## Sunday, November 11, 2007

### Algebra

We pause in our regularly scheduled NaBloPoMo reader question column for a check on Archer's mathematical progress.

I do not have a mental facility for algebra -- I pretty much always have to work it out on paper. So in most of the examples below, I didn't know ahead of time what the answers were -- I just checked Archer's answers after he provided them.

This morning, Archer asked about the final score of the UCA game last night (they shoot off a cannon in the stadium every time the home team scores, and since that's only about a seven-minute walk from our house, he spends the evening being constantly reminded about the game). I looked it up online and found that it was UCA 35, Stephen Austin 23.

"What combination of touchdowns, extra points, and field goals did we make to get 35?" I asked.

"Five touchdowns," he answered. "How many extra points?" "Five. A touchdown and extra point is 6+1," he said.

"Now what combination of touchdowns, extra points, and field goals made 23?" I challenged.

"Two touchdowns," he said.

"How many extra points?" "Two."

"How many field goals?" Triumphantly: "Three."

I added it up: 14 + 9 = 23. Yep.

While I was working it out, Archer was making up his own scores, and one of them was 62. I asked him if he could figure out how many of each kind of score went into that.

"You could do ten touchdowns with no extra points and one field goal, but that would be 63," he tried. "Maybe we could go down to nine touchdowns with no extra points and two field goals, but that's 63 too."

"Try some touchdowns with extra points," I suggested. (Even with my atrophied math skills, I knew that getting some single-points in there to allow for something other than multiples of three was the key to the answer.

"If we go down to eight touchdowns with extra points, that's 56 points, and then three field goals makes 62!" he reckoned.

Okay, now for the test. I went to ESPN.com to find another real score he could work on. The first one on the ticker was Louisiana Tech 10, LSU 58.

"How do you make 10 out of touchdowns, extra points, and field goals?" I asked.

"One touchdown, one extra point, one field goal," he answered promptly.

He thought for just a moment. "Seven touchdowns with extra points, one touchdown with no extra point, and one field goal."

I think he's grasped the concept.