Graphs and Relations
MYP Year 4 Mathematics — Number & Algebra strand: Graphs and Relations
A graph is just a frozen story — two quantities changing together, drawn so you can read the plot without watching the whole movie. The skill examiners actually test isn't plotting points (a computer does that); it's translating between three languages — the picture, the equation, and the real-world situation — without losing information crossing between them. Every question in this topic, from a cyclist's journey to a transformed parabola, is really asking: can you move fluently between graph, equation, and context?
Overview
What this topic actually covers
A relation connects two variables; a function is a relation where every input has exactly one output. Almost everything below is one of four skills applied to different graph families: reading a graph, plotting a graph from an equation, finding the equation of a graph, and predicting how a graph changes shape or position.
- Real-life graphs (distance-time, cost, temperature) test whether you can attach meaning to gradient and intercept, not just calculate them.
- The Cartesian plane is the shared language — coordinates, distance, midpoint — that every other subtopic depends on.
- Linear, quadratic, cubic and exponential graphs each have a signature shape; recognising the shape from the equation (and vice versa) is tested constantly.
- Parallel/perpendicular and transformations are really the same idea in disguise: how does changing a number in the equation change the picture?
The shape of the chapter
Command terms that drive the marks in this topic
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Interpret | Attach real-world meaning to a graph feature — say what the gradient/intercept means, not just its numeric value. | Criterion A/B | Full marks need the unit and the context sentence, not just the number. |
| Sketch | Show correct overall shape, intercepts and turning points — proportion matters more than precision plotting. | Criterion C | Missing an intercept or wrong end-behaviour loses marks even if the shape 'looks right'. |
| Determine / Calculate | Produce a specific numeric answer with working shown. | Criterion A | Method mark is separate from the answer mark — write the formula before substituting. |
| Analyse | Break down how a change in the equation affects the graph, and explain the connection. | Criterion B | A description with no algebraic link ('it's steeper') scores lower than one that names the cause. |
| Deduce | Use a given result plus reasoning to reach a new fact without re-deriving from scratch. | Criterion B | You may quote the earlier answer directly — re-doing the whole calculation wastes time, not marks, but skipping the logic link does lose marks. |
| Justify / Explain | Give a reasoned argument, not just a stated conclusion. | Criterion C | A bare 'yes' or 'no' answer without the supporting calculation earns close to zero. |
Key point
Overview