Addition as Combining Formula

The $+$ sign represents the action of combining two parts into one whole

The Formula

a + b = \text{whole}

When to use: When you pour two cups of water together, you get their combined amount.

3 red balls + 4 blue balls = 7 balls total. We combined the groups.

The + sign represents the action of combining two parts into one whole

Understanding addition as joining or combining two or more quantities to form a larger whole amount.

When you pour two cups of water together, you get their combined amount.

a + b = |A \cup B| where A and B are disjoint finite sets with |A| = a and |B| = b

easy

There are 4 yellow crayons in one box and 3 blue crayons in another box. If you put all the crayons together, how many crayons do you have?

Answer

7 crayons

Addition as combining means joining two separate groups into one big group. The total tells us how many there are altogether.

medium

Group A has 5 stickers. Group B has 8 stickers. You combine both groups. How many stickers are there in all?

Thinking addition always means 'get more' — combining a group of 3 and a group of 0 still gives 3
Struggling to combine groups of unlike objects (3 apples + 2 oranges = 5 pieces of fruit, not 5 apples)
Confusing the total with one of the parts — saying '3 and 2 is 3' instead of 5

The conceptual foundation that makes arithmetic meaningful; without this, students just follow rules blindly.

Understanding addition as joining or combining two or more quantities to form a larger whole amount.

When you pour two cups of water together, you get their combined amount.

The + sign represents the action of combining two parts into one whole

The conceptual foundation that makes arithmetic meaningful; without this, students just follow rules blindly.

Seeing addition only as 'the answer' rather than an action of combining.

Before studying the Addition as Combining formula, you should understand: counting.