![]() Part C is probably the easiest among the three, since it deals with concrete numbers. ("I told you to mark it back up by 10% they should all say $200!" etc.) It is a pretty common misconception that the before- and after-prices will be the same, so you could weave this into a tale of your boss (or maybe a nefarious manager, or whomever else) chastising you for messing up the prices. Real Life C: Suppose the jean price in A is initially $200 leaving aside whether this is an exorbitant amount to pay for a pair of pants, what will be the final price? Real Life B: Same as A but the scenario is marking down by 10% first, and back up by 10% later. Is the final price more than, less than, or the same as the original price? ![]() A few weeks pass, and she asks you to mark them back down by 10%. Real Life A: Your boss at a vintage clothing store tells you a particular brand of jeans have become very popular, and to mark them up by 10%. I phrase it below in terms of expensive jeans at a vintage clothing store, but I'm sure you can identify the underlying mathematics and modify the context as you see fit. (So, some anecdotal evidence that it was received okay!) Students seemed engaged, and one of them emailed me the next day to say:įor what it's worth: I felt like Will Hunting when I got that Red Sox ticket markup problem yesterday. The enrollees were middle school and high school teachers, who were in their first year of teaching (not having arrived with necessarily strong coursework in mathematics, but let us not diverge for the moment).īased on the interests of the (Boston-based) class, I phrased it in terms of scalping (Red Sox) baseball tickets. Here is a real-life example that I used in a class with some success. So: Be aware that even with this very practical exercise, there's an enormous difference in reaction between doing it as a theoretical exercise in class (mostly the usual "meh" reaction) and doing it in response to an immediate needy student's request (which can be "wow", etc.). ![]() Other students have complained, "Are you seriously going to be that hard on me?". In a college algebra class, I once set up the formula on the board and people were amazed and gasped and took out phones and snapped photos. Some can't accomplish it after a day of effort (even at the end of an elementary algebra course). Some students then rip off the answer in a few seconds. In almost all cases I have to remind them of our grading formula, write it down, and possibly start the substitution step. I get some surprising responses when this comes up and I respond that the asking student should be able to do it on their own. Then one can solve for the necessary F score algebraically in a straightforward fashion, but it's really hard to guess otherwise (likely involves decimals). Going into the last week, Q and T are fixed and W is known by the student's goal for overall grade (say, 90% for an A, etc.). Say the weighted formula is W = 15%Q + 50%T + 35%F, where W is the weighted total, Q the quiz average, T the test average, and F the final exam score. ![]() I now respond to that with, "Well, you're asking an algebra question, so you should be able to solve that yourself", and I've set up my grading formula specifically to make that tractable for the student. The best example I've found is the question, "What do I need on the final exam to get an in this class?" at the end of a term - which really does get asked by one or more students every semester. the question shouldn't be too easy to solve) hopefully this way they will see themselves how useful it can be to introduce variables. I'd like to begin the subject with such a question and let the students work on it together for maybe half an hour or so (i.e. There are of course loads out there in textbooks and the internet, but I haven't yet found one which is really intriguing and which could arouse the interest even of a student who has other things on his/her mind and who has a general dislike for school-mathematics.įor example questions concerning the respective speeds, distances and time-periods of two vehicles with respect to each other are classic examples motivating linear equations, but they don't really seem to occur in real life nor are they particularly fascinating (at least for someone who isn't interested in mathematics anyway). I am looking for a question from every day life (of a teenager) or a puzzle which is hard to solve without using algebra. I am going to teach some grade 9 students about solving linear and quadratic equations.
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