# teaching integers…and more

Whoa, hold up!  Detour time!  I know this is totally changing the direction here for a minute, but I have to share something for my teacher friends… Do not be scared of the math.  There’s other stuff below it.

Today, with my seventh grader (singular), I’m teaching adding and subtracting integers. And we had the following “conversation.”

Student: “Can I use a calculator?” (Reaches for calculator.)

Me:  “No.” (Sigh.) “No, you may not.”

Student:  (Crestfallen face.)But! (Tweenager whiney/grunting noise.)  Negative numbers are HARD, Miss!”

Me:  “I know, Love, but that’s why we have these!”

And I produce my plastic baggie of Integer Tiles…

Yes, that is a classroom iPad. Commence jealousy in 3, 2, 1….

After the initial introduction to the visual set up of “I have this many negatives and this many positives,” and “what if I have one positive and one negative?” and “some of them cancel out,” and “so what’s left over?” we can usually move on to solving these problems without the tiles.  But let me tell you, they help SO VERY MUCH when you’re introducing a kiddo to negative numbers.  I also use number lines, but the tiles seem to help more with the concept of canceling.  It’s also an allowable accommodation for the state test.

So, after they have the visual representation down, I spend some time going over the problems with them verbally.  For example:

1. -6 + (-6)  becomes “I have 6 negatives AND six MORE negatives. How many negatives do I have?”
2. 12 – 23  becomes “I have 12 positives and 23 negatives.  How many negatives can I cancel out?  How many negatives are left?”  (I teach them to look at the number as a positive or negative based on what sign is in front of it – it helps later when they get to solving for variables in algebra.)

Eventually, they will get to the point where they are reading the questions that way for themselves.  What’s interesting in my district right now is what I’m seeing with our current group of middle school students.  About four years ago, all of our elementary schools switched over to using “new math,” rather than teaching math the “traditional” way.  Which means that they are teaching division and multiplication in a way that I am having trouble comprehending.  It’s a program called Connected Math, and focuses more on investigation of real-life situations that represent the mathematical process being taught.  Which is awesome!  Theoretically…

Since our current 7th graders were in 3rd grade during that shift, they experienced some of the “traditional math” and some of the “new math,” and I’m noticing that they are really struggling with what we are studying in middle school math right now (which means they will struggle in high school, and be in remedial math classes in college, and isn’t that what everyone’s complaining about?! *end rant*).

We also use Connected Math at the middle school level, and every lesson also begins with an Investigation – which is difficult to do with only one student and impossible to do with 15 delinquents, but I’m sure works wonderfully in regular schools (?).  Anyway, the kiddos we have in middle school now are Lost with a capital L, and I can totally understand why.

When you learn {insert any mathematical operation} one year and it’s the old way, then the next year it’s the new way, but mom and dad at home use the old way while my teacher uses (or tries and/or is learning to use) the new way or maybe you moved from another district that doesn’t teach it this way and… Well, it is a Very Confusing Concept to learn.

Do not ask me why they did not begin with Kinder/First grade classes and build up from there when they made The Switch.  Do not ask me why they decided to begin the program in middle school when there was no proof that students got it while they were in elementary.  Do not ask me these questions because I do not want to tell you that I think it’s because this program was The Newest and because If It Is Expensive Then It Must Be Great.  Because it really is a Not Bad system that was Not Well Implemented.  But they didn’t ask me. They never do. Why is that?

don’t worry, Ryan, I don’t get it either….

Sigh.

Anyway… While my kiddo was playing working with Integer Tiles, I looked around my room and realized that it is a HORRIBLE mess, and I thought that I should clean up and make it look presentable for when The Almighty They come and ask me my opinion on the state of the district and What Would I Do differently….

Ha!  HA HA!

So nevermind.