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Criterion D is all about providing students with opportunities to use mathematical concepts and skills, to solve problems in real-life contexts. This post includes two example assessments, a break down of the five strands, definitions of the command terms and some tips to help you create your own assessment. Further guidance for creating these types of assessment can be found in this updated blog post.
To discuss the assessment strands with some context, let's look at how they may be evaluated within the following assessment. The numbers in brackets indicate which year criterion they fall under, e.g. (3) means this command term appears in the "end of year 3" assessment criterion.
Example assessment 1:
How long would it take the 2000 and 2016 Olympic gold medalist of your choice (any swimming competition) to swim around the Isle of Wight? Use your solutions to answer the question: are humans getting faster? Reflect on whether your solution makes sense in real life and on the accuracy of this answer.
Online sources to use:
Swimmer completes round the island challenge https://www.google.com/amp/s/www.bbc.co.uk/news/amp/uk-england-hampshire-37218416
Olympic records https://www.olympic.org/olympic-results
The criterion strands
i. identify relevant elements of authentic real-life situations
The first thing to consider is that in a real life context, problems are rarely handed to you with the exact information you need in the perfect format. Giving students an article, a Web page or a video will require them to interpret the question and identify what information is needed and how to manipulate it. The word "authentic" here is key! Where, possible, draw from a genuine source for the problem and/or the information needed to solve it. A fictional scenario isn't the end of the world as long as it is still reasonable (just avoid Bob going to the supermarket and buying 87 watermelons at £5.16 per kg). Plus, authentic problems can be really engaging and stimulate further inquiry!! Be sure to refine how the information is delivered to be year level appropriate - you don't want to overwhelm the younger ones with too much information!
In the example, this would mean finding the time and distance of the two Olympic athletes and the distance around the Isle of Wight. When the students get to reflecting on their answer, this would require picking up other relevant information from the news article (the swimmer was male, swam non-stop and had snacks. The article is from 2016, only 4 people have completed the route, "60" miles is a very convenient value).
ii. select appropriate mathematical strategies when solving authentic real-life situations
Once students have selected the correct values or data to use, they need to know how to manipulate it to reach and answer. This may mean forming and solving an equation, calculating a rate, converting, constructing a graph, drawing a diagram to aid the use of formulae etc.
In the example, students may calculate the speed in metres per second (as this is how distance and time is given) then convert it to mph. Or they may calculate how many 100/200/400m "fit" into 96.6km and scale up the time frame.
iii. apply the selected mathematical strategies successfully to reach a solution
This assesses how well they carry out the above. It ranges from reaching a solution, a valid solution or a correct solution. Valid could mean different things based on the context - if their strategy was to estimate or they had a choice of data to use, there may be a window of valid answers. Alternatively, if the correct approach should have lead to a single solution, you may choose to label an answer valid if it makes sense in the context (answer should show an increase from the original value, final percentages should add up to 100, the answer should show a slight profit etc.). You may want to indicate what valid means in your task specific clarification.
In the example, they need to carry out their chosen strategy to reach a window of valid solutions depending on their choice of swim event, rounding, and conversions. The correct solution would involve no errors in their chosen steps. Their answer to the question "are humans getting faster?" is yes, based on the limited data.
iv. Describe(1,3)/explain(1,3,5) /justify(5) the degree of accuracy of a solution
This is where students evaluate their methods, measurements, calculations and initial data to assess how close to the correct answer (with the given information) their final solution is. Any estimating, rounding, converting, scaling, use of inaccurate measuring tools (from a diagram, tape measure, stopwatch), outdated Internet sources etc. would affect the accuracy of their solution.
Using the example:
Describe - it is/is not accurate because...my calculations were completed with the exact values given and I did not round until the end, therefore my calculations were accurate OR not all of the original measurements were accurate as the distance around the Isle of Wight is unlikely to be exactly 60 miles.
Explain - how did looking at it from both sides lead to a conclusion about the accuracy. The Olympic page is likely to be very accurate (seconds rounded to 2dp, 100m swimming pool) as their measuring tools are exact. The distance around the island has probably been rounded to 1 significant figure. This rounding means that my answers could actually range between (x - y).
