As for not having enough gold to back the system, gold is very divisible and price does solve everything.
As for a coin themed persuasion paper, do one on what coins to collect from circulation now for profit later. Be persuasive. Sell it like you are on late night infomercials peddling pre 1982 cents.
You are investing one cent (and time. . . .) and you are guaranteed to never have that cent decline in value. It may go up based on the metal content though.
Today those cents are already worth 1.7 cents melt value. Where else can you start out with a 70% gain and an absolute guarantee that you will never lose one cent (unless of course you misplace one. . . .). Sell it hard. Stocks may go down and don't often go up 70% the moment you buy them. Is it insane to own stocks versus hoard pre 1982 pennies? If not insane, it does imply that the holder of stocks thinks there is less than zero risk and more than enough upside to pass on the 70% gain on day one.
Gloss over any concerns about the value of your time, the time value of your money, the opportunity cost of locking your money up in a copper stash in a form less usable than wire, the physical size of the stack, etc. Those are things you need to defend against in order to sell your product. It is your customer's job to decide not to buy, it is your job to persuade them otherwise.
Don't be fair, persuade them to buy your product.
Look up why coin collecting started in the first place. Gresham's Law is the answer. Basically bad or debased money drives good money out of circulation. Now that you know that debasing money caused coin collecting, learn why governments debase money in the first place. Do it before you borrow one red cent for some absolutely worthless degree.
If you want to get a better grade, do one on why teachers are underpaid.