# ICSE Mathematics Class 6 Syllabus

The syllabus consist of six themes - Number System, Ratio and Proportion, Algebra, Geometry, Mensuration, and Data Handling.

### Theme 1: Number System

Numbers

• Consolidating the sense of numberness up to 5 digits, size, estimation of numbers, identifying smaller, larger, etc.
• Place value (recapitulation and extension)
• Operations on large numbers.
• Word problems on number operations involving large numbers - 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.
• Numbers in Indian and International Systems and their comparison.

Natural numbers and Whole numbers

• Natural numbers.
• Whole numbers.
• Properties of numbers (commutative, associative, distributive, additive identity, multiplicative identity).
• Number line.
• Seeing patterns, identifying and formulating rules for operations on numbers.

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.

Sets

• Idea of sets.
• Representation of sets.
• Types of sets: Finite/infinite and empty.
• Cardinality of a set.

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).
• 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)

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 × HCF = product of two numbers.

### Theme 2: Ratio and Proportion

• Difference between fraction and ratio.
• Concept of Ratio.
• Proportion as equality of two ratios.
• Unitary method (with only direct variation implied).
• Word problems on ratio and proportions.
• Idea of percent as fraction with 100 as denominator.
• Idea of speed and simple daily life problems related to speed, time and distance.

### Theme 3: Algebra

• 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.).
• Generate such patterns with more examples and generalisation.
• Introduction to unknowns through examples with simple contexts (single operations)
• Terminology associated with algebra - like literal numbers, terms, expressions, factor, coefficient, polynomials, degree, like and unlike terms.
• Framing algebraic expressions.
• Evaluation of algebraic expressions by substituting a value for the variable.
• Introduction to linear equation in one variable.

### Theme 4: Geometry

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.
• 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.

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 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.

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).

Constructions (using Straight edge Scale, protractor, compasses)

• Drawing of a line segment.
• 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 compass.)
• Drawing a line perpendicular to a given line from a point a) on the line b) outside the line.
• Construction of circle.

### Theme 5: Mensuration

• 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 misconceptions 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.

### Theme 6: Data Handling

• 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
• Construction of bar graphs for given data interpreting bar graphs.
• Mean and median of data not having more than ten observations.