How an academy trust is building a maths curriculum using Oak

- Our trust, for the first time, has kind of been getting involved in planning lessons for teachers to have a common assessment, common materials to help with their planning and help with their time, essentially. The big thing was, we were looking at the DFE non-stat guidance, and obviously the Oak materials work alongside that. So we were thinking we wanted to position all of the schools in a place where they've got support from CPD, from the maths hubs, where they've got additional materials from Oak and other places. So when we were putting our lessons together, we were thinking about the journey, making sure it's coherent, obviously. So the materials we used, we tried to plan around making sure each lesson linked as effectively as we could. We know that, obviously, we don't know each of the individual students, so we still sort of put an expectation on the teachers that they adapt to the materials we put, and they might need to do a little bit of prerequisite checking, but the materials that we are providing, the idea being that's the basis that they can go from. So this is a lesson that is gonna come up quite early in the year seven materials. This is gonna be about multiples with integers. So we've left intentionally these do-nows blank. I know that the Oak materials do provide opportunities with the starter quizzes and exit ticket quizzes. And we've said to the teachers that if they want to use them, they can use them. But I didn't want to dictate, because it depends on obviously what's happened before for those students. But we signposted them to those starter quizzes to say, look, if that's something you want, that's there, but I'm not gonna tell you what's in those materials. So left those blank. In terms of the outcomes of the lesson, obviously they're quite clear here, just in terms of thinking about, we want the students here to be thinking about the multiples of given integers and sort of checking whether something is an integer, sorry, checking whether something is a multiple or not of a specific integer. In all of our materials, we've kind of put a link to what's come before. So we'll often use like a story slide saying, "You will have previously looked at," and I'll give you an example that we'll see in a minute. So we've talked about here this, or we mentioned earlier, sorry, about this importance of different representations. And the array is obviously one that comes up quite early for our students. And you can see at the top of the slide there, we've said, "The array is an important representation that you'll be familiar with from primary school." We really wanted to link that back. And I know that's something that, in the design materials from Oak, that there is that explicit reference to primary school before that. And throughout a lot of the materials as well there's examples and non-examples, the idea of conceptual variation. It's important to show what something is as well as what something isn't. So when talking about the array, we wanted to show, obviously, here's some examples of arrays. Here's some non-examples of arrays. So we thought that was really important to get those in, because I know in the materials that we used from Oak, for example, they talk about the array quite explicitly, and they give examples and non-examples all the way through. We also wanted to go a little bit further. So where we've adapted it is we've kind of put, why is this array in here? Why is it an important representation? We've kind of gone, to quote something from the office of coordinating mathematical success report, the forward facing methods and approaches. So for us, this was thinking about, where does this lead to as well? Well there's a cross-curricular link when thinking about computer science. Many of the students are really competent at programming, much more so than when I was at school, and so we wanted to make that reference explicit. And then also thinking about how this is gonna come up in key stage five mathematics and beyond, thinking about things like matrices, and Markov chains, and so on and so forth. So these are the bits where we explicitly use some of the oak materials. Those clear definitions that focus on language was really important for us. So you can see at the bottom here about the origins of different words. We wanted to make sure that students are really explicitly learning the terminology and that they're speaking like mathematicians. We don't want to dumb down any of our language. And we also think that etymology is really important, and that comes up, that sort of history. And that maths isn't just this western, very western centralised subject. It's something that's international. And so in some of the other materials, things that we've taken across, for example, is where it talks about the history of algebra, think about the numerical system and how that's come from the Islamic world of mathematics from the golden age of maths. So here you can see, these are things that we've taken directly across that representation, but also having it alongside the more abstract terminology. We think it's really important developing that fluency, and these materials, it shows, well here's three, here's six, here's nine, here's 12. We can see it's a 4x3, we can see it's a 3x3, but you've also then got it written explicitly in mathematical notation. So you can see them alongside each other. We want to make sure that students obviously understand this in full. So we're giving multiple examples here in terms of, well, you can list the multiples, you can physically see the multiples in terms of an array, but you can also write out the multiples by just using your times tables. This is something that we took directly, again, from the Oak materials, which is those think pair shares. And I've mentioned before about developing mathematical thinking. And this is an example where we felt like it's really easy for us to come up with think pair shares that are really broad and not focused on something specific. And this one here, with these, I'll call them talking heads, you've got the opportunity for students to actually read out these materials as well. So the students are being engaged directly as speakers and they're playing these characters. But also it's that opportunity for them to really hone in on, well what is a multiple and what is a multiple not? Earlier on in the materials there was, as I said, that key terminology about a multiple being a product of two integers. Well here we've got an integer and a non integer, so it gets students to really talk about that, and it focuses their attention, and we think that's a really important thing for them in terms of the mathematical thinking. So this gives them an opportunity