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Methods PSMT Playbook

Acuity’s comprehensive guide to ace your IA1.

Introduction


Welcome! My name is Lachy and I graduated from Terrace in 2022. This PSMT playbook comprises part of my project called Acuity. We mentor QCE students (like you!) and provide cutting-edge study support.

Your Methods IA1 is the very first test you face in Year 12. Strangely, it is also the first time you will ever complete a PSMT. Fortunately, I believe that these should be the easiest marks you will be able to access for Methods. Many students miss this golden opportunity.

This playbook will offer systems, structures, and resources. It won’t do the assignment for you. The ideas it gives you are only effective if you can implement them and dedicate consistent time to this task.

Let’s begin!

Structure

As a starting point, hopefully you’ve already seen the task sheet on Spire.

If you have, you’d know that there are three primary sections: formulate, solve, and evaluate. Rounding out the assignment is also an introduction and conclusion.

Within these sections, you have some flexibility. Ultimately, the fine-grained structure you choose is personal preference, but I would strongly recommend having some scaffold to work with. Below are my recommendations.

View Detailed Structure Guide ↓

The introduction is a really small section that you shouldn’t overthink. All you really need to do here is summarise the context given in the task sheet to form a clear objective for your report.

~100 words

Why should we care about the design of a roof?

What is the specific objective in this report?

I’d recommend leaving this to complete at the end, alongside your conclusion. Many students start with the introduction and end up spending way too much time here.

Formulate is an important section. It is overlooked by many students and is an area where marks are most commonly lost. In establishing observations and assumptions, you create for the reader a breadcrumb trail that starts at the task sheet, shows your initial interpretation, demonstrates research, illustrates how you navigated early roadblocks, and set the constraints against which your solution will be evaluated.

~350 words

Observations

Paragraph or list

Assumptions

Paragraph or list

Mathematical Concepts and Techniques

How did I interpret the task instructions mathematically?

What technology did I use?

What functions did you choose and transformations are represented?

What formulas, techniques, or constraints did you apply?

Although many students jump straight into Desmos to try and figure out there solution, I actually believe it is more advantageous to start with the formulate section first. I think trying to create a super rough draft in the formulating component is helpful to planning out your model, but don’t invest too much time here trying to perfect this section from the outset, because you’re likely to tinker with something like your assumptions constantly as your model evolves.

In terms of the actual problem-solving and modelling involved with a PSMT, this is where most of the magic happens. Your model itself should address the task criteria and align with the observations and assumptions you made in the formulate section. Your write-up must catalog a logical sequence of developments and iterations you made to go from a blank canvas to final product. Crucially, at each step, you must justify why you made that decision.

~1000 words

Modelling

Show the complete final model

Take the reader on a tour back through the modelling process, showing how each component gradually built on top of each other, and why you chose those functions, and why you decided to use them in that order

Verification

Use appropriate mathematical techniques to verify your solution against the constraints outlined in the task sheet and conditions established in your assumptions

Your solve section will take the longest amount of time by far.

If you are taking a two-model approach, use an accurate, but basic, first model, keeping your best function choices in reserve for model two.

The threshold for a complex solution is not as high as you might think. If you chase complexity by sacrificing the accuracy or practicality of your model, you’re likely losing marks overall.

Keep a record of why you make each and every decision. Even if the reason seems trivial (i.e. because the function looks nice), that is still valid rationale for why you selected it! Just note everything down as you go along and then you can always come back to make the description more agreeable and specific.

Save your Desmos files and take screenshots so you can revert to older versions if needed!!!!

You’ve now shown all the detailed maths behind your model, but now you need to interpret all the functions and calculations to draw conclusions about the quality of your solution.

~500 words

Reasonableness

Assess whether the model you designed is reasonable in light of your observations, assumptions.

Link to real-world viability as well (likely integrated within your observation or assumptions)

Strengths

Did your model meet the task requirements?

Was your solution reasonable with respect to the above section?

How would your design fare practically?

Limitations

Did your model meet the task requirements?

Was your solution reasonable with respect to the above section?

How would your design fare practically?

How did the task design restrict the viability of your model?

Would your design work under some conditions but not others?

Are there other important metrics that you haven’t considered (i.e. cost)?

This section is very methodical. Think about it like you’re writing a scientific report. You’ll do well if you keep your writing direct to the point and specific in how it addresses the criteria sheet.

Tie everything together back to the original purpose of the report.

~100 words

What was the objective of the report?

Did your solution meet the report objectives?

Was the solution reasonable?

What can we learn from this report?

Not a section that you need to overthink. Keep it concise and to the point.

Now that we have a general structure in mind, let’s dive into the specific details for this assignment ↓

Formulate

First, here are some notes I took from the task sheet:

Asks for a futuristic design

The GTPAC needs to be between 35m and 40m wide with a maximum height of 80m

The actual centre must have these constraints not the roof itself

How much additional height does a roof generally add?

How much extra width (eaves, overlapping) would a roof generally add?

Should the roof be symmetrical?

Must include exponential, logarithmic or trigonometric

Must be smooth at all points for automated cleaning

Maximum slope of 45 degrees

For me, the purpose of the formulate section is to bridge the gap between the task sheet and your model. This means identifying what hasn’t been in the task sheet, but would be an important consideration for you. Here are some ideas.

What has not been said? Therefore, what must be justified? What might I need to research?

