Does the child need to add completing the ten?

Question:

...have an other question about using your worksheets for my daughter. She is six years old - home schooled.
Currently, we are using Addition & Subtraction 2

She is able to add and subtract any numbers from 1 to 100 but when I try to explain "complete the ten" concept, she doesn't like thinking about it. She would rather solve 9+6 by counting on the finger 6 after 9 ... . She complains that I have to first subtract then add to make 10.

My question is: Should I let her complete the exercises without making her think in this manner?

It is important that she understands the IDEA in completing the ten. I gather that she does indeed understand the idea, but doesn't want to do it, since you'd have to both subtract and add, right? She just likes to do one operation, not two?

The adding though, is really easy, because you add 10 + 5 or 10 + 7 or something to ten. If she's counting with fingers, she's not yet seeing the easiness of this adding. It is also faster to do 9 + 6 by first subtracting one from 6 (getting 5), and then adding 10 + 5, because you can do 10 + 5 really easy: it is one ten and five, or we call that fifteen.

Of course she must understand place value to realize how easy that addition is.

Now, the goal is ALSO to eventually memorize the answers. You might let her know that she can't always count with fingers to find 9 + 6 but a quicker method is needed.

You can let her do some exercises "her way" for now as long as she also is able to understand and do the "complete the ten".

But come back to this idea how completing the ten makes the whole calculation easier and quicker. She WILL need to understand the idea when studying CARRYING in addition, (I mean to totally understand how it works. I realize kids can learn carrying mechanically as well.)

So you can say 1-3 months later reprint some pages and try again.

Review of Flatland: The Movie

I recently had the opportunity to watch Flatland: The Movie. It is a short, educational 35-minute animated film based on an old novel called Flatland.

I thought the movie was quite interesting and entertaining, and my husband felt the same way. We both liked watching it. The animations are excellent, the "voice acting" of the cast is very good, and the whole thing is very well made — thus very enjoyable to watch.

The storyline includes a world set in two-dimensional plane called Flatland. Its inhabitants are simple geometric shapes such as triangles, squares, pentagons, hexagons, and so on. Circles are the evil bosses of Flatland.

Arthur hears Spherius in his living room.

The main setting includes Arthur the Square who is parenting his oh-so-curious granddaughter Hex. Arthur goes to work in a "squaricle" in some office, and has (of course) a circle as a boss.

Hex starts contemplating about the third dimension, but since that is "heresy" and unimaginable in Flatland, Hex's investigations eventually get her and Arthur into trouble. But there is a "savior" — a sphere called Spherius from Spaceland who wants to educate the citizens of Flatland about the existence of the 3-dimensional world.

The interactions between these shapes express plenty of irony that makes the film fun to watch for older teens and adults — and can maybe make them think a little deeper about the prevailing "doctrines" that they are fed everywhere. Just like the shapes in the Flatland had never considered the possibility of a third dimension and rejected it as "heresy", even so we ourselves might be in a similar position (concerning something else), without realizing it.

I wouldn't recommend this movie for early elementary school or younger children because of the strong emotions expressed by the evil circles. Also, young children might not catch on to some of the main themes of the movie, the irony, nor the mathematical ideas. I couldn't put an exact age limit to this though; is up to the parents to decide, of course.

From a mathematical point of view, the movie just deals with a few concepts (after all, it is only a half-hour long). The whole theme revolves around the inability of 2-dimensional figures to grasp 3 dimensions. This is presented really well in different parts o the story. In his dream, Arthur explores all the dimensions up to 3:

• point - 0 dimensions (the King of the Pointland was really funny!)


• line - 1 dimension


• square - 2 dimensions


• cube - 3 dimensions

Also, I really liked the extra interview on the DVD which has a math professor discussing the intriguing possibility of a fourth dimension, and some neat illustrations.

Apart from the mathematical content, one could analyze this movie's themes (accepting new truth vs. sticking to the current ideology) for an English class project as well.

The website FlatlandTheMovie.com has photos, info on cast & crew, news, the trailer, and a store.

You can also see the official trailer below:



(Note: If you've read the book, you might wonder if the movie goes into gender issues and how women's position in the society is presented. This movie totally omits that part of the book. For example, Arthur's wife is a square just like Arthur is.)

Download issue

Update: The problem below has been fixed. It had to do with my server's configuration.


For my recent customers:

There is some kind of unexpected glitch in Kagi's download script. I'm working on the issue, hopefully it all gets fixed soon.

That script has been working just perfect for all these years. But not since August 30 and I'm not yet sure what happened or what is causing the problem.

Meanwhile, the download links will give a 404 error, BUT not to worry. I will email the files to you directly so you will get the book(s). If you have questions, just email me.

Maria Miller