Unique Online Classes & Pre-Recorded Courses

• Rational Numbers: Properties of rational numbers (closure, commutativity, associativity, distributive property), representation on the number line, and rational numbers between two rational numbers. 
• Linear Equations in One Variable: Solving equations with linear expressions on one side and numbers on the other, solving equations with variables on both sides, applications of linear equations, and reducing equations to simpler forms. 
• Understanding Quadrilaterals: Polygons, sum of measures of exterior angles of a polygon, different kinds of quadrilaterals (parallelogram, rhombus, rectangle, square, kite, trapezium), and their properties. 
• Data Handling: Looking for information, organizing data, grouping data, circle graphs (pie charts), and chance and probability. 
• Squares and Square Roots: Properties of square numbers, finding the square of a number, Pythagorean triplets, finding square roots through prime factorization and the division method, and square roots of decimals. 
• Cubes and Cube Roots: Cubes and cube roots of a number, finding cube roots through prime factorization. 
• Cubes and Cube Roots: Cubes and cube roots of a number, finding cube roots through prime factorization. 
• Comparing Quantities: Ratios and percentages, finding increase or decrease percent, discounts, prices related to buying and selling (profit and loss), sales tax/VAT/GST, compound interest, and applications of compound interest formula. 
• Algebraic Expressions and Identities: Terms, factors, and coefficients, monomials, binomials, and polynomials, like and unlike terms, addition and subtraction of algebraic expressions, multiplication of algebraic expressions, standard identities, and applying identities. 
• Mensuration: Area of trapezium, area of general quadrilateral, area of polygons, surface area of cube, cuboid, and cylinder, and volume of cube, cuboid, and cylinder. 
• Exponents and Powers: Powers with negative exponents, laws of exponents, and use of exponents to express small numbers in standard form. 
• Direct and Inverse Proportions: Understanding direct and inverse proportions and solving related problems. 
• Factorisation: What is factorization, division of algebraic expressions, and factorization using algebraic identities. 
• Introduction to Graphs: Bar graphs, pie graphs, histograms, line graphs, linear graphs, and their applications.

1. Review of the representation of natural numbers, integers, and rational numbers on the number
   line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.
2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers
   (irrational numbers) such as , and their representation on the number line. Explaining
   that every real number is represented by a unique point on the number line and conversely,
   viz. every point on the number line represents a unique real number.
3. Definition of nth root of a real number.
4. Rationalization (with precise meaning) of real numbers
   and (and their combinations) where x and y are natural numbers and a and b are
   integers.
5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases
   (to be done by particular cases, allowing the learner to arrive at the general laws.)

Practical Guide to Rational Numbers

Lesson Name: Rational numbers

• How to divide the pizza?
• How to divide the dough?

Lessons schedule: Monthly, 20 Classes

What you will learn: 

• Recognizing irrational expressions 
• Applying rationalisation techniques
•  Solving algebraic problems with square roots and surds 
• Avoiding common mistakes and improving accuracy 
• This session is suitable for CBSE, ICSE, and State Board students.