to actually talk about and discuss the mathematics. Now obviously we adapted a lot of these things in terms of, we didn't use all of the think pair shares, we didn't use all of the exposition stuff, but we thought it was really important to pick out the bits that we felt were most important to us. So like here, just building on that understanding of when something's a multiple and when it isn't. So we've got some examples here of other things where they're now modelling this idea of multiples, either using arrays, counting on, think about multiplication tables. And this, again, is that multiple representation idea. Now this isn't necessarily method, I think it's really easy for people to mistake the idea of a representation as a method in mathematics. We want people to see these representations, but when it comes to the actual written mathematics, this is where we might use something like an example problem pair. So this is something different that we added in that that wasn't already in the materials. There are some examples of example-problem pairs, but we were really explicit, and this is something that our teachers wanted more of. So we thought, well, if we've got all that teacher exposition beforehand about getting them to, I'll call it the orientation, we're orientating them to understand the mathematics. We also want to develop in tandem with that the procedural fluency. So this is about them really then developing, how do we write and communicate mathematics on paper rather than just verbally? Because both of those things need to happen. So this is where we put some example-problem pairs through, and we were really thinking about that metacognition as well. So what is it that people are thinking, getting 'em to reflect on what's changing. And we want to model that thinking for our students. So then when they're doing it, they've kind of got a framework to work to. So that's the stuff that we adapted and put in alongside some of those materials. When it comes to the independent practise, there is a lot of independent practise in all of the Oak materials, but in terms of some of our lessons, sometimes we use those, if we felt like it was just something we wanted to quickly do some practise on. But sometimes a lot of our teachers feel more comfortable with a sustained bit of practise. So what we did was we used some other materials from other providers where we thought that then gave them that sustained practise. Sometimes we took some of the tasks and turned them into a mini whiteboard task, or we turned them into a think pair share, for example, or maybe an extension sometimes, because sometimes we felt it was above and beyond. So you can see here, this is now where, again, this is taken from the Oak materials and this is just a development of that array and that idea. With the remainder of our materials, one of the things that our trust is really keen on, A, it's high expectations, but also the opportunity to give students the chance to study maths beyond just the curriculum. We didn't want to say, "Right, you've met the curriculum, fantastic, go and enjoy the rest of your lives." We wanted to make sure that we're giving every student the opportunity to study maths further if they want to, take part in competition maths, if that's what interests them. And so these are the bits that we added on. We still felt like we needed to add in some extension. So we've put in like some of the UKMT materials and absolute classic Don Stewart in there as well. But that's where we may maybe added in bits that we thought added a little bit of bringing it to life. And to use the phrase that I've mentioned to a number of our teachers, whilst these materials are, this is very two dimensional for them, it's still their job to make them three dimensional and bring it to life. And this is where we've tried to add in some of this stuff. We've also added in some excursions, I will say. So if there's teachers that want to go beyond, and tell some stories, and build on some of those ideas, like in the algebra section, we've really added in tales of infinity, and the background and the history of the mathematicians. And that was kind of built on, and I'll be honest, what informed me in where to start to go then researching for myself was looking at the materials. I was like, right, that's a place that I can start and build on. We've ended the lesson thinking with one final think pair share, because we thought this was a nice task to just check how well students have done with those. So I thought this was a really nice task. I hadn't decided exactly where I wanted to put it, but it was something that I didn't want to miss out. So teachers might move this earlier, but I thought this was a different type of task when thinking about the multiples, because it's not just a case of list them, it's a case of them having to understand how many gaps have happened, So halving those gaps, for example. And again, that goes back to that mathematical thinking element. Finally, where we've then adapted a little bit further, our trust is really keen on making sure that students are exposed to exam questions wherever relevant. The main reason being, we always think we've got two things to develop, develop great mathematicians, but you can be a great mathematician, but not necessarily also be exam ready. So we thought, well we've gotta cover both those bases. We didn't wanna do one in absence of the other. So this is where we thought, well, if early on we're putting in questions, just so students know, particularly for some of those lower attaining students, it gives them that confidence. So we've put in some GCSE foundation exam questions just so they can see, well, look, you've now already gained yourself a mark in a GCSE paper just from this really early year seven content. We want to push teachers away from thinking about GCSE as key stage four only. GCSE is a culmination of all the knowledge that you've ever gained from your whole maths career to that point. So we felt like if we're putting this in, it's really making that explicit. And then finally finishing an optional plenary. Or the other one is obviously, as I've mentioned, there's the exit tickets that are available on the Oak materials, which we've not put in, but we've said to teachers, if that's what you want to use, that's there. It also means they can collect data on it if they want to. So yeah, that's an example lesson of how we've thread through some of the Oak materials with a mixture of, as I've said, Don Stewart, something from some other commercial publishers, and also some things just from teachers in our own heads. But that hopefully gives you an idea of how we've maybe adapted some of these materials to support our teachers in what we think is the best way, anyway.