At a glance
Groups of three · scouted through the final unit, presented on the last day · invited guests · one exhibit, one model, one defence
What you are making
The whole course has been one idea wearing different clothes: find the function hiding in the world, name its family, and make it speak. The symposium is where you do that in public.
Your group chooses one real-world relationship worth modelling — a cooling drink, a bouncing ball, daylight hours across the year, a savings balance, a growing pattern — and builds an exhibit: the data or situation, the model, and the story of how you chose it. The catch that makes it a finale: you must audition two candidate families from different units before defending your winner. A quadratic that lost to an exponential is evidence, not waste — that judgement call is exactly What Makes a Model Good.
Guests circulate on the day. Every group answers the same two questions: why is this the right model? and where does it stop being one?
Milestones
- Phenomenon scouted and approved — real, measurable, and yours
- Two candidate families auditioned; the comparison recorded
- Winning model built, with every parameter tied to the situation
- The failure boundary found: where the model stops deserving trust
- Exhibit assembled; both symposium questions rehearsed out loud
The folded callout below stays folded until you are stuck — that is what folding is for.
If your group cannot choose a phenomenon
Pick the one you can measure by tomorrow. A modest phenomenon with real data beats a spectacular one with none, and the audition of two families matters more than the fame of the winner.
How it is assessed
The conversation is the assessment. Per How Marks Work, guests and your teacher listen for reasoning: the audition, the parameter story, and the failure boundary. Speed, polish, and poster quality are not criteria. Afterwards, Final Reflection asks what the symposium showed you about your own growth, and your Math Journal carries the record.
Success criteria
| Quality | What it looks like at your exhibit |
|---|---|
| A real phenomenon | Data or a situation your group can vouch for |
| A genuine audition | Two families tried; the loser’s failure shown |
| Parameters that speak | Every letter tied to the world, not the page |
| A known boundary | You name where the model fails before guests ask |
| Threads across units | The exhibit cites ideas from more than one unit |
Curriculum connection
A2.3
solve problems involving quadratic functions arising from real-world applications and represented using function notation Sample problem: The profit, , of a video company, in thousands of dollars, is given by , where is the amount spent on advertising, in thousands of dollars. Determine the maximum profit that the company can make, and the amounts spent on advertising that will result in a profit and that will result in a profit of at least $4 000 000.
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B3.3
solve problems using given graphs or equations of exponential functions arising from a variety of real-world applications (e.g., radioactive decay, population growth, height of a bouncing ball, compound interest) by interpreting the graphs or by substituting values for the exponent into the equations Sample problem: The temperature of a cooling liquid over time can be modelled by the exponential function , where is the temperature, in degrees Celsius, and is the elapsed time, in minutes. Graph the function and determine how long it takes for the temperature to reach 28°C.
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C2.4
solve problems involving arithmetic and geometric sequences and series, including those arising from real-world applications
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D3.5
pose problems based on applications involving a sinusoidal function, and solve these and other such problems by using a given graph or a graph generated with technology from a table of values or from its equation Sample problem: The height above the ground of a rider on a Ferris wheel can be modelled by the sinusoidal function , where is the height, in metres, and is the time, in seconds. Graph the function, using graphing technology in degree mode, and determine the maximum and minimum heights of the rider, the height after 30 s, and the time required to complete one revolution.
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