Pencils (was Radioactive decay)

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

Several unusual applications of pencils were listed by Vickie
(see below). Let me add one more; it has to do with proportional
thinking mentioned on the kinematics thread. And, like pencil
throwing-and-counting, it is appropriate for any elementary
science course.

After showing that the "number of remaining pencils" versus
the "step number" curve is not a straight line ask students to
place ten new pencils on the scale and to determine the weight.
Then to remove one pencil and find the new weight. Then to
remove one pencil and find the new weight, etc. Let them plot
the relation ( W versus i) and ask some questions, such as:

1) What do these two curves have in common?
   (N or W go down.)
2) Predict the value of W (before using the scale) after two
    pencils are removed? (The weight of each pencil is given.)
3) Predict the N after two throwing steps.
4) What makes the predictability of W possible and what
    prevents us from making predictions about N?
5) Then talk about deterministic and probabilistic relations.
    The concept of probability can be introduced and used to
     make reasonable probabilistic predictions, for example,
     about simple betting games or investments. Knowing
     probabilities is better than knowing nothing.
6) How can probabilities be determined?

What else can be done with a set of pencils to promote
children's learning?

"Frohne, Vickie" wrote:

> I've done this quite a few times, and the "decay curve" from a handful
> of M&M's works out beautifully. The only hitch is when students have
> a few M&M's left over that have no writing on either side. This is
> when I introduce the concept of "background subtraction."
>
> M&M's are slightly cheaper to purchase than pennies, and they are
> preferred when you are asking the students to eat their apparatus.
> However, if you consider that you can use pennies year after year, use
> them in numerous other experiments (measurement, density, voltaic pile,
> etc.), and that you can recover 100% of their initial cost when you recycle
> (by spending) the used pennies, you can't beat the price of pennies.