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 Perla Perez. Her topic, from Algebra: multiplying binomials.

B1. How can this topic be used in your students’ future courses in mathematics or science?

As students progress through different levels of math, they will continue to utilize tools, such as multiplication of binomials. When I give students the solutions to a quadratic function and ask them to find the equation, I expect for them to know how to multiply the binomials. For example: find the quadratic equation with the solution x=-2,2. The students are to set up as: (x+2)(x-2) and go forth. The students can also be given a quadratic equation, x^{2}+6x+8 and are to find the solutions in representation (x+2)(x+4). In order to arrive at the answer, the students will have to factor the original equation. To check their work, they can just multiply the answer that they get. Multiplying the binomials is a more complex form of the distributive property. It’s a building block for more challenging math concepts. Multiplying binomials essentially does the opposite of factorization, which students will learn later on in their algebra class. Binomials are also used in sciences, such as physics, biology, and computer science, so it helps for students to have a strong foundation on this topic.

B2. How does this topic extend what your students should have learned in previous courses?

I’ve seen students panic when a new concept, equation, or definition is introduce. Before they begin thinking again that math is some sort of sorcery, showing them something familiar will help ease the students into a new topic that is an extension of what they previously learned. Students learn about distributive property in their pre-algebra course. In order for students to multiply binomials students need to understand distributive property. Distributive property is a building block that is needed for the multiplication of binomials. It works with singles terms being multiplied, where as binomial multiplication works with two. In a way it is like learning how to add single digits to double digits. In order to teach this, I would first reintroduce 4-5 problems they’ve seen in their previous class using distributive property with single terms such as 4(x+5). Once they begin to recognize and solve the problems, I will begin to introduce two terms rather than just one. When they compare their previous knowledge to this new idea they will see that it is not very different.

A1. What interesting (i.e., uncontrived) word problems using this topic can your students do now? (You may find resources such as http://www.spacemath.nasa.gov to be very helpful in this regard; feel free to suggest others.)

Students often find it difficult to understand why we use certain tools, such as the multiplication of binomials. Word problems are a good solution when introducing a new topic. There are many methods for multiplying binomials, such as the FOIL and the CLAW methods, and it is important that student learn them; however, students who struggle with the topic need new information to be presented in a different way. The website mathisfun.com has a great word problem for multiplying binomials.

I like this problem because it divides the topic into separate steps, making it easier for the student to understand what to do. With this particular word problem, the teacher can begin to see where the students are having difficulties. This allows the teacher to see what areas need to be revisited, such as order of operations, the multiplication of a negative or positive number etc. Word problems also help teachers evaluate the critical thinking skills of their students.

My References are:

https://www.mathsisfun.com/algebra/polynomials-multiplying.html

http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111c.html