Mathematics and Science: Content Plus Pedagogy for the 60-Mark Paper
For the Mathematics and Science teacher, this section is 60 marks: 30 Mathematics and 30 Science, each roughly half content and half pedagogy. Content follows the Classes VI–VIII syllabus; pedagogy items describe a classroom situation and ask for the appropriate strategy.
Mathematics map
Number system and operations, HCF/LCM, ratio and proportion, percentage, profit and loss, simple and compound interest, exponents, algebraic expressions and identities, linear equations, lines and angles, triangle congruence, circles and constructions, mensuration (area, surface area, volume), data handling, symmetry. Pedagogy: Van Hiele levels (visualisation → analysis → informal deduction → deduction), concrete → pictorial → abstract sequencing, Polya's four steps (understand, plan, carry out, look back), error analysis, mathematics laboratory and manipulatives.
Science map
Food and its components, materials and separation techniques, acids and bases, plant and animal life, respiration, reproduction, motion and force, light, sound, electric circuits, natural phenomena, environment. Pedagogy: process skills (observing, classifying, hypothesising, experimenting, inferring), the 5E model (Engage, Explore, Explain, Elaborate, Evaluate), activity-based and inquiry learning, laboratory safety.
Worked example
Two numbers are in the ratio 3 : 4 and their HCF is 8. Numbers = 3 × 8 = 24 and 4 × 8 = 32. LCM = 8 × 3 × 4 = 96. Check: 24 × 32 = 768 and HCF × LCM = 8 × 96 = 768. Reasoning: the HCF rule product = HCF × LCM holds only for two numbers, and the ratio terms must be coprime - 3 : 4 is.
Traps
- Applying HCF × LCM = product to three numbers.
- Unit slips: 1 m/s = 3.6 km/h; 1 hectare = 10,000 m².
- Confusing mass with weight in science items.
- Placing an ammeter in parallel or a voltmeter in series.
- Describing Van Hiele level 1 as "pre-visual" - it is visualisation.