# Transcript of What's new – number and algebra

Katherin Cartright: Thank you very much. So welcome, everyone, to our third session of Syllabus PLUS for this term, this year, and today's session is on 'What's new: number and algebra'. I'm here with Chris Francis. You can hopefully see her just in the background. And we'll start our session now. So, welcome.

So today's session is on what's new for number and algebra. This is the first one of three, I guess, in our little tiny series within our larger series that's going a little bit deeper into each strand of the K-6 maths syllabus. So today is on number and algebra. Next week is on measurement and geometry. And then the last session, the week after that, is on statistics and probability. So our syllabus states that number is about quantifying and describing the world. That's how we use numbers in everyday. So our students are encouraged to develop number sense, to use mental computation strategies in all stages, and to explore number and prealgebra concepts. So this is sort of the essence of what number and algebra is about. And, as people might know from our current syllabus, number and patterns and algebra were separate strands and they've now been combined back into one as in line with the Australian curriculum. So we haven't lost patterns and algebra, it just exists as a substrand within numbers and algebra.

So if I have a look at the organisation of content, we're used to this kind of concentric circles diagram in primary, and you can see that number and algebra sits down the bottom. So the diagram shows the scope of the strands and the substrands and it also shows that central role of working mathematically. You can also see that our diagram now has the 7-10 substrands. They were previously referred to as 'topics'. They've now taken on board the same terminology that we use about substrands, and I think this is really helpful to see where some of these substrands, or topics, go and develop into Stage 4 and, obviously, then into Stage 5 and into Stage 6. The picture, if you're not familiar with it, is not indicative of the time spent on each of those substrands. We do still see number and algebra as the most important strand, so it probably gets a bit more priority than the other two. But just so you have an understanding of the whole scope, this is a great diagram to have a look at.

So overall, what's new for number and algebra in Early Stage 1? So there's not a whole lot of changes for Early Stage 1 in our new syllabus. Most of the information and the content is the same as what you're currently teaching. But in whole numbers, there's a bit more of a focus on correspondence between collections, so the idea that the students compare how many they have in comparison to how many somebody else has, so maybe the person sitting next to them. So that example there of "I have four counters, you have seven." So it's seeing the difference, whether they're using addition or subtraction or just visually looking at that, that's something that's a little bit new for Early Stage 1. The use of the term "is the same as" to express equality of groups. Now, this isn't particular new. It exists already in Early Stage 1, but it's been moved to whole number. So that used to exist in another substrand, so it's been moved across. And it is also something that continues through our whole syllabus, which we'll have a look at in a moment. But that whole idea around seeing the equal sign as actually like a balance, I guess, thinking that "is the same as", so both sides need to match - not be exactly the same, but that they have the same value. Also in patterns and algebra there's the use of the word 'classify'. They have to be able to classify groups of objects into smaller groups, and they have to be able to explain how they've classified the objects. Now, straightaway when we read this, we had a link straight to 3D objects. So we think that is somewhere that it could match up nicely if you're looking to scope and sequence whole numbers...sorry, patterns and algebra, you could do it with 3D space, because that whole idea of sorting is something that's also mentioned in that strand.

So I mentioned that term "is the same as". So in our session today we're just going to show you a few examples of learning development. So it's not necessarily the learning continuum through the one substrand, but some of these topics or concepts appear again and again throughout the syllabus, and particularly with things that are new, it's really important to see, well, where do they go or where have they come from? Particularly if you're in a different stage than what you're used to, you need to have an understanding of how that concept develops not only within its substrand but across substrands. So I mentioned that in Early Stage 1, it's now in whole numbers, "is the same as". In Stage 1, it now appears in multiplication and division, and it talks about how 3 groups of 4 is the same as 4 plus 4 plus 4, so it's relating grouping strategies with repeated addition. In Stage 2 it appears in addition and subtraction, where we're looking at "is the same as" when you're looking at two sides of an equals symbol. So you've got 32 take away 13 is the same as 30 take away 11. And our students do struggle with that idea of balance on either side of the equals sign. They're so used to seeing it as the answer and not as that balance. So we need to really bring that out in our teaching and show them examples of what we mean when we say "is the same as". In Stage 2 it also appears in multiplication and division. And it appears when we're talking about factoring. So when you see 5 times 8, they can then factor 8 down to 2 times 4 to then help with your working out. If you don't know what 5 times 8 is, you can change it to become 10 times 4, and that might be something that's easier to work out because the student knows, you know, on the decade counting. So there's a really flexible use of this concept within number and algebra as a whole strand. We also see it in Stage 2 in fractions. So it starts to talk about, you know, that 0.1 is the same as 1 tenth. So there's not...it doesn't just sit in one substrand. And then in Stage 3 it actually starts to apply to other areas. So in this example here, it's looking at time, and that 15 minutes is the same as 15 sixtieths of an hour, which is the same as a quarter of an hour. So it's looking at units of time as well, and that equivalent fractions, so there's a whole lot of other concepts that match up together that you could teach around this kind of concept.

