I teach basic (very) statistics to prisoners in a medium/high security prison and would like to demonstrate the Central Limit Theorem. The classroom has no resources beyond a white board. I can only bring in paper and writing implements. Any suggestions on a simple demonstration?
I assume that by "demonstration" you mean, "showing what it's about", not a mathematical demonstration.
I would draw a Galton board on the black-board, and simulate what happens as you drop balls, making a random choice each time. You can even ask the students to pick "left or right" randomly a few times, to make it clear that the process is random and you're not deliberately choosing the path (though you should probably do so, in order to get better convergence).
You could also ask all the students their height, and plot a histogram. Why does it look like a bell curve? It's a contribution of many random effects.
If you are in US, this url has statistics on US prisons
Perhaps you could explore it to see whether some manifestation of the CLT emerges in there.
tell the people to choose papers (or cards) from a pack of cards where each card has a number from -2 to 2.
Also have 5 boxes (A, B, C, D, E).
At first time tell them to choose only one card each.
Then tell them to place their cards into one of the boxes.
When everyone (including you if you want) has placed her card(s) in a box, count the sum of each box and draw a histogram, this wil be very crude.
Then tell the people to choose more than one card (make sure there are enough cards for the experiment) and place their cards on a box (or even different boxes).
Repeat the counting process, draw a new histogram
Repeat once again with people having even more cards each, repeat the counting process, draw histogram.
One can repeat this process as many times as one wants.
Observe the histograms and their shapes.
Can you bring in dice? (or maybe they already have access to dice). Then have them throw the dice (many times, they have the time ...), draw histograms, calculating mean number of eyes, drawing histograms of that for different $n$, so on ...
With many dice you can even build the histogram directly with the dice. We got this in class: