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Graphs of Relationships

CAPS Senior Phase Mathematics (South Africa): Grade 8–9

8 ready-made resources for teaching Graphs of Relationships, written for CAPS Senior Phase Mathematics. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where learners usually go wrong, free to read whether or not you sign up.

Independently rechecked. These files were written to the specification from our own topic maps, then put through a separate recheck pass from the one that wrote them, which found and fixed real errors. A subject teacher has not signed them off individually, so give them your usual read before you teach from them.

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What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Worksheet (Grade 8 & 9)Word, editable
Worksheet mark schemeWord, editable

Grade 8

Describe a real-world situation by interpreting a graph of that situation, with explicit attention to its trends and features: whether it is linear or non-linear, increasing or decreasing, has a maximum or minimum, and is discrete or continuous.
Draw a graph from a written description of a situation, showing the same trends and features.
Use ordered number pairs to draw graphs on the Cartesian plane, working in the first quadrant only.

Grade 9, in addition

Draw graphs on the Cartesian plane directly from given equations, new coordinate-geometry content, not a continuation of the Grade 8 situational-graph skill. This includes constant-form equations (e.g. x = -4, a vertical line; y = 2, a horizontal line), straight lines via a table of values, and simple non-linear graphs (e.g. y = 2x², y = -6/x), note that the general straight-line form y = ax + q and its gradient/intercept meaning is Grade 10 content, deliberately not required yet.
Informally investigate gradient as a constant rate of vertical-to-horizontal change along a line, without yet using the formal y = ax + q formula.
Determine an equation from a given graph: the reverse process.

Where learners go wrong

Describing a graph's trend using everyday language that doesn't match its actual shape (e.g. calling a curve "increasing" throughout when it has both an increasing and a decreasing section).
Confusing "discrete" data (separate, countable points, not joined) with "continuous" data (a connected line), and joining points that should be left separate or vice versa.
At Grade 9, substituting a value into an equation incorrectly when generating points to plot, particularly with negative x-values.
Assuming every graph must pass through the origin, when only certain relationships do.

How it gets asked in the exam

"Describe the trend shown in the graph", "Sketch a graph to show ...", "Draw the graph of [equation] on the Cartesian plane" (Grade 9), "Determine the equation of the graph shown" (Grade 9).

Key vocabulary

Graph, linear, non-linear, increasing, decreasing, maximum, minimum, discrete, continuous, Cartesian plane, equation, coordinate.

Assumed prior knowledge

Plotting ordered pairs on the Cartesian plane, first quadrant (Grade 7-8 content, extended to four quadrants in the Geometry strand's Position and Movement topic).
Substituting values into a formula or equation (Patterns and Relationships topic).
Solving a simple equation (Algebraic Equations topic): needed to find missing coordinate values.

How Speca scaffolds this topic

Use a consistent three-step routine at Grade 9 for drawing a graph from an equation, "make a table of values," "plot the points," "join with a straight line or smooth curve", so the process is identical regardless of the specific equation.
For Grade 8's situational graphs, provide a small gallery of labelled example shapes (linear increasing, linear decreasing, curved with a maximum, a discrete step graph) as a visual reference bank before learners attempt to sketch or describe their own.
Keep the vocabulary list (linear/non-linear, increasing/decreasing, maximum/minimum, discrete/continuous) visible and consistently colour-coded whenever a graph is discussed, so the descriptive language becomes automatic rather than re-taught each time.
South African decimal convention: use a comma as the decimal separator wherever a decimal value appears (e.g. 2,5, not 2.5); coordinates use a semicolon, e.g. (3;-4), not a comma.

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