Single Digit Addition. No new concepts. That's not really true. We're going to combine previous concepts to handle more complicated carries. You'll need to be able to do this eventually, but these examples will be simplified in the next lesson.
We'll start with an easy example: six plus seven. Start with two fists. Set six by adding a finger and the thumb to the right hand. Seven is two plus five. Add the two of the seven by adding two fingers. You want to add the thumb, but the thumb is already set. So subtract five (the thumb) and add ten (a finger on the left hand). Read the answer: thirteen.
Let's add eight plus nine. Two fists, then set three fingers and the thumb on the right hand. Nine is five plus four. You want to add the four, but you don't have four fingers to add. So, you subtract the Five's Complement of four, which is one. You want to add the five (from the Five's Complement), but you already have that set. So, you must subtract five (the thumb) and add ten (a finger on the left hand). Then, you must go back and add the five from the nine. So add the right thumb. Read the result: seventeen.
Now, let's do the really hard one. That's right, the dreaded seven plus eight. Start with two fists, then set the two right hand fingers and the thumb. Eight is three plus one. You want to add three, but can't, so you subtract the Five's Complement of three, which is two - which is done by subtracting both right fingers. You want to add five, but already have a thumb set. So, you subtract five (the thumb) and add ten (a finger on the left hand). Now you need to go back and add the five from eight (the right thumb). Read the result: fifteen. That's ten (the left finger), plus five (the right thumb) and zero (the right fingers).
At this point, you can add any two single digit numbers. There are a few examples to try below. But none of the books have enough examples. Since you can't have too many examples, you are referred to an example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. Bookmark the link.
| 6 + 4 10 | 3 + 3 6 | 4 + 6 10 | 8 + 5 13 | 4 + 8 12 | |||||||||||||||
| 9 + 8 17 | 6 + 2 8 | 7 + 8 15 | 4 + 3 7 | 5 + 8 13 | |||||||||||||||
| 1 + 5 6 | 7 + 9 16 | 3 + 6 9 | 6 + 1 7 | 5 + 6 11 | |||||||||||||||
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2 comments:
Here's another idea just to add up to 9 + 9 with this system. No numbers more than 10 are allowed.
Say 7 + 8. One hand shows thumb and two fingers. Other hand shows thumb and three fingers.
The trick: put your thumbs against each other to realize they make ten. The rest of your fingers are five, so total ten and five, fifteen.
This idea is inspired by the special coloring by fives on the abacus offered by RightStart mathematics.
The next lesson gets us there without using up your other hand, and without having to remember to add the other five. Stay tuned.
This finger math series borrows from Chismbop and the Japanese abacus: the Soroban.
I've never used an abacus with ten beads per rod. They had them in kindergarten, but there was no mention of the use of it. It was as if the teachers didn't know how. This could be true. In any case, your reference is straight forward.
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