## Monday, August 29, 2016

### Math Don't Break

Integer operations are always an interesting endeavor with 7th grade students because they come pre-loaded with so many rules.  So. Many. Rules.

We've been talking about making our own rules, so we have this sequence of products and I ask students to discuss what patterns they notice.

-3 (3) = -9
-3 (2) =  -6
-3 (1) = -3
-3 (0) =  0
-3 (-1) = ??

Stuff we noticed:

"It starts with a -3 every time."
"It goes down by 1."
"It changes by 3."

I zero in to the apparent contradiction in going down by 1 and changing by 3 so we can clean up the language a bit.  This starts an nice little exchange about whether or not going from -9 to -6 is an increase or decrease.  We conclude it's actually an increase.  I have to remember to take my time here because this isn't an insignificant point:  Kids seem to think in absolute value.

So what comes next?

I wrote down everything I heard.

"3".  "-3".  "4".  "-4".

"Wow!"  I say.  "We've got a great argument about to happen.  This is awesome!  So many different opinions.  So which is it?"

Some minds change when groups start to discuss.  The students who thought 4 or -4 were thinking of sums and not products.  That leaves 3 or -3.

"Ok, so which is it?"

If I had a dollar for every time a student said "A negative times a negative is a positive" followed by "because my teacher told me", I'd have all the dollars.

But then Isaac offers a reason worth looking at.

"I think it's -3, because positive 3 times positive 1 is positive 3, so negative 3 times negative 1 is negative 3."

So I write the following on the board:

(pos) (pos) = pos
(neg) (neg) = neg

Jordan speaks up, "I don't think so.  It has to be positive three so that it doesn't break the pattern."

"Which pattern is that?"

"The pattern goes from -9 to -6 to -3 to 0.  It's increasing by 3 each time so the next answer has to be 3."

"Why would that be so?" I ask.

Then Vanessa chimes in.

"Because math don't break."

#### 1 comment:

Mike Kaechele said...

David,

Long time, no tweet :) I am really glad that you are actively blogging again. I have taken a new position teaching 6th grade math. I really like these posts where you share how you frame discussions in your class instead of just direct instruction. This is something that I want to get better at and seeing your examples is very helpful. So thanks for sharing!

Go Tigers!
Mike