Scheming, Part 1: Sequencing Topics and Prerequisites

I have probably spent about 40 hours in the past two weeks working on my scheme of work.

I started with the base scheme of work from my first school in Highgate. It stands out amongst schemes because it spends just 2-3 lessons on each ‘unit’ before moving on. This isn’t because it tries to pack in the whole syllabus into two years, but because each ‘unit’ consists of just one major new idea.

I really enjoyed teaching this way and was surprised when I first found out that other schools spend around a month teaching one narrow around area of maths before moving on to a different area. I wonder how on earth the students are going to remember a topic that they last studied two years ago. If you teach in small blocks, the difficulty is that pupils may not remember the prerequisite material. However, this forces you to constantly recap and provides spaced-practice by default.

So, what have I done to improve (in my opinion) on Highgate’s scheme? I have put a lot of effort into checking that the topics flow well from year to year, with each new ‘unit’ introducing a similar amount of new material. I have referred to some other schemes in the process:

I used these mostly to give me an idea of what year group pupils usually meet a topic. Jemma’s scheme in particular gave me new ideas of the key points within a topic and helped me to break down some of my topics more carefully. Where I needed more help on this, I also asked for help on twitter. This poll was the culmination of loads of great suggestions I received on teaching HCF and LCM, which led to me introducing a section on algebraic forms of these as a prerequisite to factorising, adding algebraic fractions and more.

Some of my considerations in designing the scheme were:

I don’t want to recover material that pupils have already learned at primary school, so I haven’t included the lessons on basic number and geometry that many secondary schemes do. Instead, I will check pupils’ prior understanding when introducing new topics as part of my planned mastery approach.

I want my scheme to only list each new idea once. Of course, there will be need for review and if necessary, reteaching, but in general, I really dislike schemes which have exactly the same ideas in two different places. I want to know what the pupils should have already learned (even if they haven’t fully learned it!) and what’s new.

I tried to put at least one bit of each ‘topic area’ in each year group. I feel that this is generally a good idea, as pupils have to see a topic each year and so have an opportunity to recap it. It’s also particularly important in my international context, as we have a higher turnover of pupils, so it will allow me to get new pupils up to date with each topic.

I don’t want to accelerate higher-attaining pupils and I don’t want to finish teaching before Easter in year 11, so the ideas are spread evenly throughout the 5 years.

I used specifications to mark the topics which only feature on the higher tier. With a few exceptions, I made sure these topics are in year 10 and 11 so that if I decide to enter pupils for the foundation tier, they will be able to spend more time on the other topics in these final two years.

So, the final product… You can see / download it here:

I’d really welcome any criticism to this as it’s definitely still a work in progress.

In particular, I’m working through the geometry tabs to check that I have listed all the relevant prerequisites. I’m also aware that while the topics are very interleaved, there is little genuine interweaving of them.

3 thoughts on “Scheming, Part 1: Sequencing Topics and Prerequisites”

  1. In answer to a question I was asked on twitter about how I decided which primary topics to exclude (

    I tried to exclude all the ideas that are explicitly covered in primary, but I may have missed some. I used schemes of work from our school’s primary section, which is our main feeder. I am still planning to confirm a few question marks with the primary maths lead.

    One specific case: adding fractions, does feature in our primary scheme, but I wanted to include it (in fact twice) as pupils often arrive in secondary without full understanding of this.
    In such cases, a try to add a new idea which they should not have met at primary, in this case using the LCM to find the best denominator.

    I agree that it’s sometimes the case that pupils arrive at secondary without secure understanding of some of the primary curriculum. But they also arrive in year 10 without secure understanding of year 9. As I mentioned in my blog, I’ll be checking prior knowledge at the start of every topic, and teaching those who need it. But this way, I won’t be encouraged to repeat a topic with a whole class, of whom many have met all the ideas before.

    1. Thank you for your reply.
      When going through our Y7 SoW we realised that probably half or more was Y6 work. We are looking at doing something similar to you – recapping these topics in a homework a couple of weeks before we would have taught the section to allow us to move quicker for work they can recall and to teach work they aren’t as secure with. We haven’t started yet but I do predict that we will have a mixture of those who are fully secure and those who haven’t a clue. How we make sure we can still move quicker than before whilst not leaving the strugglers behind is our next consideration.

      1. Recapping a few weeks before sounds like a good idea.
        I don’t think you have to move quicker as a result of this, you can spend longer on the ideas which are genuinely new to ensure that they’re really well understood.
        I expect to have to reteach some of the ideas which are covered in primary, but only to those pupils who need it. Whilst doing that, I’ll give the others extension tasks on those primary topics, bringing everyone together before introducing the new concept. This will take time.. I hope I’ve left enough but I will be flexible if I can’t get through my full schedule in y7.

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