Students compare simple models with real outcomes (taxi fares, trip times, exchange rates), name the assumption that failed, and refine the model with a starting charge, stops or fees (AC9M8M07, node 2).
Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.
Predict and Run 8 min · Investigate 8 min · Modify 10 min · Practise and Make 9 min
Do the Run board yourself first. Students need rate models (previous lesson).
The one idea: when a model and real life disagree, look for the assumption that did not hold, then refine. The common mistake is blaming correct arithmetic (Sam's mistake).
The board's starting charge (base) shows a refined model: a fixed amount plus a rate. The taxi fare, plumber's prices and exchange rate are round examples, not real tariffs.
Wider: compare a simple tax model (one rate for everyone) with the bracket model from Money models; constant versus changing exchange rates.
Separating the maths from the model. When an answer is 'wrong', ask students to check the arithmetic first, then ask what the model took to be true.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student says the maths is wrong. | Is the calculation right? What did the model assume? | Check the arithmetic, then name the assumption. |
| A student forgets the fixed charge when working backwards. | What do you pay before the meter starts? | Take the fixed part off first, then divide by the rate. |
| A student cannot name an assumption. | What would have to be true for the answer to be exact? | That is the assumption. |
One possible solution for each task. Other correct programs are fine.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Stretch: Find a real taxi or rideshare fare structure for your city and build its model. What does it still leave out (waiting time, surge pricing)?
Support: A frame: The model assumes … In real life … So the answer … A better model would …
For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.
You are a patient maths coach for a Year 8 student in Australia. Help me understand ONE idea only, from the lesson "Checking a model". The idea: Reviewing model appropriateness: I can Students evaluate whether a ratio or rate model is appropriate for a given situation, identify assumptions, and suggest improvements. What understanding looks like: - Identifies at least one assumption made in a given model. - Explains how the assumption affects the model's accuracy. - Suggests a reasonable refinement to the model. Mistakes students often make here: - A student says the maths is wrong. - A student forgets the fixed charge when working backwards. - A student cannot name an assumption. How to coach me (rules from the Waypoints Kit coach): - Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question. - Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit). - If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go. - If I seem to be missing the idea that comes before this one (Formulating and solving ratio/rate models), check it quickly, then come back. - Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back. - After you help, ask me one reflective question, such as how I know my answer is right or what I would check. - Praise my effort and method, not my ability. - You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so. - Use simple words. - Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Checking a model".
A model says 4 kg of apples at $3.50 per kg cost $14. The shop charges $12.60 for 4 kg. Name a possible assumption that failed.
A fixed price per kg: the shop may give a discount for buying more (a bulk price).
This completes AC9M8M07.
Where it leads: linear models with a starting value (Linear relations: y = mx + c), and modelling in Years 9 and 10.