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Patterns and Relationships Between Variables

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

8 ready-made resources for teaching Patterns and Relationships Between Variables, 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

Investigate and extend numeric and geometric patterns: including patterns shown physically or in diagrams, patterns from natural or cultural contexts, patterns learners design themselves, and patterns that are not limited to a constant difference or ratio.
Represent a pattern algebraically for the first time (Grade 7 represents patterns in words, diagrams and tables only, not yet algebraically).
Determine input and/or output values of a relationship using a verbal description, flow diagram, or table (carried forward from Grade 7), and now also using a formula or an equation: both new at Grade 8.
Recognise when a verbal description, flow diagram, table, and equation all describe one and the same relationship, and move confidently between these forms.

Grade 9, in addition

Explain and justify a rule generated from a pattern using formal algebra, rather than describing it in the learner's own words as in Grade 7 and 8: a genuine shift in the standard of justification expected.
Extend the equivalence-of-representations work to include reading and drawing the same relationship as a graph on the Cartesian plane, alongside the verbal, flow-diagram, table, and equation forms already met.

Where learners go wrong

Continuing a pattern by only looking at the last two terms, rather than checking the rule holds consistently across the whole sequence.
Writing an algebraic rule for a pattern that works for the first few terms shown but breaks down further along the sequence (a rule found by insufficient checking).
Confusing an input-output table's rule with a fixed starting value, rather than a rule that must be applied consistently to every input.
At Grade 9, treating a graph as a completely separate representation rather than recognising it shows the same relationship as the table or equation already found.

How it gets asked in the exam

"Determine the next three terms in the pattern", "Determine a formula/rule for the pattern", "Complete the table of values", "Determine the output value when the input is ...", "Represent the relationship as a graph on the Cartesian plane" (Grade 9).

Key vocabulary

Pattern, sequence, term, rule, input, output, flow diagram, formula, equation, Cartesian plane, relationship.

Assumed prior knowledge

Confident work with number sequences and simple patterns (Grade 7 content, expressed non-algebraically).
Substituting a value into a simple formula.
Plotting points on a Cartesian plane (first quadrant at Grade 7, extending to four quadrants elsewhere in the Geometry strand).

How Speca scaffolds this topic

Use a consistent input-output "function machine" visual across verbal, flow-diagram, table, and (at Grade 9) graph representations, so the same underlying relationship is always recognisable in a new format.
For patterns, a colour-coded difference-row written directly underneath a numeric sequence, the same scaffold already used elsewhere in this taxonomy for algebraic pattern work, helps learners spot the rule before attempting to write it algebraically.
Chunk the move from "describe the rule in words" to "write the rule algebraically" as its own explicit step, since this is the main new cognitive demand at Grade 8, not the pattern-spotting itself.
South African decimal convention: use a comma as the decimal separator wherever a decimal value appears (e.g. 2,5, not 2.5).

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