## MILESTONE 2: Addition

One may easily learn to add numbers mentally up to one hundred using the procedures given here.

**MATH MILESTONE #A2: ADDITION**

Addition is an extension of counting. For example, by counting you know that you have 3 marbles. By counting again you know that you got 4 more marbles from your friend. You put all these marbles in a box and count them together. You find that you now have 7 marbles.

**Addition is counting together.**

In the initial stages one learns to add small numbers by counting on one’s fingers. For larger numbers, one may use abacus. The first concept that one learns here is “carry-over” across the place values. After gaining sufficient familiarity with objects, one may add on paper using digits.

It is easy to visualize addition with objects. We may also visualize addition using a number line. Basic addition is demonstrated in the following video from Khan Academy.

Basic Addition

When we have larger numbers we may add them more easily by column. See the demonstration in the following videos from Khan Academy

Addition 2

Level 2 Addition

Addition 3

Addition 4

Here are some comments on addition.

(1) Addition depends on the concept of the same units. For example, we may add 2 cats and 3 cats to come up with the sum of 5 cats. However, we cannot express the sum of 2 cats and 3 dogs in terms of a single unit, unless we change the unit to “animal”, which is inclusive of both cats and dogs.

(2) Mathematical units may be the same, but units in the real world are never exactly the same. For example, any two oranges would never be exactly be the same in all aspects including the number of atoms they contain.

Thus, mathematics may come very close to describing the physical universe, but it is never exact.

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