Mathematics
Mathematics tests content up to upper primary and the pedagogy of building number sense, geometry and data handling. Strong answers connect a procedure to the underlying idea and anticipate children's errors.
Core rules
- Place value is base ten; operations, fractions, decimals, LCM and HCF depend on it. Equivalent fractions, ratio, proportion and percentage are connected representations.
- Commercial arithmetic: profit and loss are calculated on cost price; discount is calculated on marked price; simple and compound interest use different bases.
- Geometry and mensuration: angle types, triangle properties, perimeter, area and volume; keep units consistent and convert squared and cubed units correctly.
- Data handling: mean, median and mode; read tables and bar graphs accurately.
- Pedagogy: use a concrete-representational-abstract sequence, manipulatives, error analysis and problem-solving heuristics rather than algorithm-first drilling.
Worked example
A shopkeeper marks an item 25% above cost price and then gives a 10% discount. Let cost price be 100. Marked price is 125. Selling price is 90% of 125, which is 112.5. Profit is 12.5 on cost price 100, so profit percent is 12.5%. A common wrong answer, 15%, comes from subtracting 10 from 25; that ignores the different bases.
Traps
- Applying discount to cost price instead of marked price.
- Using the wrong base for percentage change.
- Confusing perimeter with area, or cm with cm².
- Converting units without squaring or cubing the factor.
- Averaging already-averaged values without weighting.