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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,585

Here's some dot patterns that can be visualized with your eyes closed.

Enjoy some dot patterns for adding numbers one to nine.

I like these and others because then you can add in your head without remembering any answers!

Click on the picture below to make it larger.

*Last edited by John E. Franklin (2006-05-17 09:00:59)*

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,585

Here are some interesting shapes

I came up with.

I would have drawn them with X's in a "code" box except that the spaces are not the same width as characters I don't think.

Tiny! Can you see it?

**igloo** **myrtilles** **fourmis**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,559

John E. Franklin wrote:

I like these and others because then you can add in your head without remembering any answers!

OK ... that needs more explaining ... Expound!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,585

Well, it all depends on what your definition of "remembering answers" is.

Like if I can recognize certain shapes like a 4x4 matrix as 16, at what point

is this memorization, or just ingrown knowledge. For example, if you see

three points in an "L" shape, you know it is 3 dots, but do you call this remembering

the answer. I don't really, because I have known it since I was a small child, so it just seems

second nature. So if I become very familiar with certain shapes of dots such as the

bowling pins setup as 10 pins, then I can add 6 and 4 in my head by combining

the six triangle of 1-2-3 rows with the back row of 4. So I guess what I am trying to

do is make adding a visual process in my mind instead of just memorizing the

answers. For example, we know that 8 + 6 is 14, but you can see in your

head a 2x4 grid and a 2x3 grid below it and touching it. Then you can notice it

is almost a 4x4 grid except and 2x1 grid is missing, so 16-2 is 14 and then that

reinforces our knowledge that it is 14.

The possibilities are endless, especially if you get to point like Rainman where you

probably have memorized many setups of objects at strange angles.

Its all just a bunch of silliness, but I like going back to basics sometimes to see if

I might find out something I missed in first grade...

**igloo** **myrtilles** **fourmis**

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