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Ratio and Rate

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

8 ready-made resources for teaching Ratio and Rate, 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

Solve real-life problems involving ratio and rate, including problems involving time, distance and speed: the same core skill introduced in Grade 7, applied to more complex or realistic contexts at Grade 8.
Simplify a ratio to its simplest form.
Increase or decrease a quantity in a given ratio.
Share an amount in a given ratio.

Grade 9, in addition

Continue solving real-life ratio, rate, time/distance/speed problems at a more advanced level.
Understand and use direct proportion: recognising when two quantities increase or decrease together at a constant ratio, and solving problems involving this relationship.
Understand and use indirect (inverse) proportion: recognising when one quantity increases as another decreases in a fixed pattern (e.g. more workers taking less time to complete the same job), and solving problems involving this relationship.

Where learners go wrong

Simplifying a ratio incorrectly by dividing by the wrong number, or dividing only one part of the ratio.
Confusing a ratio (comparing two quantities of the same kind) with a rate (comparing two quantities of different kinds, such as distance and time).
At Grade 9, assuming every proportional relationship is direct, when the context actually describes an indirect/inverse relationship.
Applying the speed formula (speed = distance ÷ time) with mismatched units, e.g. mixing kilometres with minutes without converting.

How it gets asked in the exam

"Determine the ratio of ... to ...", "Calculate the speed/distance/time ...", "y is directly proportional to x. Determine ...", "If it takes ... workers ... days, how long would it take ... workers?" (indirect proportion in context).

Key vocabulary

Ratio, rate, speed, distance, time, direct proportion, indirect (inverse) proportion.

Assumed prior knowledge

Simplifying fractions and ratios (using the highest common factor).
Confident multiplication and division, including with decimals.
Unit conversion, particularly for distance, time and speed problems (e.g. converting minutes to hours, or centimetres to metres, before comparing a ratio or rate).

How Speca scaffolds this topic

A bar-model visual for ratio sharing, and a formula-triangle for speed/distance/time, give concrete anchors for the Grade 8 core skill before Grade 9 introduces the more abstract proportion language.
Provide a sentence-starter prompt for Grade 9 ("as ___ increases, ___ ...") to help learners decide direct versus indirect proportion before attempting to solve, rather than guessing which relationship applies.
Anchor examples in concrete real-world contexts (recipe scaling, work-rate problems, map scales) rather than abstract numbers alone.

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