Factoring Quadratic Trinomials (Day 2 of 2)

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SWBAT factor trinomials using the method of their choice, and check their answers by multiplying the factors.

Big Idea

For students to have a choice in the method they use to factor trinomials and check their success of applying their method of choice to a set of problems.

Presentations of Different Factoring Methods of Trinomials

20 minutes

This is day two of a two day lesson on Factoring Trinomials.  Students are to be ready to present their examples of their assigned method at the beginning of the class period.  Students were assigned one of the methods below on the previous day.

1.  Factor a Trinomial by Trial and Error

2.  Factor a Trinomial by the Box Method

3.  Factor a Trinomial by Grouping

I draw three columns on the board for students to present their method.  These will be posted, one method in each column while students are working today.  If other pairs of students add another example, or extra input, I try to have them place it neatly in the same column.  

As instructed to the students in day one of this lesson, I have students take notes on each of the methods.  The goal of this two day lesson is for students to be exposed to all three of these methods, and choose a method that they prefer to practice on today's assignment.  The assignment is for the students to be able to use the method of their choice to factor Trinomials independently.

I call on a pair of students that I select the previous day while monitoring their work.  The students are not aware of the groups that I select on the first day of the lesson. After a pair of students present the method, depending on the clarity of the presentation, I may have another group present another example of the same method.  I also call on other groups that have the same method to add extra input that I write on the board in the same column.  Then we proceed to column two and then column three using the same process to present the  other methods.

Independent Practice

20 minutes

After students have presented all three methods, I hand each student an Independent Practice to complete.  I expect the students to take about 20 minutes to complete the 10 problems on the Independent Practice.  I instruct students to write the method that they choose to factor the trinomials at the top of the page.  

The Independent Practice is a mix of problems that include, Greatest Common Factors, and Leading Coefficients where a is equal to one or greater than one.  Students apply the method of their choice from the Presentations and practice that method.  

I walk around to monitor students while they are working and to provide prompts to move students forward if they are stuck.  The students still have the notes from the Presentations on the front board to assist them, as well as the notes that they took during the Presentations.

After providing students with about 20 minutes of work time, I have students move on to the Peer Feedback.  I assign the problems not completed as homework.  Students must show their work on all problems, therefore students may need to complete the work on their own paper.

Peer Feedback

10 minutes

With about 10 minutes left in the period, I instruct students to find a student that chose the same method as them.  Then compare the factors of the Trinomials that they have completed.  If one of the students complete five problems, then students will compare those five problems only.  If any factors are different, students should multiply the factors to check that the trinomial is the product of the factors.  

After comparing and checking their factors, students should look for the mistakes made on factors that were incorrect.  Students that are completing the factors correctly should provide feedback to students that are struggling.

In this lesson, I do not separate trinomials that have a leading coefficient of one or greater than one.  I want the students to know that these methods work to factor any trinomial after the Greatest Common Factor is factored out.  One of the disadvantages of the Box Method that we discuss in this lesson, is that it will not work if the Greatest Common Factor is not done first.  When using the Trial and Error Method and the Factor by Grouping Method, students may recognize to factor additional terms out later in the problem.