Transcript of New content in the stage 6 mathematics standard syllabus

Mathematics new content

Speaker: Amy Birungi

Hello, everyone. Welcome to this afternoon's session - New Content in the Stage 6 Mathematics Standard syllabus. My name's Amy Birungi. I'm the mEsh project officer for mathematics and I'm here... You can see her in the background there. I'm here with Ruth Glasgow, who's the mathematics adviser for 7 to 12. So there is a chat pod going to be open throughout the presentation and then there'll be an opportunity for you to ask questions at the end. So the purpose of this session is to provide information about the new content in the syllabus. We have put up there that we recommend that you have a copy of the new syllabus and a highlighter for this session. However, if you don't, you can still participate. A recording of the session will be put up at the end so that you can go back and watch it again if you need to.

OK, so let's get started. We're going to go through in order, from Year 11 onwards. So the main changes to the new syllabus, first of all, is that there is some new content that's not been covered in either Year 11 or 12. And the other thing that's happened is that there is some similar content to our previous syllabus, but it's been taught in a different year to previously. We're not going to touch on that in this session, but I'll talk to you about how you can access a supplementary recording that shows you that content. So we're just going to go through the new content today.

We're going to go through it very systematically and hopefully slowly enough for you to be able to get it all down if you happen to have a copy of your syllabus with you. One thing that we do want to talk about before we get into the syllabus, though, is the use of the phrase 'including but not limited to', which appears at least about 13 times across Year 11 and 12 in the new syllabus. I've got an example of where that appears that's from MS-A1 Formulae and Equations, which is in Year 11.

What you'll notice is that this is a dot point that asks students to review the substitution of numerical values and nonlinear algebraic expressions and equations. And in that last dash point there, it asks students to solve problems involving formulae "included but not limited to", and then it goes on to give examples of the types of problems that you might look at there. What we are encouraging teachers to interpret that as meaning is that we would advise that you look at all of the examples that appear at the end of that dot point. So we would suggest that you solve problems involving formulae to do with calculating distance, speed and time, or calculating stopping distance of vehicles using a suitable formula but to not restrict yourself to only looking at those. So we would encourage you to look at those plus others that you might think would be relevant to you and to your students and your context. We're not going to touch upon where those appear throughout the syllabus today. But as I said, it appears about 13 times throughout, the first example of which being from MS-A1.

OK, so starting with Year 11, what I'm going to do is just present, basically, the pages that have new content as they would appear in your syllabus. I've put the page link at the top so you can flick to the relevant page and highlight the relevant sections. So the first new content appears in MS-A2 Linear Relationships, which can be found on page 30 of your syllabus. So in that last dash point of the first dot point, it asks students to construct straight-line graphs and what you'll see, the new content there is "with and without the aid of technology". So a lot of the technological applications previously were in the Suggested Applications section of the support document, but they've now been included within the syllabus. OK, looking at MS-M1 Applications of Measurement that can be found on page 32 of the syllabus, students are required to investigate types of errors. For example, human error or device limitations.

We accept that a lot of teachers might have looked at this in the past. But this is... [INAUDIBLE]. Just in that note there on the third dot point, there's a new standard form. And you'll see the note there says "standard form replaces scientific notation." So the terminology of scientific notation is no longer used and we're going to go direct with a standard form from now on. In the first dot point in 1.2, it says...just a note there to say that, with regards to composite shapes, previously... [INAUDIBLE] ..composite shapes made up of two shapes. It doesn't put that explanation in, so we could assume that it could be more than two shapes.

OK, looking at MS-M1 Applications of Measurement on page 33. You'll see now that Year 11 students are required to derive the Trapezoidal rule for a single application and then use it to solve a variety of problems. In Units of Energy and Mass, students have to use metric units of energy to solve problems, use units of energy and mass to solve problems and use units of energy to solve problems. And you've got some examples for each there. OK, looking at MS-M2 Working with Time, which can be found on page 34, students are required to review using units of time, converting between 12-hour and 24-hour clocks and calculating time intervals. So, note that this is a review topic. It's something that students would have looked at in Stage 4, but we're now giving students the opportunity to go back and look at that again.

Another new inclusion is for students to review how to interpret timetables - for example, bus, train and ferry timetables - and to use them to solve problems. OK, moving to MS-F1 Money Matters, which can be found on page 36. In that first subsection on interest and depreciation, students are required to use a spreadsheet to calculate and graph compound interest as a recurrence relation involving repeated applications of simple interest. Going further on in Money Matters, students, under the section on calculating income tax, are going to be looking at tax deductions. And most of those deductions are things that students have considered before. However, not previously stated in the previous syllabus was HECS repayments. That is a new inclusion.