So an example from Early Stage 1 - we wanted to give a little example of lessons you could still use. So this is a lesson from our 'Talking about patterns & algebra' CD or ebook, as it now exists. That little image on the left there is actually a hyperlink, so if you want to click on that now or later on, you can, to be taken to where you can download that ebook. So this is a resource that currently fits with our current syllabus, but you can also use it within the new outcomes context. So this activity is all about using the term "is the same as". And the students make posters to describe different ways that we can represent the number four. Now, obviously you can make that a lot more complex for as you go into higher grades, and particularly when we talked about fractions and decimals, you could make a poster or cards that represent those as well. So it's a nice visual activity that helps students understand what that term really means.

So we see it in Stage 1, where they have to be able to use both of the partitioning standards of...standard and non-standard forms. But we're just giving you some examples here of the non-standard partitioning. So 32 can be seen as 32 ones or 2 tens and 12 ones, as well as just the usual 3 tens and 2 ones. So it's just using it for a different purpose. In Stage 1 it also appears in addition and subtraction where they're partitioning numbers to aid with addition and using their place value knowledge to help with that. It also appears in Stage 2 addition and subtraction, where they're again using non-standard forms with 3-digit and 4-digit numbers to aid with addition. So it's just another one of those skills and strategies we want to build within our students, different to "count by one" strategy, or different from just partitioning because it's in tens, hundreds or ones. Also it appears in fractions and decimals, so they also now need to be able to partition decimals up to two decimal places into non-standard forms, so it's seeing how that decimal appears as a whole number and a fraction, or part of a whole number as well. And in Stage 3 it appears in whole numbers as the numbers get larger, of any size. But not only are they asked to do it, to present the numbers in non-standard forms, it's to aid in their mental calculation, so it's actually giving a purpose and a use for doing that. And we really want to encourage that throughout the whole of the syllabus as you present the idea of non-standard partitioning into different...different ways that the students are problem-solving. So it's definitely something that's new and it's a concept that will need to be developed along with standard partitioning.

So this is a little bit more in-depth into the changes. I won't go through this in a large detail during today's session because it's a short session today, but you can go back and have a look at this later or if you came or watched the first of our series, I gave you a document, an Excel spreadsheet, that had a lot more detail around this. This is just highlighting some of the ones that we think are really important. There will be links, as mentioned, in the chat today to the previous sessions, sent out with the link to this session. So you won't miss out if you haven't seen the previous two sessions. So you can just see I've just broken it into the substrands within Stage 1, what it looks like in the current syllabus, and if there's nothing there, it means that that content doesn't exist currently in our syllabus, and then where it appears in the new syllabus. So there are some things in there that are a little bit new for Stage 1. Particularly around equivalent values of money, there's some moved content from patterns and algebra. There's that difference between sharing and grouping. fractions now includes eighths. And there's also a little section there about combinations in addition and subtraction - that it's not just combinations of 10, it's up to and including 9, and from 11 up to and including 12.

