Addition

Welcome to the Class 1, Addition lesson plan.

Learning Objectives

Introduction to mathematical operations
Addition up to 120 numbers
Relate counting forwards to addition
Making and separating numbers
Addition using unknowns of two digits (60 + ____ = 90)
Addition up to four one- and two-digit numbers (30 + 10 + 5 = 45)
Properties of Addition (Commutative and Associative Laws)

About Patiganita (पाटीगणितम्)

Let us now learn more about numbers, place value system and how they are used in calculations.

In earlier days paper was scarce, so they used wooden boards called phalaka or patta and chalk or soap-stone (pandu-lekha or svetavarni) to write on them. Till as recently as 19^th century, boards were used to do number based ganita. Hence such mathematics was called Patiganita. Patti means “board” and ganita as you know means “science of calculation”. It means science of calculation which requires the use of writing materials. Now, it was sometimes called dhulikarma (dust work) because numbers or symbols were written using sticks on dust or find sand spread on a board or ground. Much of the mathematical calculations used to depend on memory. People recited shlokas and even number problems in those days as writing material was not widely available. Indian mathematicians had difficulty in carrying out long calculations using these tools.

Well! How do we know all this? Because the terms patiganita and dhuli-karma were translated into Arabic language of travellers who took this great science to the Arabic world from India.

Mathematical Operations

Every person uses mathematics in his daily life in one form or the other. However, from early times all Indian mathematicians recognized a very simple view that all mathematical operations are variations of two fundamental operations, namely

Joining together (addition)
Taking away (subtraction)

So, it comes down to doing two things – more or increasing and less or decreasing of something. For example,

Put sugar in milk in the morning (to increase sweetness)
Give two puris from your lunch box (from four) to your friend (less lunch)
Neatly arrange stacks of newly washed clothes (have more in stack)
Take out and wear washed clothes to go to school (less in stack)

And this list goes on and on forever for everyone.

Definition of Addition

Acharya Aryabhata – 2 in his Mahasiddhanta, explains that bringing in one or several numbers is addition. It makes a new total. The shloka and it's explanation are given below.

संख्यावतां बहूनामेकीकरणं तदेव संकलितम् । (म सि. 14.2)

बहूनां संख्यात्मकपदार्थानामेकीकरणं सपिण्डनं (सम्मेलनं) तदेव सङ्कलितम्।

The words saamkalana (making together), sammelana (mingling together), samyojana (joining together) and many other such terms are all used for Addition.

Recall how we counted numbers forward and backward.

Putting together 66 flowers and one more flower makes it 67.

Bringing in one flower more to 67 makes it 68!

Thus, we keep adding one more flower to the other… by the operation or activity called Addition.

Representing Addition Operation

Addition operation is represented by the plus symbol.

It can be written in the form of an equation.

In words we say, one plus one equals two.

Example: When we add 3 and 4, we get 7. We write this as 3 + 4 = 7.

What happens in addition?

We use any two numbers
The numbers may be same or different
We get an increase in total number after addition
The total number obtained after addition is called the sum
We can represent it in the form of an equation
Left hand side should be equal to what we write in Right hand side of equation.

In words we say, ten plus five equals fifteen.

We also say, the sum of ten plus five is fifteen.

Activity: Adding up health

Number Exercise – Introduction of addition and equal to symbols, relate counting to addition