CBSE Class 6 Syllabus for Mathematics

Number System (60 hrs)

(i) Knowing our Numbers:

Consolidating the sense of numberness 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 factorisation, 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 X 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 numbers (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 Intergers

How negative numbers arise, models of negative numbers, connection to daily life, ordering of negative numbers, representation of negative numbers on 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 whole, Representation of fractions (pictorially and on 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 in fractions) Review of the idea of a decimal fraction, place value in the context of decimal fraction, inter conversion 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)

Algebra (15 hrs)

INTRODUCTION TO ALGEBRA

• Introduction to variable through patterns and through appropriate word problems and generalisations (example 5 X 1 = 5 etc.)

• Generate such patterns with more examples.

• Introduction to unknowns through examples with simple contexts (single perations)

Ratio and Proportion (15 hrs)

• Concept of Ratio

• Proportion as equality of two ratios

• Unitary method (with only direct variation implied)

• Word problems

Geometry (65 hrs)

(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.

• Interior and exterior of closed 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 opposite sides (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 Line segment

• Measure of angles

• Pair of lines

      - Intersecting and perpendicular lines

      - Parallel 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 locating in the surroundings

• Elements of 3-D figures. (Faces, Edges and vertices)

• Nets for cube, 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 60o, 120o (Using Compasses)

• Angle bisector- making angles of 30o, 45o, 90o etc. (using compasses)

• Angle equal to a given angle (using compass)

• Drawing a line perpendicular to a given line from a point a) on the line b) outside the line.

Mensuration (15 hrs)

CONCEPT OF PERIMETER AND INTRODUCTION TO AREA

Introduction and 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 Counter examples to different misconcepts related to perimeter and area. 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 generalisation.

Data handling (10 hrs)

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

(ii) Collection and organisation of data - examples of organising 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+.

SYLLABUS

Summative Assessment- I

1. Knowing Our Numbers
2. Whole Numbers
3. Playing with Numbers.
4. Basic Geometrical Ideas.
5. Integers
6. Understanding Elementary shapes.
7. Fractions
8. Data Handling

Summative Assessment- II

1. Decimals
2. Practical Geometry
3. Mensuration
4. Algebra
5. Ratio and Proportion
6. Symmetry (Only Lab Activity)

Test Papers

1 MCQ

2 Model test paper – Summative Assessment-I (Solved)
3 Model test paper – Summative Assessment-I (Unsolved-1)
4 Model test paper – Summative Assessment-I (Unsolved-2)
5 Model test paper – Summative Assessment-II (Solved)
6 Model test paper – Summative Assessment-II (Unsolved-1)
7 Model test paper – Summative Assessment-II (Unsolved-2)
8 Revision Worksheets

SCHEDULE FOR FORMATIVE ASSESSMENTS:
FORMATIVE ASSESSMENT-I [50 Marks]
MCQ [25 Marks]
HOLIDAY HOMEWORK [15 Marks]
LAB ACTIVITIES [10 Marks]

FORMATIVE ASSESSMENT-II [50 Marks]
PEN & PAPER TEST [30 Marks]
MCQ [10 Marks]
CLASS PERFORMANCE/
NOTEBOOK ASSESSMENT [10 Marks]

FORMATIVE ASSESSMENT-III [50 Marks]
PEN & PAPER TEST [30 Marks]
MCQ [10 Marks]
ACTIVITIES [10 Marks]

FORMATIVE ASSESSMENT-IV [50 Marks]
MCQ [20 Marks]
PROJECT WORK [15 Marks]
LAB ACTIVITY [10 Marks]
NOTEBOOK ASSESSMENT [5 Marks]

MODULES

Module – 1
Chapter : Knowing Our Numbers
Contents:
(i) Comparing Numbers
(ii) Ascending/Descending Order
(iii) Place Value
(iv) Estimation
(v) Roman Numerals

Learning Objectives:
Students accquire knowledge of whole numbers and natural numbers.
Key Terms:
Natural numbers, Whole numbers

Module – 2
Chapter : Whole numbers
Contents:
(i) Introduction of Natural and Whole Numbers
(ii) Definitions of Key Terms
(iii) Successor / Predecessor
(iv) Define operations
(v) Properties of Addition, Subtraction, Multiplication and Division
(vi) Examples and related questions
(vii) Distributive property

Learning Objectives:
Students acquire knowledge of operations possible on whole and natural numbers and properties of these operations. They apply the knowledge and develop skills in using properties on whole numbers in different kinds of problems.
Key Terms:
Natural numbers, Whole numbers

Module – 3
Chapter : Playing with numbers
Contents:
(i) Define Factors and Multiples
(ii) Properties of factors and multiples
(iii) Prime and composite numbers
(iv) Odd and even numbers
(v) Perfect numbers
(vi) Divisibility test for 2, 3, 4, 5, 6, 8, 9, 10, 11
(vii) Properties of divisibility
Learning Objectives:
Students learn about factors and multiples. They develop understanding of different
kinds of numbers and also acquire knowledge of applying different divisibility tests.
They also learn about Prime factorization and develop ability to find HCF & LCM
and their problem sums.
Key Terms:
Factors, Multiples, Perfect number

Module – 4
Chapter: Playing with numbers (contd.)
Contents:
(i) Prime factorization
(ii) LCM & HCF
Learning Objectives:
Students learn about Prime factorization and method to find HCF and LCM of the given numbers.
Key Terms:
Prime factorization, HCF and LCM

Module – 5
Chapter: Playing with numbers (contd.)
(i) Properties of LCM & HCF
(ii) Problem sums

