Topics
Number System
Sets
 Concept of Sets
 Representation of Sets
 Types of Sets: Finite/Infinite and Empty
 Cardinality of a Set
Number System(Consolidating the Sense of Numberness)
 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.
Estimation
 Concept of Estimation
 Estimation of Outcome of Number Operations
Numbers in India and International System (With Comparison)
 Numbers in Indian and Comparison
 Numbers in International Systems and Comparison
Place Value
 Concept for Place Value  Recapitulation and Extension
Natural Numbers and Whole Numbers (Including Patterns)
Negative Numbers and Integers
 Negative and Positive 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
Number Line
 Operation of Whole Numbers on Number Line
 Seeing Patterns for Operations on Numbers.
 Identifying And Formulating Rules for Operations on Numbers.
HCF and LCM
 Concept for HCF and LCM
 Prime Factorization for HCF and LCM
 Division Method for HCF and LCM
 Property HCF x LCM = Product of Two Numbers
Playing with Numbers
 Arranging the Objects in Rows and Columns
 Simplification of Expression by Using Brackets
 Factors and Multiples
 Concept of Even and Odd Number
 Concept for Coprime Numbers, Prime Factorisation
Ratio and Proportion
Ratio
 Concept of Ratio
 Difference Between Fraction and Ratio.
Proportion (Including Word Problems)
 Proportion as Equality of Two Ratios
 Concept of Ratio
 Concept of Proportion
Unitary Method
 Concept for Unitary Method (With Only Direct Variation Implied)
Fractions
 Concept of Fractions
 Concept of Fraction as a Part of Whole
 Representation of Fractions (Pictorially and on Number Line).
 Concept for Fraction as a Division.
 Concept of Proper Fractions
 Concept for Equivalent Fractions
 Concept of Fractions
 Operations on Fractions (Avoid Large and Complicated Unnecessary Tasks). (Moving Towards Abstraction in Fractions).
Decimal Fractions
 Concept of Decimal Numbers
 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).
Percent (Percentage)
 Concept of Percent and Percentage
 Idea of Percent as Fraction with 100 as Denominator
Idea of Speed, Distance and Time
 Relation Between Speed, Time and Distance
 Idea of Speed and Simple Daily Life Problems Related to Speed, Time and Distance
Algebra
Fundamental Concepts
 Fundamental Concepts for Algebra
 Introduction to Constants, Variable and Unknown Through Patterns
 Concept for Appropriate Word Problems and Generalisations
Fundamental Operations (Related to Algebraic Expressions)
 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)
Substitution (Including Use of Brackets as Grouping Symbols)
 Concept of Substitution
Framing Algebraic Expressions (Including Evaluation)
Simple (Linear) Equations (Including Word Problems)
 Concept of Simple (Linear) Equations (Including Word Problems)
 Linear Equation in One Variable
Geometry
Fundamental Concepts
 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
Angles (With Their Types)
 Types of Angles Acute, Obtuse, Right, Straight, Reflex, Complete and Zero Angle.
 Measure of Angles
 Types of Angles Acute, Obtuse, Right, Straight, Reflex, Complete and Zero Angle.
 Introduction to Lines and Angles
Properties of Angles and Lines (Including Parallel Lines)
 Concept of Properties of Angles and Lines
 Measure of Line Segment
 Pair of Lines – Intersecting and Perpendicular Lines, Parallel Lines
Triangles (Including Types, Properties and Constructions)
 Concept of Triangles  Sides, Angles, Vertices, Interior and Exterior of Triangle
 Classification of Triangles (On the Basis of Sides, and of Angles)
Quadrilateral
Polygons
 Concept of Polygons  Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
 Simple Polygons (Upto Octagons Regulars as Well as Nonregular).
 Sum of Angles of a Polynomial
 Sum of Exterior Angles of a Polynomial
 Regular Polynomial
The Circle
Revision Exercise Symmetry (Including Constructions on Symmetry)
 Concept of Revision Exercise Symmetry (Including Constructions on Symmetry)
 Concept of Reflection Symmetry
 Concept of Observation and Identification of 2d Symmetrical Objects for Reflection Symmetry.
 Operation of Reflection (Taking Mirror Images) of Simple 2d Objects
 Recognising Reflection Symmetry (Identifying Axes).
Recognition of Solids
 Concept of Recognition of Solids
 Identification of 3d Shapes: Cubes, Cuboids, Cylinder, Sphere, Cone, Prism (Triangular and Square), Pyramid (Triangular and Square)
 Identification and Locating in the Surroundings.
 Faces, Edges and Vertices
 Nets for Building 3d Shapes  Cube, Cuboids, Cylinders, Cones, Pyramid, and Prism
 Faces, Edges and Vertices
Mensuration
Perimeter and Area of Plane Figures
 Concept of Perimeter
 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 Viceversa
 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.
Data Handling
Data Handling (Including Pictograph and Bar Graph)
 Concept of Data Handling (Including Pictograph and Bar Graph)
 Collection of Data to Examine a Hypothesis
 Collecting Data
 Concept of Pictograph
 Organisation of Data
Mean and Median
Definition
Place value: Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.
Notes
Place Value:
1. Place value of the whole number:

