Viva ICSE Mathematics 6

Contents:

Chapter 1. Numbers • Numeral, Numeration and Hindu-Arabic System of Numeration, Face Value and Place Value, Indian and International Place Value Charts, Expanded Form of a Number, Comparison and Formation of Numbers, Operations on Large Numbers, Estimation (in Sum, Difference, Product and Quotient)

Chapter 2. Natural Numbers and Whole Numbers • Natural Numbers and Whole Numbers, Addition, Subtraction and Multiplication of Whole Numbers on a Number Line, Properties of Whole Numbers, Division Algorithm

Chapter 3. Negative Numbers and Integers • Need for Negative Numbers, Connection of Negative Numbers in Daily Life, Integers and their Representation on a Number Line, Ordering of Integers, Absolute Value of an Integer, Addition and Subtraction of integers

Chapter 4. Playing with Numbers • Simplification of Brackets, Factors and Multiples, Types of Numbers (Even, Odd, Prime, Composite), Sieve of Eratosthenes, Divisibility Tests of 2, 3, 4, 5, 6, 8, 9, 10 and 11, Common Factors and Common Multiples, Co-prime Numbers, Prime Factorization, Highest Common Factor (HCF), Lowest Common Multiple (LCM), Relation between HCF and LCM of Two Numbers

Chapter 5. Fractions • Fraction as Division, Types of Fractions (Proper, Improper, Mixed and Equivalent), Like and Unlike Fractions, Simplest Form of Fractions, Conversion of Fractions (Mixed to Improper and vice versa, Unlike to Like), Fractions on the Number Line, Comparison of Fractions, Operations on Fractions and Word Problems

Chapter 6. Decimals • Decimals, Decimal Fractions, Decimal Notation, Like and Unlike Decimals, Equivalent Decimals, Decimals on Number Line, Comparison of Decimals, Conversion of Fractions into Decimals, Conversion of Decimals into Fractions, Operations on Decimals and Word Problems

Chapter 7. Set Theory • Idea of Sets, Representation of Sets, Types of Sets: Finite, Infinite and Empty, Cardinality of a Set

Unit 2: Ratio, Proportion and Arithmetical Problems

Chapter 8. Ratio, Proportion and Unitary Method • Ratio, Difference between Fraction and Ratio, Simplification of Ratio, Dividing a Quantity in a Given Ratio, Comparison of Ratios, Proportion, Unitary Method

Chapter 9. Percentage • Percentage, Expressing One Quantity as a Percentage of the Other, Finding Percentage of a given Quantity, Finding the Number from its Given Percentage, Applications of Percentage

Chapter 10. Speed, Distance and Time • Speed, Units of Speed, Conversion of Units of Speed

Unit 3: Algebra

Chapter 11. Fundamental Concepts of Algebra • Constants and Variables, Matchstick Patterns, Use of Variables, Terms (Constant, Like, Unlike), Coefficient, Algebraic Expressions, Monomials, Binomial and Trinomial, Polynomial

Chapter 12. Operations on Algebraic Expressions • Addition, Subtraction and Multiplication of Algebraic Expressions, Use of Brackets as Grouping Symbols, Evaluation of Algebraic Expressions by Substituting a Value for the Variable

Chapter 13. Linear Equations in One Variable • To Write a Given Statement in Algebraic Form, To Write a Statement for a given Algebraic Form, Transposition of Terms of an Equation, Solution of an Equation, Solving Linear Equations in One Variable, Word Problems

Unit 4: Geometry

Chapter 14. Fundamental Concepts of Geometry • Introduction to Geometry, Point, Line, Line Segment, Ray, Plane and Space, Parallel, Intersecting and Perpendicular Lines, Perpendicular Bisector, Open and Closed Figures, Interior, Exterior and Boundary of Closed Figures, Curvilinear and Linear Boundaries, Collinear and Non-collinear Points, Concurrent and Non-concurrent Lines

Chapter 15. Angles • Angle–Vertex, Arm, Naming, Interior and Exterior, Magnitude, Types of Angles, Special Angles, Special Pairs of Angles, Measurement of a Line Segment, Measurement of an Angle, Construction of an Angle using Protractor

Chapter 16. Constructions • Construction of Line Segments, Construction of Perpendicular Bisectors of Line Segments, Construction of Bisectors of Angles, Construction of Angles (60°, 120°, 90°, 30°, 45°, 135°), Construction of Angle Equal to a Given Angle, Construction of Perpendicular to a Line

Chapter 17. Triangles and Quadrilaterals • Polygon and Types of Polygon, Triangle—Sides, Vertices, Interior and Exterior, Angles, Median and Altitude of a Triangle, Classification of Triangles, Quadrilateral—Sides, Vertices, Angles, Adjacent and Opposite Sides, Adjacent and Opposite Angles, Diagonal, Interior and Exterior, Types of Quadrilaterals

Chapter 18. Circles • Circle—Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Construction of Circles

Chapter 19. Three-dimensional Shapes • Classification of Objects: 1D, 2D and 3D, Elements of a 3D Shape - Faces, Edges and Vertices, 3D Shapes: Cube, Cuboid, Cylinder, Cone, Sphere, Prism, Pyramid, Nets of 3D Shapes, Visualizing Solid Objects

Chapter 20. Symmetry • Symmetry and line of Symmetry, Reflection and Symmetry, To Construct a Point Symmetric to a Given Point with Respect to a Line, To Construct a Line with Respect to which Two Given Points are Symmetric

Unit 5: Mensuration

Chapter 21. Perimeter and Area • Concept of Perimeter, Perimeter of a Rectangle, Square and Triangle, Different Shapes with the Same Perimeter, Area of a Square and a Rectangle (Using a Squared Paper), Conversion of Units

Unit 6: Data Handling

Chapter 22. Data Handling • Data: Collection and Organization, Interpreting and Constructing Pictographs, Interpreting and Constructing Bar Graphs, Measures of Central Tendencies: Mean and Median

Self-Testing Exercises

Concepts’ Glimpse

Formula Sheet

Question Bank

Subject Integration

Answers

About the Authors:

Monicaa Abhijit, with teaching experience of over 25 years, is currently teaching in St. Thomas School, New Delhi.

Ajay Kumar, with teaching experience of over 15 years, is currently heading the Mathematics Department in St. Mary's School, New Delhi.