- 1. From Abstract to Contextual Graphs
Recognize that straight-line graphs carry real-world meaning when axes represent named quantities, and read values directly and in reverse from simple contextual graphs.
- 2. Reading Beyond the Graph: Scaling and Extrapolation
Extend a proportional relationship beyond the plotted range of a graph using ratio tables and proportional scaling; extrapolate values from conversion graphs.
- 3. The Gradient is a Rate of Change
Calculate the gradient of a contextual graph using vertical rise and horizontal run, and interpret it as a real-world rate of change.
- 4. The Graph as a Decision Tool
Use a conversion graph to compare two quantities expressed in different units or currencies, convert to a common unit, and construct a justified real-world decision.
- 5. The Graph as a Decision Tool
Use a conversion graph to compare two quantities expressed in different units or currencies, convert to a common unit, and construct a justified real-world decision.
- 6. Graphs That Don't Start at Zero: The Fixed Charge
Recognise non-origin contextual graphs; interpret the y-intercept as a fixed charge; read totals; decompose cost into fixed and variable parts; contrast proportional vs fixed-plus-rate contexts.
- 7. The Equation as a Contextual Model (y = mx + c)
Write contextual linear models as y = mx + c; interpret m and c in context; derive equations from intercept and gradient; substitute to find totals or usage; use meaningful variable names (C, t, d, n).
- 8. Drawing Conversion Graphs from a Rate
Calculate coordinate points from a rate, determine an appropriate scale, and accurately plot proportional conversion graphs.
- 9. Drawing from Data and Dual-Line Comparison
Plot data to verify collinearity, draw dual lines on shared axes, and interpret intersections as break-even points to make financial decisions.
- 10. Speed as a Compound Measure
Define speed as a compound measure, understand 'per' in speed units, and distinguish distance from time within speed measurements.
- 11. Calculating Speed: Integer Cases and the Ratio Table
Calculate speed for integer and half-hour times using a ratio-table structure to identify the unit rate.
- 12. Speed with Unit Conversion
Calculate speed when the given time is in minutes by scaling to hours, and perform multi-step conversions across units.
- 13. Reading Distance-Time Graphs: The Two Fundamental States
Interpret horizontal and diagonal lines on a distance-time graph, and understand that a downward slope represents returning toward the start.
- 14. Speed as the Gradient of a Distance-Time Graph
Recognize that the gradient of a distance-time graph represents speed, by extracting the rise and run and using a ratio table.
- 15. Your Pay, Your Graph: Wages and Hourly Rates
Construct and interpret wages graphs, identifying the hourly rate as the gradient, and compare job offers with and without hour limits.
- 16. Bills and Tariffs: What You Pay Before You Start
Construct and read a contextual graph for a two-part tariff — fixed charge plus variable rate. Draw two tariff lines on the same axes to identify the break-even point and determine which tariff is cheaper for a given usage.
