Open your mind to something exciting -- relearn what you know already, the "whole numbers", in a refreshing new form.
• grouping to form place-value
• regrouping or carry over
• de-grouping or borrowing
• First principles of comparison, addition, subtraction, multiplication, and division
• Procedural Simplifications by place-value
• numerical expressions and precedence order
Numerals 0 to 9
This page quickly reviews the numbers 0 to 9 and introduces
• digits, numerals, numbers
• numbers given in abstraction
The lesson is critical to properly understand the place-value system and whole number arithmetics. These lessons take hardly mins. Learners are advised to go through them noting how numbers are represented with units blocks, tens blocks, hundreds blocks, etc. This helps in understanding explanation of various concepts in numerical arithmetics.
This page quickly reviews the numbers from to and introduces grouping of units to ten. The grouping is further explained to understand units, tens, hundreds, etc. This is an important concept to understand numerical arithmetics.
Expanded form of Numbers
This page introduces concept of 2-digit numbers, 3-digit numbers, etc. The expanded forms in hundreds, tens, units and number in words are explained with examples. For large numbers with 5 digits or more, the Indian and International systems of numbers are explained.
Face and Place Values
This page introduces the face value and the place value of a digit in a number.
Approximation and Estimation
This page introduces approximation of a number to a given degree of approximation. The same is also referred as estimation for measurement of an object.
Comparing two Whole Numbers
In this page, comparing two whole numbers to find one as larger, equal or smaller is explained.
The comparison in first principles is explained and it is extended to comparison as ordered sequence.
A simplified procedure based on place-value of large numbers is explained.
Number-line (Whole Numbers)
This page establishes the concept of smaller or larger between two quantities. The comparison is extended to the numbers in abstraction.
The ordered sequence of whole number and the representation of the order using the number-line is discussed.
Predecessor and Successor (Whole Numbers)
It was earlier studied that the numbers are in an ordered sequence. In this page, the predecessor and successor of a number is explained.
Largest or Smallest (Whole Numbers)
In this page, finding largest or smallest number among three or more whole numbers is explained.
Ascending and Descending Orders (Whole Numbers)
In this page, arranging three or more whole numbers in ascending or descending order is explained.
Addition: First Principles
This page explains that combining two quantities and counting or measuring the combined quantity is addition in first principles. Addition is also explained using number-line.
Addition: Simplified Procedure for Large Numbers
This page extends the addition in first principles into a simplified procedure for addition of large numbers, which is called as addition by place value with regrouping.
Subtraction: First Principles
This page explains that taking away from a quantity, a part of a quantity is subtraction in first principles. Subtraction is also explained using number-line.
Subtraction: Simplified Procedure for Large Numbers
This page extends the subtraction in first principle into a simplified procedure for subtraction of large numbers, which is called as subtraction by place value with de-grouping.
Multiplication: First Principles
This page explains the multiplication in first principles as repetition of a quantity, with examples in count or measure of quantities and in the number-line.
Multiplication : Simplified Procedure for Large Numbers
This page extends the multiplication in first principles into a simplified procedure for multiplication of large numbers, which is called multiplication by place-value with regrouping.
Division: First Principles
This page explains the division in first principles as splitting of a quantity, with examples in count or measure of quantities and in the number-line.
Division : Simplified Procedure for Large Numbers
This page extends the division in first principles into a simplified procedure for division of large numbers, which is called division by place-value with de-grouping.
In this page, numerical expressions are introduced as statement of a number using multiple numbers and arithmetic operations between the multiple numbers.
Precedence of Arithmetic Operations
In this page, the precedence order of arithmetic operations in a numerical expression is explained. That is, multiplication and division has higher precedence to addition and subtraction.
Sequence in Arithmetic Operations of Same Precedence
In this page, the sequence in arithmetic operations of same precedence in a numerical expression is explained. That is, multiple operations of same precedence are evaluation from left to right.