Engaging students: Dividing polynomials

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 again comes from my former student Sarah Asmar. Her topic, from Algebra/Precalculus: dividing polynomials.

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

Many high school students are introduced to Polynomials in Algebra I. They are taught how to factor and to even graph Polynomials. In Algebra II, students are asked to add, subtract, multiply and divide Polynomials. Dividing Polynomials is challenging for many students because they are not only dividing numbers, but now they have added letters to the mix. There are two ways to divide Polynomials: Long Division and Synthetic Division. Since this is a topic that most students find difficult to grasp, I would split the students into groups of about 3 or 4 and provide each group with Algebra tiles. I would then provide each group with an index card with a specific Polynomial for them to divide. The index card will have a dividend and divisor for the students to use in order for them to create find the answer using the Algebra tiles. First, they will need to create a frame. Then, the dividend should be formed inside the frame while the divisor is formed on the left hand side outside of the frame. The answer will be shown with the tiles on the top line outside the frame. I will do an example with them first and then have them do the problem provided on their index card with their group. This activity will provide the students with a visual representation on how dividing polynomials would look like in order for it to be easier for them on paper.

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

Students are introduced to dividing Polynomials in Algebra II. Most would never like to see this topic again, but unfortunately that is not the case. Dividing Polynomials is revisited in a Pre-Calculus class. However, it is taught at a much deeper level. Students are required to divide using long and synthetic division. Synthetic division is taught as a short cut for dividing Polynomials, but it doesn’t always work and students would have to divide using long division. Synthetic substitution is taught as well to find the solution of the Polynomial given. Synthetic substitution is as easy as just plugging in the given number for the variable provided in the Polynomial. Dividing Polynomials is also used in Binomial Expansion in Pre-Calculus. Along with all of these topics in Pre-Calculus, dividing Polynomials appears in all future basic Math courses such as Calculus. A real life example that uses Polynomials is aerospace science. These equations are used for object in motion, projectiles and air resistance.

How can technology be used to effectively engage students with this topic?

I was searching the Internet and I came across this video. I thought that this video would be an amazing tool to help the students understand how to divide polynomials without me just lecturing to them. It is sung to the tune of “We Are Young” which is a very popular song in the pop music culture. Using something like this would show a visual representation, but it will also drill the steps in their head. Our brains can easily remember songs even after listening to a song just once. The fact that dividing polynomials is put into a song makes it more likely for a student to remember the steps they need to take in order to perform the indicated operation.

References:

http://www.doe.virginia.gov/testing/solsearch/sol/math/A/m_ess_a-2b_1.pdf

http://polynomialsinourlives.weebly.com/polynomials-in-the-real-world.html