Addition is an operation which allows us to find out how many we have when we combine two or more sets of objects. We can only add like objects, and when we use addition to combine two sets of different types of objects, we need to give them a common name. For example, if we combine three apples with two oranges we have five pieces of fruit (fruit being a common name for apples and oranges). If we add three inches and two feet, we first change the two feet to 24 inches, and then extend the 24 inches by three inches to get 27 inches.

The numbers representing the parts in an addition problem are called terms. (There are older words for these parts, but they are seldom if ever used today.) The answer is called the sum. Thus, in

• 2 + 3 = 5

the terms are 2 and 3 and the sum is 5.

We use addition when we make a deposit to our bank account, when we find how many comic books we now have when we put ten more comic books into our collection, and when we add the price of a coke and a sandwich plus the tax to see if we can afford to buy lunch.

We now come to one of the two hard tasks in elementary mathematics, memorizing addition facts. The other hard task is memorizing multiplication facts. In both cases, there are 100 facts to memorize, though various short cuts can reduce this by half.

Most of mathematics we can figure out, which reduces the need to memorize. We could figure out the addition and multiplication facts, but it would take too long. Once we have them memorized, we can do quick mental arithmetic while driving a car or standing in the check out line in a store.

In most schools, addition facts are taught while children are still young enough to memorize easily, and so few students fail to remember their addition facts. On the other hand, multiplication facts are taught after students are too old to memorize easily, and so many students have trouble memorizing their multiplication facts. If you are a parent, using this book to teach your children, teach them their addition facts when they are five and their multiplication facts when they are six. (Do not teach both at the same time -- children will get them confused.) Always use exactly the same words in teaching rote addition and multiplication. "Two plus three is five." "Two threes are six."

In Chapter One, you learned to count to 100. To add one, just count up. 3 + 1 = 4. 10 + 1 = 11.

Since 3 + 1 is the same as 1 + 3, you now know 19 out of the 100 addition facts. By the way, the rule that 1 + 3 = 3 + 1 is an example of the commutative law. Picture the 1 commuting to where the 3 lives, and the 3 commuting to where the 1 lives.

When you first begin to add, it is tempting to add two by counting up twice. This works, but is too slow. Instead of thinking: to add 3 + 2 I start with three and count four five, you need to memorize "three plus two is five". After you do that, every time you see 3 + 2, the number 5 will instantly pop into your mind. We therefore need to bite the bullet and begin to memorize. You memorize these addition facts by saying them over and over and over until you know them by heart.

"two plus two is four, three plus two is five, four plus two is six, five plus two is seven, six plus two is eight, seven plus two is nine, eight plus two is ten"

Read this twenty times a day until you've got it. Flash cards are another good way to learn addition facts. Keep practicing, and at some point the addition facts will move from short term memory (where we keep locker combinations) to long term memory (where we keep the names of our parents). Then you will have them forever, and the effort will be worth while.

Teachers in every grade should make sure that all of the their students know all of their addition and multiplication facts.

You didn't need to relearn one plus two is three. And the commutative law almost doubles the new facts you have learned, so you have learned 13 new fact which together with the 19 facts about adding one means you have learned 32 of the 100 addition facts.

Adding a number to itself

For the sake of variety, let's next learn how to add a number to itself. You already know that one plus one is two and that two plus two is four. Here are the rest of those facts. Memorize them.

"three plus three is six, four plus four is eight, five plus five is ten, six plus six is twelve, seven plus seven is fourteen, eight plus eight is sixteen, nine plus nine is eighteen."

You now know 39 of the 100 addition facts.