Addition of Two Digit Numbers
A response to the question:
My nephew is having problems with two digit addition operations. How can I assess what he already knows and how can I help him with what he needs to learn?
First of all, let me commend you for wanting to assess what he knows before you begin. Children learn best by finding something they can "hook" the new information to. By knowing what he understands, you can help him increase his knowledge base.
To assess what he understands, generate a set of problems that he can solve. They should be different types of addition problems, some that need regrouping (we used to call that "carrying" when I was a student) and some that do not. For example, 15 + 42 does not need to be regrouped, but 15 + 68 does, and so does 15 + 97 (in both the tens and the ones). Throw in a few with a zero in the ones place, like 60 + 73.
Then, when he solves these, you can see where the mistakes are occurring, and focus on that sort of problem as you help him.
You might also approach this from the other direction... instead of having him add two given numbers and find a sum, you could have him search for two numbers that would give him a specific sum, say, 53.
So, he could try two numbers, and see what their sum was, and then try two more, looking for just the right pairs. Many (most) students will blindly guess when doing this, so you may want to guide him a bit, too. For example, if he is looking for sums of 53, using two digit numbers, he might try 41 and 32, and upon adding discover that their sum is 73, which is too large. He should adjust both addends (the 41 and 32) to get a smaller sum. What is important here is that HE be the one doing the adjusting, not you. As adults, we have a lot of background knowledge about how our number system works that our children haven't had time to amass yet. If you tell him how to adjust the numbers (by making them smaller) then he is cheated out of a chance to explore the numbers and discover how they work together.
So, he changes the two amounts to 21 and 12 (because he sees that the ones place digit is working) and now he gets 33, which is too small. That should tell him something. 41 and 32 were too large, and 21 and 12 are too small. That means the numbers he is looking for are somewhere in between those two pairs.
Eventually, if you help him organize his guesses, he will find that these 2-digit pairs will give him a sum of 53.
10 + 43 11 + 42 12 + 41 13 + 40 14 + 39 . . . all the way to 43 + 10
In hunting for the sums, he will get a lot of addition practice, and he will become familiar with how our place value system works.
-Gail, for the T2T service
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