# ICSE Mathematics Class 7 Syllabus

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

### Theme 1: Number System

• Multiplication and division of integers
• Properties of operations on integers: Commutativity, associativity, existence of identity and inverse and distributivity
• Problem solving using operations on integers
• Solution of word problems involving integers (all operations)
• Introduction to rational numbers (with representation on number line)
• Word problems on rational numbers (all operations)
• Decimal representation of rational numbers
• Problem solving using operations on rational numbers and decimal fractions
• Fraction as an operator
• Reciprocal of a fraction
• Multiplication and division of decimal fractions
• Exponents only natural numbers.
• Laws of exponents (through observing patterns to arrive at generalisation.)
• Application of laws of exponents in simple daily life problems
• Revision idea of sets
• Equal, equivalent, universal sets
• Cardinal property of sets

### Theme 2: Ratio and Proportion

• Ratio and proportion (revision)
• Unitary method continued, consolidation, general expression for unitary method
• Percentage - an introduction.
• Understanding percentage as a fraction with denominator 100
• Converting fractions and decimals into percentage and vice-versa.
• Application to profit and loss (single transaction only)
• Application to simple interest (time period in complete years).
• Speed, distance, time

### Theme 3: Algebra

• Terms related to algebra like constants, variable, terms, coefficient of terms, like and unlike terms, etc.
• Generate algebraic expressions
• Performs operations (addition and subtraction) on algebraic expressions with integral coefficients only
• Simple linear equations in one variable (in contextual problems) with two operations.
• Inequalities and solution of simple inequalities in one variable

### Theme 4: Geometry

Understanding shapes

• Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite)
• Properties of parallel lines with transversal (alternate, corresponding, interior, exterior angles)

Properties of triangles

• Angle sum property
• Exterior angle property
• Pythagoras Theorem (Verification only)

Symmetry

• Recalling reflection symmetry
• Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (90°, 120°, 180°)

Representing 3-D in 2-D

• Identification and counting of vertices, edges, faces, nets (for cubes cuboids, and cylinders, cones).
• Mapping the space around approximately through visual estimation.

Congruence

• Congruence through superimposition
• Extend congruence to simple geometrical shapes e.g. triangles, circles.
• Criteria of congruence

Construction

• Construction of a line parallel to a given line from a point outside it
• Construction of simple triangles.

### Theme 5: Mensuration

Revision of perimeter and Idea of Circumference of Circle

Area

Concept of measurement using a basic unit area of a square, rectangle, triangle, parallelogram and circle, rings and combined figures.

### Theme 6: Data Handling

• Collection and organisation of data - choosing the data to collect for a hypothesis testing
• Mean, median and mode of ungrouped data - understanding what they represent
• Constructing and interpreting bar graphs
• Feel of probability using data through experiments. Notion of chance in events like tossing coins, dice etc.
• Tabulating and counting occurrences of 1 through 6 in a number of throws.
• Comparing the observation with that for a coin. Observing strings of throws, notion of randomness.