Chapter: 2. Basic Geometrical Ideas
Contents:
(i) Concept of Point, Line and Plane
(ii) Definition of Line, Line Segment and Ray
(iii) Introduction of curves and its types
(iv) Polygons
(v) Angles
(vi) Triangles
(vii) Circles and its parts

Learning Objectives:
Develop ability to find HCF & LCM and their problem sums. They also develop understanding on basic geometrical concepts, different types of curves, polygons and other basic geometrical shapes.
Key Terms:
HCF, LCM, Point, Line, Line segment, Intersecting lines, Parallel lines, Ray,Polygons, Angles, Triangles, Circles

Module – 6
Chapter : Integers
Contents:
(i) Need of integers and their introduction
(ii) Representation of integers on number line
(iii) Ordering of integers
(iv) Addition and subtraction of integers

Learning Objectives:
Students develop understanding of integers and operation on integers. Develop skills in using and solving operations on integers.
Key Terms:
Ordering, Additive Inverse

Module – 7
Chapter : Understanding Elementary Shapes
Contents:
(i) Measurement of Line segments
(ii) Angles - Its kinds and measurement
(iii) Perpendicular lines
(iv) Classification of Triangles
(v) Quadrilaterals and types of Quadrilaterals
(vi) Polygons and its classification
(vii) Three dimensional shapes

Learning Objectives:
Students get indepth knowledge of Line segment, Angles, Triangles, Polygons and Quadrilaterals including their classification and measurements.
Key Terms:
Quadrilaterals, 3–D shapes

Module – 8
Chapter : Fractions
Contents:
(i) Concept of fractions
(ii) Types of fractions
(iii) Equivalent fractions
(iv) Simplest form of fractions
(v) Like and unlike fractions
(vi) Comparison of fractions
(vii) Addition & subtraction of fractions

Learning Objectives:
(i) Imparting knowledge of fractions and its types.
(ii) Students learn more about fractions and its operations i.e. Addition and subtraction.
Key Terms:
Equivalent fractions, Proper and improper fractions

Module – 9
Chapter : Data Handling
Contents:
(i) Recording and organization of data
(ii) Pictograph
(iii) Drawing and interpretation of Pictograph
(iv) Bar graph
(v) Drawing and interpretation of bar graph

Learning Objectives:
(i) Students learn recording and organization of data. They also acquire knowledge of drawing and interpretation of pictograph.
(ii) Students acquire knowledge about the concept of bar graph and its interpretation from the data.
Key Terms:
Data, Pictograph, Bar graph

Module – 10
Revision For Half Yearly Examination

Module – 11
Chapter : Decimals
Contents:
(i) Concept of Decimals
(ii) Fractions as decimals and vice versa
(iii) Place values
(iv) Comparison of decimals

Learning Objectives:
Students learn the concept of decimals and its comparison.
Key Terms:
Decimal and Number line

Module – 12
Chapter : Decimals (contd…)
Contents:
(i) Application of decimals
(ii) Addition and subtraction of decimals

Learning Objectives:
Imparting knowledge on use of decimals in simple daily life problems and operations of decimals.
Key Terms:
Money, length, weight

Module – 13
Chapter : Practical Geometry
Contents:
(i) Construction of a circle
(ii) Construction of a line segment
(iii) Constructing a line segment equal to the given line segment
(iv) Draw a perpendicular to a given line through a point.
(a) Lying on it
(b) Not lying on it
(iv) Draw the perpendicular bisector of a given line segment
(v) Construct an angle equal to a given angle
(vi) Construction of angles of measure 600, 300, 900, 450, and 1200 .

Learning Objectives:
(i) Students develop skills to draw figures using ruler and compass.
(ii) Students acquire skills to draw correct and accurate figure from the given data.
Key Terms:
Perpendicular bisector

Module – 14
Chapter : Mensuration
Contents:
(i) Perimeter of square and rectangle
(ii) Area of square and rectangle
(iii) Perimeter and area of irregular figures
(iv) Problem sums

Learning Objectives:
Students get knowledge about concepts of Perimeter and Area which are of great practical utility.
Key Terms:
Area, Perimeter

Module – 15
Chapter : Algebra
Contents:
(i) Concept of constants and variables
(ii) Use of variables
(iii) Expressions with variables
(iv) Use of expressions practically
(v) Introduction of an equation
(vi) Solving an equation

Learning Objectives:
Students develop an understanding of literal numbers and operations of literal numbers. Gain knowledge of algebraic expressions. Develop skill in simplifying and solving the equation.
Key Terms:
Like / unlike terms, grouping symbols, exponential form, literal numbers, linear equation.

Module – 16
Chapter : Ratio and Proportion
Contents:
(i) Concept of ratio and proportion
(ii) Extreme and middle terms
(iii) Express in ratio form
(iv) Express in proportion form

Learning Objectives:
Develop understanding of ratio and proportion. Students learn the method of comparing two quantities with the help of ratio and proportion.
Key Terms:
Ratio, Proportion, Extreme and middle term

Module – 17
Chapter : Ratio and proportion contd.
Contents:
(i) Unitary method

Learning Objectives:
Students develop ability in understanding and solving problems based on unitary method and direct variation.
Key Terms:
Unitary method.

Chapter : Symmetry (ACTIVITY BASED)
Contents:
(i) Concept of Linear Symmetry
(ii) Figures with 2 lines of symmetry

Learning Objectives:
Students get an idea about the symmetrical objects in daily life.
Key Terms:
Line of Symmetry