[PS] Guitar Hero
October 16th, 2010 by Dan Meyer
Algebra I (Illinois Edition), Prentice Hall, a Pearson subsidiary.
Pseudocontext
Is there anything inherent to buying an electric guitar that would lead to that equation ever?
[via Ryan Buck]
Transcription:
A music store sells a copy of a deluxe electric guitar for $295. This is $30 more than 1/3 the cost of the deluxe electric guitar it is modeled after. What is the cost of the deluxe electric guitar?
Assignment:
- Scan an example of pseudocontext.
- Email it to dan@mrmeyer.com
- List the textbook title, edition, and publisher.
- Give me your interpretation of the term "pseudocontext."
- Let me know if you'd like credit (name, blog or twitter) or if you'd prefer anonymity.
This one actually looks okay to me. I plugged it into Excel, and it agreed:
=if(guitar, “real”,”")
“You bought a used deluxe electric guitar from an online store for $295, shipping included. The seller told you it was a great deal because he was selling it for just one third of the original selling price, plus thirty dollars to cover shipping. If that’s true, how much did the guitar originally cost?”
My word. That … almost does the job.
I like Zeno’s version. It’s a reasonable application, and it also avoids the triple repetition of the awkward phrase “deluxe electric guitar.”
The other real-life variant of this kind of problem is the small retail operation: “You bought widgets wholesale at $14.37 each. Your store’s standard retail mark-up is 150% above the wholesale price, and you want to round to the nearest $0.50 price point so you don’t have to deal with pennies. How much should you price each widget?” I did a lot of that math at various jobs…
Worse to me, here, is the process in setting up and solving the problem. What’s presented by the text suggests that a student can only solve the problem by “relating” in the specific way dictated above (eventually writing an equation). But what happens when the words change, or the order of the information changes? Lots of kids seem to botch this type of problem when they’d be fine if the cost of the original guitar were given and they were asked to find the cost of the model…
Nice job by Zeno of cleaning this up, and I shudder if kids end up thinking this is the type of work they might do at an actual music store.
Zeno did do a good job cleaning up the problem. The only change I would make is the verb “told” in the second sentence. I think that “wrote” would be better because the transaction is taking place online. I know that this is picking nits.
LOL at Zeno’s question…you must hang out in the same guitar forums as my husband!
My biggest beef with the original problem is the flippant use of the commutative property of addition. If the problem was written $30 less than instead of $30 more than, the $30 would come AFTER the subtraction sign. I am thinking in an Algebra I class, the commutative property would have been discussed by now? Ideally, put the $30 after the operation, be it addition OR subtraction.
I like Zeno’s suggestion, I’d just change the ending to “how much would you actually save over buying it new”.
“A friend will sell you his Gibson for a fraction of the original cost. That fraction is 3/2. Should you buy it?”
[...] be anything else in the world? And who has a favorite orange anyways? Another example would be the guitar problem. Sure we can set up equations and solve to find the cost of a guitar, but this problem won’t [...]