Official syllabus: 2025–2027 · version 3. Read the authoritative syllabus. Summary checked against its assessment overview on 5 October 2026. Administrative zone and centre-specific entry options remain unconfirmed.
Core: Papers 1 and 3, 80 marks and 90 minutes each. Extended: Papers 2 and 4, 100 marks and 120 minutes each. Each paper contributes 50%; Papers 1/2 prohibit calculators, Papers 3/4 require a scientific calculator.
For each proposed week: one 50-minute guided lesson, one 40-minute supported practice session and approximately 60 minutes of independent work. The appointed teacher must adjust pace from the initial diagnostic, map the complete syllabus and confirm accommodations before delivery. This sample is only the opening six-week sequence.
Each guided lesson uses: 5 minutes retrieval; 10 minutes explicit modelling; 15 minutes guided practice; 15 minutes independent response; 5 minutes exit check. Keep a plain-text copy and accept agreed low-bandwidth work. Collect only authorised learner records; no live learner records are included here.
Before week one, use the first unit’s questions without grading for certification. Record the method as well as the result. Identify a specific gap, teach one smaller example and retry a parallel question. After two unsuccessful supported attempts, the future teacher refers the learner to the academic coordinator with the work sample and the support tried. This is a proposed workflow; named staff are not yet appointed.
Represent a quantity as a fraction, decimal and percentage; justify the conversion.
Use a hundred-square drawn on paper. Shade 35 cells, label the fraction 35/100, simplify to 7/20 and convert to 0.35. Explain why every representation names the same quantity. Model 3/8 by division and comparison with 1/2. Have learners explain a mistaken claim that 0.35 equals 3.5%.
Convert 7/20 to a decimal and percentage. Order 0.6, 5/8 and 62%. Explain why 3/8 is less than 0.4.
7/20=0.35=35% (2 marks). Order: 0.6, 62%, 5/8=62.5% (3 marks). 3/8=0.375<0.4 with valid working (2 marks).
Use hundred-squares and written division for support; extend with recurring decimals without assuming finite conversion.
Retain the authorised work sample, annotate the specific criterion met or missed, give one actionable feedback point and check a parallel response. A mark alone does not demonstrate improvement. Log the next lesson’s adaptation.
Scale a ratio and check a proportional model against a context.
Model a paint mix of blue:white=2:3 using five drawn parts. A 20-litre batch has four litres per part, hence eight blue and twelve white. Compare additive and multiplicative changes; adding equal amounts does not generally preserve the ratio. Ask what must remain constant for a price model to be proportional.
Split R450 in the ratio 2:3. Three notebooks cost R54 at a constant unit price; calculate the cost of five. Explain why a delivery fee prevents total price being directly proportional to notebook count.
R180 and R270 using five equal parts (3 marks). R90, with R18 per notebook (2 marks). A fixed fee adds a non-zero intercept (2 marks).
Provide part diagrams; extend by deriving y=kx and a contrasting y=kx+b.
Retain the authorised work sample, annotate the specific criterion met or missed, give one actionable feedback point and check a parallel response. A mark alone does not demonstrate improvement. Log the next lesson’s adaptation.
Calculate a percentage change and identify the correct base.
Start with a R240 item and a 15% reduction. Model 15/100 of R240=R36, then R204. Explain the multiplier 0.85. Compare a reduction followed by a rise: the bases differ, so equal percentages do not cancel. Estimate the direction and magnitude before calculation.
Find a 15% discount on R240 and the final price. Increase R200 by 10%, then reduce the result by 10%. Explain the final difference from the original.
R36 discount and R204 final (3 marks). R220 then R198 (3 marks). The second percentage uses R220; overall decrease R2 (2 marks).
Use a labelled original/change/final table; extend to reverse percentages.
Retain the authorised work sample, annotate the specific criterion met or missed, give one actionable feedback point and check a parallel response. A mark alone does not demonstrate improvement. Log the next lesson’s adaptation.
Translate a simple pricing rule into an equation and solve for an unknown.
A fictional taxi model charges R12 plus R4 per kilometre. Write C=12+4d, label variables and units, and calculate three values. Demonstrate solving 12+4d=40 by undoing operations in reverse. Discuss why this simplified rule may not model all real journeys.
Write the rule, find the cost at 5 km, solve for distance when cost is R40 and identify one modelling limitation.
C=12+4d (2 marks); R32 (2 marks); d=7 km (3 marks); plausible limitation such as waiting time or variable tariffs (1 mark).
Provide balance diagrams and operation arrows; extend to comparison of two linear models.
Retain the authorised work sample, annotate the specific criterion met or missed, give one actionable feedback point and check a parallel response. A mark alone does not demonstrate improvement. Log the next lesson’s adaptation.
Select an area calculation and preserve units through a compound shape.
Draw an L-shaped floor as a 6 m by 4 m rectangle with a 2 m by 1 m corner removed. Calculate the large area before subtracting the cut-out. Compare a second method that splits the shape into rectangles. Ask why perimeter cannot be obtained by subtracting areas.
Calculate the L-shaped area. At R75 per square metre, calculate material cost ignoring waste. State one reason a real quotation could be higher.
24−2=22 m² with working (3 marks); R1650 (2 marks); allowance for waste, labour or other stated cost (1 mark).
Supply a labelled scale-free diagram; extend to an algebraic expression for a variable cut-out.
Retain the authorised work sample, annotate the specific criterion met or missed, give one actionable feedback point and check a parallel response. A mark alone does not demonstrate improvement. Log the next lesson’s adaptation.
Calculate summaries and explain what a small data set can and cannot show.
Use fictional journey times 12, 14, 14, 15, 25 minutes. Model sorting, median, mean and range. Explain how the high value affects the mean while the median describes the central ordered value. Require a sentence tying the choice of measure to the question rather than declaring one measure always better.
Find mean, median and range. Compare with 12,14,14,15,15. Explain why neither five-value set establishes the usual journey time for an entire town.
Mean 16, median 14, range 13 (3 marks); second mean 14, median 14, range 3 (3 marks); small/context-limited sample with reason (2 marks).
Use ordered cards or plain text; extend by describing a fairer sampling method.
Retain the authorised work sample, annotate the specific criterion met or missed, give one actionable feedback point and check a parallel response. A mark alone does not demonstrate improvement. Log the next lesson’s adaptation.
For the six-week review sample, combine one task from weeks 1–2, one from weeks 3–4 and one from weeks 5–6. State the purpose and local rubric before use. These are original practice tasks, not Cambridge examination questions, grade thresholds or official mark schemes.
All four remain required before formal teaching opens. School admissions and fees remain launch-gated.