Teaching Ratio to Low Attaining Students

Last week was internal observation week at Sidney Stringer Academy. After the stress last year of a looming Ofsted inspection (which we passed with flying colours), this term's observations were met with a lot less panic. The maths department certainly seemed more laid back than usual.

 

For mine, I was being observed with my year ten class. This class is aiming for grades G, F or E at GCSE. Most of them have a Roma background, and they all have their own barriers to learning to overcome. I have taught this class for over two years now, so we know each other pretty well.

 

The topic I was due to teach was ratio. I had a double lesson, and spent the first hour introducing the idea of ratio. In the second hour, of which the first thirty minutes were observed, I taught them how to share a quantity in a ratio.

 

My observers graded the lesson as "outstanding", so I thought other people might be interested to know exactly how I taught it.

 

My class had recently been working on times table facts, factors, and multiples. I knew that these areas were fairly strong for them. I also knew that the concept of proportionality, including fractions and scale factors, was a weak area for them.

 

I gathered the class around one big table in the middle of the room. I like doing this because it feels a bit primary school-y. There are only 14 students in the class so this wasn't too squashed. The students did not bring their books with them, there was no need for them to take notes.

 

I handed out a whiteboard and pen to three specifically chosen students. They were chosen because they were unlikely to contribute to the discussion, either because they were too shy, or likely to be disengaged.

 

I told the class I wanted to share a bag of 24 sweets (counters) between the oldest and youngest member of the class. These two girls were conveniently sitting on opposite sides. I explained that I didn't want to share them equally, because I thought the older girl deserved more than the younger girl. They seemed to be happy with this idea. I said I wanted to share them in the ratio of 3:5. They had seen this notation in the previous hour (remember, this was the second half of a double) and knew vaguely what this meant.

 

The three whiteboard holders had the job of recording what was going on. One student was to record the number of counters that the youngest had, one recorded the oldest's number, and the third recorded the total number of counters that had been given out.

 

I started to give out the counters. I gave 5 to the eldest, and 3 to the youngest. The recorders dutifully wrote 5, 3 and 8. Then I gave out another lot of 5 and 3. The numbers were changed to 10, 6 and 16. Then I gave out another lot and we had 15, 9 and 24. I asked the students to comment on any patterns they had noticed. Many of them spotted the 5 times table and the 3 times table, and amazingly they even noticed the 8 times table. I took a mini whiteboard and drew a little table to show the numbers at each stage. This was me modelling how to lay out their working out when it came to doing it themselves.

 

Next I told those with the boards to pass them to someone else, and I took back the counters and added some more to the pile. I picked another two students to share between. I picked a new ratio, and again said the older of the two should get more (please tell me I'm not the only teacher who has memorised their students' birthdays! Not on purpose, I hasten to add). I did the same thing again, and students were telling me the numbers before I even managed to give the counters out. That showed me that the students had managed to move away from the concrete towards the abstract already. Again, I modelled how to write down the solution. Then I said to them, "Are you ready to do this by yourselves?" and they all responded yes. Then they all went back to their seats and did just that. They tackled the questions wonderfully. They were all happy to have a go.

 

Here are the worksheet used and some examples of the students' work:

 

 

This student was very confident with the method.

The sentence at the bottom of the page demonstrates that this student knew what they were doing.



This student did the times tables up as far as they thought they needed, and ended up with too many to add to make 50. This doesn't matter though, they can cross out the ones they don't need. "Mistakes" aren't punished in my class.

 

In my feedback, I was told that this lesson was effective because:

• It was very simple
• Every student was engaged
• Every student was motivated and eager to learn
• The lesson was pitched at the right level
• The method built on the students' prior knowledge.

I know this is not the traditional method for sharing in a ratio. It is long winded and a bit ridiculous when it comes to numbers over 100. But I knew my students would understand it. The normal method is to see 3:5 as 8 "parts" and to divide the quantity by the number of parts to work out how much is in each part, then multiply by 3 and 5. Can you see that this method is a lot more abstract, as it talks about "parts"? Although this can be faster, I feel that it is more confusing, and hence difficult, unless you understand the rationale behind it. For a group whose average KS3 level was a 2a, my method was a lot more appropriate.

 

I hope this lesson "plan" can be of some use to you. My actual formal lesson plan is available on request: email me at ecooke.staff (at) Sidneystringeracademy (dot) org (dot) uk. (I'm writing this weirdly to avoid spam robots).