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Mathematics transcends from basic skill to an in-depth analysis of the quantities around the students by this stage. The syllabus focuses on various new concepts and delving deeper into the pre-existing concepts. The students have gradually developed a better sense of the subject by the end of the year.

The curriculum for the academic year 2022-2023 is based on the guidelines given by CBSE. The syllabus is based around the main book suggested by CBSE. The layout of the book changes drastically too, focusing more on learning.

Mathematics - textbook for class VI

The Chapters / Contents of the book

Chapter 1: Knowing Our Numbers | 1.1 Introduction 1.2 Comparing Numbers 1.3 Large Numbers in Practice 1.4 Using Brackets 1.5 Roman Numerals |

Chapter 2: Whole Numbers | 2.1 Introduction 2.2 Whole Numbers 2.3 The Number Line 2.4 Properties Of Whole Numbers 2.5 Patterns in Whole Numbers |

Chapter 3: Playing With Numbers | 3.1 Introduction 3.2 Factors and Multiples 3.3 Prime and Composite Numbers 3.4 Test For Divisibility Of Numbers 3.5 Common Factors and Common Multiples 3.6 Some More Divisibility Rules 3.7 Prime Factorisation 3.8 Highest Common Factor 3.9 Lowest Common Multiple 3.10 Some Problems on HCF and LCM |

Chapter 4: Basic Geometrical Ideas | 4.1 Introduction 4.2 Points 4.3 A Line Segment 4.4 A line 4.5 Intersecting Lines 4.6 Parallel Lines 4.7 Ray 4.8 Curves 4.9 Polygons 4.10 Angles 4.11 Triangles 4.12 Quadrilaterals 4.13 Circles |

Chapter 5: Understanding Elementary Shapes | 5.1 Introduction 5.2 Measuring Line Segments 5.3 Angles-’Right’ and ‘Straight’ 5.4 Angles- ‘Acute’, ‘Obtuse’ and ‘Reflex’ 5.5 Measuring Angles 5.6 Perpendicular Lines 5.7 Classification of Triangles 5.8 Quadrilaterals 5.9 Polygons 5.10 Three Dimensional Shapes |

Chapter 6: Integers | 6.1 Introduction 6.2 Integers 6.3 Addition of Integers 6.4 Subtraction of Integers with the help of a Number Line |

Chapter 7: Fractions | 7.1 Introduction 7.2 A Fraction 7.3 Fraction on the Number Line 7.4 Proper Fractions 7.5 Improper and Mixed Fractions 7.6 Equivalent Fractions 7.7 Simplest Form of a Fraction 7.8 Like Fractions 7.9 Comparing Fractions 7.10 Addition and Subtraction of Fractions |

Chapter 8: Decimals | 8.1 Introduction 8.2 Tenths 8.3 Hundredths 8.4 Comparing Decimals 8.5 Using Decimals 8.6 Addition of Numbers with Decimals 8.7 Subtraction of Decimals |

Chapter 9: Data Handling | 9.1 Introduction 9.2 Recording Data 9.3 Organisation of Data 9.4 Pictograph 9.5 Interpretation of a Pictograph 9.6 Drawing a Pictograph 9.7 A Bar Graph |

Chapter 10: Mensuration | 10.1 Introduction 10.2 Perimeter 10.3 Area |

Chapter 11: Algebra | 11.1 Introduction 11.2 Matchstick Patterns 11.3 The Idea Of A Variable 11.4 More Matchstick Patterns 11.5 More Examples of Variables 11.6 Use Of Variables in Common Rules 11.7 Expressions with Variables 11.8 Using Expressions Practically 11.9 What is an Equation? 11.10 Solution of an Equation |

Chapter 12: Ratio and Proportion | 12.1 Introduction 12.2 Ratio 12.3 Proportion 12.4 Unitary Method |

Chapter 13: Symmetry | 13.1 Introduction 13.2 Making Symmetric Figures: Ink-blot Devils 13.3 Figures With Two Lines of Symmetry 13.4 Figures with Multiple Lines of Symmetry 13.5 Reflection and Symmetry |

Chapter 14: Practical Geometry | 14.1 Introduction 14.2 The Circle 14.3 A Line Segment 14.4 Perpendiculars 14.5 Angles |

(i) Knowing our Numbers: Consolidating the sense of numbers up to 5 digits, Size, estimation of numbers, identifying smaller, larger, etc. Place value (recapitulation and extension), connectives: use of symbols =, <,> and use of brackets, word problems on number operations involving large numbers up to a maximum of 5 digits in the answer after all operations. This would include conversions of units of length & mass (from the larger to the smaller units), estimation of outcome of number operations. Introduction to a sense of the largeness of, and initial familiarity with, large numbers up to 8 digits and approximation of large numbers)

(ii) Playing with Numbers: Simplification of brackets, Multiples and factors, divisibility rule of 2, 3, 4, 5, 6, 8, 9, 10, 11. (All these through observing patterns. Children would be helped in deducing some and then asked to derive some that are a combination of the basic patterns of divisibility.) Even/odd and prime/composite numbers, Co-prime numbers, prime factorization, every number can be written as products of prime factors. HCF and LCM, prime factorization and division method for HCF and LCM, the property LCM × HCF = product of two numbers. All this is to be embedded in contexts that bring out the significance and provide motivation to the child for learning these ideas.

