BEDMAS as real world teaching

Part of the Gr. 7 curriculum is to 'evaluate expressions that involve whole numbers and decimals, including expressions that contrain brackets, using order of operations"--which inevitably leads us to 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.

Ultimately BEDMAS/order of operations is a communications tool. Sure, you can solve the problem as a two step and organize your response that way...or you could use a BEDMAS expression--you'll end up with the answer either way. But the advantage of BEDMAS is that is an easy way to communicate the order of steps to others, in an efficient one line.

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!