Factoring Trinomials

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Objective

SWBAT factor a quadratic trinomial expression.

Big Idea

This lesson will help students extend their understanding of multiplying and factoring to polynomial expressions.

Launch

15 minutes

For today's warmup, I will project the tasks from trinomial_factoring_launch on the board at the front of the room.

Slide 1

I let students work individually for a minute to determine the factors of both 10 and 15.  Most students will be familiar with this terminology from middle school.  Once students find the factors. I have them do a think pair share to determine what the meaning of factors is.  Students can jot down a definition and then turn and talk with their partner to compare definitions.  When students are sharing out, I guide them towards the understanding that factoring a number means to take it apart.  Factors are the numbers that make another number by multiplication.

Slide 2

I begin by having students turn-and-talk about this slide.  Students can try to come up with a metaphor to describe factoring and multiplying.  Examples that I have heard are:

Factoring - knocking down a block tower, taking an engine apart, etc.

Multiplying - building a block tower, putting the engine back together, etc.  

This slide will allow students to deepen their understanding of the vocabulary terms through repetition, variation and depth of thought.

Slide 3

Students should complete all three multiplication questions with their partner.  Students can draw an area model or use the distributive property as needed.

Slide 4 

This slide asks student to investigate their answer more closely.  Students should look at the structure of their answer to determine where the individual terms originated (MP2 and MP7). Have students turn and talk to compare ideas with their partner.  Encourage them to cite specific numbers in the original expression when giving their answer.  Call on several students to share ideas.  As each student shares have others build on their idea until the class can all understand where each of the three terms originated in the first expression.  Guide students towards the understanding that the x^2 term comes from the x and x being multiplied.  The 11x term comes from the sum of the 5x and the 6x term and the 30 comes from multiplying the 5 and 6.

Practice

20 minutes

This factoring lesson is all about taking expressions apart. The trinomial_factoring_practice worksheet lets students work backwards and forwards with various quadratic expressions.  Students can build on the discussion from the Launch to analyze the structure of an expression (MP7) and determine how it can be broken into two binomial factors. Remind students that the "taking apart, putting back together" operations help them to identify and understand the structure of each expression by identify simpler, components (factors) of an polynomial.  

I have students work in pairs so that they can discuss ideas for factoring each of the expressions. I want students to share ideas and approached (MP3).  I encourage students to "think out loud" with their partner so that each can benefit from hearing the others ideas.  

Teacher's Note: Today's practice lesson deals with all positive terms. The emphasis is on finding factors that will generate the given polynomial. I deliberately avoided the increased difficulty of positive and negative values for today's work. 

Close

5 minutes

Today's closing activity asks students to get creative and design a factorable polynomial of their own (MP2).  Then, it asks students to create a trinomial that cannot be factored.  I have students work on each of these prompts for about 3 minutes.  If time permits at the end of class have a few students share their trinomial that could not be factored, and, explain how they designed it (MP3).