As a buyer, you could also ask: “Is there a number of money ducks that I could buy so that I am guaranteed to make money?”

On the flip side, the seller might ask, “Where do I need to price the money duck to ensure that I make a profit overall?”

Today I learned I’m not one of Dan’s favorite curriculum designers ;)

My favorite question here would be to set a price for the duck and ask the seller’s question, what distribution should I use for the bills? But only after the kids have determined that an equal distribution is profitable for the buyer.

Some of my thoughts:
How many days of cleanliness could you get out of this bar of soap?
How many days of sudsy clean do we lose with the money inside? I’m not real keen on rubbing dirty money on myself, even if it’s been sitting inside a bar of soap.
If it cost $10 and the bar contained the $20 or $50, how many regular bars of glycerin soap would that afford me?

(obviously, i realize that most people buy this kind of product for the novelty of it, but these are some questions that we could explore with students.)

Seems like this might be a fun little project:

Your friend Dan walks in with 5 money ducks. Each of the ducks has some money hidden inside – one has $1, one has $5, one has $10, one has $20, and one has $50. You do not know which duck has what amount of money, but Dan does.

He suggests a couple of games:

(1) You pick any of the ducks you want and get to keep the money inside of it. How much money do you expect to win playing this game one time?

(2) You pick any of the ducks you want and then Dan tells you the lowest amount of money remaining in one of the 4 ducks that you didn’t pick (without telling you which one of the ducks contains that lowest amount of money). He then lets you pick a new duck if you want. Would you rather play this game or game (1)? Why?

(3) Same as (2), but after your first selection Dan tells you the highest amount of money that remains in one of the four ducks that you didn’t select instead of the lowest. He then lets you pick a new duck if you want. Would you rather play this game or game (2)? Why?

Depending on how advanced the students are, you could ask for expected values in games (2) and (3), too, but even without calculating an exact number, the discussion about which games people would rather play would be interesting.

Alas all so many good ideas already!

You, your friend Dan and 3 other friends each have a Money Duck. Dan finds out his has a 1$ bill (sorry Dan). One friend then asks you to switch ducks with them. Should you? (Easiest variation – 5 ducks, 5 prizes as indicated on the packaging).

This is a really good expected outcome scenario that could be explored in a multitude of different ways.

I would look into the overall cost of production of the duck – materials, manufacturing, packaging, distribution and the money prize, compared with the actual price asked for the duck. From this students could create different distributions of money prizes that still makes the product profitable to the company.

I just wish I could get hold of some of these actual values…

Say every student of mine bought just one Money Duck and we pooled the hidden duck money together. Would my students be willing to evenly divide the hidden money (profit or loss)? At what point in the process should they commit to their decision?

The actual cost of the product on Amazon.com is $9.94 plus $4.99 shipping.

http://www.amazon.com/Duck-Money-Soap-Each-Contains/dp/B00E9E4PAE/ref=sr_1_1?ie=UTF8&qid=1398947912&sr=8-1&keywords=money+duck

My 2nd grader wants to know how many baths he has to take before he gets to the money.

I’d split the class in half and have half the class discuss one question and then the other half discuss the other. Then I’d have kids share what their groups came up with. You could break kids up into smaller groups within the halves and then do a “jigsaw activity” where groups them split off into new groups and come together to discuss.

What a great classroom debate this would make with half of the class representing buyers and half representing sellers. Students would have to realize that buyers and sellers have competing interests, but the price must make both of them happy in order to have a viable product that will appeal to the consumer and generate profits for the seller. (Possibly a collaboration with the Economics teacher)

I presented the Money Duck to my grade 4/5 class this morning with the question: “What is the most that you would pay for a Money Duck bar of soap?” Group conversations were animated as was the class discussion.

Questions that students raised included: “How likely would it be for the package to have 10, 20 or 50 dollars?”, “Is the money planted in the middle of the soap? If so, would someone break the soap to get at the money?” [in which case the soap didn’t matter at all in the pricing] and “What is the quality of the soap?” [If it was a good quality soap many were willing to pay more]. Some students started taking the seller’s point of view and gave ideas how they could increase profits.

The discussion lasted nearly half an hour. Incidentally, the average price the students were willing to pay was $5. (Figuring that the soap itself was worth 3 or 4 dollars, and then factoring in the minimum prize of 1 dollar).
Clearly this idea has potential at multiple grade levels.
Thanks!

Nothing to add to the awesome suggestions above.

From what I’ve heard, nearly all of the ducks are $1 ducks. It’s like buying a lottery ticket — you expect to lose, but it can be fun for some people anyway.

I am expecting an Act III that involves a ridiculous amount of high speed hand washing.

My first instinct is that students will be more interested in taking the buyer’s point of view, but some entrepreneurial souls may jump on the question from the seller’s point of view. I like the suggestions to split the class and do the problem from both perspectives.

When thinking about the question from the buyer’s perspective, I’d want to know the distribution of currencies in the ducks. In real life, that information is probably not knowable (as the buyer). But for the sake of designing a math problem you could either 1) provide a distribution if the students determine its necessary or 2) have them guess what they think the distribution is likely to be (which is what a real buyer must do). And then they could answer the question–Is it worth it?–allowing and encouraging students to put a value on the soap, the expected value of the currency, and its novelty.

