A chapter-wise, continuously updated handbook of key formulas, definitions and concepts from the Class 6 NCERT Maths textbook (Ganita Prakash, 2026-27 edition). Each section below is added as the corresponding chapter’s Solutions/Extra Questions/Revision Notes are published.
Chapter 1: Patterns in Mathematics (Ganita Prakash)
- Triangular numbers: 1,3,6,10,15,… — nth term = n(n+1)/2.
- Square numbers: 1,4,9,16,25,… — nth term = n².
- Cube numbers: 1,8,27,64,125,… — nth term = n³.
- Virahanka numbers: 1,2,3,5,8,13,21,… — each term is the sum of the two before it.
- Key identity: sum of first n odd numbers = n².
- Complete graph with n points has n(n-1)/2 connecting lines.
Chapter 2: Lines and Angles
Chapter 3: Number Play
Chapter 4: Data Handling and Presentation
Chapter 5: Prime Time
Chapter 6: Perimeter and Area
- Perimeter of rectangle = 2 × (length + breadth)
- Perimeter of square = 4 × side
- Perimeter of regular polygon = number of sides × side length
- Area of rectangle = length × breadth
- Area of square = side × side
- Area of triangle = ½ × base × height
- Same perimeter can give different areas; same area can give different perimeters (square-like shapes minimise perimeter for a given area)
Chapter 7: Fractions
- Fraction = numerator/denominator; unit fraction has numerator 1
- Proper fraction: numerator < denominator. Improper: numerator ≥ denominator. Mixed: whole + proper fraction
- Equivalent fractions: multiply/divide numerator and denominator by the same number
- Simplest form: divide by HCF of numerator and denominator
- Comparing unlike fractions: convert to a common denominator (LCM), then compare numerators
- Addition/subtraction (Brahmagupta’s method): like fractions — add/subtract numerators directly; unlike fractions — use common denominator (LCM) first
Chapter 8: Playing with Constructions
- Circle: set of all points at a fixed distance (radius) from a fixed centre
- Rectangle/square construction: base (ruler) → 90° perpendiculars (protractor) → mark breadth → join points
- Rectangle splits into n identical squares only if longer side = n × shorter side
- A rectangle’s diagonal splits each corner’s 90° angle into two parts summing to 90°
- 45°/45° diagonal split ⇒ the shape must be a square
- A rhombus can have all sides equal without being a square
Chapter 9: Symmetry
- Line of symmetry: a line along which a figure folds into two matching mirror halves
- Rotational symmetry: figure matches itself after rotating less than 360° about a fixed point (centre of rotation)
- Angle of symmetry must be a whole-number factor of 360°; order of rotational symmetry = number of such angles
- Regular polygon with n sides: n lines of symmetry, rotational order n, angle of symmetry = 360°/n
- Circle: infinite lines of symmetry, infinite angles of symmetry
Chapter 10: The Other Side of Zero
- Integers: positive numbers, negative numbers, and zero (addition/subtraction only at this level)
- Additive inverse: number that sums with a given integer to give 0 (inverse of +4 is -4)
- On the number line, values increase left to right; among negatives, closer to zero = greater (-2 > -5)
- Subtracting a negative = adding the positive: a – (-b) = a + b
- Token model: a “+” and a “-” token together form a zero pair, worth 0
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