Justify - what could validate this answer? Multiple calculations here could validate the answer. Using different methods to find the solution e.g. the difference in Olympic times scaled up by distance gives the same time as working out both athletes independently and finding the difference. Justify that this is as accurate as the answer can be with the given values.
v. State (1)/describe(1,3)/discuss(3,5)/explain(3,5)/justify(5) whether a solution makes sense in the context of the authentic real-life situation.
Some more analysis of the answer reached in the context of the original problem - an accurate answer does not always make sense. Comparing against an estimate, a hypothesis, common sense or information given in the context of a question. This also gives the student an opportunity to discuss the limitations of their answer. Real life scenarios can not always be modelled exactly by linear, quadratic or exponential functions - in real life would you expect the answer to be higher or lower and why? If any information was missing, what assumptions did you make?
Using the example:
State - yes or no it makes sense/it does not make sense
Describe - it makes sense because my 2016 swimmer had a shorter time than my 2000 swimmer both in the Olympic records and when I calculated the Isle of Wight time OR It does not make sense because it was very different to the Isle of Wight swimmer's time.
Discuss - a view from both sides. It does not make sense in real life because the swimming pace for a minute can not be maintained across several hours.
Explain - how did looking at it from both sides lead to a conclusion of it making sense/not making sense? Scott Dawson's time was longer because his pace would be slower. The Olympic swimmers are trained for short distances so may not even complete the route. Explain why the conclusion was reached that humans are getting faster - what discussion points were weighed up?
Justify - what could validate this conclusion? Use information from the newspaper and website to back up explanations. If within the scope if the assignment, perhaps additional research into the average time taken/speed to swim the route. Are humans getting faster? One comparison can not answer this question - there could be other reasons for the 2000 to 2016 improvement (better measuring tools, individual performance, looked at different swimming styles etc.). The answer of "yes" could be justified with greater research and improvements (compare more sports, across more years. Have a set, measured route around Isle of Wight. Develop a model which accounts for current and wind etc.)
Command terms
Apply - Use knowledge and understanding in response to a given situation or real circumstances. Use an idea, equation, principle, theory or law in relation to a given problem or issue.
Describe - Give a detailed account or picture of a situation, event, pattern or process.
Discuss - Offer a considered and balanced review that includes a range of arguments, factors or hypotheses. Opinions or conclusions should be presented clearly and supported by appropriate evidence.
Explain - Give a detailed account including reasons or causes.
Justify - Give valid reasons or evidence to support an answer or conclusion.
Select - Choose from a list or group.
State - Give a specific name, value or other brief answer without explanation or calculation.
What it says in the guide
Opportunities to use mathematical concepts to solve real-life problems. For example, modelling or curve fitting tasks based in authentic contexts. (Page 31)
Mathematics can be used to model many situations (for example, painting a room, analysing mobile telephone tariff plans, triangulation, diet plans). (Page 31)
In reference to the e-assessment: Applying mathematics in real-life contexts: The second task assesses students’ ability to apply mathematics in a real-life context, which is typically connected to the global context for the session. Students may be required to produce pieces of extended writing to evaluate and justify the validity of mathematics models. (page 47)
Answers will require an appropriate use of significant figures or decimal places based on the demands of the question. Unless otherwise indicated, final answers are to be given correct to three significant figures. Estimation is to be completed by rounding; truncation will not be rewarded. Correct use of subscript and superscript is expected in all relevant mathematical contexts. (page 47)
Good practice and tips
Within the unit it would be beneficial to focus on developing the following ATL skills, depending on the requirements of the assessment: critical thinking, reflection, information literacy, transfer skills.
Be mindful of how many lessons it will take, especially if criterion c is being assessed too.
Task specific clarification are always useful, but for your sake, and the students, establish what you mean by describe, explain and justify and give opportunities for reflection within the questions.
As always, your assessment should be linked to the statement of inquiry. However here it should be really obviously connected to the global context.
Keep your eyes open for inspiration - the news, pop culture, questions your students ask, even your own life and interests.
This is a great opportunity to tie in or even compare information from around the world - architecture in other countries, currencies, unique cultural practices etc.
View more tasks complete with assessment rubric, task-specific clarifications, sample student answer and marking guidelines.
