# Mathematics Class 6 ICSE CISCE Topics and Syllabus

## Syllabus

1 Number System
1.1 Sets
• Idea of sets.
• Representation of sets.
• Types of sets: Finite/infinite and empty.
• Cardinality of a set
1.1 Number System(Consolidating the Sense of Numberness)

Consolidating the sense of numberness up to 5 digits, size, estimation of numbers, identifying smaller, larger, etc.

1.2 Estimation

Estimation of outcome of number operations.

1.3 Numbers in India and International System (With Comparison)

Numbers in Indian and International Systems and their comparison

1.4 Place Value

Place value - recapitulation and extension

1.5 Natural Numbers and Whole Numbers (Including Patterns)
• Natural numbers
• Whole numbers
1.6 Negative Numbers and Integers
• Need for negative numbers.
• Connection of negative numbers in daily life.
• Representation of negative numbers on number line.
• Ordering of negative numbers, Integers.
• Identification of integers on the number line,
• Operation of addition and subtraction of integers,
• Addition and subtraction of integers on the number line
• Comparison of integers,
• ordering of integers.
1.7 Number Line
• Number line.
• Seeing patterns, identifying and formulating rules for operations on numbers.
1.8 HCF and LCM
• HCF and LCM, prime factorization and division method for HCF and LCM, the property LCM × HCF = product of two numbers
1.9 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.
2 Ratio and Proportion
2.1 Ratio

Difference between fraction and ratio.

Concept of Ratio.

2.2 Proportion (Including Word Problems)
Proportion as equality of two ratios
Word problems on ratio and proportions
2.3 Unitary Method

Unitary method (with only direct variation implied).

2.4 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
• Operations on fractions (Avoid large and complicated unnecessary tasks). (Moving towards abstraction in fractions).
2.5 Decimal 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).
2.6 Percent (Percentage)

Idea of percent as fraction with 100 as denominator

2.7 Idea of Speed, Distance and Time

Idea of speed and simple daily life problems related to speed, time and distance

3 Algebra
3.1 Fundamental Concepts

Introduction to constants, variable and unknown through patterns and through appropriate word problems and generalisations (For example 1+3=22, 1+3+5=32,
1+3+5+7=42 , sum of first n odd numbers = n2.).

3.2 Fundamental Operations (Related to Algebraic Expressions)

Terminology associated with algebra- like literal numbers, terms, expressions, factor, coefficient, polynomials, degree, like and unlike terms

Introduction to unknowns through examples with simple contexts (single operations)

3.3 Substitution (Including Use of Brackets as Grouping Symbols)
3.4 Framing Algebraic Expressions (Including Evaluation)

Framing algebraic expressions.

Evaluation of algebraic expressions by substituting a value for the variable.

3.5 Simple (Linear) Equations (Including Word Problems)

Introduction to linear equation in one variable.

4 Geometry
4.1 Fundamental Concepts

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

Line, line segment, ray.

Open and closed figures.

Interior and exterior of closed figures.

Curvilinear and linear boundaries

Angle — Vertex, arm, interior and exterior.

4.2 Angles (With Their Types)

Measure of angles

Types of angles- acute, obtuse, right, straight, reflex, complete and zero angle.

4.3 Properties of Angles and Lines (Including Parallel Lines)

Measure of Line segment

Pair of lines – Intersecting and perpendicular lines, Parallel lines.

4.4 Triangles (Including Types, Properties and Constructions)

Triangle — vertices, sides, angles, interior and exterior, altitude and median.

Classification of triangles (on the basis of sides, and of angles).

Quadrilateral — Sides, vertices, angles, diagonals, adjacent sides and opposite sides (only convex quadrilateral are to be discussed), interior and exterior of a quadrilateral.

4.6 Polygons

Simple polygons (introduction) (Upto octagons regulars as well as non-regular).

4.7 The Circle

Circle — Centre, radius, diameter, arc, sector, chord, segment, semicircle, circumference, interior and exterior.

4.8 Revision Exercise Symmetry (Including Constructions on Symmetry)

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).

4.9 Recognition of Solids

Identification of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone, prism (triangular and square), 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.

5 Mensuration
5.1 Perimeter and Area of Plane Figures
• 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
• Conversion of units (Mass, time, money, and capacity) from to smaller to larger and vice-versa
• 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.
6 Data Handling
6.1 Data Handling (Including Pictograph and Bar Graph)

Collection of data to examine a hypothesis

Collection and organisation of data - examples of organising it in tally bars and a table.

Pictograph- Need for scaling in pictographs interpretation & construction of pictograph

6.2 Mean and Median

Mean and median of data not having more than ten observations