Mathematics For Grade 7

Introduction

Grade 7 math deepens students' understanding of mathematical concepts and prepares them for advanced study. Students work extensively with proportional relationships, percentages, and linear equations, building algebraic skills. Geometry covers the properties of two- and three-dimensional shapes, including angles, scale drawings, and surface area and volume calculations. Data analysis is expanded with an introduction to probability and statistical concepts. Rational numbers, including operations with integers, fractions, and decimals, are explored in depth. Critical thinking and problem-solving are central, enabling students to apply mathematical reasoning to real-world challenges and academic pursuits.

All Chapters & Topics

1.  Number System

• 1.1.  Integers
• 1.1.1.  Properties of Integers
• 1.1.2.  Operations on Integers
• 1.1.3.  Additive and Multiplicative Inverses
• 1.1.4.  Applications of Integers
• 1.2.  Rational Numbers
• 1.2.1.  Definition of Rational Numbers
• 1.2.2.  Properties of Rational Numbers
• 1.2.3.  Operations on Rational Numbers
• 1.2.4.  Standard Form of Rational Numbers
• 1.3.  Decimals
• 1.3.1.  Operations on Decimals
• 1.3.2.  Converting Between Fractions and Decimals
• 1.4.  Powers and Exponents
• 1.4.1.  Laws of Exponents
• 1.4.2.  Simplifying Expressions with Exponents
• 1.4.3.  Scientific Notation
• 1.5.  Roots
• 1.5.1.  Square Roots
• 1.5.2.  Cube Roots

2.  Algebra

• 2.1.  Expressions
• 2.1.1.  Algebraic Expressions
• 2.1.2.  Simplifying Expressions
• 2.1.3.  Evaluating Expressions
• 2.2.  Linear Equations
• 2.2.1.  Solving Simple Equations
• 2.2.2.  Applications of Linear Equations
• 2.3.  Algebraic Identities
• 2.3.1.  Expanding Using Identities
• 2.3.2.  Simplifying Using Identities

3.  Ratio and Proportion

• 3.1.  Ratios
• 3.1.1.  Understanding Ratios
• 3.1.2.  Simplifying Ratios
• 3.1.3.  Equivalent Ratios
• 3.2.  Proportion
• 3.2.1.  Concept of Proportion
• 3.2.2.  Direct Proportion
• 3.2.3.  Inverse Proportion
• 3.3.  Unitary Method
• 3.3.1.  Solving Problems Using the Unitary Method

4.  Geometry

• 4.1.  Lines and Angles
• 4.1.1.  Types of Angles
• 4.1.2.  Pairs of Angles
• 4.1.3.  Properties of Parallel Lines and a Transversal
• 4.1.4.  Angle Bisectors
• 4.2.  Triangles
• 4.2.1.  Types of Triangles
• 4.2.2.  Angle Sum Property
• 4.2.3.  Exterior Angle Property
• 4.2.4.  Pythagoras Theorem
• 4.3.  Congruence of Triangles
• 4.3.1.  Criteria for Congruence
• 4.3.2.  Applications of Congruence
• 4.4.  Quadrilaterals
• 4.4.1.  Types of Quadrilaterals
• 4.4.2.  Properties of Parallelograms
• 4.4.3.  Special Quadrilaterals
• 4.4.4.  Properties of Rectangles and Rhombuses

5.  Mensuration

• 5.1.  Perimeter and Area
• 5.1.1.  Perimeter of Plane Figures
• 5.1.2.  Area of Plane Figures
• 5.1.3.  Area of a Trapezium
• 5.1.4.  Area of a Parallelogram
• 5.1.5.  Area of a Circle
• 5.1.6.  Area of Composite Figures
• 5.2.  Surface Area and Volume
• 5.2.1.  Cubes and Cuboids
• 5.2.2.  Surface Area of Cylinders
• 5.2.3.  Volume of Prisms and Cylinders
• 5.2.4.  Volume and Surface Area of Cones

6.  Data Handling

• 6.1.  Data Collection
• 6.1.1.  Organizing Data
• 6.1.2.  Frequency Distribution
• 6.2.  Graphical Representation of Data
• 6.2.1.  Bar Graphs
• 6.2.2.  Double Bar Graphs
• 6.2.3.  Pie Charts
• 6.2.4.  Histograms
• 6.2.5.  Line Graphs
• 6.3.  Probability
• 6.3.1.  Simple Events
• 6.3.2.  Experimental Probability
• 6.3.3.  Theoretical Probability

7.  Practical Geometry

• 7.1.  Construction of Triangles
• 7.1.1.  Constructing Triangles Given Side Lengths
• 7.1.2.  Constructing Triangles Given Side and Angle
• 7.1.3.  Constructing Right-Angled Triangles
• 7.2.  Construction of Quadrilaterals
• 7.2.1.  Quadrilaterals Given Side Lengths and Angles
• 7.2.2.  Constructing Parallelograms and Rectangles