Mathematics
Mathematics in CTET is split across two papers. Paper 1 (Classes 1–5) tests primary number sense, basic geometry, measurement and the pedagogy of teaching maths to young children. Paper 2 (Classes 6–8) extends into integers, algebra, mensuration, data handling and the pedagogy of upper-primary maths. Both papers ask 30 questions — about 20 on content and 10 on pedagogy. These 17 topic notes cover the full official syllabus, with the pedagogy emphasis the exam actually demands.
Paper 1 — Mathematics (Classes 1–5)
Primary mathematics — number sense, basic operations, shapes, measurement, money and the pedagogy of teaching maths to young children.
Geometry — Shapes, Spatial Understanding & Solids
Children grasp 3D before 2D — handle solids first, then trace faces. Van Hiele levels 0–1 at primary, with symmetry through rangoli (NIOS 504, Unit 6).
MP1-02Numbers — Concept, Place Value & Number Sense
Hindu-Arabic decimal system with zero as place-holder. Pre-number concepts (matching, one-to-one) precede formal counting. Place value through bundles of sticks (NIOS 504).
MP1-03Addition & Subtraction
Addition combines, subtraction takes away. Addition is commutative and associative; subtraction is neither. Children develop 'counting-on' before written algorithms (NIOS 504, Unit 5).
MP1-04Multiplication & Division
Multiplication is repeated addition; arrays show commutativity. Two types of division — partition (equal sharing) and quotition (grouping). Distributive law as mental-maths tool (NIOS 504, Unit 5).
MP1-05Measurement — Length, Weight, Time & Volume
Length and mass conservation develop before area and volume. Children start with non-standard units (handspan, cubit) before SI units. Estimation is central (NIOS 504).
MP1-06Data Handling (P1)
Collection → tally marks → pictograph → bar graph. Mode introduced informally through pictographs; mean comes later. Surveys drawn from children's own lives (NIOS 504, Unit 8).
MP1-07Patterns & Money
NCF 2005: 'regularity is the essence of mathematics'. Pattern recognition is the precursor to algebra. Rangoli and money problems make decimals meaningful.
MP1-08Nature of Mathematics & Children's Mathematical Thinking
Five characteristics — logical, symbolic, precise, structural, abstract. NCF 2005's broader aim is mathematisation, not just content (Wheeler, Polya — NIOS 504 Unit 2).
MP1-09Mathematics Pedagogy — Evaluation, Errors & Remedial Teaching (P1)
Concrete → Pictorial → Abstract (Bruner's CPA). Maths phobia comes from abstract symbols too early. NCF 2005: assess understanding, not preciseness of answers.
Paper 2 — Mathematics (Classes 6–8)
Upper-primary mathematics — integers, fractions, algebra, geometry, mensuration, statistics and the pedagogy of teaching maths to older children.
Number System — Knowing & Playing with Numbers, Whole Numbers
Lakhs to billions, primes, HCF/LCM, squares, cubes, exponents. Brahmagupta and Virahaṅka named as Indian originators (NCERT Ganita Prakash Cl. 6–8).
MP2-02Negative Numbers, Integers & Fractions
Brahmagupta's laws for integers and fractions (628 CE) frame the whole topic; spiral from Class 6 intuition to Class 8 percentages (NCERT Ganita Prakash).
MP2-03Algebra — Introduction, Ratio & Proportion
NCERT 2024 calls variables 'letter-numbers' to ease the jump. Algebra = generalised arithmetic. Distributive law + proportional reasoning (Ganita Prakash Cl. 7–8).
MP2-04Geometry — Basic 2D Ideas & Elementary Shapes (P2)
Lines, angles, triangles, congruence, quadrilaterals. NCERT 2024 co-attributes Pythagoras to Baudhāyana (Sulba Sūtras, ~800 BCE) — direct IKS integration.
MP2-05Symmetry, Construction & Mensuration
Symmetry, compass-ruler construction, perimeter→area→volume, and fractals. NCERT 2024 calls symmetry 'ubiquitous in Mathematics and beyond' (Ganita Prakash Cl. 6, 7 P2, 8 P2).
MP2-06Data Handling & Statistics (P2)
Cl. 6 collection → Cl. 7 mean/median/mode (Connecting the Dots) → Cl. 8 line graphs and pie charts. Spiral curriculum in one strand (NCERT Ganita Prakash).
MP2-07Nature of Maths & Pedagogy (P2)
The 'dual role' — intuition + rigour, exploration + best methods (NCERT Ganita Prakash). Middle Stage bridges Preparatory → Secondary (NCFSE 2023). NEP 2020: computational thinking + IKS.
MP2-08Evaluation, Remedial Teaching & Problems of Teaching Maths (P2)
NCERT 2024: 'classroom should not expect blind application of algorithms'. Algebra-anxiety and the 'multiplication makes bigger' alternative conception both fail at Middle Stage.