# Mathematics (M 707) - Grade 7

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

Unit 1 |
Integers | 05 | Read more |

Unit 2 |
Fractions and Decimal | 05 | Read more |

Unit 3 |
Introduction to Rational Numbers | 10 | Read more |

Unit 4 |
Powers | 10 | Read more |

Unit 5 |
Algebraic Expressions | 10 | Read more |

Unit 6 |
Ratio and Proportion | 10 | Read more |

Unit 7 |
Understanding Shapes | 05 | Read more |

Unit 8 |
Symmetry | 05 | Read more |

Unit 9 |
Representing 3D in 2D | 10 | Read more |

Unit 10 |
Congruence | 10 | Read more |

Unit 11 |
Menstruation | 10 | Read more |

Unit 12 |
Data Handlings | 10 | Read more |

Total Marks |
100 |

# Unit 1

**Multiplication and Division of Integers**

- Introducing multiplication and division of integers through patterns. Showing that division by zero is meaningless.

**Properties of Integers**

- Properties of addition and multiplication of integers viz closure, commutative, associative, distributive through patterns Counter examples to show that the properties do not hold good for subtraction.

**Application of Number Operations**

- Word problems on number operations for integers.

**BODMAS**

- Recapitulating and applying the BODMAS rule.

# Unit 2

**Multiplication of Fractions**

- Recapitulate the concept of fractions and its types; addition, subtraction and comparison of two or more fractions. Multiplication of two given fractions

**Fraction as an Operator**

- To apply fraction as an operator, to find part of a given quantity, reciprocal of a fraction

**Division of Fractions**

- To define division of fractions, to apply division of fractions in terms of reducible to multiplication

**Applications of Fractions in Problem Solving**

- Word problems involving fractions including mixed fractions; understanding the importance of fractions in real world problems

**Multiplication of Decimals**

- Recapitulate the concept of decimals as a fraction; addition, subtraction of two or more decimals Multiplication and division of decimal fractions

**Conversion of Units**

- Application of decimal fraction in conversion of units of length and mass

**Applications of Decimals in Problem Solving**

- Word problems involving decimal fractions understanding the importance of fractions in real world problems. Application of the BODMAS rule in solving the problems involving fractions and decimals

# Unit 3

**Introduction to Rational Numbers**

- Introduction to rational numbers and its need as an extension of fractions.

**Operations on Rational Numbers**

- Addition, subtraction, multiplication and division of rational numbers with reference to the operations on fractions.

**Representation of Rational Number as Decimal**

- Represent rational number as a decimal, as an extension of representation of fraction, as decimal.

**Representation of Rational Numbers on the Number Line**

- Recapitulate the representation of fractions on the number line and extend the same for rational numbers (simple cases only).

**Applications of Rational Numbers in Problem Solving**

- Word problems involving rational numbers using all the operations.

# Unit 4

**Exponents**

- Defining 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:
- am an =am+n

(am) n =amn

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

- am an =am+n

**Applications of Laws of Exponents**

- Applying the laws of exponents to solve the problems with different operations. Writing large numbers in standard form using the laws of exponents and vice versa

# Unit 5

**Formation of Algebraic Expressions**

- Recapitulate algebraic expressions and terms involved. Generate simple algebraic expressions involving one or two variables. Identify constants, variables, coefficients, powers.

**Like and Unlike Terms**

- Defining like and unlike terms through examples; defining degree of an algebraic expression (degree ≤3).

**Operations on Algebraic Expressions**

- Addition and subtraction of algebraic expressions with integral coefficients. Multiplying single term over a bracket, taking out single term common factors, expanding the product of two linear expressions (binomial by binomial)

**Define and Distinguish between Various Terms used with Algebraic Expressions**

- Distinguish between the terms equation, formula, expression and identity

**Linear Equations**

- Simple linear equations in one variable with two operations (avoid complicated coefficients) Verification of the accuracy of the answer by substitution. To set up and solve simple linear equations in which unknown appears on both sides

# Unit 6

**Definition of Ratio**

- Recapitulate the concept of ratio. Ratio in simplest form, comparison of ratios.

**Definition of Proportion**

- Recapitulate the concept of proportion. Continued proportion, Mean proportional.

**Unitary Method**

- To understand the concept of unitary method and apply it in various problems.

**Percentage**

- Introduction to the concept of percentage Understanding percentage as a fraction with denominator 100. Converting fractions and decimals into percentage with denominator.

**Conversions Into/from Percentage**

- Converting fractions and decimals into percentage and vice-versa.

**Applications in Problems Solving**

- Applications of ratio and proportion, and percentage in profit and loss (single transactions only). Applications to simple interest (time period in complete years).

# Unit 7

**Angles**

- Understanding the concept of an angle, pairs of angles viz. linear, supplementary, complementary,adjacent, vertically opposite (Verification of these angles)

**Parallel Lines**

- Properties of parallel lines with transversal; alternate angles, corresponding angles, interior and exterior angles

**Triangles**

- Properties of triangles; angle sum property (with notions of proof and verification through paper folding) Exterior greater then the angle property. Sum of two sides of a triangle is >third side

**Pythagoras Theorem**

- Verification of Pythagoras theorem and its applications

# Unit 8

**Definition**

- Recapitulate symmetry and various lines of symmetry, recalling reflection symmetry

**Introduction Rotational Symmetry**

- Introduction to the concept of rotational symmetry, observations of rotational symmetry of 2-D objects (90°,120°,180°). Operation of rotation through 90° and 180° of simple figures. Examples of figures with reflection and rotational symmetry

# Unit 9

**2D and 3D Figures**

- Drawing 3D and 2D figures in 2D showing all the faces

**Identification 3D figures**

- Identifying 3 D pictures of various objects and matching them with their names

**Components of 3D figures**

- Identification and counting of vertices, edges and faces; nets(for cubes, cuboids, cylinders and cones)

# Unit 10

**Introduction to the Concept**

- Introducing the concept of congruence through examples of superimposition. Extend congruence to simple geometrical shapes e.g., triangles, circles

**Properties of congruence**

- Introduction to the properties of congruence viz. SSS, SAS, ASA, RHS. Verification of the properties

**Constructions**

- Constructions using scale, protractor and compass: Construction of a line parallel to a given line and from a point outside it (Simple proof as remark with the reasoning of alternate angles)

# Unit 11

**Perimeter**

- Recapitulate the concept of perimeter. Introduce the idea of Circumference of a circle

**Area**

- Recapitulate the concept of area, introduce area of a circle, square, rectangle, parallelogram

**Area Bounded between two Figures**

- Area between two rectangles and two concentric circles

# Unit 12

**Collection and Organisation**

- Collection and organization of data- choosing the data to collect for a hypothesis testing

**Mean, Median and Mode**

- Mean, Median and Mode of an ungrouped data under standing what they represent

**Bar Graph**

- Constructing bar graph and reading the same

**Case Study**

- Specify a problem; plan and carry out the four stages of data handling process: Plan, collect, organize and interpret. Identify what further information may be needed to answer the enquiry Identify the primary data that needs to be collected in discrete data: collect, organize and tabulate data

**Probability**

- Informal introduction to 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 of a coin. Notion of randomness