# Mathematics (M 807) - Grade 8

Unit | Area Covered | Marks | |
---|---|---|---|

Unit 1 |
Rational Numbers | 05 | Read more |

Unit 2 |
Exponents and Powers | 10 | Read more |

Unit 3 |
Squares and Square Roots; Cubes and Cube Roots | 20 | Read more |

Unit 4 |
Linear Equations in One Variable | 05 | Read more |

Unit 5 |
Linear Understanding Quadrilaterals and Constructing Quadrilaterals | 10 | Read more |

Unit 6 |
Mensuration | 10 | Read more |

Unit 7 |
Algebraic Expressions, Identities and Factorization of algebraic expressions | 05 | Read more |

Unit 8 |
Comparing Quantities | 10 | Read more |

Unit 9 |
Direct and Inverse Proportion | 10 | Read more |

Unit 10 |
Representing 3 D in 2D | 05 | Read more |

Unit 11 |
Playing With Numbers | 05 | Read more |

Unit 12 |
Data Handling | 05 | Read more |

Total Marks |
100 |

# Unit 1

**Definition and operations on rational numbers**

- 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.

**BODMAS**

- Recapitulating and applying the BODMAS rule.

**Applications of rational numbers in problem solving**

- Word problems involving rational numbers using all the operations.

# Unit 2

**Exponents**

- Recapitulate an exponent for natural numbers only.

**Laws of exponent**

- Arriving to the generalization of laws of exponents through patterns. Statements of the laws of exponents:

(i) am ×an =am+n

(ii) (am) n =amn

(iii) am/an = am-n, where m – n is a natural number

Extending the above laws for negative exponents and large exponents. Defining Multiplicative inverse w.r.t. exponents.

**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

**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**

- Through examples, generalize the properties of squares.

**natural numbers**

- 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 generalizing the number of digits in a perfect square number. Finding the square root of a perfect square and non perfect square by long division method. Square root of a decimal number.

**Estimation of square root**

- Estimating the square root of a given whole number to the nearest whole number.

**Applications of square and square root of a number**

- Word problems involving squares and square roots; understanding its importance in real world problems.

**Introduction to Cube of a number**

- Recapitulate the concept of cubes of numbers in reference to the powers of 3. Defining a perfect cubic number.

**Properties of cubes of natural numbers**

- Through examples, generalize the properties of cube of natural numbers.

**Cube Root of a given number**

- Find the cube root of a perfect cube (both 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**

- 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 Equations**

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

**Applications of Linear Equations**

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

# Unit 5

**Introduction to term polygon and its types**

- Explain the difference between polygons and non polygon figures; convex and concave polygons through examples. Classification of the types of polygons, with their names up to 10 sided polygons with a special reference to quadrilateral and its types.

**Angle sum property of a polygon**

- Generalizing the angle sum property of a polygon from that of a triangle through paper folding.

**Types of Quadrilaterals with their properties**

- Definition of trapezium, kite and their properties. Definition of parallelograms and its properties as a recapitulation of parallel lines and its properties with the transversal.

**Types of parallelograms**

- Defining a rhombus, rectangle and a square as a special parallelogram. Properties of the above.

**Construction of Quadrilaterals**

- Construction of a Quadrilateral when

i. Four sides and one diagonal are given

ii. Two diagonals and three sides are given

iii. Two adjacent sides and three angles are given.

iv. Three sides and two included angles are given

# Unit 6

**Area of 2-dimensionals**

- Recapitulate the concept of area, area of a square.

**Figures**

- 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 figures**

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

**Volume of 3 dimensional figures**

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

**Applications of volume and surface area**

- Apply the formulae of the volume and area of a cube, cuboid and right circular cylinder in practical problems.

# Unit 7

**Algebraic expression**

- Recapitulate an algebraic expression, constant, variable, like and unlike terms. Addition and subtractions of algebraic expressions.

**Multiplication of algebraic expressions**

- Multiplication of two monomials, a monomial with a binomial, a binomial with a binomial and a trinomial with a binomial.

**Algebraic Identities**

- Defining an Identity through examples. Arriving at the formulae through paper cutting lab activities for the following identities:

**(a+b) , (a-b) , a2 – b2**

Applications of the above identities to solve numerical and algebraic problems.

**Factorization**

- 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
- The method of common factors and by regrouping
- As an application to the above identities and
- Factorization of trinomials of degree 2 by the method of splitting the middle term (simple cases only)

**Division of two algebraic expressions**

- Dividing two polynomials by factorization method (simple cases only).

# Unit 8

**Ratio and Proportion**

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

**Percentage**

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

**Profit and Loss**

- Application of percentage to find the profit percentage and loss percentage.

**Sales Tax and Value added tax (VAT)**

- Application of percentage to find Sales Tax and Value added tax (VAT).

**Compound Interest**

- Recapitulate the concept of Simple Interest. Introduce compound interest as an extension to simple interest. Calculation of compound interest with rate of interest compounded annually and semi annually.

# Unit 9

**Direct Proportion**

- Introduction to direct Proportion. Application of direct Proportion in real life situations.

**Inverse Proportion**

- Introduction to inverse Proportion. Application of inverse Proportion in real life situations.

**Mixed problems**

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

# Unit 10

**Identification of 3-D objects**

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

**Different views of 3 –D 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.

# Unit 11

**General form of a number**

- Writing the expanded form of a number and the that of the number formed by reversing its digits.

**Letters for digits ( decoding the digits from letters)**

- Using letters for digits to solve puzzle games.

**Divisibility tests**

- Applying the divisibility rules to find the value of unknown number.

# Unit 12

**Graphical representation of data**

- Recapitulate the representation of ungrouped data in a bar graph. Introduction to double bar graph and reading the same.

**Grouped data**

- Grouping data by frequency distribution table. Frequency distribution table for ungrouped data and grouped data. Class interval, upper and lower limit class size (continuous class intervals only).

**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.