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 2-d Symmetrical Objects for Reflection Symmetry.
- Operation of Reflection (Taking Mirror Images) of Simple 2-d Objects
- Recognising Reflection Symmetry (Identifying Axes).
Recognition of Solids
- 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.
- Faces, Edges and Vertices
- Nets for Building 3-d 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 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.
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
