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 Lucy Grimmett. Her topic, from Algebra I: multiplying binomials like 
How could you as a teacher create an activity of project that involves your topic?
There are tons of activities that could be created with this topic. The first thing that came to mind was giving each student a notecard when they walked in the room. Each notecard would have a binomial on it. Students would be asked to find a partner in the classroom and multiply their binomials together. They would be able to assist one another, discuss possible misconceptions, and ask questions that they might not want to ask in front of an entire class. This could be a quick 5-minute warm up at the beginning of class, or could turn into a longer activity depending on how many partners you want each student to have. This wouldn’t involve much work on the teacher’s part; all you would have to do is create 30 differing binomials. If you feel the need to create a cheat sheet with answers to every possible pair you can, but that would involve more work then necessary.
How does this topic extend from what your students should already have learned in previous courses?
In previous courses and chapters in algebra, students are set up with knowledge of combining like terms. The most common idea of combining like terms is adding or subtracting, for example 2-1=1 or 2+1=3. Students don’t realize that in the elementary school they are combining like terms. This is a key tool used when multiplying binomials. As future math teachers, we know that when we see 2x + 3x we can quickly combine these numbers to get 5x. This simplifies an equation. Students will struggle with this at first because they will not be used to having a variable, such as x, mixed into the equation, literally. This will be a similar issue when discussing multiplying binomials. Students will have to get used to seeing (4x+1)(3x-8) and turning it into the longer version 
How can technology be used to effectively engage students with this topic?
Algebra tiles are a great tool for students and teachers to use. Even better is an online algebra tile map. This allows a teacher to show students how to use algebra times from a main point, such as a projector, rather then walking around the room and individually showing them. Teachers can have students work individually with their iPad’s (if they have them) or use actual algebra tiles. This would be a great engagement piece for a day when students are recapping distributing or “FOIL” as many teachers like to call it. This can also be a great discovery lesson when students are learning how to multiply binomials. This all depends on if students have used algebra tiles before, and how comfortable the teacher is with implementing a lesson like this in the classroom. Another idea is pairing students and giving them binomials to multiply, which they will present to the class in a short presentation using their online algebra tile tool.
Here’s the link for the online algebra tiles:
http://technology.cpm.org/general/tiles/
Mean Green Math 