Sep 13, 2009

Adding & Subtracting Integers

I've held off cooking a nice dinner, am hungry, am angry, am missing a new episode of Entourage. At this point, I've accumulated a small fortune of years of lessons to fall back on. However, I've spent the past couple hours designing a lesson on adding & subtracting integers. Reason? I've sucked at it. There are multiple methods and multiple models and I can't seem to find which is the best.

I also want to avoid restricting ourselves to rules that serve to negate a sound conceptual understanding of number sense. For example, every year I find several students hoping to apply this rule:
1. If the signs are the same, add the numbers and keep the same sign.
2. If the signs are different, subtract the numbers and take the sign of the larger number.
I'm not trying to create computing machines here, I want thinkers who understand what they're doing.

So, just to share, this is what I'll try tomorrow:

Share 2 models of adding integers:
1. Adrian Peterson's total yardage calculated with losses and gains.
2. Mr. G's bank balance calculated with deposits and withdrawals.
Share 2 methods of adding integers:
1. Number line
2. Counters
Share 1 method of subtracting integers:
1. Add the opposite (meaning, when we see the subtraction sign, let's change the operation to addition and oppositize the second number), then use one of the 2 methods above.

I've contemplated the benefits of showing number line, counters, AND the difference model with subtraction but am afraid sharing those will do one of two things: scare students or confuse students.

Therefore, I go with what I've seen produce the most clarity and success. After we got these methods down for a day or so, THEN I'll show the other stuff. How's that sound? Anybody else got something that's worked real well for them?

Or maybe I'll just show this video:

And lastly, whatever happens tomorrow. I'm no doubt leaving a minute or two to show Kanye's infamous diss. Gotta buy your students' attention, you gotta. Also, I wanna see reactions. Sorry Taylor.


Natalie said...

I'm not a teacher, bhen I was little we used a song to the tune of Jingle Bells:

Like signs add,
Like signs add,
Add and keep the sign.

Unlike signs,
Subtract this time,
and keep the larger sign.

I don't know if that was particularly the best way of teaching math (we used songs for multiplication and to this day I still have trouble with it), but the songs have definitely stayed with me!

And also, Team Taylor!

Mindy said...

When I teach this in fifth grade, we think of "I'm happy about this" and "I'm sad about this" combined with the number line.

3 + 4...I start at 3 on the number line (or in my head). I'm adding 3 positives. Yea! I'm happy. I'm moving up the number line to 7.

3 + -4...I start at 3 on the number line. I'm adding 4 negatives. Yuck! I'm sad about adding negatives. I move lower on the number line to -1.

3 - 4...I start at 3 on the number line. I'm taking away 4 positives. Yuck! I'm sad about taking away positives. I move down the number line to -1.

3 - (-4)...I start at 3 on the number line. I'm taking away 4 negatives. Yea! I'm happy about getting rid of negatives. I move up the number to a higher value of 7.

Of course, I talk to them about how positive and negative don't mean happy and sad. We are actually happy about taking away negatives in the case of debt relief.

I think this helps them think about value and what they are doing with the subtraction of negatives.

Eyawn said...

These are both great suggestions! Anything that helps students remember mathematical rules is useful. I myself sing the quadratic formula for my students when the time comes.

Mindy, I can see several of my students benefiting from this way of thinking. I think I'll give it a go for students that need re-teaching.