What is a polynomial?
1 The Hook - Video from Brainpop
Students watch the video on Classifying Polynomials on the Brainpop website as a class. I suggest playing this video as an introduction to the topic. The teacher can pause the video as needed to add any additional thoughts or clarification. Although there may be a few times I pause the movie to add some more detail, this video gives the students a much more interesting way to learn the necessary vocabulary than from a list or textbook. Students may have some questions when the video is over, as it goes fast and gives a lot of information.
2 Direct Instruction - Notability
At this point it is important to make sure that the information in movie made sense to my students. Students take notes and do practice that I have provided for them on the board, based on the information from the movie. (You can also do this on paper if your students do not have iPads.) We do the first few examples together, setup in a chart type form or list.
- I start off with something simple like 2x^2 (Quadratic Monomial) and then build onto that to make another expression like 2x^2 + 2x (Quadratic Binomial).
- I then do an example like 2x^2y^3 + 2x - 1 (5th degree trinomial).
- I keep expanding my expression so that the students see how the name of the polynomial changes when I change the degree and the number of terms of the expression.
- After doing a few examples together, I ask my students to participate and use the vocabulary to give the answers to the next group of examples.
My students record their notes using the app Notability. They each have a virtual folder/notebook for all their math notes using Notability. When taking notes, some students will take a picture of the examples on the board, while others will write the problems using their finger or stylus. Either way, they should end with notes that look something like this:
3 Guided Practice - IXL
Students can practice this same skill (classifying polynomials) using the IXL app or website at their own pace. The teacher can see how long the students have practiced and what types of errors the students made, if any. Depending on how much time I have left after the previous steps, I have either use IXL to have the students do individual practice in class or they can use the IXL app for homework. (This is also a great application for formative assessment.)
When students log into IXL, they need to go to the Algebra 1 tab to find the practice on Classifying Polynomials. The page looks like this if you are on the webpage:
The page looks like (before you click on A1 for Algebra 1) this if you are using the iPad:
Specifically the skill they want to practice is Z1, Polynomial Vocabulary.
I like my students to practice the skill until they have mastered it. BUT if they are struggling for any reason then I ask them to stop after 20 minutes. (They can always go back another time to master the skill.)
After the students have completed the assignment (or the 20 minutes), I am able to go into the teacher part of IXL and view their answers - both incorrect and correct. Depending on your needs you can use the other data provided by IXL to help differentiate moving forward.
4 Formative Assessment - Socrative
As a follow up to the previous steps in my work-flow, I have my students take a non-graded assessment at the end of the lesson using Socrative. I usually do this as they enter the classroom the next day following the initial lesson.
Previous to the time the students take the assessment, I create a quiz using Socrative. I will either write in polynomials with multiple choice answers that contain the vocabulary or I will create open ended questions where I ask the students to create a certain type of polynomial. For example, I would ask my students to create Quadratic Trinomial. After each student has entered their answer, I would then share all of the students' answers with the entire class while being projected on the screen. We would go through each one together and decide if the expression given by each student was in fact a Quadratic Trinomial. (It should be noted that I am the only one in the class who can see the student names. Socrative is great at sharing as a group without embarrassing anyone.)
Socrative is flexible and fun. It does take some time to set up the questions, and sometimes it is difficult to write in math fonts. This application is both web-based and as an app. So it works on any device.