Ramblings for the classroom – Week 14 – Final for 2019!
This week I took a bit of a leap and have used my Cuisenaire Rods and the visualiser to model different areas of ratio. I hadn’t really planned to use my ‘concrete’ representations in class this term and had bought them after reading ‘Teaching for Mastery’ by Mark McCourt (@EmathsUK) and ‘Visible Maths’ by Peter Mattock (@MrMattock) over the summer and actively wanted play about them when I tried out different techniques.
Whilst i am thanking people another massive support has been the great website created by Jonathan Hall (@StudyMaths) as this site has really helped me in making this leap to using visuals in my teaching. Using the equation solver has been a highlight in my teaching this year.
The first lesson of the ratio topic I had used the bar modelling on the above site and showed how to simplify and express in the form 1:n. As I was just about to start delivering dividing into ratio I spotted my visualiser and the Cuisenaire rods in the corner of my eye and decided to model with them.
I had not pre-planned this so the examples I am using, on reflection, would have been slightly smaller number wise to save all the blocks. I started by putting this on the board.
Whilst most students could give me the answer 9:15 when I then further probed their understanding their general response was that they had been taught a method of adding 3 and 5 and then dividing and then multiplying the ratio. They had no concept of what 3:5 actually meant.
I started with single white blocks then formed the bars underneath.
Above is the finished modelling on this first example with students explaining why their were three rows. I felt at this point that some students were still struggling to see the value of the green, yellow and brown bars so did one further example and really focus on my explanation throughout the steps.
I wrote share £48 in the ratio 2:4 on the board and started with the following model.
We had a discussion then about simplifying the 2:4 to 1:2 but decided to leave it as 2:4 for this example. I showed that if we took the red 2 block as 1 unit then 4 would be equivalent to 2 red blocks in effect 1:2. Once we had decided to use 2:4 (we could have used 1:2) we then had a discussion about why we combined the 2 and 4 parts.
As we had now modelled two of these examples together the students were beginning to want to generalise their approach. So I took a snapshot of the visual from the visualiser and then annotated over the top of this.
We then finished off by modelling the more abstract steps clearly embedding the visual steps.
The students then worked through some questions independently and I revealed answers at regular intervals. All the ratio questions are available on the site here.
I can hear some teachers in the edutwitter world thinking why would you just not model the example on the board? It would be covered in five minutes instead of this which took around 15 minutes. My argument would be that none of my students really understood what a ratio was and I was building on sand which meant when I was looking at different types of ratio question they would then struggle I just learn another method they could retain but any variance to that would stump them. I remember a couple of years ago when the ratio ‘difference’ questions started in the new GCSE I was initially stumped – Adam and Ben shared money in the ratio 2:5. Ben got £33 more than Adam. What did Adam receive? I admit I solved this be counting up in equivalent ratios until there was a gap of 33.
Once this lesson had finished I felt I needed to connect the visual to the process slightly more clearly and a twitter conversation I had with Dave Taylor (@taylorda01) earlier in the year about modelling the visual and the method side by side. The next sets of slides show the second lesson.
We started by discussing why a fourth bar was not needed for this type. The importance of labelling each ratio part above it. The aim to get £18 for Ben and then the associated number of rows. I then took a snip of this and then annotated the numbers over the top to reinforce the solution.
The final lesson was looking at the ratio ‘difference’ questions
I started modelling with same routine from the first two lessons. Then put Ben and Charlie’s rods side by side to prompt a discussion. As this was the key teaching point I then moved to annotating on the board over the next few steps.
As I then wanted to check student understanding I used a KAGAN routine of Sage and Scribe where student pairs take it in turns to explain the question (Sage) to their partner (Scribe) and they then write the steps in their books. You can also see the modelling I left on the board to support.
Bit of a thought vomit of a blog this week probably due to the brain being a bit scrambled after 14 weeks of teaching! I think these 3 lessons have now totally converted me into the power of using models in the classroom as they show very clear connections across multiple areas of maths and the similarity of methods within topics too.
Thanks again to all the educators I’ve engaged with this year and wish everyone a good last week in school. Bring on 2020!