PSMTs: Maths Problem-Solving and Modelling Tasks

student bored or confused in classroom

New open-ended maths focus in Queensland schools needs students and teachers to adapt and think differently

Thanks to the spike in anxiety levels of Years 7 to 10 children, many parents are aware of the shifting school maths curriculum. It’s moving away from:

  • Clear tasks with a well-defined procedure from start to end, with one expected right-or-wrong answer,

and towards:

  • More real-life tasks that each student will approach differently, and then justify their conclusions.

This is causing big headaches because neither students nor parents (nor some teachers) are used to this type of task. Unless students are introduced to expectations and working habits in very early secondary – or better yet, in primary school – they face a painfully radical change in mindset if they are to cope with this style of assessment.

There are things that you can do to help your child face open-ended maths assignments. But first…

What is a PSMT?

The Queensland curriculum calls them PSMTs, though it’s alarming how many students don’t realise this stands for Problem Solving and Modelling Task.

The old, straight-forward, one-track assessments do not resemble the kind of situations students will meet outside classroom walls. Employers don’t want to have to lay out tasks step-by-step for employers to follow blindly. So why train students to do that in school?

Employers would much prefer to mention a problem they have and be able to trust their employee to formulate a plan, consider all the options, and present only the best solutions for the boss’s consideration. So the thinking behind the shift in focus is to build students capacities for real-world problem-solving skills which students can apply to their life and careers beyond school.

The task sheets for these open-ended tasks are often convoluted, as teachers find a balance between making tasks too broad or too narrow.  But to give you an idea, here are some recent examples of tasks we’ve seen.

maths problem solving area volume surface

Junior and middle years PSMTs:

  • Year 6 – Estimate how many lollies are in this jar in two ways, using measurements and volume calculations; explain which estimate is probably better.
  • Year 7 – Using area calculations, suggest a shape and layout for a barn in a paddock which allows a tethered goat to reach the most grass.
  • Year 7 – Create a report which analyses data collected about a students age cohort, such as hand span, height, hair colour, etc, and compares themselves to their peers.
  • Year 8 – Redesign your school’s vegetable garden to improve its usability, compare the new and old design using charts to show improvements, and calculate the cost of materials.
  • Year 10 – Design a skateboard course to meet criteria, using linear, quadratic and simultaneous equations to create an exact plan for the builders.

Year 11 and Year 12 QCE PSMTs:

  • Specialist Maths – Mathematically recreate the path of a basketball shot taking into account, angle of launch, velocity, air resistance, gravity, etc.
  • Mathematical Methods – Choose a section of coastline or mountain range to model as closely as possible using  linear, quadratic, cubic and hyperbolic functions.
  • Mathematical Methods – Develop a model of a hanging chain that might be used in programming graphics for a video game. (See and example task and student response.)
  • General Maths – Analyse the queues at your school canteen, as well as the canteen procedures, and justify suggested improvements to the system using networks and queueing theory.
  • General Maths – Decide which school is better by statistically analysing and comparing test results for various subjects at each school.
  • Essential Maths – Provide advice comparing the scenarios of buying a house with a mortgage verses renting and investing over the same period.
  • Essential Maths – Create itineraries and budgets for two possible holiday which try to balance the conflicting criteria of the friends you’ll travel with, and present the benefits and drawbacks of each.

Students must produce a multi-page report explaining their interpretation of the problem, the procedure they developed, why their solution is/isn’t reasonable, and what could be done differently next time.

Of course, mathematical procedures need to be shown, but in a PSMT report equations are secondary to analysing, explaining and justifying in words.

Queensland Curriculum and Assessment Authority mandates that schools create maths assessments to be solved like this in Year 11 and 12 mathematics:

PSMT flowchart. The QCAA process for completing a maths problem-solving and modelling task.

Once mastered, this process can be used all through high school to Year 12, and beyond.

QCAA also provide annotated samples of completed PSMTs, showing how students met the criteria to earn high marks, which can be valuable for students to learn from:

What you should do

Some schools have been transitioning students into the ways of thinking and working needed to take on this new kind of assignment.

But even then, the shift has been too sudden for some students who are used to the (unhelpful yet ubiquitous!) idea that maths is about following a pre-set path to come to one conclusion.

These old habits need to be broken. Ease your child’s transition by helping them realise sooner rather than later.

Some critical points to reiterate to your children:

  • First, understand the whole task. We see that students who don’t “begin with the end in mind” are wasting a lot of time and effort on unnecessary work which won’t translate into a higher mark. In the past, students could step their way through an assignment, section by section, to arrive at the end without ever considering how all the parts relate to each other as a whole. Not with a PSMT!
  • Pay attention to the details and guides on the task sheet. Information on task sheets is often presented haphazardly, so extract the details and write it in dot points to check off as you go. In lower year-levels, there is often a suggested problem-solving process chart included for students to follow to develop their solution, but it never lists the whole process necessary for an A grade. Also check the marking rubric to see what needs to be included for the teacher to award high marks.
  • Discuss the PSMT with teachers, family and friends. The more that students explain the task to others, and hear others’ perspectives, the better the path they will develop to their solution. However, even though the task sheets are presented as open-ended, and for students to find their own unique solutions, some teachers have very set ideas about how they want the task done. Ultimately, students must please the person who will mark the work, which means getting feedback from teachers.
  • Start immediately. PSMTs can eat TIME while students figure out how to tackle them, and those who used to be able to leave tasks until the last few days are not finishing these kinds of tasks.
  • Finish early. Pretend the due date is a week before it actually is so that there is time spare for last-minute changes or additions. FINISH the assignment fully by the DRAFT submission date so that teachers have the opportunity to give feedback on the WHOLE assignment.

Encourage your child to follow this advice from as early as possible.

girl writing maths in book

How ELC can help

We’ve never let the school system dictate what ELC students study session by session. We hit students’ current school content only when absolutely necessary – conscious that, in the long run, ELC time is far more effectively spent working ahead of school.

We want our students to discuss their tasks with us and present their work for our feedback. But there is not enough time to complete these assignments solely within ELC sessions. So, we give feedback on progress made between sessions, and prioritise our precious 75 minutes to continue learning the most important maths content ahead of school.

Our students:

  • Read the whole task sheet before attending ELC
  • Start developing ideas and questions immediately
  • Form an overview of the whole task before beginning
  • Make as much progress as humanly possible between ELC sessions so that we can give feedback on work done each week.
  • Bring their ‘finished’ assignment to their ELC session prior to the due date for a final feedback opportunity.

Open-ended maths assessments don’t have to cause the huge stress that some students are feeling. But the right habits do need to be instilled from early on!

If you’re not already any ELC family, talk to us about how ELC can help manage your child’s learning, to prepare them well for a ‘less-stress’ school future, and success beyond.

Call 54781172.     Email

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About the Author: Dan Blore
Dan Blore manages and teaches at Extended Learning Centres. He has spent 20 years in education, having studied secondary education at University of the Sunshine Coast. He has taught in Australia and Germany and studied at university in Italy. He most enjoys teaching and studying mathematics and languages, both of which he focused on at university.

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