I start this lesson with a set of Polynomials that are factored, but missing the plus or minus sign in each factor. Some of the Polynomials are review of factoring binomials from the previous lesson, and should help students access their prior knowledge. Other problems in this Warm Up are given trinomials that students will learn how to factor in this lesson if they have difficulties during the Warm Up. I expect the students to take about 10 minutes to complete this Warm Up and for me to review with the class. My purpose of this Warm Up is for students to focus on the signs of the terms when distributing to create the given product. Then later in the lesson, students will focus on the signs and the numbers that are used to create the original trinomial.
In this Partner Activity, I assign each pair of students one method to research to factor trinomials. The purpose of this research is for students to be able to present their method to the class. Not all groups will present, I will randomly pick groups to present until I feel the method has been presented clearly to meet the objective. It may be one group for each method, or I may have an additional pair of students present the same method again. It depends on the clarity of the first students presentation, and if students are understanding the method. I will not indicate to students which groups will be present, I just state that they will be sharing and presenting their methods. I have narrowed this lesson to three methods in order to not to confuse the students with too many methods. However, to also provide students options for success. The three methods are listed below:
1. Trial and Error
2. The Box Method
3. Factor by Grouping
I post the three methods on the board, and assign students the methods to present. I assign Trial and Error to higher level groups. I have students in the class already assigned in homogeneous pairs. I assign the Box Method and the Factor by Grouping Method to the middle and lower level students. The reason I assign methods in this way is from past experience. In previous years, most students that struggle with factoring use the Box Method or Factor by Grouping. I provide one video of each method for students to begin their research, but I instruct students that they may research other videos and information about their method. The starting video I provide for each method is listed below.
Factoring Trinomials by:
I instruct students that they have 30 minutes to identify an example and create a clear way to present their assigned method. All members of the group should participate, and be prepared to present their part.
I chose the two additional methods, the Box and the Factor by Grouping Method because they begin with the same steps. The intermediate steps are also the same, just set up into different representations. The box method is set up in a box, and the Factor by Grouping method is set up in a linear fashion. Some students relate well to the Box Method because it is similar to the Punnett Squares that they have used in Science.
All of the methods above, I believe provide students with the conceptual understanding of how the factors multiply to equal the original problem. Some other methods that I did not choose provide students with tricks where the math behind it is difficult to see. At this point, I do not distinguish between when a is equal to one, or when a is greater than one. If students do not discover the difference on their own in this lesson, I will present it later in this unit.
Students should recognize and check that multiplying and factoring are inverses of each other, and I expect some students to state this in their presentations. That will be a point I will emphasize also during their presentations when providing feedback and questioning as a whole class.
In closing of day one of this lesson, I inform students to be prepared to present at the beginning of class the following day. I post this list on the board that students should have the following:
I inform students again that the purpose of this two day lesson is for students to explore different options to factor trinomials and select a method that works best for them. Students should be able to decide after the presentations on the following day which method they prefer to practice during the Independent assignment the following day.
If time permits, I have students present their method to another pair of students. Then the pair can present their method to them as well. I instruct students to provide quick feedback about if their presentation is clear. Any suggestions may be used to improve their presentation, or not used if the pair of students prefer.