Let’s Talk Addition

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I’ve been watching my 4th grade daughters homework since the school year started with the new Common Core Standards being taught. Camille brought home some math homework the other day that was really basic addition with some other division problems that I will talk about in another post. Since I have a math background and have written on her learning what a rectangle was in Kindergarten I thought that this would be an interesting post. Turning 55 this year it has been interesting to see how she is being taught in the subjects that I love. Here is the problem and solution as it was taught:

9 + 6 = x

9 + (1 + 5) = x

(9 + 1 ) + 5 = x

10 + 5 = 15

While that is correct, to me it is an interesting way to factor to the answer. Now if we replace the non 9 number, which in this case was 6 with y this is how it was done when I was her age. Take 1 off y and add it to the first digit to the left of the 9 and replace the 9 with the new y. I am using 49 instead of 9 to show it with a bigger number below, but with the single digit 9 there is no number in front of it so you assume to add the 1 + 0 where I am using 49 instead of 09.

49 + y = x

49 + 6  = x

6 – 1 = 5

4 + 1 = 5

x = 55

It’s still 3 steps but the answer is the numbers from the two other equations. Lets try it with 3 digits

189 + 8 = x

8 – 1 = 7

8 +1 = 9

x = 197

or when you are in the 3 digits or more in the 90’s, 900’s, etc.

199 + 9 = x

9 – 1  = 8

9 + 1 = 10

Here is the extra step with the carry over 1 in 3 digits or above where you need to take the 1 and add it to the number in front of the second 9.

1 + 1 = 2

x = 208

Carry over is taught in 3rd grade, so students should know how to do that when taught larger numbers. Of course all of this is a matter of opinion, whose teaching and who is the supposed expert at knowing what is the best method. I don’t think there is a best method, but it was curious to me coming from a math background through college Calculus of the changes from when I was younger. The other big difference from when I was younger is that we memorized addition and multiplication tables so we could rattle and answer off without using a piece of paper, whereas I have not seen one flash card or memorization technique from Camille. Not that I’m worried about her because she got a perfect score on in math on the FCAT in 3rd grade last year.

Just some fun math and interesting differences from 1967.