Mathematics Mastery Program for Classes 1–10 by Uzma Shaikh

Phase 1: Primary School Foundation (Classes 1 to 5)

​This phase focuses on building fundamental number sense, basic operations, and geometric awareness.

Key Focus Areas:

• ​Number System & Operations:

  • ​Class 1 & 2: Counting, number names (1-100), simple addition and subtraction (up to two digits), concept of zero, comparing numbers.

  • ​Class 3 to 5: Place value (up to thousands/lakhs), four basic operations (\times, \div), properties of operations, estimation, mental math.

​Fractions & Decimals:

• ​Introduction to fractions (parts of a whole), comparing and simple operations with fractions (Class 5).

• ​Introduction to decimals (tenths and hundredths).

• ​Measurement:

  • ​Units of length, mass, capacity (non-standard and standard units).

  • ​Time (reading clocks, calendar).

  • ​Money (basic calculations).

• ​Geometry:

  • ​Introduction to 2D and 3D shapes.

  • ​Spatial understanding (position, direction).

  • ​Perimeter and Area of simple shapes (Class 4 & 5).

• ​Data Handling:

  • ​Collecting and organizing data, pictographs, and bar graphs.

​Phase 2: Middle School Transition (Classes 6 to 8)

​This phase introduces abstract concepts like Algebra, Integers, and Rational Numbers, transitioning students from arithmetic to higher mathematics.

​Key Focus Areas:

• ​Number System Deep Dive:

  • ​Integers: Operations and properties.

  • ​Fractions and Decimals: Detailed operations, conversion.

  • ​Rational Numbers: Introduction, representation on the number line, operations.

• ​Algebra:

  • ​Introduction to Variables and Expressions (Class 6).

  • ​Linear Equations in one variable (Class 7 & 8).

  • ​Algebraic Identities and factorization of simple polynomials (Class 8).

• ​Geometry:

  • ​Basic geometrical concepts (lines, angles, triangles, quadrilaterals).

  • ​Congruence (Class 7) and Similarity (Introduction).

  • ​Understanding 2D and 3D shapes (Mensuration).

• ​Mensuration:

  • ​Area and Perimeter of standard shapes (Rectangle, Square, Triangle).

  • ​Surface Area and Volume of Cuboid and Cube.

• ​Commercial Mathematics:

  • ​Ratio and Proportion.

  • ​Percentage, Profit and Loss, Simple and Compound Interest (Class 8).

• ​Data Handling:

  • ​Frequency distribution, Histograms, and Pie Charts.

  • ​Introduction to Probability.

​ Phase 3: Secondary School Pre-Board (Classes 9 & 10)

​This phase is critical for board exams, focusing on rigorous proofs, theorems, and advanced algebraic and geometric topics.

​Key Focus Areas:

• ​Algebra:

  • ​Polynomials: Zeros, factor theorem, remainder theorem, factorization.

  • ​Linear Equations in Two Variables (Graphical and algebraic methods).

  • ​Quadratic Equations (Factorization, completing the square, quadratic formula).

  • ​Arithmetic Progressions (A.P.) (Class 10).

• ​Geometry:

  • ​Euclid's Geometry (Class 9).

  • ​Triangles: Congruence, Similarity Theorems (especially Thales Theorem/BPT).

  • ​Circles: Properties of chords, tangents, and angle subtended by an arc.

  • ​Constructions (Dividing a line segment, tangents to a circle).

• ​Trigonometry (Class 10):

  • ​Trigonometric Ratios (sin, cos, tan).

  • ​Trigonometric Identities.

  • ​Heights and Distances (Application of Trigonometry).

• ​Coordinate Geometry:

  • ​Distance Formula, Section Formula, Area of a Triangle.

• ​Mensuration:

  • ​Surface Areas and Volumes of combinations of solids (Cone, Cylinder, Sphere, Hemisphere).

  • ​Area related to Circles.

• ​Statistics & Probability:

  • ​Statistics: Mean, Median, Mode (grouped data).

  • ​Probability: Theoretical probability and related problems.