CBSE Class 6 Maths
NCERT Ganita Prakash • Chapter-wise Theory • Questions • Solutions
Explore Class 6 Mathematics through chapter-wise theory, clear explanations, worked examples, practice questions and step-by-step solutions based on NCERT Ganita Prakash for the 2026–27 academic session.
What is CBSE Class 6 Maths?
CBSE Class 6 Maths is the Grade 6 foundational mathematics curriculum based on the official NCERT textbook Ganita Prakash (Reprint 2026–27). It encompasses 10 core chapters spanning number patterns, geometric building blocks (lines, angles, constructions), arithmetic games, data handling, prime factorization, perimeter, area, fractions, symmetry, and integers. The curriculum prioritizes experiential exploration, logical reasoning, and puzzle-based inquiry that bridge mathematical thinking directly with the emerging field of Computational Thinking.
Class 6 Maths Overview
The Class 6 Mathematics curriculum bridges the Preparatory and Middle School stages. Rather than expecting passive memorization of formulas and mechanical algorithms, Ganita Prakash introduces students to mathematics as an exploratory art. Learners actively investigate number sequences, geometric configurations, symmetric transformations, arithmetic games, and real-world data collection.
Chapter-Wise Theory
In-depth conceptual breakdowns, formal definitions, and intuitive explanations for all 10 chapters.
Worked Examples
Step-by-step mathematical problem walkthroughs modeling clear analytical thinking.
Interactive Practice
Multiple-choice conceptual questions with instant grading, hints, and explanatory solutions.
Visual Geometry & Symmetry
Interactive geometry explorations covering lines, angles, protractor measurements, and constructions.
Empirical Data Handling
Hands-on data collection, tally tables, pictographs, bar graphs, and critical infographic evaluation.
Computational Thinking Bridge
Direct integration with algorithmic decomposition, patterns, invariants, and logic puzzles.
Class 6 Maths Chapters
Patterns in Mathematics
Number Sequences, Visual Lattices & Geometric Relationships
Explores mathematics as the creative search for patterns. Covers sequences of numbers (counting, odd, even, triangular, square, cube, powers of 2 and 3, and Virahānka numbers) and their surprising geometric interrelations.
- •What is Mathematics? (The search for beautiful patterns and explanations)
- •Whole number sequences and growth rules
- •Triangular numbers (1, 3, 6, 10, 15...) and dot representations
- •Square numbers (1, 4, 9, 16, 25...) and odd number summation
Lines and Angles
Geometric Building Blocks, Rays & Angle Measurements
Introduces the foundational elements of geometry: points, line segments, rays, and intersecting/parallel lines. Explores angle formation through turns, rotational measures, protractor usage, and angle classifications.
- •Points, line segments, lines, and rays (naming conventions)
- •Intersecting, collinear, and parallel line relationships
- •Angles as measures of rotation and turns
- •Classification: Zero, Acute (<90°), Right (90°), Obtuse (90°–180°), Straight (180°), and Reflex angles
Number Play
Supercells, Palindromes, Kaprekar's Constant & Game Strategies
A playful mathematical adventure featuring grid supercells, number line estimation, digit permutations, palindromes, D.R. Kaprekar's magic constant 6174, the Collatz 3n+1 conjecture, and winning strategies in arithmetic games.
- •Supercells in rows and 2D orthogonal grids
- •Patterns and interval spacing on the number line
- •Digit sums and digit frequency distributions
- •Palindromic numbers and reverse-and-add algorithms
Data Handling and Presentation
Surveys, Tally Tables, Pictographs, Bar Graphs & Aesthetic Integrity
Covers the complete data handling lifecycle: collecting empirical facts, organizing with tally marks into frequency tables, drawing pictographs with scale keys, constructing column and bar graphs from a zero baseline, and guarding against misleading visual infographics.
- •What is data? Distinguishing empirical collection from fixed facts
- •Tally marks in bundles of five (卌) and frequency tables
- •Ascending order data organization and threshold queries
- •Pictographs: Unit keys, multi-unit scales, and fractional symbols
Prime Time
Prime Numbers, Factorization, Sieve of Eratosthenes & Divisibility
Explores prime numbers as the atomic building blocks of whole numbers. Covers factors, multiples, prime vs composite classification, the Sieve of Eratosthenes, prime factorization trees, divisibility tests, and HCF/LCM computation.
- •Primes (exactly 2 factors) vs Composite numbers (>2 factors)
- •The uniqueness of 1 (neither prime nor composite) and 2 (only even prime)
- •The Sieve of Eratosthenes systematic prime discovery algorithm
- •Prime factorization and factor tree decomposition
Perimeter and Area
Boundary Lengths, Grid Coverage & Shape Optimization
Deepens conceptual understanding of boundary length (perimeter) versus surface coverage (area). Uses grid squares, rectilinear polygons, and spatial puzzles to illustrate that shapes with equal perimeters can have different areas.