And that's where our example comes from for Stage 1. So we've titled it "Friends of everyone!" So we're not just trying to teach friends of 10, we're trying to teach friends of all those numbers all the way through really to 20, but particularly of 6, 7, 8 and 9. So, often we find that we just teach friends of 10 and it's great, the students end up knowing these combinations, but then don't really know what to do with them. Well, what are they used for? So again, this is a little activity from the 'Talking about patterns & algebra' ebook that's really quite useful. So it's just rainbow relationships, and you can see the picture there. They're just making a little coloured rainbow to find the pattern and to look for combinations to 7. But, obviously, you can do it for all of those numbers. And, you know, what do we use them for? Why do we need to know how to partition those sort of numbers? And, you know, I've got that little example there. If I know that 2 plus 5 equals 7, then I want to be able to use this knowledge to solve more difficult problems. So if I had the problem 18 plus 7, we want them to be able to see, "Well, I can break that 7 into the 2 and the 5, and I can then see 18 plus 2 plus the 5, and they might then, you know, add the 18 and 2 to get 20 and then add the 5 on. So another strategy they can use. And there's a little example there that's helping them see that it is the same as. You know, 18 p;us 7 is the same as 18 plus 2 plus 5. So it's just another non-"count by one" strategy that we really want to build up with our students.

So our example of learning development here is that idea of using concrete materials or visuals to aid in understanding fractions. So I mentioned there was a lot more pictures or visuals in the syllabus, and here are just a few of them. So in Stage 1 they're asked to record the halves using drawings. In Stage 1 in fractions and decimals they're also asked to use concrete materials to model half, quarter or an eighth of a whole object. In Stage 2 they're asked to model the fractions and to model the objects, shapes and collections using concrete materials and diagrams. So it's really asking them to get that visual representation first before they actually do anything with the fractions. And then in Stage 3, they're asked to express mixed numerals as improper fractions through the use of diagrams and number lines. And it's leading to a mental strategy, so that idea of being able to visualise first helps them understand, "I'm making a picture in my mind when I'm trying to do this in my head." So I think that's really, really important and I love that they're using more and more diagrams for fractions, because it's definitely an area that our students struggle with.

So what's new for number and algebra overall in Stage 2 you can see from the current syllabus and the new syllabus. They now use 5 digit numbers. That partitioning is strong again in Stage 2. They're calculating equivalent amounts of money. That focus on fractions and unit fractions. Percentages have moved. And they're asked to make these generalisations about number patterns, including multiples and odd and even numbers.

There's also a new focus on using the area model as one way of showing a visual representation of how to multiply two numbers together. So if this is something new to you, it's really good to start investigating, "Well, what is it? How do I do it? And how do I use it with my students?" So it's basically just...it helps link to that algorithm. So I think we don't want to jump too quickly. The algorithm doesn't appear until, I guess, the later part, so the part 2 in Stage 2. And there's a reason for that - we really want students to understand the concept and the place value of those numbers. So, often when students jump into, like, vertical algorithms, they start seeing them as single digits again and start having that conversation around, "Oh, I just put the zero here," not understanding why they're doing it. So if you want more information on that area model, I've created a little "how to" video. That's not a hyperlink there, just a reminder that you can download my video from the file pod at the end of the session today.

Stage 3 - as I mentioned, large amount of content change for Stage 3. There's been movement of a few concepts from Stage 4, OK? The Australian Curriculum wanted to have those as a focus for Stage 3, and so we had to move content down to Stage 3 from Stage 4, remembering that they still deal with this again in Stage 4. They're not going to have a gap that they're not going to fill ever, so any of these topics are touched again in Stage 4, so things like factors, order of operations, some work with decimals, and the cartesian plane. So there's also a large number of key ideas and concepts in fractions and decimals, so again that focus on fractions and decimals. And there's also a bit of a focus around modelling and representing strategies when they're solving fraction problems. And as I mentioned before, percentages have moved up to Stage 3 only.

So there's some information there. There's quite a lot of this information. I've got two slides representing information for Stage 3 just to give you a fuller understanding of what's new and what's not. There's some terminology as well around integers, and some more partitioning that's happening, factors, highest common factors and lowest common multiples. And I think these kind of focuses are a really nice opportunity to link in with your feeder high school, or if you are a K–12 school, if you're a central school, get in touch with those people that are teaching the upper grades and maybe get a few lessons from them about how they effectively teach these topics within their classrooms.