Mathematics Class 7 ICSE CISCE Topics and Syllabus

• Concept of Integers 
• Multiplication and Division of Integers 
• Properties of Operations on Integers 
• Concept for Commutativity, Associativity, Existence of Identity 
• Inverse and Distributivity 
• Problem Solving Using Operations on Integers 
• Statement Problems on Integers Using All Fundamental Operations. 

• 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)

• Concept of Rational Numbers 
• Word Problems on Rational Numbers (All Operations) 
• Decimal Representation of Rational Numbers 
• Concept for Problem Solving Using Operations on Rational Numbers 
• Concept of Decimal Numbers 

• Introduction to rational numbers (withrepresentation on numberline)
• Word problems onrational numbers (alloperations)
• Decimal representation of rational numbers
• Problem solving using operations on rational numbers and decimal fractions

• Concept of Fractions 
• Concept for Fraction as an Operator 
• Concept for Reciprocal of a Fraction 

• Fraction as an operator
• Reciprocal of a fraction

• Concept of Decimal Numbers 
• Concept for Multiplication 
• Division of Decimal Numbers 
  • Decimal Division through models.

• Multiplication and
  division of decimal
  fractions

• Concept of Exponents 
• Concept for Exponents Only Natural Numbers. 
• Laws of Exponents (Through Observing Patterns to Arrive at Generalisation.) 
• Concept for Application of Laws of Exponents in Simple Daily Life Problems 

• Exponents only natural numbers.
• Laws of exponents (through observing patterns to arrive at generalisation.)
• Application of laws of exponents in simple daily life problems.

• Concept of Ratio 

• Ratio and proportion (revision)

• Concept of Unitary Method (Including Time and Work) 
• Unitary Method Continued, Consolidation, General Expression for Unitary Method . 
• Relation Between Speed, Time and Distance 

• Unitary method continued, consolidation, general expression for unitary method .
• Speed, distance, time

• Concept of Percent and Percentage 
• Concept for Understanding Percentage as a Fraction with Denominator 100 
• Converting Fractional Numbers to Percentage 
• Converting Decimals to Percentage 

• Percentage- an introduction.
• Understanding percentage as a fraction with denominator 100
• Converting fractions and decimals into percentage and vice-versa.

• Concept of Discount 
• Concept for Application to Profit and Loss (Single Transaction Only) 

• Application to profit and loss (single transaction only)

• Concept of Principal, Interest, Amount, and Simple Interest 
  • Simple Interest for one year
  • Simple Interest for multiple years
• Concept for Application to Simple Interest (Time Period in Complete Years). 

• Application to simple interest (time period in complete years).

• Fundamental Concepts 
• Terms, Factors and Coefficients of Expression 
• Algebraic Expressions 
  • Variable
  • Constant
  • Algebraic Expressions
  • Value of Expression
  • Number line and an expression
• Performs Operations (Addition and Subtraction) on Algebraic Expressions with Integral Coefficients Only. 

• 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 
• Concept for Inequalities 
  • The sign > means, "is greater than" i.e.; if 'a' is greater than 'b', we write : a > b.
  • The sign < means, "is less than" i.e.; if 'a' is less than 'b', we write : a < b.
• Concept for Solution of Simple Inequalities in One Variable 

• Simple linear equations in one variable (in contextual problems) with two operations.
• Inequalities and solution of simple inequalities in one variable

• Concept of Set Concepts 
• Concept for Revision Idea of Sets 
• Concept for Universal Sets 
• Concept for Cardinal Property of Sets 

• Revision idea of sets
• Equal, equivalent, universal sets
• Cardinal property of sets

• Introduction to Lines and Angles 
• Concept for Pairs of Angles 
• Concept for Properties of Parallel Lines with Transversal 
  • Interior angle theorem
  • Corresponding angles and alternate angles theorem
• Construction of a Line Parallel to a Given Line from a Point Outside It . 

Understanding shapes:-

•             Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite).
•             Properties of parallel lines with transversal (alternate, corresponding, interior, exterior   angles).     
•             Construction of a line parallel to a given line from a point outside it .

• Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle 
• Concept for Angle Sum Property 
• Concept for Exterior Angle Property 
• Concept for Construction of Simple Triangles. 

Properties of triangles:-

• Angle sum property
• Exterior angle property
• Construction of simple triangles.

• Right-angled Triangles and Pythagoras Property 

• Pythagoras Theorem (Verification only)

• Concept of Symmetry 
• Concept of Reflection Symmetry 
• Concept for Idea of Rotational Symmetry, Observations of Rotational Symmetry of 2-d Objects. (900, 1200, 1800) 

Symmetry:- 

• Recalling reflection symmetry
• Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (900, 1200, 1800)

• Concept of Recognition of Solids 
• Faces, Edges and Vertices 
• Concept for Mapping the Space Around Approximately Through Visual Estimation. 

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 of Triangles 
• Concept for Congruence Through Superimposition 
• Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles. 
• Criteria for Congruence of Triangles 

 Congruence :- 

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

• Mensuration 
• Concept of Perimeter 
• Circumference of a Circle 
• Concept of Area 
• Concept of Measurement Using a Basic Unit Area of a Square, Rectangle, Triangle, Parallelogram and Circle, Rings and Combined Figures. 

• 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.

• Concept of Data Handling 
  • Data Handling
  • Data
  • Types of Data
• Concept for Collection and Organisation of Data – Choosing the Data to Collect for a Hypothesis Testing 
• Concept of Median 
• Concept of Mode 
• Concept for Constructing 
• Interpretation of Bar Graphs 

• 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

• Basic Ideas of Probability 
• Concept for Feel of Probability Using Data Through Experiments. 
• Concept for Notion of Chance 
• Concept for Tabulating and Counting Occurrences 
• Comparing the Observation with that for a Coin. Observing Strings of Throws, Notion of Randomness. 

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.