OK, still in MS-F1 Money Matters. We're now on page 37. Students, in the dot point "planning for the running and maintenance of a car", are asked to investigate other running costs associated with the ownership of a vehicle. For example, the cost of servicing, repairs and tyres. They're also asked to calculate and compare the cost of running different vehicles using a spreadsheet, so this is an elaboration upon the previous syllabus's focus study on mathematics and driving. OK, looking at MS-S1 Data Analysis.

We're now on page 39. You'll note down the bottom there where it says, "display categorical data in tables and, as appropriate, in both bar charts or Pareto charts". If you need some insights into what a Pareto chart is, the syllabus does come with a glossary that provides an explanation and there's also a wealth of information on the internet that you could look up as well. OK, still in Data Analysis.

We're now on page 40. In the dot point "interpret and compare data by considering it in tabular and/or graphical representations", students are required to choose an appropriate tabular and/or graphical representation to enable comparisons. In MS-S1 Data Analysis, we're still on page 40, but we're now in S1.2, which is exploring and describing data arising from a single continuous variable. Students are required to describe the distinguishing features of a population and sample. They're asked to define notations associated with population values and sample-based estimates, including the population mean, the population standard deviation, the sample mean and the sample standard deviation. And down the bottom there, students are required to investigate real-world examples from the media, illustrating appropriate and inappropriate use or misuse of measures of central tendency and spread. OK, looking at MS-S2 Relative Frequency and Probability.

We're on page 41. Students are asked to identify factors that could complicate the simulation of real-world events. All the rest is things that they would have looked at before. OK, so we're moving into Standard 1. This is the course that replaces Mathematics General 1, which was typically the... well, it's a non-ATAR course. So we're going to go through what's new in that course. The first topic in Standard 1 is MS-A3 Types of Relationships and can be found on page 45. So in this topic, students are asked to develop a pair of simultaneous linear equations to model a practical situation. In section A3.2, "Graphs of practical situations", they're asked to "Use values of physical phenomena. For example, the growth of algae in a pond over time, or the rise and fall of the tide against the harbour wall over time to plot graphs and make predictions."

Now, obviously, the type of graph that we would be drawing, say, to exact... to show the growth of algae in a pond over time would be exponential. Formerly, students were only asked to draw linear and quadratic equation graphs of linear and quadratic equations in General 1. Student need to sketch the shape of a graph from a description of a situation. They need to determine the best model - linear or exponential - to approximate a graph by considering its shape, using digital technology where appropriate, and they're also asked to identify the strengths and limitations of linear and non-linear models in given practical contexts. In MS-M3, Right-angled Triangles, which you can find on page 47, students are required to work with angles as previously, but this time they're being asked to answer either to the nearest degree and/or minute. This was previously only done in the General 2 course.

OK, looking at MS-M4 for Rates, which we can find on page 48, students are asked to use rates to solve practical problems. We've included this as new content because, previously, students were only asked to calculate rates. This time, they're actually being asked to apply their calculations to solving practical problems. OK, MS-M5 is Scale Drawings, which can be found on page 49. And the new inclusion there is that students are required to use ratio to describe map scales. So scale...scale drawings and reading scale drawings is not new, but it's the use of the ratios to describe them that is.

OK, looking at MS-F2 on investment, which you can find on page 51, students are asked to compare the growth of simple interest and compound interest investments numerically and graphically using digital technology. Likewise, they're asked to investigate the effect of varying the interest rate, the term of the compounding period on the future value of an investment using digital technology. In MS-F3 Depreciation and Loans, which you can find on page 52, the first dot point there asks students to calculate the depreciation of an asset using the declining-balance method. That's not essentially new content. It was previously in Year 11. But it was formerly only related to cars. Now that limitation's been taken away and it could be applied to... to a range of items. Students are asked to use digital technology to investigate depreciating values either numerically or graphically, and that is new content. When looking at reducing balance loans, they're asked to use a spreadsheet, and it's the use of a spreadsheet which is new.

OK, looking at MS-S3 Further Statistical Analysis, which you can find on page 54, you'll see the new content there is that students are asked to implement the statistical investigation process to answer questions that involve comparing the data across two or more groups. You can see that the... the steps involved in the statistical investigation process are listed in the dot point above. In S3.2, "Exploring and describing data arising from two quantitative variables", you'll see that students are required to construct a bivariate scatterplot and there's no specification as to what sort of context to look at that in. That's new, because formerly it was only applied to body measurements.

OK, MS-S3 Further Statistical Analysis. Still in that same place, but we're now on page 55. Students are asked to collect data, interpret, and construct graphs using context. For example, sustainability, household finance and the human body. So MS-N1 Networks and Paths is an entirely new topic in the syllabus, which is why the whole thing is highlighted. You can find that on page 57. OK, so we're moving to Year 12 Standard 2 now. This is the course that replaces Mathematics General 2 and it's the course, typically, that students followed who were pursuing an ATAR. So just a word of caution, in the old syllabus, Mathematics General 2 was listed before Mathematics General 1.

