Engaging students: Adding and subtracting 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 Christian Oropeza. His topic, from Algebra: multiplying polynomials. How could you as a teacher create an activity or project that involves your topic?

The activity would consist of each student being given a bowl with 20 pieces of candy, which has multiple colors (e.g., Skittles or M&M’s) and a worksheet, which by the end will show students how to add and subtract polynomials(Reference 1). The objective for each student is to group all of the pieces of candy by the same color. Once this has been completed, the students will write down on the worksheet for “Part 1”, how many pieces of candy are in each group. Next, the students would be given 10 more pieces of random colored candy. Then, the students will regroup the new pieces of candy and write down the new number of candies in each group for “Part 2”. For “Part 3”, students will eat(or put away) 10 of their candies randomly. Finally, the students will write down the new number of candies in each group. Then the students would be asked, “What did each one of you do to put the candies in groups?”, “what operation was used for Part 2 of the worksheet”, and “what operation was used for Part 3 of the worksheet”. The students’ responses should be somewhere along the lines of “group the candies by the same color”, “addition”, and “subtraction”. Then the students would be told to relabel each group of colored candies into a different variable. For example, green=x, red=x2, yellow=k, blue=y, etc. Knowing the previous information, the students will next repeat the Part 1, 2, and 3, but using the assigned variables instead of the colors. The purpose of this activity is to show students that each variable in a polynomial must be grouped by like terms when performing addition or subtraction. How does this topic extend what your students should have learned in previous courses?

This topic relates to previous math classes by activating students’ prior knowledge on the concept of adding and subtracting integers. This means knowing the rules of addition and the rules of subtraction. For example, students should know that a 3+2=5=3+2, but 3-2=1 $\ne$2-3 (i.e., commutative property). Students should also know that the when subtracting a negative integer, the signs cancel out and all that is left is the addition of a positive integer (e.g., -(-2)=2). Students should also be familiar with grouping anything into specific groups. For example, if students were given colored tiles, then the students should be able to group the tiles into different colored groups. The distributive property is a topic the students should have covered before, which helps out when trying to simplify an expression involving parenthesis (e.g., 2(3+a)=6+2a. The idea of closure for integer properties and operations is the key to adding and subtracting polynomials, so students must have understood this concept prior in order to use the operation of addition and subtraction on like terms. 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.

Technology is always a great way to engage students especially with the newer generation of students where technology is part of their everyday life. The website mathisfun.com (Reference 2) is an excellent piece of technology to introduce this topic to the students because the website breaks down the idea of adding and subtracting polynomials piece by piece in easy manner that will help students see patterns and activate prior knowledge. With the inclusion of examples and non-examples students will learn where to minimize their potential errors. Some of the examples are animated with colors to help the more visual students understand and recognize the pattern for each problem. Another example of effective technology is the website Khan Academy (Reference 3,4,5). Khan Academy has great videos that thoroughly explains this topic. Reference 3 defines the word “polynomial” in math language by breaking the word into two words, which will help students remember and recognize this topic more easily. Also, Reference 2 goes over the vocabulary associated with adding and subtracting polynomials (e.g., coefficients, monomial, binomial, trinomial, and degree). Reference 4 goes over an example of adding a polynomial by going through step by step procedures. Reference 5 does the same thing as Reference 4, but over an example of subtracting polynomials.

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