- •Perimeter as total distance around the closed boundary of a 2D shape
- •Area as the measure of surface region enclosed within boundary lines
- •Calculating perimeter for regular polygons (squares, rectangles, equilateral triangles)
- •Finding area by counting unit square grids and partial squares
Fractions
Parts of a Whole, Fraction Strips, Equivalence & Operations
Builds intuitive fractional understanding starting from unit fractions (such as 1/10 and 1/4). Uses visual fraction strips, number lines, proper/improper fractions, mixed numbers, equivalent fractions, and like/unlike fraction addition and subtraction.
- •Fractions as equal parts of a whole or a collection
- •Unit fractions (1/n) as the foundation of rational quantities
- •Proper fractions (<1), improper fractions (≥1), and mixed numbers
- •Representing fractions accurately on the number line
Playing with Constructions
Ruler & Compass Geometry, Bisectors & Precision Circles
A hands-on geometric construction laboratory using a ruler and compass. Guides students through drawing circles of given radii, constructing line segment copies, perpendicular bisectors, angle bisectors, and special angles (60°, 90°, 120°).
- •Geometric drawing instruments: Ruler, compass, divider, and set-squares
- •Constructing circles and concentric circles with specified radii
- •Constructing a line segment equal in length to a given segment
- •Constructing perpendicular lines and perpendicular bisectors of line segments
Symmetry
Reflection Lines, Rotational Symmetry, Rangoli & Natural Patterns
Explores symmetry as an artistic and mathematical principle across nature, architecture, and art. Covers lines of symmetry (reflection symmetry), ink-blot and paper-folding designs, multiple lines in regular polygons, and rotational symmetry.
- •Line symmetry (bilateral/reflection symmetry) and mirror axes
- •Identifying lines of symmetry in letters, natural leaves, and architecture
- •Lines of symmetry in regular polygons (an equilateral triangle has 3, square has 4, regular hexagon has 6)
- •Completing symmetric figures given a partial drawing and mirror line
The Other Side of Zero
Negative Numbers, Integers, Bela's Building & Brahmagupta's Laws
Introduces directed numbers and negative integers through real-world models (Bela's Building of Fun elevators, temperatures below zero, sea levels, and financial balances). Culminates in Brahmagupta's 628 CE formal rules for addition and subtraction of integers.
- •The necessity of numbers below zero in physical contexts (temperatures, basements, depths)
- •The set of Integers: Positive integers, zero (neutral), and negative integers
- •Representing integers on the number line and ordering relationships (-5 < -2 < 0 < 3)
- •Opposite numbers / additive inverses (x + (-x) = 0)
Class 6 Maths Theory
Select any chapter below to explore its foundational principles, mathematical vocabulary, core theorems, and pedagogical takeaways:
Patterns in Mathematics
Explores mathematics as the creative search for patterns. Covers sequences of numbers (counting, odd, even, triangular, square, cube, powers of 2 and 3, and Virahānka numbers) and their surprising geometric interrelations.
Comprehensive Concepts in this Chapter:
Recognizing repeating sequences, iterative step rules, and invariant algebraic properties.
Class 6 Maths Questions & Solutions
Test your mathematical understanding with chapter-representative questions derived from Ganita Prakash concepts. Select an option to receive immediate feedback, hints, and complete step-by-step solutions:
What is the sum of the first 6 consecutive odd whole numbers (1 + 3 + 5 + 7 + 9 + 11)?
What angle is formed by the hands of a standard 12-hour clock at exactly 3:00?
In the 1949 Kaprekar routine for 4-digit numbers with distinct digits, which unique invariant constant is always reached?
In a pictograph where 1 Book Symbol = 10 Books, how many books are represented by 3 complete symbols and 1 half symbol?
Which of the following numbers is a prime number?
A rectangular garden has length 15 m and breadth 8 m. What is its perimeter and area?
Which fraction is equivalent to 3/4 with a denominator of 20?
Which tool combination is strictly used for classical geometric constructions of bisectors and standard angles?
How many lines of symmetry does a regular pentagon have?
What is the value of (-8) + (+15) + (-7)?
Mathematics and Computational Thinking
As emphasized in the Foreword and introduction of Ganita Prakash, learning mathematics is not just memorizing algorithms—it is discovering patterns, formulating logical arguments, and developing structured problem-solving habits that lead directly into the emerging discipline of Computational Thinking and Artificial Intelligence.
Observing patterns, arithmetic rules, and geometric relationships.
Reasoning why properties hold, finding loopholes, and generalizing rules.
Decomposition, step-by-step instructions, invariants, and abstraction.
Training models on structured data to recognize complex real-world patterns.
Practice Computational Thinking with Class 6 Maths
After learning the relevant mathematical concepts, students can apply systematic reasoning and problem-solving through Computational Thinking questions.
Practice Class 6 Computational Thinking Questions →