## Unit 1: Rational Numbers

Definition and operations on rational numbersPractise Now

Recapitulate the definition of rational number; addition, subtraction, multiplication and division of two rational numbers.

Properties on Rational Numbers

State and verify the properties of addition, subtraction, multiplication and division of rational numbers.

Representation of rational numbers on number line

Representing a given rational number on the number line; representing the sum and difference of two rational numbers (with same denominator) on a number line.

Finding two or more rational numbers between two given rational numbers

Given two rational numbers, find another rational number between them by mean method and more than two by the method of equivalent rational numbers.

Applications of Laws of Exponents

Applying the laws of exponents find an unknown exponent. To solve the problems involving exponents with different operations. Writing very large and small numbers in standard form using the laws of exponents and vice versa.

## Unit 3: Squares and Square Roots; Cubes and Cube Roots

Introduction to squares

Recapitulate the concept of squares of numbers in reference to the powers of 2. Defining a perfect square number.

Properties of squares of natural numbers

Through examples, generalize the properties of square of natural numbers. Introduce Pythagorean Triplet

Square Root of a given number

Recapitulate the term prime factors and find the square root of a perfect square (natural numbers and non negative rational numbers) by prime factorization method. Through examples

positive and negative numbers) by prime factorization method.

Applications of cubes and cube root of a number

Word problems involving cubes and cube roots; understanding its importance in real world problems.

## Unit 4: Linear Equations in One Variable

Linear EquationsPractise Now

Recapitulation of Linear Equations in one variable. Solution of a linear equation with linear expression on one side and numbers on the other and extending the concept to variables on both sides of the equation.

Solution of Linear EquationsPractise Now

Extend the concept to solution of linear equations expressed in terms of rational expressions. Solution of equations reducible to linear form.

Applications of Linear EquationsPractise Now

Applying linear equations in one variable to solve the real life problems.

Construction of QuadrilateralsPractise Now

Construction of a Quadrilateral when:

- Four sides and one diagonal are given
- Two diagonals and three sides are given
- Two adjacent sides and three angles are given
- Three sides and two included angles are given

## Unit 6: Mensuration

Area of 2-dimensional figuresPractise Now

Recapitulate the concept of area, area of a square, area of a rectangle, area of a circle and area of a parallelogram. Introduce area of a triangle, trapezium, quadrilateral, parallelogram and regular polygon.

Area of 3 dimensional figuresPractise Now

Lateral/ Curved Surface Area of a cuboid, cube, right circular cylinder.

Volume of 3 dimensional figuresPractise Now

Volume of a cuboid, cube, right circular cylinder(solid right circular cylinder and hollow right circular cylinder)

FactorizationPractise Now

Recapitulate factorization of natural numbers. Factorization of monomials, finding the H.C.F. of monomials. Factorization of the expressions which are other than monomials by:

i. the method of common factors and by regrouping

ii. as an application to the above identities and

iii. factorization of trinomials of degree 2 by the method of splitting the middle term (simple cases only)

Division of two algebraic expressions

Practise Now

Dividing two polynomials by factorization method (simple cases only)

## Unit 8: Comparing Quantities

Ratio and Proportion

Recapitulate ratio and proportion. Recapitulate the applications of the above in daily life problems.

PercentagePractise Now

Recapitulate the concept of percentage. Introduce increase or decrease of percentage

Mixed problems

Identifying the questions on direct and inverse.Proportion and application of the same.

## Unit 10: Representing 3D in 2D

Identification of 3D objects

Recapitulation of the components of various 3-D objects including prisms and pyramids

Different views of 3D objects

Finding out different vies of 3-D objects from different positions

Introduction to Map

Identify different symbols in a given map, draw simple route maps

Polyhedron

Introduction to polyhedron with a special reference to prism and pyramid and its components

Euler's Formula

Introduction to Euler's formula through activities

Histogram

Graphical representation of grouped data using frequency distribution table. Concept of Jagged line to be introduced

Pie Chart

Construction of pie chart using central angle of a sector as a fraction of the area of the circle

Probability

Recapitulate the concept of probability. Formal introduction to probability using the terms random experiment and equally likely outcomes. Building the definition through examples.