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 Andy Nabors. His topic, from Algebra: multiplying binomials.
A2. How could you as a teacher create an activity or project that involves your topic?
Multiplying binomials is an interesting concept because there are so many ways in which this can be done. I can think of five ways that binomials can be multiplied: FOIL, the box method, distribution, vertical multiplication, and with algebra tiles. I would incorporate these methods into one of two different ways. In either case, I would split the class into five groups.
- In the first way, I would assign each group a different method of multiplication. The groups would each be responsible for exploring their method, working together to master it. Then each group would be responsible for making a poster describing their method in detail. Then would then present their poster to the class, and the students not presenting would be taking notes. Already having one concept of binomial multiplication, the students would be seeing other methods and deciding which makes most sense to them.
- In my second idea, I would have five stations in the classroom each with their own method. The groups would rotate station to station figuring out the different methods collaboratively. The groups would rotate every 7-10 minutes until they had been to every station. Then the class would discuss the strengths/weaknesses of each method compared to the others in a class discussion moderated by the teacher.
These activities rely on the students being able to work and learn in groups effectively, which would present difficulty if the class was not used to group work.
B1. How can this topic be used in your students’ future courses in mathematics or science?
I had the privilege of teaching a multiplying binomial lesson to a freshmen algebra one class in CI last spring. My partner and I focused on the box method first, and then used that to introduce FOIL. The box method was easier to grasp because of the visual nature of it. In fact, it looks a lot like something that the students will definitely see in their biology classes. The box method looks almost identical to gene Punnet Squares in biology. In fact, my partner and I used Punnet Squares in our Engage of that lesson. We reminded the students of what a Punnet Square was, and then showed them a filled out square. We went over how the boxes were filled: the letter on top of each column goes into the boxes below and the letters to the left of the box go in each box to the right. Then we showed them an empty Punnet Square with the same letters before. We inquired about what happens when two variables are multiplied together, then filled out the boxes with multiplication signs in between the letters. The students responded well and were able to grasp the concept fairly well from the onset.
E1. How can technology be used to effectively engage students with this topic?
The internet is fast becoming the only place students will go for helpful solutions to school problems. This activity is designed to be a review of multiplying binomials that would allow students to use some internet resources, but make them report as to why the resource is helpful. The class will go to the computer lab or have laptops wheeled in and they will be given a list of sites that cover binomial multiplication. They will pick a site and write about the following qualities of their chosen site: what kind of site? (calculator, tutorial, manipulative, etc.), how is it presented? (organized/easy to use), was it helpful? (just give an answer opposed to listing the steps), did it describe the method it used?, can you use it to do classwork?, etc.
This is a sample list, I would want more sites, but it gives the general idea I’m going for. (general descriptions in parentheses for this project’s sake)
http://www.mathcelebrity.com/binomult.php (calculator, shows basic steps of FOIL of inputted problem)
http://www.webmath.com/polymult.html (calculator, shows very detailed and specific steps of FOIL of inputted problem)
http://calculator.tutorvista.com/foil-calculator.html (calculator, shows general steps of FOIL, not the inputted problem)
http://www.coolmath.com/crunchers/algebra-problems-multiplying-polynomials-FOIL-1.html (calculator but only problems it gives itself, more of a practice site)
http://www.mathwarehouse.com/algebra/polynomial/foil-method-binomials.php (FOIL tutorial site with practice problems with hidden steps)
http://www.themathpage.com/alg/quadratic-trinomial.htm (wordy explanation, lots of practice problems with hidden answers)
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying-binomials/v/multiplying-polynomials-2 (many tutoring videos, just the writing no person)
http://www.zooktutoring.com/now-available-my-very-first-instructional-math-video/ (many tutoring videos, tutor is seen with the work)
http://illuminations.nctm.org/Activity.aspx?id=3482 (algebra tile manipulator)
I will assume as a teacher that my students already look for easy solutions online, so I want to make sure they look in places that will help them gain understanding. I would stress that calculator sites are dangerous because if you just use them then you will not be able to perform on your own, but could be helpful to check your answer if you were worried. At the end of the lesson they would have a greater understanding of how to use internet sources effectively and have reviewed multiplying binomials.