# Addition (Addition Facts)

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*:

$3+5=8$

When counting all, the child counts up 3 fingers, 1, 2, 3 on one hand, then counts up 5 fingers on the other hand, 1, 2, 3, 4, 5. Then, the student counts all of the fingers for the final answer: 1, 2, 3, 4, 5, 6, 7, 8.

**Most students quickly figure out that there's an easier way to add, "counting on."**

*Example*:

$3+5=8$

When counting on, the child counts up 3 fingers, 1, 2, 3 on one hand, then counts up 5 fingers on the other hand, 1, 2, 3, 4, 5. Then, the student starts at 3 (the quantity already known from the first hand, and counts up from there, using the five fingers on the second hand: 4, 5, 6, 7, 8.

You can see how this is more efficient, especially when the second number is smaller:

$5+2=7$

The student holds up five fingers and holds up two fingers, then starting with five, counts on: 6, 7.

**Eventually, students start to "count on" while holding the first number in their head.**

*Example*:

$3+5=8$

The student says 3, then holds up 5 fingers and counts up on them: 4, 5, 6, 7, 8.

This strategy works even if the first number is quite large:

$92+5=97$

The student holds 92 in her head, then counts up through 5 fingers: 93, 94, 95, 96, 97.

**Once students have mastered "counting on while holding a number in their heads," it's time to start memorizing math facts. Give them tricks:**

- Commutative property: 3+5 is the same as 5+3, that halves the number of facts they have to memorize!
- Identity property: adding 0 to any number gives you the same number (think about it, you have 1 cookie, I give you no cookies, how many cookies do you have?)
- Adding 1 = counting up by 1
- Adding 2 = counting up by 2 (or going to the next odd or even number)
- 5+5, 4+6, 3+7, 2+8, 1+9 all = 10 (knowing the addends for 10 is super helpful! Memorize these early!)
- Doubles are helpful! 5+5=10, 4+4=8, 3+3=6, 2+2=4 1+1=2

Mastering the tips above gives students great scaffolding for learning the rest of the facts. If you know that 5+5=10 and 4+4=8 and 4+6=10, then knowing that 4+5=9 is pretty obvious. For more practice, print out the flashcards below. They are designed to be printed two sided (questions on one side, answers on the other). We start with the doubles!

**Why are 0-10 addition facts so important?** We live in a base-10 system. Once we master the 0-10 addition facts (and learn the algorithm for adding in columns) we can add anything! So get these down perfectly.

**Why are fingers super handy?**

- They are always nearby.
- We have 10 of them... helpful in a base-10 system.
- Almost everyone has 5 on each hand, always... so it's easy to create rules that will always hold true.
- Even very young kids learn what different numbers look like on their fingers. Ask a 3-year-old and he'll show you 3 on his hands. So, you can build on that fact that most kids could do the first part of $3+5$ on their hands without even counting out the 3 and the 5 (try it, a kid who would count out 5 manipulatives will probably instantly raise 5 fingers).
- Fingers are visual. A student who might struggle to remember $3+5=8$ in the abstract might be able to visualize 3 fingers and 5 fingers equals 8 fingers. That's a math fact!

For some people, the manual dexterity required to work with fingers is too much. If someone struggles with fingers, feel free to use manipulatives. There are specifical math manipulatives (little cubes, counting bears), but you can use money (real or pretend), pencils, or even little pieces of paper, anything that students can use to hold their place when their counting.