The idea, step by step
Which inputs are allowed?
Discrete inputs come in separated choices. If an input counts people or whole tickets, 2.4 is not an allowed count.
Continuous inputs can take values between marked numbers. Elapsed time during steady filling may be 2 min, 2.5 min or 2.53 min.
A connecting line makes a claim
Joining points claims something about the values between them. A straight segment assumes a constant rate between its endpoints; use it only when the context and model support that assumption.
A few measurements do not prove a real process followed straight lines. State when a line is an approximation. Category names, such as colours, are not a continuous numerical scale.
A common trap
Joining every plotted set simply because the dots line up.
Instead: Check the input's meaning before deciding to join points.
See the thinking
Whole tickets
Tickets cost 6 dollars each. Is (2.5,15) an allowed ticket-count/cost pair?
- 2.5×6=15 is correct arithmetic.
- But only whole tickets are sold.
- 2.5 is not an allowed input.
Between readings
An empty tank fills steadily at 4 L/min. Is (1.5,6) part of the time/volume model?
- 1.5 minutes is a possible time.
- 4×1.5=6 litres.
- The continuous model includes intermediate times.
Check your understanding
A shop sells only whole apples. Is 3.7 apples an allowed input in its apple-count cost model?
Show answer
No.
The number of whole apples is discrete.
Your turn
6 questions · 15 marks · Work at your own pace.
Read the questions online
- Is the number of whole cars in a car park discrete or continuous? Explain.2 marks
- Rope is sold by measured length. Is length discrete or continuous in a mathematical model?2 marks
- Tickets cost 8 dollars each and only whole tickets are sold. Is (1.5,12) allowed?2 marks
- An empty tank fills steadily at 2 L/min. Find the volume at 2.5 min and classify the model.3 marks
- The temperature is 20°C at noon and 24°C at 2 pm. Must it have been 22°C at 1 pm? Explain.3 marks
- Why should the tops of bars for red, blue and green not be joined to claim a continuous numerical relationship?3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Is the number of whole cars in a car park discrete or continuous? Explain.2 marks
Only whole-number car counts are possible.
Discrete. - Rope is sold by measured length. Is length discrete or continuous in a mathematical model?2 marks
Intermediate lengths such as 1.25 m are possible.
Continuous. - Tickets cost 8 dollars each and only whole tickets are sold. Is (1.5,12) allowed?2 marks
1.5×8=12, but 1.5 tickets cannot be bought in this model.
No. - An empty tank fills steadily at 2 L/min. Find the volume at 2.5 min and classify the model.3 marks
2×2.5=5.
Times between whole minutes are allowed.
5 L; continuous. - The temperature is 20°C at noon and 24°C at 2 pm. Must it have been 22°C at 1 pm? Explain.3 marks
The actual temperature may change unevenly.
No. That is a straight-line model's prediction, not a fact established by two readings. - Why should the tops of bars for red, blue and green not be joined to claim a continuous numerical relationship?3 marks
A numerical halfway point between the colour categories has no meaning here.
The inputs are categories, not a numerical measurement scale.
Curriculum reference & lesson scope
Australian Curriculum v9.0 / South Australian Curriculum
Year 7 coordinate, pattern and authentic-graph interpretation scope. Includes prerequisite four-quadrant plotting; formal gradient/intercept techniques are not required here.
Official curriculum source ↗