Engaging students: Factoring quadratic 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 comes from my former student Kelsie Teague. Her topic, from Algebra I and II: factoring quadratic polynomials.

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What interesting things can you say about the people who contributed to the discovery and/or the development of the topic?

In Renaissance times, polynomial factoring was a royal sport. Kings sponsored contests and the best mathematicians in Europe traveled from court to court to demonstrate their skills. Polynomial factoring techniques were closely guarded secrets.


When reading this article, I found the fact that this topic was considered a royal sport very interesting. Students would also find that interesting because it would get their attention with the fact that kings thought this was very important. We could even have our own royal game for it. I think we could start off with a scavenger hunt to work on factoring just basic integers. Also, I think we could use the same idea to start the explore except to do it backwards and give them the polynomial already factored and have them FOIL it and get their polynomial. I want to see if they can see how to do it the other way around without being taught how. This game could show them that factoring is just the reverse of foiling.

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How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?

I looked up factoring quadratic polynomials on Khan Academy and I found some really great videos. They have videos that show detail steps and also after a few videos they have parts where you can practice what you just watched and see if you understand it.  This website is great for at home practice or in class practice because with the practice sections it tells you if you are correct or not and will also give you hints if you don’t know where to start. Also, if you don’t have a clue how to do the problem given, you can hit “show me solution” and it will redirect you to a similar problem in a video to help out. I think this website is a great tool to let students know about to learn and practice.

Also I found a great video on YouTube it’s a rap about factoring that would certainly get gets engaged.

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Students first learn about the basic idea of factoring in elementary school and continue to learn and use this topic all the way through college. You need to factor polynomials in many different contexts in mathematics. It’s a fundamental skill for math in general and can make other calculations much easier. You use factoring for finding solutions of various equations, and such equations can come up in calculus when find maxima, minima, inflection points, solving improper integrals, limits, and partial fractions.  Students will need to know factoring all the way up in to their higher-level math classes in college, and also be able to use it in a career that is related to engineering, physics, chemistry and computer science.


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