 4, the other made up of very weak pupils - struggling to get a level 3 in their KS2 SATs.

I know I could teach it better. Each year I try a slightly different approach. I guess the problem is that I find the topic very intuitive and I fight the urge to tell them 'it's obvious!'

so, anyone have any sure-fire ways of teaching this topic, particularly to lower ability pupils?

(thank you)

2. ### a long half term

table method

9 girls for every 4 boys

16 boys how many girls

boys girls
4 9
16 ?

what do you do to 4 to get 16? x4 etc

not always easy with lower ability but i did in a y6 booster tonight and they liked

have done it lots of times over the years - i find it the best way

you can add a total column to it too

3. ### a long half term

hmmmm just read the post properly - not sure if this is a winner for really low ability - but could you rote teach it? (sorry lads!!!!)

alternative is - do you need to teach ratio with such a low ability group???

could you not concentrate on 4 operations and their strengths(shape and space)

i have found with my bottom set y8 they respond to stuf they 'like' and find easy (i did level 6 construction with them for an observation - they are all level 4 at best) and they responded brilliantly.

i have decided im gonna teach them stuff i like, they like and also the basics!

any use?

4. ### williamj555

Is it possible to teach it as a by-product of trigonometry i.e. talking about similar triangles having set ratios of side length?

5. ### 1 45

I would teach it like a long half term to my Y6 group but they are much higher ability. My lower ability Y5 would probably do it all with counters or pictures. Grouping together different counters to show x2, x3 etc.

Alternatively I did a Christmas one that was based around decorations where they had to colour in baubles on a Christmas tree in the correct ratio.

6. ### moved

I liked what my bottom set did - like your example - where they used others in the room to create patterns, and while they had that visual picture in front of them, they were fine.

I find the problem comes when trying to formalise the work, particularly when it comes to ideas such as simplifying the ratios

7. ### 1 45

Can they do equivalent fractions? I'm sorry if this is not correct but I show them how, as in equivalent fractions, one side of the ratio increases by, say x3, the other side must do the same. Suddenly light bulbs go on.

8. ### moved

re post 3: how do you mean by rote teaching it?

as for your other comments - I understand where you are coming from, but I feel that this is something I need to improve. Even this ability are fab at some aspects of algebra, and I think a lot of this is down to my confidence - I know how I'm going to present the material, how to cover the objectives, and can be enthusiastic about it - which makes a big difference!

I'm also still considering your question about whether they should be taught it at all - I can undertstand why one might not, but my gut instinct is yes, they should. By not at least offering it to them so they can start to become familiar with a topic, I would feel I am restricting their progress - the pupils I will still be teaching next year will be ok as I will know what they haven't covered this year, but what of those that move up? Also, what about the pupils who don't struggle with the topic? Should they just miss out because some of their classmates might struggle? And if I miss out ratio for fear of them struggling, what else should I miss out on?

re post 4: who said maths teachers have no sense of humour!!

9. ### moved

1 45 - yes, very simple fractions anyway!

I, too, make the connection between simplifying fractions and simplifying ratios - but I don't want them to just have a method that, if we're lucky, they'll remember for the next test. I'd like something or some way of presenting the topic that makes sense to them in order to deepen their understanding, if you know what I mean

10. ### wibble73

Ummmm - given that it is Level 5 to do the following:

"They reduce a fraction to its simplest form by cancelling common factors and solve simple problems involving ratio and direct proportion."

At present I think you should be happy with them using manipulatives.

I've just taught it to my bottom set Year 8 and we used multi-link blocks for all the lessons and speaking to them they used coloured counters or similar to find equivalent ratios at home. The majority of the class didn't sit their KS2 SATs. We're moving forward slowly... Next year I hope to move away from manipulatives.

11. ### STCoop

E.g make a stick using 3 red and 2 blue cubes. You can then see that the FRACTION of red cubes is 3/5 & of blue is 2/5 but the RATIO is 3:2. Can then make other sticks and discuss if they are equivalents ratios. Also do problems where just the red section is shown and ask how many blue there would be & vice versa. Can extend to different ratios & 3 colours.

Did lesson like this with low ability year 7s and it went well.

12. ### brookes

I think this may be too advanced for your class, but I've used making up squash as a context for ratio. I don't drink tea or coffee, so this is a pretty important use of ratio in my (real) life and it's funny how strongly the kids can feel about squash being too strong/weak.

We discuss how we like our squash making - how much water and how much cordial. What's the ratio of cordial to water? Which ratios lead to a strong drink, which to a weak drink etc. If Miss Brookes likes a ratio of cordial:water of 1:4 and uses 50ml of cordial, how much water does she need?

14. ### moved

thank you to everyone for all of your suggestions

I think it is a topic we will revisit - things have a tendency to fit together better 2nd time round regardless of ability, don't you think!

(Moomz - thank you for the link, I had a look and followed the number link, then 'Lisa's method - ratio. I think you need to make a couple of changes as the example on there is wrong - sorry, hope you don't mind me pointing it out)

16. ### Moomz

Thanks moved. Not my website but will pass the info on.

Really liked your article cffoster!! Have you written others?

18. ### hardlife

What a great set of articles Mr Foster - very prolific! Loved the one about your school phone number - sounds like a great lesson. How an earth did you go about producing the formula?

19. ### Owen Bentley

With low ablility groups why not rum a betting shop with various runners at variious prices (start at eens 2:1 3:1 5:1 10:1, then if they get good at that then you could introduce odds on ie 1:2 1:5 etc. It gives them a very good insight on how ratio is used to divide up quantities.

20. ### cffoster

hardlife - it was a while ago; I think I found a website which would fit a polynomial to a curve and used that, to save time, if I remember rightly. 'm sure I could find it, or something similar, again - happy to do your phone number for a small fee!