BEDMAS (Brackets, exponents, division OR multiplication and addition OR subtraction).
Students quite enjoy the puzzle nature of cracking a BEDMAS equation like the one demonstrated in this Khan academy video:
8 + (5 x 4) - (6 + 10 divided by 2) + 44
I've also had students create questions like this for their peers to solve...they enjoy the challenge of both designing and 'cracking the code'.
Inevitably, though, students ask me--as they SHOULD--how does this relate to real life? When am I ever going to use BEDMAS in real life?
"Well, I'm soooo glad you asked," says I. Usually, a student asks me about 'real life' right from the get go whenever we start a new math unit but I typically plan to demonstrate real life applications anyway, because they are so necessary to solidifying math understanding. No one likes learning things one believes have no use! Math is too easily done in the head, abstractly, without connection to anything, just floating in the ether of logic and rationality. I've a few students that like to live in this math bubble, they enjoy the logic for logics sake and the puzzle for the sake of puzzling. But for the vast majority, math, at least at this level, needs to be grounded in reality or students disconnect.
Anyway, I initially wasn't so sure how to make BEDMAS 'real'. When I learned it, way back when, it was simply a matter of tackling a sheet full of questions by applying BEDMAS...and that's it.
Luckily, I found a selection of word problems online here and also this question that I found in the textbook.
The Cross Country Team ran timed circuits. Here are their times: 15.8 min, 12.5 min, 18.0 min, 14.2 min, 13.9 min, 16.0 min, 16.2 min, 17.5 min, 16.3 min, 15.6 min. Find the mean (average) time.
We had done mean previously, so they understand the HOW (add up a set of #'s and divide by the total # in the set). They just had to make the connection between 'multi step problem' and BEDMAS as a way of representing the multi-step procedure in a single expression!
Students solved this, and other word problems...but they had to write up their solution using the BEDMAS expression format, in other words communicate the order of steps as a single expression, as it would apply to that particular real life problem.
It is pure enjoyment to a teacher's ears to hear the various 'a-ha's' that went off around the room today as students realized that the order of operations/BEDMAS procedure was actually just a way of representing multistep operations...rather than just being this obscure, occasionally entertaining math question.
They were familiar with mutli step word problems... What they usually did was figure out the first step...then figure out the second step seperately. Now they could use order of operations/BEDMAS to a) put those steps all in one line/equation and b) effeciently COMMUNICATE to others the way to solve the problem...what to do first and what to second, and so on, by applying the BEDMAS rules.
Something so mundane as 'order of operations' turned into a real a-ha moment for my students today as they not only made the connection between math and real life but also the variety of ways math can be communicated...and how to be most efficient in the use of 'math language'. BEDMAS is just such an efficient and streamlined--dare I say elegant?-- way to communicate. Math tends to favour elegant simplicity!
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Monday, 25 February 2013
In math, we should be finished order of operations (BEDMAS) and should get started on integers before the break--we will likely continue them after the break. Continue to check out the math page on this blog to see what we are doing daily in math class!
Inanimate Alice, various media representations of fictional narrative for us to evaluate and interpret, a Skype interview with my author friend, Kevin McGill (author of Nikolas & Co) and, of course, the creation of a narrative piece (a fictional short story). More details to come after the break!
Wednesday, 6 February 2013
In my last post, we developed criteria for judging the effectiveness of a video game (such as quality of graphics, music/sound, multiplayer, etc) and then applied that criteria to a game. Students were encouraged to be as specific as possible in their judgements...to provide specific detail from the game to support their positions. For example, if they found the sound effects too annoying, then they had to give an example to back that up: "the woop, woop, woop for every power up sounds squeaky and is too repetitive".
After that, we looked at a review written on that game and evaluated it according to this checklist. Students had to explain what was done effectively (or not) according to the criteria on this checklist. (The reviews were written by prior students or by me).
The ability to evaluate and judge is considered a higher order thinking skill. It is a skill I am really pushing students to utilize in this unit, as not only are they evaluating a game/movie and text but also the reviews written about each of those things.
After the video game, we went through the same process for films. We developed criteria and then applied that to 3 short films, using our graphic organizer.
The 3 short films we watched were:
Alternatively, others liked the ending. They thought it was a good resolution because it twisted your expectations... I encourage everyone to watch it and make up their own mind!
Again, after going through the process of critically evaluation the films and determining our own opinions, we looked at a review written on a movie (Mission Impossible: Ghost Protocol) and evaluated it according to the checklist.
After that, students are to start the process of creating their own review on a game, movie or fiction text of their own choice.
I look forward to reading student reviews!