However, in this syllabus, Mathematics Standard 1 appears before Mathematics Standard 2. OK, so looking at MS-A4 Types of Relationships, you can find that on page 60. Students are asked to develop a pair of simultaneous linear equations to model a practical situation. So as you go through, you will find that some of the dot points are very similar or the same as what's in Standard 1, but you may find that they are within different topics or subtopics. Students are asked to construct and analyse a quadratic model to solve practical problems involving quadratic functions or expressions of the form y = ax2 + bx + c. For example, braking distance against speed. They're asked to recognise the shape of a parabola, and that it always has a turning point and an axis of symmetry. And they're also asked to consider the range of values for x and y for which the quadratic model makes sense in a practical context. That's on page 61. OK, looking at MS-M6.

We're now into Non-right-angled Trigonometry, which is on page 63. When students are determining the area of any triangle, they are still using the rule area = 1/2absinC. However, now they're also going to be given an opportunity to use Heron's formula when they have three sides. Again, Heron's formula is listed in the glossary at the back of the syllabus. Students are... What's new also here is that students are required to investigate navigational methods used by different cultures, including but not limited to those of Aboriginal and Torres Strait Islander peoples and they're also asked to work with angles correct to the nearest degree and/or minute.

Moving on to MS-M7 Rates, which is on page 64. Students are now asked to know that a watt is the International System of Units' derived unit of power and is equal to one joule per second. Likewise, like Mathematics Standard 1 down the bottom there, you'll see they're asked to use ratio to describe map scales. OK, looking at MS-M7 rates, which is on page 65, you'll see that some students are asked to calculate the perimeter or area of a section of land using the Trapezoidal rule. Remember that that was a new inclusion in the Year 11 syllabus. They were only asked to use it to one application.

Moving forward to MS-4 Investment and Loans, page 67, you'll see the new content there is that students are required to compare the growth of simple interest and compound interest investments numerically and graphically, linking graphs to linear and exponential modelling using digital technology, investigate the effect of varying the interest rate, the term or the compounding period on the future value of an investment using digital technology. So there's an increased inclusion of the use of digital technology, particularly in the financial mathematics and graphing topics. So it's going to be important to consider those in your programming.

Continuing on with Investment and Loans. We're looking at section F4.2 - Depreciation and Loans, found on page 68. So, again, calculating the depreciation of an asset. This was the same in Standard 1. They've done declining-balance method before, but formerly it was only related to cars. They're also asked to solve practical problems involving reducing-balance loans. For example, determining the total loan amount and monthly repayments. That is not new. However, previously, that was only related to cars and students were only required to use a table or an online calculator.

In that last dot point, which is about credit cards, new content here for students is they're asked to compare credit card interest rates with interest rates for other loan types. They need to interpret credit card statements, which is not essentially new. However, with that, they're asked to recognise the implications of only making the minimum payment. They need to understand what is meant by an interest-free period and they're asked to calculate the compounding interest charged on a retail purchase transaction or the outstanding balance for a given number of days using digital technology or otherwise. OK, looking at MS-5 Annuities.

We're on page 69 now. You'll see there that new content is that students are required to use digital technology to model an annuity as a recurrence relation and investigate either numerically or graphically the effect of varying the amount and frequency of each contribution, the interest rate or the payment amount on the duration and/or future value of the annuity. So MS-N2 and MS-N3 have to do with networks. They are entirely new topics within the syllabus, so you'll see that pages 76 and 77 should be entirely highlighted. We are, in one of our later Adobe Connect sessions, going to be looking specifically at networks, what we're supposed to be doing with them according to the syllabus, and how we might approach them with our...with our classes.

So that completes our session - or at least the presentation - on the new content. As I said at the beginning of the presentation, there has been stuff that has moved between 11 and 12. I've actually made a supplementary recording similar to what I've just done for the new content that shows what's moved from Year 11 and 12 and some content that's moved between Mathematics General 1 and Mathematics General 2 in the HSC. So we'll keep this screen that you're looking at now up following this session.

You'll see that we have a link to last week's recording, which was Unpacking the New Stage 6 Mathematics Standard Syllabus. Following the session today, we will upload the new link for this session as well as the link for the recording for the content that has been moved between Year 11 and 12. Next week we're going to look at how to monitor assignments and investigation-style tasks. That'll be on Tuesday, 20 June, starting at 3:30. And then on Thursday, 29 June, which is the week following, we'll be looking at networks. So all sessions are accessible via this page.

As I said, we'll keep this screen open so that people can access the links. If you have any further details, please don't hesitate to contact either Ruth or myself on our email addresses there. But we do have a question-and-answer pod at the bottom of the screen. If people had any questions that they'd like to ask now, we can answer them. But we thank you for your participation in today's session and we look forward to seeing you, hopefully, next week for Tuesday's session. Thanks very much.

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