In maths, every digit in a number has a place value.

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

In 574, 5 is in hundred's place and its place value is 500,
7 is in ten's place and its place value is 70,
4 is in one's place and its place value is 4.
2. Place value of a decimal number:
Decimal numbers are fractions or mixed numbers with denominators of powers of ten.
In a decimal number, the digits to the left of the decimal point represent a whole number. The digits to the right of the decimal represent the parts. The place value of the digits becomes 10 times smaller.
The first digit on the right of the decimal point means tenths i.e. `1/10`ths.
In 27.356,
27 is the whole number part,
2 is in ten's place and its place value is 20,
7 is in one's place, and its place value is 7.
There are three digits to the right of the decimal point,
3 is in the tenth's place, and its place value is 0.3 or `3/10`
5 is in the hundredth's place, and its place value is 0.05 or `5/100`
6 is in the thousandth's place, and its place value is 0.006 or `6/1000`.
Example
Write the following decimals in the place value table.
0.4
Hundreds  Tens  Ones  Tenths  Hundredths  Thousandths 
0  0  0  4  0  0 
Example
Write the following decimals in the place value table.
0.467
Hundreds  Tens  Ones  Tenths  Hundredths  Thousandths 
0  0  0  4  6  7 
Example
Write the following decimals in the place value table.
10.408
Hundreds  Tens  Ones  Tenths  Hundredths  Thousandths 
1  0  4  0  8 
Example
Given the place value table, write the number in decimal form.
Hundreds  Tens  Ones  Tenths  Hundredths  Thousandths 
0  0  2  5  7  0 
2 × 10 + 5 × 1 + `7/10`
= 20 + 5 + `7/10`
= 25 + `7/10`
= 25 + 0.7
= 25.7
Example
Given the place value table, write the number in decimal form.
Thousands  Hundreds  Tens  Ones  Tenths  Hundredths  Thousandths 
0  1  9  7  6  8  0 
1 × 100 + 9 × 10 + 7 × 1 + `6/10 + 8/100`
⇒ 100 + 90 + 7 + `6/10 + 8/100`
⇒ 197 + `(60 + 8)/100`
⇒ 197 + `68/100`
⇒ `197 68/100`
⇒ 197.68
Example
Given the place value table, write the number in decimal form.
Thousands  Hundreds  Tens  Ones  Tenths  Hundredths  Thousandths 
7  3  2  1  0  8  9 
7 × 1000 + 3 × 100 + 2 × 10 + 1 × 0 + `8/100 + 1/1000`.
= 7000 + 300 + 20 + 1 + 0 + `8/100 + 1/1000`.
= 7321 + `(80 + 9)/1000`
= 7321 + `89/1000`
= `7321 89/1000`
= 7321.089