Investigating Integers -- why do the rules work?

Today we spent our session getting some practice graphing more linear equations. I think you guys are really starting to get the hang of it!

One of the things I noticed during today's session is that our integer work isn't as strong as it needs to be. When our integer work isn't solid, solving and graphing linear equations can be a big challenge!

So, I decided to blog about integers, and give you guys an opportunity to investigate integers more deeply.

First of all, what is an integer?

An integer is any of the natural numbers, positive or negative, including zero. For example, [-2, -1, 0, 1, 45, -30] are all integers.

When we worked with our linear equations today, we sometimes had to add or subtract integers, and sometimes we even had to multiple or divide by integers! I could tell that at times, things got a little perplexing!

Here are some rules we learned:

(1)--whenever adding integers with LIKE signs (either both positive or both negative), you simply add them and keep the same sign

(2)--Whenever adding integers with UNLIKE signs (a positive and a negative), you subtract the smaller number from the larger number, and you KEEP the SIGN of the LARGER number

(3)--Whenever multiplying or dividing two integers, you following these two simple rules: LIKE signs will give a POSITIVE answer; UNLIKE signs will give a NEGATIVE answer


There are a couple of online videos I want you to watch. When you watch them, please feel free to pause the video and really look at what they are talking about, so that you can make sure you understand before going on.

The math can get pretty heavy in these videos, I don't expect you to understand everything you see in the video. But I know that you guys are so amazing that you WILL understand A LOT of what you watch.

And finally, here is a challenge for you! After watching any of the videos I have posted, pick one of the "RULES" listed above (1, 2, or 3) and explain in your own words why it is true. You can post your explanation in the comment box on this blog. THANKS!

VIDEOS (cut and paste address into your browser):

Adding and Subtracting Integers:
http://www.khanacademy.org/solovideoview.jsp?id=32&uid=C38B33ZywWs

Multiplying and Dividing Integers
http://www.khanacademy.org/solovideoview.jsp?id=31&uid=d8lP5tR2R3Q

Proof that a Negative TIMES a Negative is a Positive:
http://video.google.com/videoplay?docid=-8882864739933366607&q=why+is+a+negative+times+a+negative+a+positive%3F&ei=A_dTSLYdi6aqA4qJ-N8O


These videos are bettwen 6 and 9 minutes each. They are stictly math videos (not the cool animations in brainpop! But, interesting!)