Teaching addition to kids: part 2

I'm starting with part 2 because, I'm teaching this to my 7yr old right now. She is not a math-natural and it seems to be working like a charm. This part is about numbers whose sum is greater than 10. Part 1 is about numbers whose sum is less than or equal to 10.

In part 1, which isn't yet posted--sorry!, we emphasized "magic friends add to ten." The short story here is that every number has a friend that will sum to ten.

1 and 9
2 and 8
3 and 7
4 and 6
5 and 5

The kids should know this very well before proceeding.

Step 1 to this process is teaching kids what 10 + another number is. They should know 10+1 is 11. They don't necessarily need to understand ones place and tens place to get through this though it is helpful. If they can count to twenty, they can recognize that 10 + 2 is twelve.

In order to teach this, I start at the top.

10 + 9 is 9 teen. Emphasize the teen here.
10 + 8 is 8 teen.

Do this down to 16. They'll hear the pattern.

Next, tell them that 13 and 15 are very similar but we just pronounce them funny.

5 teen is fifteen
3 teen is thirteen
Don't forget to mention 14.

When you get to 12 and 11, mention that these numbers are got named differently since 12 is such an important number, i.e. 12 months in a year, 12 hours in a day/night, 12 in a dozen.

2 teen is twelve
1 teen is eleven


Practice adding 10 + another number until this is easy for them to do. No paper is necessary for this work.

(If the child doesn't, yet, understand that 20 + another number is just twenty and the other number, now is a good time to alert them to that fact as well. We teach that
twenty = twoty
thirty = threety
fifty = fivety
etc.

Notice, the strange naming practices end at the same spots. Twenty and Twelve have odd spelling when compared to sixty and ninety. Also, look up twelve and eleven in wiki and you'll see some interesting stuff to make math come alive for the linguists among us.)

The second step has two sub-steps and that is the end, I promise.

2a)the smaller of the two numbers in need of addition is decomposed into two smaller yet numbers (one of which is the magic friend of the larger number)

2b)the resulting 3 numbers are added pointing out that two of them are magic friends.

And example will clarify what I mean.

7 + 8

Take 7 and decompose it into 2 and 5. Then since the 2 is the magic friend of 8, the 2 and 8 make a 10. Now just add the 5 to 10 yielding five teen--15.

The key to this is knowing the magic friend of 8. And then being able to decompose 7 into that magic number and another number.

That is the concept, but now to how to teach it to a child.

First, start with the problem, I'll use a different example. 6 + 9

Write it out with lots of space below. Ask the child to recognize which of the numbers is bigger (9) and draw a line straight down from it and rewrite 9.

Now, from the smaller number, draw two lines that angle away like you would use for a family tree. Construct these lines such than when you write a number at the end of the lines, they will be level with the 9. We will be creating a new equation with the numbers beneath the lines.

Now, ask the child to give you the "magic friend" of 9. Write that number in the position that is nearest the 9. In our problem, we'll have a 1 in that position.

Ask the child what number is needed with the 1 to sum to 6 and of course that is a 5. Write that beneath the line that is empty. Put + signs between all the numbers.

So now in our new equation we have 5 + 1 + 9. Circle the 1 and the 9. Point out that this sums to 10 and then ask them to sum 5 and 10 which is of course five teen or 15.

(Note: I always find the magic friend of the larger number because 1) decomposing smaller numbers is easier than larger numbers and 2) the magic friend is smaller as well. You don't have to do it this way, but I find it works more easily.)

After they have the idea and can do this on paper easily, have them practice in their heads. Any math that can be done in the head, should be done in the head.