With the Clarity of Mud

Oh man did I ever have to eat crow today. One of the middle school teachers insists on the students turning all of their integer problems into addition problems, like this...

4 - 8 =

and then they would have to turn that into this...

4 + (-8) =

and then they would have to solve it...

4 + (-8) = -4

This used to make me so mad, until I found that I had to explain it to my students using different colored dice. In class today, for the above problem, I took four green dice and eight white dice (green was positive, white was negative) and showed them that the white outnumbered the green by four, and therefore the answer was negative (white) four.

In order to do it this way, it really helps if you turn all of the problems into addition problems like I did above.

More for instances:

(-5) + 6 = 1

3 + (-9) = -6

(-7) + (-6) = -13

Here's a kind of a tricky one to turn into addition, because the two negatives in a row actually transform them both into positives...

4 - (-16) =

Which becomes 4 + (+16) = which of course is equal to 20.

I told the kids for their homework tonight to take pennies and dimes, little pieces of construction paper, or whatever you have around the house and use them the way I did the dice this afternoon, to see what balances out to what.

The homework tonight (there are 54 problems, but I think the repetition will be good for them, plus they're all fairly simple) already has all of the problems converted to addition problems. Hopefully any problems have been wrinkled out!

SO SORRY that the book report STILL hasn't been given out! It's on its way! It just seems to be on the slow train here!