K's Math Concepts

By Daddy K:

The ingenuity of youth is endlessly amazing. Our eldest daughter, K, came up with a few Math concepts on her own that simply blew me away. I was so amazed that I had to make my first addition to the Blog.

The first concept was chronologically second, but is the easier concept to understand. It was a Saturday and I woke to hear her getting out of bed. I decided to join her downstairs assuming we would be watching some variety of show she likes. Instead, she sat down with the dry erase board and starting drawing squares. She then wrote numbers above and below them and circled one of them. She then turned to me with a serious eye and said, “I know how to find the number in the middle”.

She sat down to explain it to me. She drew 5 boxes. Above each box she wrote the numbers one through five in ascending order. Below the boxes she wrote the numbers one through five in descending order. Where the two numbers are the same is the middle. In the case below the middle number is 3 since both above and below the number is the same.

I had to ask the question, "What if I had six boxes?" This stumped her as she understands what one half of something is, but she didn’t seem to grasp the difference between half and the middle. I sat down to explain it to her using her own created concept. You write the numbers the same as before. Instead of looking for one box with the same numbers above and below you find the two boxes that have the same two numbers, whether it is above or below, and draw a line between those two boxes. She instantly knew that I had cut it in half. I then asked “But what is the middle?”. She thought about it for a few minutes, then shrugged her shoulders. I explained that in this instance we could use either .5 or ½ to represent the line and that it was friends with the lower number. She then told me that 3 ½ was the middle.

The other concept was her self-created Math function. A little history is needed to understand it. K will at times make up words for everyday items and state, “That’s what it’s called on Jalar.” Jalar is an imaginary world she created. She came to me one day and asked if I would like to learn Math from Jalar. I entertained her and accepted the invitation.

She sat down and wrote “+ +” on the dry erase board. I was informed that what I was looking at was the symbol for “siren”. Siren is a Jalarian math expression. To teach me how to do Sirens she wrote it out on the board.


To solve for this expression you subtract the second number from the first. In our example this would be one. At this point she thought for a minute and then told me that we add that number to it again and add a zero when we’re done.

In the above example you would get the following:

1) Subtract the second from the first

8-7 =1

2) Add it to itself

1+1 = 2

3) Multiply by 10

2 * 10 = 20

Thus the answer to 8 siren 7 is 20.

Siren in OUR math language would be written as 20(X – Y).

Now initially I thought this was just an amusing one shot deal. I loved that my daughter taught me an original math concept. I was more amazed when two weeks later I asked her to solve for 6++4 and she came up with the correct answer. In five years she may not remember how to solve the Siren of two numbers but I will never forget it.

* 6++4 = 40 for those of you playing along at home.

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