(iii) Whole numbers: Natural numbers, whole numbers, properties of number (commutative, associative, distributive, additive identity, multiplicative identity), number line. Seeing patterns, identifying and formulating rules to be done by children. (As familiarity with algebra grows, the child can express the generic pattern.)

(iv) Negative Numbers and Integers: How negative numbers arise, models of negative numbers, connection to daily life, ordering of negative numbers, representation of negative numbers on a number line. Children to see patterns, identify and formulate rules. What are integers, identification of integers on the number line, operation of addition and subtraction of integers, showing the operations on the number line (addition of negative integer reduces the value of the number) comparison of integers, ordering of integers.

(v) Fractions: Revision of what a fraction is, Fraction as a part of a whole, Representation of fractions (pictorially and on a number line), fraction as a division, proper, improper & mixed fractions, equivalent fractions, comparison of fractions, addition and subtraction of fractions (Avoid large and complicated unnecessary tasks). (Moving towards abstraction infractions) Review of the idea of a decimal fraction, place value in the context of decimal fraction, interconversion of fractions and decimal fractions (avoid recurring decimals at this stage), word problems involving addition and subtraction of decimals (two operations together on money, mass, length, and temperature)

Introduction to Algebra

- Introduction to a variable through patterns and through appropriate word problems and generalizations (example 5 × 1 = 5 etc.)
- Generate such patterns with more examples.
- Introduction to unknowns through examples with simple contexts (single operations).

- Concept of Ratio
- Proportion as equality of two ratios
- Unitary method (with only direct variation implied)
- Word problems

(i) Basic geometrical ideas (2 -D): Introduction to geometry. Its linkage with and reflection in everyday experience.

- Line, line segment, ray.
- Open and closed figures.

*figures*.- Curvilinear and linear
*boundaries* - Angle — Vertex, arm, interior, and exterior,
- Triangle — vertices, sides, angles, interior and exterior, altitude and median
- Quadrilateral — Sides, vertices, angles, diagonals, adjacent sides and the opposite side (only convex quadrilateral are to be discussed), interior and exterior of a quadrilateral.
- Circle — Centre, radius, diameter, arc, sector, chord, segment, semicircle circumference, interior, and exterior.

ii) Understanding Elementary Shapes (2-D and 3-D):

- Measure of a Line segment
- Measure of angles
- Pair of lines

- Types of angles- acute, obtuse, right, straight, reflex, complete and zero angle
- Classification of triangles (on the basis of sides, and of angles)
- Types of quadrilaterals – Trapezium, parallelogram, rectangle, square, rhombus.
- Simple polygons (introduction) (Upto octagons regulars as well as non-regular).
- Identification of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone, prism (triangular), pyramid (triangular and square) Identification and located in the surroundings
- Elements of 3-D figures. (Faces, Edges, and vertices)
- Nets for cubes, cuboids, cylinders, cones, and tetrahedrons.

(iii) Symmetry: (reflection)

- Observation and identification of 2-D symmetrical objects for reflection symmetry
- Operation of reflection (taking mirror images) of simple 2-D objects
- Recognising reflection symmetry (identifying axes)

(iv) Constructions (using Straight edge Scale, protractor, compasses)

- Drawing of a line segment
- Construction of circle
- Perpendicular bisector
- Construction of angles (using protractor)
- Angle 60°, 120° (Using Compasses)
- Angle bisector- making angles of 30°, 45°, 90°, etc. (using compasses)
- Angle equal to a given angle (using a compass)
- Drawing a line perpendicular to a given line from a point

a) on line b) outside the line.

Concept of Perimeter and Introduction to Area Introduction and a general understanding of perimeter using many shapes. Shapes of different kinds with the same perimeter. Concept of area, Area of a rectangle and a square Counterexamples to different misconceptions related to perimeter and area.

The perimeter of a rectangle – and its special case – a square. Deducing the formula of the perimeter for a rectangle and then a square through pattern and generalization.

(i) What is data - choosing data to examine a hypothesis?

(ii) Collection and organization of data - examples of organizing it in tally bars and a table.

(iii) Pictograph- Need for scaling in pictographs interpretation & construction.

(iv) Making bar graphs for given data interpreting bar graphs+.