Addition (whole numbers)

Once students learn their additional facts, they should learn to add multiple numbers. 

There are many ways to add columns of numbers.  Of course, the strategies of counting up and counting on (holding a number, or sum, in your head while counting on another number) always work. 

However, once students know their math facts, they can work faster than that.  And, if students know the pairs that add up to nicely added-to numbers (like 10), they can work even faster. 

Example: 

$7+5+3=$

Once you have learned to add with regrouping, you can add numbers of any size. The process that you use with multi-digit numbers is the same as the process used with two-digit numbers, you just keep moving over, place value by place value.

Addition with regrouping (also called addition with carrying) is one of the first complicated math algorithms that most students learn.  

When we first start to teach students to add multi-digit numbers, it's important to teach them to write problems vertically and line up place values.  Setting addition problems up vertically, even when there is no regrouping or carrying, helps students prepare for the next step: regrouping! And, understanding that place values line up also sets the groundwork for more advanced skills (such as lining numbers up properly when numbers have decimals!).

We add all the time -- often without even realizing that we're adding.  The student who has 2 pencils, grabs another and calls out, "Now I have 3 pencils!" just did mental addition without even thinking about it!

Learning addition is a process.  Most people start that process on their fingers (any object will work... but fingers are handy and there are some cool patterns that kids can learn with fingers). 

The most basic form of finger (or object addition) is "counting all."

Example:

$3+5=8$