LESSON 2
ADDITION
Combining Numbers to Find a Total
What is Addition?
Addition is the process of combining two or more numbers to find their total, or sum. It is one of the four basic arithmetic operations and one of the first operations we learn after counting.
The symbol for addition is the plus sign (+). When we write 3 + 4 = 7, we are saying that combining 3 and 4 gives us a total of 7.
Basic Addition
Basic addition involves combining small numbers. Start by counting all the objects together. For example, if you have 2 apples and someone gives you 3 more, you count all 5 apples.
Adding Larger Numbers
When adding larger numbers, we line them up by place value — ones under ones, tens under tens, hundreds under hundreds — and add each column from right to left.
Carrying (Regrouping)
When the sum of a column is 10 or more, we write the ones digit and carry the tens digit to the next column. This is called carrying or regrouping.
Properties of Addition
Addition has important properties: Commutative (a + b = b + a), Associative ((a+b)+c = a+(b+c)), and Identity (a + 0 = a). These rules make addition flexible and powerful.
Key Facts
The plus sign (+) was first used in mathematics by Johannes Widmann in 1489.
Addition is commutative — the order of the numbers does not change the sum.
Adding zero to any number always gives back that same number (identity property).
The result of an addition problem is called the 'sum'. The numbers being added are called 'addends'.