Topics
Number System
Sets
Number System(Consolidating the Sense of Numberness)
Estimation
Numbers in India and International System (With Comparison)
Place Value
Natural Numbers and Whole Numbers (Including Patterns)
Negative Numbers and Integers
 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
Number Line
HCF and LCM
Playing with Numbers
Ratio and Proportion
Ratio
Proportion (Including Word Problems)
Unitary Method
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
Percent (Percentage)
Idea of Speed, Distance and Time
Algebra
Fundamental Concepts
Fundamental Operations (Related to Algebraic Expressions)
Substitution (Including Use of Brackets as Grouping Symbols)
Framing Algebraic Expressions (Including Evaluation)
Simple (Linear) Equations (Including Word Problems)
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)
Properties of Angles and Lines (Including Parallel Lines)
Triangles (Including Types, Properties and Constructions)
Quadrilateral
Polygons
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)
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