Learning intention and success evidence
We are learning to connect a linear equation, graph and planning interpretation without treating a model as reality.
- I identify m and c from a table or graph.
- I attach units and contextual meaning to both constants.
- I state one justified prediction and one limitation.
Exact Phase 4 curriculum anchor
- Interpreting and graphing linear equations in the form y = mx + c, using the gradient and y-intercept - Calculating the gradient and y-intercept of a line, using a graph - Comparing the relative magnitude of m in two or more linear graphs, using the concept of steepness and relating it to the magnitude of m - Finding the equation of a line, given two points or the gradient and a single point - Determining the effect on graphs in the coordinate plane of changing the coefficient of x2 and the fixed value c, for a range of quadratic equations of the form y = ax2 or y = x2 + c, where a is a positive integer and c is an integer
Preparation
Print: learner pack page L4. The visitor counts are deliberately synthetic. Define t as hours after 9:00 am and V as the modelled number of visitors passing a fictional checkpoint during that hour.
60-minute runsheet
- Whakaoho — read the constants (5 min): display V=30t+50. Learners annotate what 30 and 50 could mean and name their units.
- Build from a table (12 min): Model A gives (t,V): (0,40), (1,75), (2,110), (3,145), (4,180). Find the constant difference, equation and intercept.
- Graph and verify (15 min): plot Model A, use two points to calculate gradient, then check a non-adjacent table value by substitution.
- Compare models (18 min): Model B is V=25t+70. Find when A and B predict the same count and explain which model grows faster and which starts higher.
- Model boundary (7 min): test predictions for t=9 and t=24. Learners write why opening hours, capacity and changing behaviour make indefinite linear extrapolation unsafe.
- Exit evidence (3 min): complete: “In V=35t+40, the gradient means ___; it does not prove ___.”
Worked checkpoints
- Model A: V=35t+40.
- 35 visitors per hour is the synthetic constant rate of change; 40 visitors is the modelled count at t=0.
- 35t+40=25t+70 gives t=3, V=145.
Evidence standard: a bare equation is incomplete. Require the graph, units, interpretation and limitation.