  • How much additional height does a roof generally add?
  • How much extra width (eaves, overlapping) would a roof generally add?
  • Should the roof be symmetrical?
  • Should the eaves be of equal length either side?
    • 2.5m excess eaves? What is standard?
  • How many functions should I use?
  • How do I quantify smoothness?
  • Does the design need to be continuous?
  • What would be the optimal width? Does it matter at all?
  • Is there an ideal shape for the eaves?
  • Where would you want more gradient? Where would you prefer less?
  • Does concavity matter? Should you consider whether leaves can be trapped and accumulate in the roof?
  • How many different types of functions should be used?
  • Are there functions that are best off being used in tandem?
  • Is there a preferred maximum gradient?
  • What constitutes a futuristic design?
  • Is there preferred minimum gradient?
  • Which cross-section are we designing?
  • How does the 3D shape differ to the 2D representation?
  • What issues could occur in 3D versus 2D?
  • Could we do anything in the model to address these?
  • What software would be best for modelling this problem?
    • Why was Desmos selected?
  • Should sliders be used? Why?
  • Should we consider the cross-sectional area of the roof for any reason? Insulation? Storage space?
  • Should we consider how the roof adheres to or connects to the actual building? What angles and surface exposure?
  • Should I use a piecewise function or individual functions?
  • Should cost be considered at all?
  • What coordinate system are you using? What is the scale of your model?
  • Does the roof have to begin at height zero?
    • What does height zero represent?
    • Can it start below height zero?
    • Would this affect calculations?

Consider which of the previous questions you care about for your design, plus any other you think of. Not everything can be factored in, but those which you believe are important will need observations and assumptions to unpack them further. You don’t have to, but I often feel like it helps you meet the justified criteria and have a more cohesive flow to your report.

Example: should the roof be symmetrical?

  • If yes:
    • Make observations from actual research to inform a more nuanced perspective.
    • Use this nuance to create an assumption about what you believe is an important constraint to guide your assignment and aligns with what you might value in a futuristic roof design.
  • Observations can also include comments about the shape of specific functions based on preliminary modelling.
    • Example: when the slider B is set close to zero, the period increases and the gradient significantly dampens in a sine curve (show diagram screenshot)

Unlike observations and assumptions, this is a section I would suggest leaving until after the model is completed and you know what concepts and techniques you actually employed. That being said, here are a list of things you should consider including in this section:

  • Use of Desmos
  • Differentiation used to confirm smoothness of function intersections
  • The actual functions used and how your translations affect the base function
  • Any differentiation techniques (chain rule, quotient rule, product rule) used
  • How you verified that functions intersected in a continuous manner
  • Constraints that were used to guide coordinates in Desmos

These ideas will make more sense after we discuss the solve section, so let’s take a deep dive into that now…

Solve

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Evaluate

Overall, the evaluate section requires methodical and precise writing to collect full marks. Before starting on this section, make sure you go back and refine the observations and assumptions you made in the formulate component. You’ll definitely need to reference these here.

For me, I feel like the criteria sheet clearly outlines what your evaluate section should include:

Although it doesn’t matter where you decide to place your verify results section, I generally prefer this at the end of the solve section, rather than in evaluate, as I feel like it flows on more cohesively from the heavy maths content there. In terms of fulfilling this criteria though, you can have it either in the solve or evaluate section.

Now, touching on the next four dot points. As outlined earlier, I think it makes a lot of sense to split your evaluate write-up into three short sections: reasonableness, strengths, and limitations. Under reasonableness, use two separate sub-paragraphs to distinguish clearly for the marker between your assumption and observation discussions.

Ultimately, the evaluate section will vary widely depending on the specifics of your model and the guiding assumptions you set out for yourself earlier in the assignment. Keep your writing to the point with these criteria in mind and you should score well here.

Use the structure and questions provided here as stimuli for getting started with this section.

Completing the Report

Congratulations! If you’ve now completed the actual model, verified that it meets the task constraints, and then built cohesive formulate and evaluate sections around it, you’ve pretty much finished a rock-solid draft. Your job isn’t quite finished yet though.

As the finishing touches for your assignment, you’ll also need an introduction and conclusion. Collectively all these sections are really asking is for you to place your solution in context. Make the objective of your report clear, evaluate whether your model is reasonable based on the task constraints, and give a little insight into why this report could be relevant.

You don’t need to labour over these sections too much, but you can find clear guidelines for how I would approach them here.

Elegant home office desk setup with a laptop and a plant near a window. Ideal for remote work.

Final Advice and Resources

Here are just a few things I think deserve a little extra emphasis, plus some broader snippets of advice:

  • Almost every criterion uses the word justified, meaning: show or prove something to be right, reasonable or valid.
    • The more evidence you can use to support your decisions, the better.
  • Really make an effort to take advantage of this assessment item. The rest of your marks throughout Year 12 Methods are significantly more difficult to acquire, so this assignment is a blessing for many students
  • Collaborate with your peers. You won’t be offered much teacher-led feedback for this assignment, so drafting things with your peers can be a great idea. Brainstorming ideas for the model, in particular, can be really useful.
    • Do not collude though! Your models can use similar mathematical concepts, but they, of course, cannot be the exact same thing.
  • I know I have said this a few times, but please make sure you save your Desmos model…

As a guide that you can follow for both your modelling work and report write-up, you can access my actual, full 20/20 assignment, plus a Desmos continuity and smoothness template here.

What Next?

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The Road Ahead

NOVEMBER

~Week 7: Submit your final PSMT report (20%)

January

Week 1: Year 12 begins for real.

March

~Week 10: Methods IA2 Exam (15%)

July

~Week 3: Methods IA3 Exam (15%)

OCTOBER

~Week 4: External Exam (50%)

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