About this unit
How can algebra describe, and prove, facts about shapes on a grid?
Sections in this unit
Factual
- Which form of a straight line is most useful, and when?
- How do you find the equation of a line through two given points?
- What is the condition for two lines to be perpendicular?
Conceptual
- Why do perpendicular gradients multiply to minus one?
- How is dividing a segment in a ratio like sharing money in a ratio?
- Which facts are enough to prove what kind of shape you have, and which only fit it?
Debatable
- Is a proof from coordinates better than a proof from a diagram?
Skills
Students should be able to:
- Select and apply an appropriate technique in an unfamiliar situation.
- Move between representations: read the same line as an equation in three forms, as a graph and as two points.
- Justify why a result must hold, choosing facts that settle the question rather than facts that merely fit.
- Use technology deliberately — to check reasoning already argued on paper, and say what it has confirmed.
How you are assessed
- Unit assessment
Before you start
Students arrive with:
- Plotting points, drawing straight-line graphs, and gradient as rise over run.
- Gradient-intercept form, recognised if not yet fluent.
- Reflections and translations as transformations, from Year 9.
- Sharing a quantity in a given ratio, which the final lesson starts from.
- Pythagoras' theorem, underlying the distance formula.
- From Unit 3, rearranging equations and solving systems — the intersection of two lines is a system, and the do-now routines keep the algebra live.
Check what you remember
Plotting points and gradient
Solving linear simultaneous equations using elimination or substitution