18 December 2009

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.

16 December 2009

Wordless Wednesday

Peter Pan

Last night K finished reading an adapted version of Peter Pan. We started it a few weeks ago, and read roughly half of it taking turns reading aloud. I would read a chapter, she should read part of a chapter, and then she would finish the chapter silently before bed. After about chapter 5 or so, she just started reading it by herself. Last night she read the last four chapters and then came downstairs to let me know that she had finished it. She is now going through our Treasury of Illustrated Classics collection to pick out her next book. I think she is going to end up with Black Beauty as her next quest.

04 December 2009

Weekly Report - Week #10-11

With the recent holidays I have been very busy, so I'm now going to get caught up with a double weekly report. (We did not have school the week of Thanksgiving.)

First of all, I don't think I mentioned the report cards in my last post. For our first term K received E's (excellent) in all of her graded subjects. H received E's for phonics & reading and spelling, but a S (satisfactory) for science, which is graded subjectively. Sometimes she doesn't want to participate when I'm trying to tell them things, but she is getting better.

K has been doing a lot better at her math lately. We have backed up to a point that gives her a nice challenge without being too hard for her to do on her own for the most part. Yesterday, I even taught her a place value lesson from H's math, and she seemed to enjoy working with the Math-U-See blocks. In her Math Mammoth, she did some problems of subtracting in columns.

I just picked up a new reading workbook from Barnes & Noble a few weeks ago, and we have been working out of that along with our other reading workbook. It's called Reading for the Gifted Student. There have actually been a few things that have presented a challenge to her, mostly answering questions that require her to come up with answers that are not clearly stated in the reading selections.

H's reading is still getting better and better. We have now completed the first 46 lessons of McRuffy. She has doubled up on the lessons several times, since the lessons are somewhat short. We will complete a lesson and then she will look ahead at the next page and decide that she wants to do that, too. She is also starting to really get into Starfall, and will play on that site a few times per week.

We have also completed the first eight lessons of H's Math-U-See. We have moved onto lesson 9, which is Place Value: Units and Tens. (That's the lesson I taught K yesterday.) I have not taught the lesson to H yet, as we have been working on making a lapbook to go along with it. We were having so much fun working on it, K decided to help, too. She drew a car to go along with it for me to cut out. Here are some pictures of the project still in progress. I have to pick up a few items this weekend to be able to finish it next week.

I think that about covers it for what we have done in the last couple school weeks. I will be sure to post some more pictures of the lapbook once it's completed.