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This blog post will provide practical guidance for designing MYP Mathematics criterion D (applying mathematics in real-life contexts) tasks. It will start by detailing different points to consider, then provide a simple ABC format to follow in the design process before outlining three examples of tasks for a unit. If you are completely new to these assessments, start by reading this initial blog post about criterion D assessments.
Elements to consider
Initially, you would need to consider the content from the unit and the global context exploration to identify where students could use what they had learnt in a real-life context. However, even after narrowing down your unit in these areas, there are still a large range of ways to assess your students. For example, a unit focused on the concepts of area and volume with a global context exploration of environmental sustainability could lead to assessment tasks ranging from:
- an interdisciplinary project with Science and Design where students create compost bins based on the amount of waste produced in their household;
- a report comparing different companies packaging choices of a similar product e.g. cartons of milk and suggesting ways to minimise the amount of material used;
- calculating the yield of crops per square metre in a community garden.
The route you choose to go down will depend on a range of considerations, all of which are valid and dependent on your desired outcomes for the unit balanced with any constraints. These considerations are outlined on the spectrums below.
Suggested structure (ABC)
Regardless of the selected placement of the various elements on the spectrums above, the following format can be used to construct an assessment task sheet.
Aim: give an overview of the task - state the goal of the process, ideally using a command term, and outline the intended outcome, product or performance.
Background: direct students to the information needed to better understand the context. This can be a fictional scenario, a video, an article, screenshots of data, links to online sources, suggestions of key words to search for or the necessity to conduct primary research in their own context.
Clarification of criteria: regardless of the nature of the task, the strands for criterion D are consistent and must each be assessed at least twice per year. The way students address these strands may vary from specific questions to answer to just a reminder of the strands to be addressed in their final product/performance. It is helpful to identify and share with the student what level of rigour is needed in order to progress from state, to describe, explain and justify.
If you are struggling to write task-specific clarifications, here are some questions to ask yourself when considering each strand:
identify relevant elements of authentic real-life situations - how well have they interpreted the task and identified the correct contextual clues from the background information? E.g. did they collect data for a week to work out how much food waste their family produces? Did they select different shaped milk cartons to compare? Did they identify the correct dimensions of the garden from the diagrams given?
select appropriate mathematical strategies when solving authentic real-life situations - did they use the wording of the question to select which topic/skill from the unit was relevant for setting up the working out process? E.g. the bin's volume should correspond to the amount of waste. The surface area of each carton would need to be calculated to find out how much material was used. The area of each vegetable patch would need to be scaled to 1 square metre to compare yield.
apply the selected mathematical strategies successfully to reach a solution - how correctly have they carried out this method? Is their final solution completely correct or have some errors in process led to a valid in size but incorrect answer, or a completely unreasonable answer?
explain (1-3) justify (4-5) the degree of accuracy of a solution - how well can they evaluate the accuracy of the background information, their chosen strategy/modelling process, their calculations and how they presented their final values? You could ask them to focus on specific areas (e.g. how accurate is the amount of material used by each manufacturer?) and specify the quantity of valid comments needed to reach the different command terms. Explain may be one-sided with one comment e.g "accurate because I measured each side of the carton to the nearest mm instead of cm". While justify might be two-sided with values to support reasoning e.g. "the answer is accurate because I used the correct surface area formula instead of estimating but it is inaccurate because I did not consider the overlapping tabs at the bottom of the carton. Overall, my conclusion about who used the least material per 100ml is accurate because they probably would have had similar amounts of overlapping material so this would not have affected the final comparison much."
describe (1), explain (2-3) justify (4-5) whether a solution makes sense in the context of the authentic real-life situation - did they reflect on any non-mathematical factors to consider? Either from the background information, general knowledge or from exploration through the unit. E.g. should the compost bins be a smaller size to speed up the decomposition process or bigger to accommodate the fortnightly bin collection? Would it be big enough during school holidays when everyone is eating at home more during the day?
Three examples assessments
Unit overview
Year: MYP5
Title: Optimised Decisions
Key concept: Relationships
Related concepts: models, quantity, validity
Global context and exploration: personal and cultural expression - creative entrepreneurship
SOI: Modelling the relationships between quantities supports valid decisions in creative ventures
Content: Function notation, quadratic functions.
