Today is rung 5 of 6 on this topic
Modelling with linear functions
Can do: Builds a linear model from a real situation and interprets both parameters and the prediction.
Why it matters
It's the point where algebra becomes useful, and interpretation is exactly what exams reward and students skip.
What it looks like when it's wobbly
Produces the equation and stops, never interpreting the numbers or sanity-checking the prediction.
⏱️ Two-minute check
"A tank has 200 L, draining 5 L/min. Write the model. When is it empty? Is 60 minutes sensible?"
Solid looks like: y = 200 − 5x, 40 minutes, and 60 rejected as impossible.
The full activity for this topic · 30 minutes
Model Something Real
- 1Measure at regular intervals and record the data.
- 2Plot it and decide whether a linear model fits.
- 3Find the equation from two points and state what each parameter means.
- 4Predict a future value, then wait and check it.
- 5Discuss where the model stops being valid and why.
If it's too hard
Given data that's exactly linear, find and interpret the equation.
If it's too easy
Data that's nearly linear — fit a line, discuss residuals, and quantify the error.
Say this
"What does the −5 mean, in tank language? And when does this model stop making sense?"