Units and Topics
- Concept for Number System(Consolidating the Sense of Numberness)
- Consolidating the Sense of Numberness up to 5 Digits, Size, Estimation of Numbers, Identifying Smaller, Larger, Etc.
Consolidating the sense of numberness up to 5 digits, size, estimation of numbers, identifying smaller, larger, etc.
Place value - recapitulation and extension
- Concept of Negative Numbers
- Need for Negative Numbers
- Connection of Negative Numbers in Daily Life
- Representation of Negative Numbers on Number Line
- Ordering of Negative Numbers, Integers.
- Representation of Integers on the Number Line
- Operation of Addition and Subtraction of Integers
- Addition of Integers
- Comparison of Integers
- Concept for Ordering of Integers
- Need for negative numbers.
- Connection of negative numbers in daily life.
- Representation of negative numbers on number line.
- Ordering of negative numbers, Integers.
- Identification of integers on the number line,
- Operation of addition and subtraction of integers,
- Addition and subtraction of integers on the number line
- Comparison of integers,
- ordering of integers.
- Operation on of Whole Number on Number Line
- Seeing Patterns for Operations on Numbers.
- Identifying And Formulating Rules for Operations on Numbers.
- Number line.
- Seeing patterns, identifying and formulating rules for operations on numbers.
- Introduction of Playing with Numbers
- Simplification of Expression by Using Brackets
- Factors and Multiples
- Concept of Even and Odd Number
- Concept for Co-prime Numbers, Prime Factorisation
- Simplification of brackets.
- Multiples and factors,
- divisibility rule of 2, 3, 4, 5, 6, 8, 9, 10, 11. (All these through observing patterns. Children would be helped in deducing some and then asked to derive some that are a combination of the basic patterns of divisibility)
- Even/odd and prime/composite numbers, Co-prime numbers, prime factorisation, every number can be written as products of prime factors.
Unitary method (with only direct variation implied).
- Concept of Fraction as a Part of Whole
- Representation of Fractions (Pictorially and on Number Line).
- Concept for Fraction as a Division.
- Types of Fraction
- Concept for Equivalent Fractions
- Equivalent Fractions
- Cross Product
- Concept for Equivalent Fractions
- Concept of Fractions
- Operations on Fractions (Avoid Large and Complicated Unnecessary Tasks). (Moving Towards Abstraction in Fractions).
- Revision of what a fraction is.
- Fraction as a part of whole.
- Representation of fractions (pictorially and on number line).
- Fraction as a division.
- Proper, improper & mixed fractions.
- Equivalent fractions
- Comparison of fractions
- Operations on fractions (Avoid large and complicated unnecessary tasks). (Moving towards abstraction in fractions).
- Concept of Decimal Numbers
- Place Value in the Context of Decimal Fraction.
- Concept for Inter Conversion of Fractions
- Word Problems Involving Addition and Subtraction of Decimals (Two Operations Together on Money, Mass, Length and Temperature).
- Review of the idea of a decimal fraction.
- Place value in the context of decimal fraction.
- Inter conversion of fractions and decimal fractions (avoid recurring decimals at this stage).
- Word problems involving addition and subtraction of decimals (two operations together on money, mass, length and temperature).
Idea of percent as fraction with 100 as denominator
- Relation Between Speed, Time and Distance
- Idea of Speed and Simple Daily Life Problems Related to Speed, Time and Distance
Idea of speed and simple daily life problems related to speed, time and distance
- Fundamental Concepts for Algebra
- Introduction to Constants, Variable and Unknown Through Patterns
- Concept for Appropriate Word Problems and Generalisations
Introduction to constants, variable and unknown through patterns and through appropriate word problems and generalisations (For example 1+3=22, 1+3+5=32,
1+3+5+7=42 , sum of first n odd numbers = n2.).
- Operation on Algebraic Expression
- Algebra Terminology - Literal Numbers, Terms, Expressions, Factor, Coefficient, Polynomials, Degree, like and Unlike Terms
- Concept for Unknowns Through Examples with Simple Contexts (Single Operations)
Terminology associated with algebra- like literal numbers, terms, expressions, factor, coefficient, polynomials, degree, like and unlike terms
Introduction to unknowns through examples with simple contexts (single operations)
- Algebraic Expressions
- Algebraic Expressions
- Value of Expression
- Number line and an expression
- Evaluation of Algebraic Expressions by Substituting a Value for the Variable.
Framing algebraic expressions.
Evaluation of algebraic expressions by substituting a value for the variable.
Introduction to linear equation in one variable.
