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I give this substitution problem every year in my summer Algebra I refresher class. The mistake they almost all make, is a classic PEMDAS problem. So I teach order of operations rather strictly as illustrated in the example below. Here are 2 things essential things I teach them:
Here is a typical PEMDAS mistake students make:
Our Department abolished the phrase “Cancels out” a long time ago, and now we use phrases such as “reduces to 1“, “divides to 1 over 1“, etc. which demonstrates the math operation not some magic. We also always replace numbers and variables that reduce with a number even if it’s one (see below right). I actually start my students on Day 1 teaching them the fundamentals of both derivatives and integration. I can’t stress enough how important extra help is to being successful in Math. Some of the highest average students in my Honors sections got there because they came regularly to extra help. Another benefit is that a teacher that you might feel is not very approachable, is usually a lot more so at extra help where they aren’t trying to manage a large class. The problem sometimes is that students don’t know how to get the most out of extra help. I started teaching AP Calculus (AB) for the first time about 10 years ago. My students didn’t do so well my first 2 years (the class average grade was below 3). The third year I taught the class I started seeing much better grades. Now our AP scores average is above 4.0. Here are 3 things that I did differently that I think made all the difference:  A place to record problems you struggled with One of the tricks I suggest to all my students is to create a page filled with all the problems you struggled with or got wrong during the past unit. (I call it the “I got pwned page” – pwned is teen-speak for getting destroyed by something). I suggest students use the last page of your notebook because it’s always easy to find. They should record either a reference to the problem (problem #, worksheet, etc.) or simply copy the problem down. The night before the test (or a couple of nights before the test!) they should do all of these problems first as part of their practice. Hopefully they have solutions to these problems in their notes. They then check the solution v. their work. If they get it right, just cross it off! If they don’t, come back to it after doing all of the other problems and try again. Contrary to popular opinion, I feel that students should be doing math more often than taking notes. A binder (3 ring) should be used for the technique described below. Note taking should be minimal (better to watch the teacher more and then eventually do problems yourself!) and here is how I teach all my students to do it. Welcome and this post is probably a complete waste because no one is visiting yet! Well – it’s my way of congratulating myself for getting this blog up and running. |
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Matter and anti-matter cancels out (violently I might add). The airlines can cancel your flight. You can’t cancel out in Math (instead you “reduce” or “divide”). If you do try to cancel out, bad things can happen. Let me explain.