Option 1: authentic application (long term project)
Aim:
Explore the effect of ticket pricing on the potential money raised for an organisation as part of your service as action project. Create a presentation for your tutor to fully understand how your estimated amount fundraised would be reached.
Background:
Indirect action for service as action can involve raising money for an organisation so that they can continue helping a cause. Money can be fundraised by selling tickets to events such as a comedy performance, music concert, entrance to a raffle, activity fair, film viewing or a workshop. Generally, the aim of fundraising would be to maximise the amount of money made, however, if the event also aims to raise awareness, for example by having a volunteer from the organisation in to speak, a priority may be to allow access to as many people as possible, even if a smaller profit was made.
In general, as the price of a product decreases, more people would be willing to pay for it. Therefore, theoretically, this relationship of price and number of sales can be modelled using a linear function. Points fitting the function can be estimated by asking a sample of the target audience if they would be willing to pay certain prices. Revenue can be calculated by multiplying the amount of tickets sold by the selling price and therefore modelled using a quadratic function. The money fundraised and donated to the organisation would be the revenue generated, less any costs for the running of the event.
Clarification of criteria:
Identify relevant elements of authentic real-life situations: gather appropriate primary data from your peers.
Select appropriate mathematical strategies when solving authentic real-life situations: use appropriate functions to model the expected revenue at various price points.
Apply the selected mathematical strategies successfully to reach a solution: interpret your functions correctly to suggest a theoretical “ideal” price and expected revenue.
Justify the degree of accuracy of a solution: identify aspects of your data collection, model and further calculations which affected the accuracy of your estimated amount to fundraise and justify to what extent.
Justify whether a solution makes sense in the context of the authentic real-life situation: consider the recommended price to charge from the model and reflect on what other considerations should be reflected on when making this choice.
Criterion C (communication) would also be assessed.
Option 2: simulated scenario (2-3 lessons)
Aim:
Model on Desmos what a trajectory of a leap on Earth would look like elsewhere in space. You will need to explain your process and the accuracy of your solution in a report.
Background:
As part of a sports gaming development team, you want to program a feature which will allow a person’s motion on Earth to be visualised as it would play out in space. Here is a similar feature which shows generally how high a person/kangaroo can jump in space depending on gravity. Here is a video showcasing Michael Jordan’s “hang time” in different areas of space. You will need to show the trajectory of an original leap on Earth and the translated leap for somewhere in space on Desmos, explain the relationship and reflect on the accuracy and limitations to the rest of your team.
Information you may want to further look into:
Gravity on different planets
How gravity affects parabolas
How to input images/videos into Desmos
Clarification of criteria:
Identify relevant elements of authentic real-life situations: identify the relevant background information for the planet/moon of choice.
Select appropriate mathematical strategies when solving authentic real-life situations: select appropriate strategies to model a leap on Earth as a quadratic function.
Apply the selected mathematical strategies successfully to reach a solution: use the relationship with the background information to correctly show the trajectory of the leap on another planet.
Justify the degree of accuracy of a solution: justify strengths and limitations of the approach.
Justify whether a solution makes sense in the context of the authentic real-life situation: use the background information to explain why the solution is reasonable.
Criterion C (communication) would also be assessed.
Option 3: transfer skills test (1 lesson)
Aim:
Calculate the dimensions of a window design which let in the most light.
Background:
A window design is to be made from a maximum 510cm of frame, indicated by the 5 black lines in the 3 versions of the design below. Thick, red stain glass triangles will be placed from the midpoints of the lengths as shown, and no light will shine through these. The rest of the window will be clear, allowing light in. The height and width of the windows must be integer values.
Clarification of criteria:
Show that if the height of the window was 50cm, the width could be a maximum of 180cm.
Show that, in this case, the total area of light allowed through is 6750cm^2.
Using h to represent the height of the window, write down a quadratic function for the area a(h) of light which can shine through.
Sketch the function a(h) for 0 < h < 200, clearly showing critical points.
Hence, or otherwise, find the maximum area of light that can be let through as well as the height and width for this design.
Explain why your dimensions and/or area make sense using the background information.
Justify why a quadratic function in this form corresponds to the context of the real-life problem and identify any limitations/restrictions/misrepresentations of the graphical model.
Justify which elements of your calculations, methods and/or given information means that if the design was created according to your chosen dimensions, this exact area of light would/would not be the result.
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