- Concepts of Fundamental (Geometry)
- Concept for Basic Geometrical Ideas (2 -d)
- Concept for Linkage with and Reflection in Everyday Experiences.
- Concept of Line
- Concept for Open and Closed Figures.
- Concept for Interior and Exterior of Closed Figures.
- Curvilinear and Linear Boundaries
- Concept of Angle - Arms, Vertex, Interior and Exterior Region
Basic geometrical ideas (2 -D): Introduction to geometry. Its linkage with and reflection in everyday experiences.
Line, line segment, ray.
Open and closed figures.
Interior and exterior of closed figures.
Curvilinear and linear boundaries
Angle — Vertex, arm, interior and exterior.
- Measure of Angles
- Types of Angles- Acute, Obtuse, Right, Straight, Reflex, Complete and Zero Angle.
- Introduction to Lines and Angles
Measure of angles
Types of angles- acute, obtuse, right, straight, reflex, complete and zero angle.
- Concept of Properties of Angles and Lines
- Measure of Line Segment
- Pair of Lines – Intersecting and Perpendicular Lines, Parallel Lines
Measure of Line segment
Pair of lines – Intersecting and perpendicular lines, Parallel lines.
- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Classification of Triangles (On the Basis of Sides, and of Angles)
Triangle — vertices, sides, angles, interior and exterior, altitude and median.
Classification of triangles (on the basis of sides, and of angles).
- Interior and Exterior of a Quadrilateral.
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
Quadrilateral — Sides, vertices, angles, diagonals, adjacent sides and opposite sides (only convex quadrilateral are to be discussed), interior and exterior of a quadrilateral.
- Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
- Simple Polygons (Upto Octagons Regulars as Well as Non-regular).
- Sum of Angles of a Polynomial
- Sum of Exterior Angles of a Polynomial
- Regular Polynomial
Simple polygons (introduction) (Upto octagons regulars as well as non-regular).
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Circle — Centre, radius, diameter, arc, sector, chord, segment, semicircle, circumference, interior and exterior.
- Concept of Revision Exercise Symmetry (Including Constructions on Symmetry)
- Concept of Reflection Symmetry
- Concept of Observation and Identification of 2-d Symmetrical Objects for Reflection Symmetry.
- Operation of Reflection (Taking Mirror Images) of Simple 2-d Objects
- Recognising Reflection Symmetry (Identifying Axes).
Observation and identification of 2-D symmetrical objects for reflection symmetry.
Operation of reflection (taking mirror images) of simple 2-D objects
Recognising reflection symmetry (identifying axes).
- Concept of Recognition of Solids
- Identification of 3-d Shapes: Cubes, Cuboids, Cylinder, Sphere, Cone, Prism (Triangular and Square), Pyramid (Triangular and Square)
- Identification and Locating in the Surroundings.
- Nets for Building 3-d Shapes - Cube, Cuboids, Cylinders, Cones, Pyramid, and Prism
- Faces, Edges and Vertices
Identification of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone, prism (triangular and square), pyramid (triangular and square), Identification and
locating in the surroundings.
Elements of 3-D figures. (Faces, Edges and vertices).
Nets for cube, cuboids, cylinders, cones and tetrahedrons.
- Concept of Perimeter
- Shapes of Different Kinds with the Same Perimeter.
- Concept of Area
- Conversion of Units (Mass, Time, Money, and Capacity) from to Smaller to Larger and Vice-versa
- Counter Examples to Different Misconcepts Related to Perimeter and Area.
- Perimeter of a Rectangle
- Deducing the Formula of the Perimeter for a Rectangle and Then a Square Through Pattern and Generalisation.
- Concept of perimeter and introduction to area
- Introduction and general understanding of perimeter using many shapes.
- Shapes of different kinds with the same perimeter.
- Concept of area, Area of a rectangle and a square
- Conversion of units (Mass, time, money, and capacity) from to smaller to larger and vice-versa
- Counter examples to different misconcepts related to perimeter and area.
- Perimeter of a rectangle – and its special case – a square.
- Deducing the formula of the perimeter for a rectangle and then a square through pattern and generalisation.
- Concept of Data Handling (Including Pictograph and Bar Graph)
- Collection of Data to Examine a Hypothesis
- Collecting Data
- Concept of Pictograph
- Organisation of Data
- Ungrouped Data
- Grouped Data
Collection of data to examine a hypothesis
Collection and organisation of data - examples of organising it in tally bars and a table.
Pictograph- Need for scaling in pictographs interpretation & construction of pictograph
Mean and median of data not having more than ten observations
Books For All Subjects
- Selina Concise Mathematics - Middle School for Class 6