At a glance
Pairs · launched with the sinusoid recipe, due on the modelling day · one model, four letters explained, one prediction defended
What you are making
Twice a day, the ocean breathes. You will receive a genuine tide table — heights and times for one Canadian station over several days — and your job is to catch that breathing in an equation:
You finish with the fitted model, a paragraph for each letter explaining what it means in water — half the tidal range, the length of a tidal cycle, when high tide arrives, the average sea level — and one defended prediction: the water height at a time your data never recorded, plus the answer to the harbour question that comes with your station: between which hours is there enough depth to cross?
Milestones
- Data plotted by hand; period, amplitude, and axis estimated from the picture before any formula appears
- The four letters assembled into a first-draft equation, using the recipe from Sinusoidal Functions
- Model plotted against the data in Using Desmos and adjusted until the disagreement is small and stated
- Each letter translated into a sentence about water
- Prediction and harbour answer written and defended
How it is assessed
Per How Marks Work, the reasoning is the product: a model that misses slightly, with the miss measured and explained, outranks a perfect curve with silent letters. On the due date your pair defends the prediction out loud. The Math Journal entry on where your model disagreed with the data completes the evidence.
Success criteria
| Quality | What it looks like in your work |
|---|---|
| Picture first | Amplitude, period, and axis read from the plot |
| Letters that speak | Every parameter tied to something wet |
| A measured miss | Model-versus-data disagreement stated in metres |
| A brave prediction | An unmeasured time, with reasoning shown |
| A useful answer | The harbour question answered in clock hours |
If the wave will not fit
Check the period before anything else — tides run on roughly a 12.4-hour cycle, so a period of exactly 12 will drift out of phase across your data window. A cosine form may also fit more naturally than sine: same wave, different starting point.
Curriculum connection
D2.8
represent a sinusoidal function with an equation, given its graph or its properties Sample problem: A sinusoidal function has an amplitude of 2 units, a period of , and a maximum at . Represent the function with an equation in two different ways.
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D3.3
determine, through investigation, how sinusoidal functions can be used to model periodic phenomena that do not involve angles Sample problem: Investigate, using graphing technology in degree mode, and explain how the function approximately models the relationship between the height and the time of day for a tide with an amplitude of 5 m, if high tide is at midnight.
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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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