# Engaging students: Order of operations

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Chais Price. His topic, from Pre-Algebra: order of operations.

How could you as a teacher create an activity or project that involves your topic?

With a concept as foundational as the order of operations, an interactive activity involving precise directions given from the teacher to the class would be appropriate and hopefully engaging. To clarify on this topic, imagine a teacher that explains to the class that we have a problem to solve. That problem could be that there is a hidden homework pass locked away inside a box. The only way to unlock the box to get the homework pass out is by following a set of simple instructions in order (possibly even a scavenger hunt). After the class completes the instructions, they are then to vocalize what they just did emphasizing he order. The Teacher can start off with saying from this point on everything I say is fair game as far as any directions I give you. So everyone stand up. Take off your shoes left shoe first then right. Next bring your shoes to the front of the class room and return to your desk. Do 5 jumping jacks and spin around twice and be seated. After students do this and recite back verbally their actions in order the teacher can then ask them do repeat the given directions backwards.

• How can this topic be used in your students’ future courses in mathematics or science?

The topic of the order of operations will be used in all high school math classes and most undergraduate math courses. It is truly a fundamental topic. Without knowing the order of which operation to apply first, the challenge remains. How then can our solution be correct?If you add or subtract before you apply an exponential or division step then the answer will be incorrect. If the answer is correct then it is purely coincidence. One example of this is anywhere the quadratic formula is used which is quite often. Any time something doesn’t factor nicely we use the quadratic formula. Just take what is inside the radical for instance. B^2-4ac. If b = 2, a= 2, and c=-2 and we apply the b^2- 4 before we multiply 4ac then we are left with a 0 inside the radical which would not be correct. We need to apply the order like this: b^2= 4 and -4ac = – ((4)(2)(-2)). Thus we have 4+16= 20 inside the radical if we did the steps in the order we were supposed to.

How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic? Note: It’s not enough to say “such-and-such is a great website”; you need to explain in some detail why it’s a great website.

I personally use technology such as YouTube and other sites where I can find videos of certain topics. I find these sites to be an abundant source of learning material. Take the topic of order of operations like we are discussing today. Each student has somewhat of a different learning style. With resources such as YouTube you are certain to find someone who can explain the topic to meet an individual learning style. These sites can be composed of lectures, examples, and misc. They are not put out just by teachers but students as well. When I searched order of operations on YouTube I found about 20 different videos on the first page. They ranged from beginning order of operations to multiple lessons building upon the concept. One video was even taken in the classroom with actual students (hopefully with permission). In addition I also found this video that I thought was pretty interesting. I will let you be the judge of that.

Mister, C. [learningscienceisfun]. ( 2010, October 31). PEMDAS- Order of Operations RAP [Official Music Video] Mister C. Retrieved from https://www.youtube.com/watch?v=OWyxWg2-LTY