From the seller’s perspective, I might flip the question around. A seller would likely come up with a price first that they think buyers would find reasonable (let’s say $10) and then determine the distribution from there. This kind of problem is so open-ended that you might have to put some constraints on it. Say, in a lot of 200 ducks, how many of each bill would you use? And then ask students to come up with 3 different distributions. One distribution would have to equal $10, the second distribution would have to yield the highest profits for the company, and the third distribution would strike a balance between the two and offer buyers some hope of landing that $20 or $50 (which would encourage more sales).

Many great ideas here! Taking a spin on M Ruppel’s idea about giving them a pictoral representation of 100 ducks with their payouts, it could be neat to give the “sellers” a piece of paper that has ~50 small pictures of ducks. They are told that every duck must have a $1, 5, 10, 20, or 50 in it; and that each duck costs $2 to produce. Their task is decide how many of each bill to use, and then to decide the individual selling price along with a marketing campaign to lure the “buyers” to choose their product. They can write the dollar amount payouts on each duck as a very concrete representation of how much money they are giving away in total. In the end, the different “seller” groups could present their selling price and marketing campaign, and also their expected profit.

1) Owning and playing aren’t binary, and kids understand this but at 16:40, the teacher doesn’t acknowledge it. Like Mr. K suggested, after setting a price we don’t just want to ask, “Would you buy this?” but also, “How many of your classmates would buy this?” then find out. This starts us down the path of mean v. median v. mode , right skew, utility, and gambler’s fallacy, for instance. Kids can craft a game that balances popularity/appeal among their peers with profits better than I.

2) Feedback! After #1, rip open 10 ducks then ask students to come up with a better price or distribution. How? Either simulate in Excel or build a $10 quincunx , placing dollar values at the bottom.

3) Set up shop like Dan Anderson suggested. Two groups of producers sell ducks while four groups of consumers decide how many from each producer to buy, if any. Stop along halfway through to balance the books, write Yelp reviews, and adjust schemes.

pose 2 questions to the class. If you knew that 200 ducks were made;

Would you buy if all ducks except 1 had only $1 (and the payoff duck had $101)

or

Would you buy if you knew that at least 15 of the ducks had $10 and some contained nothing?

If the average amount per duck stays the same, at what point does the possible payoff make the situation more tempting?

Sorry Dan, I couldn’t find the problem I was thinking of. I was remembering a classroom lesson I had observed and I thought it was based on a Math Forum PoW, but looking through the library it seems like they were using a problem from another source and using “I Notice, I Wonder” as the launch activity and that’s what I was there to observe. The problem was something like this: http://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.271158.html (I’m sorry it’s such an ugly website).

I noticed that your suggested treatment lets students start from their buyer perspective at first, and shifts them towards a seller’s perspective as things get more formal and quantitative, which makes sense to me. I wonder which kids might have more and less trouble making that transition.

Did you really get a $50.00 after six purchases? They still made money off of you…

I found that my first question after watching the video was: “How much money will Dan make if he buys a LOT of ducks? Or will he lose money?”

From Dan Meyer: “The marketplace idea (proposed by several of you) seems pretty tantalizing and also really tough to pull off. One reservation I have is that at any given moment one half of the class seems not to be doing much of anything which, if true, is a management problem as well as a waste of a bunch of brains….
Is there a way we could have everybody in the class play both sides — producing and consuming?”

You’re right. I suppose a bette setup of the marketplace would allow all groups to make their own product, and then allow all the individuals to be the buyers. The most interesting mathematical time would be the initial setup of the product and the breakdown after the marketplace has concluded.
I don’t think that there’d be an extended marketplace amount of time, enough to set the flan, but not enough burn it.

Also from Dan M.: “Extra credit: say you were in a 1:1 classroom, how could our friends at Desmos facilitate this kind of classroom marketplace? (Imagine everybody is a seller and buyer of soap. Everybody has a bank account with cash in it. Now what ….)”

This might be an efficient and fun way of setting up a marketplace, allow each group to set the odds of each bill appearing, and set a price (they’d need to divulge the probabilities).
After the marketplace was setup, then give students a bankroll and allow them to buy bars of soap. What business would make the most money? What buyer would (luckily) get the biggest reward?
I think the danger here, like many online forays into the teaching of math, is not letting the computers do _all_ the interesting math. Know what I mean?

I’m probably coming at this from more of a probability angle (because I’m teaching it right now), but I like the co-mingling of theoretical and experimental probability, represented by the producers and consumers tasks. The producers need to have probabilities that add to 1, and the consumers will potentially grasp that even though the $20 bill should show up once every 10 soap bars, it takes a long long time for the probabilities to play out. Computer simulations are a natural extension to this experimental probability.
Dan

You compute this and manually adjust your bankroll for a stretch but after a time, the computer does it for you freeing you up to attend to limiting behavior and other global foci.

Yea, and have the students originally keep track of the probabilities and then have the computers take over and track the outcomes.
Is this marketplace idea too open ended for a full computer simulation?

believe it or not my little girl pulled a 50$ bill out last night. I was putting under lights because I was in disbelief but it is legit money. Just a lucky ducky:)

my school got some. one for each class and we are getting feedback from our other classes then we voted and my teacher gave away a money duck to who ever did the best based on the class vote