I can remember being 11 or 12 years old and my dad taking me to the bowling alley to keep score for his bowling team. At first I was a bit intimidated. I had been bowling for a few years already and could keep score quickly and accurately. There were 5 men on each team, they bowled fast, and they expected an accurate accounting of their scores. I had no calculator to help me, but as long as I was accurate they were happy, and they paid me accordingly. At the end of an evening I would have about $5.00 in change in my pockets, and was the richest kid on the block in 1958 or 1959.
The reason I tell the story, is not because of the money I made, but the speed addition that I had learned that made it possible. Today, when we go to the bowling alley, a computer keeps score for us. Many people do not even know why they have the score they have, and would not know how to figure out their own score, based on the number of pins they have knocked down each frame. However, even if we never enter a bowling alley, we can learn to add quickly by tens, and to use tens to add quickly.
For the first thought ADDING QUICKLY BY TENS we can look at a few examples.
1. 24 + 18 = ? In our mind we count 24, 34, 44, because 44 is 20 more than 24
Now 18 is 2 less than 20, so we need 2 less than 44, or 42,
Thus we can say from 24; 34 then 42.
2. 59 + 35 = ? Again, in our head we think 59, 69, 79, 89 + 5 = 94
Or we can think 69, 79, 89, 99, less 5 = 94
Either one is fine, but by using 10's we can get there quickly and accurately
3. 137 + 27 = ? Nothing changes after 100, so think 137; 147, 157, 167
but 27 is 3 less than 30 so we get 164.
Or 147, 157, + 7 = 164
Our first and second graders can become quite good at this with a lot of practice, and with it they will develop a clearer feeling for subtraction. Now what about USING 10'S TO ADD QUICKLY.
When I visited a Kindergarten class last year, I was given small groups ( 4 or 5) and I gave them a test.
I had 9 squares with the numbers 1 to 9 on them. I spread them out on a table and ask them to put them in pairs that would add to 10. All of the groups had no trouble finding the pairs that made 10. They even asked me for another 5 so that the left out 5 they had would have a partner to make 10. Then we lined them up: 1 – 2 – 3 – 4 – 5 9 – 8 – 7 – 6 – 5
I then said when adding always look for your 10 pairs it makes it easier. There is a pattern here to be observed and remembered, and with practice it makes larger groups of adding easier. I believe that we can take this further by looking for 3 digits to make 10 or even 4 digits to make ten. With these patterns we build confidence in math, eliminate the the anxiety that we see in so many children, and doing problems can become enjoyable, not stressful.
I finish with this story. When I was studying for my Math degree, I gave my dad a sum to do. It was five, 4-digit numbers. He placed his fingers on the top number and slowly moved his hand down. He then proceeded to write down the correct answer that I had already tabulated. I said, "Dad, how did you do that so fast?" He said, "I just captured all the 10's and the rest was easy, doesn't everybody do it that way?" "No", I said. His comment was, "you see son, that is the way I was taught in the 1920's". Have we gone the wrong direction since then. Arithmetic has not changed. For all those youngsters who are today just learning to count to 10, and those who are adding, subtracting, and multiplying their way through the basics. Give them the advantages of the patterns of Math, and they will fly through the concepts.
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