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Class 9

Mathematics: Ganita Manjari Part 1

73 lessons in 8 chapters, explained in plain words.

Orienting Yourself: The Use of Coordinates

  1. Grids before graphs
  2. Reiaan's room on a grid
  3. Axes, origin and points on the axes
  4. The four quadrants
  5. Planning a room with coordinates
  6. Distance between two points
  7. Reflection keeps lengths
  8. Distance at work
  9. Midpoints and trisection (enrichment)

Introduction to Linear Polynomials

  1. Terms, variables and coefficients
  2. Polynomials and their degree
  3. Linear patterns
  4. Linear equations and input-output
  5. Stage n: the general term
  6. Linear growth and linear decay
  7. Finding y = ax + b from two facts
  8. Graphs of y = ax: slope
  9. The y-intercept and parallel lines

The World of Numbers

  1. The need to count
  2. Śhūnya: when nothing became a number
  3. Fortunes and debts
  4. Rational numbers
  5. Arithmetic of rational numbers
  6. Rationals on the number line
  7. √2 is irrational
  8. Building √n, and π
  9. Terminating or repeating?
  10. Repeating decimals and the real numbers

Exploring Algebraic Identities

  1. Identities, and why (a + b)² works
  2. Squaring with (a + b)²
  3. Factorising perfect squares
  4. (a + b + c)² and a² – b²
  5. Algebra tiles and (x + a)(x + b)
  6. Splitting the middle term
  7. Cubes: (a + b)³ and (a – b)³
  8. Sums and differences of cubes
  9. Simplifying rational expressions
  10. Using factorisation

I’m Up and Down, and Round and Round

  1. What a circle is
  2. Circles through two points
  3. Three points and the circumcircle
  4. Equal chords, equal angles
  5. The perpendicular from the centre
  6. How far is a chord from the centre?
  7. Angles subtended by an arc
  8. Concyclic points and cyclic quadrilaterals
  9. Reasoning with circles

Measuring Space: Perimeter and Area

  1. Perimeter, and why relays have staggers
  2. The story of π
  3. Arcs, and a 400 m track
  4. Perimeter puzzles
  5. Areas of parallelograms and triangles
  6. Heron's formula
  7. Brahmagupta's formula and squaring a rectangle
  8. Area puzzles
  9. The area of a circle
  10. Areas with circles and copies

The Mathematics of Maybe: Introduction to Probability

  1. Chance and randomness
  2. The probability scale
  3. Experimental probability
  4. Theoretical probability
  5. Using data; the long run
  6. Sample spaces and events
  7. Tree diagrams
  8. Probability problems

Predicting What Comes Next: Exploring Sequences and Progressions

  1. Sequences and their terms
  2. Explicit rules
  3. Recursive rules
  4. Arithmetic progressions
  5. Adding up an AP
  6. Geometric progressions
  7. Fractals, bounces and GP problems
  8. Progressions puzzles