Claudette Tucker

Instructional Unit

Lesson Four: Factoring Trinomials

ax2+bx+c

Key Standards

 

GPS:  MM1A2 

Students will simplify and operate with radical expressions, polynomials, and rational expressions.

(f) Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below.  (Please see standards for formulas.)

 

Materials

Algebra tiles

Paper

Pencil

Ruler

Computers with access to GSP

 

(Note:  Basically, this lesson is a continuation of lesson three.  The only difference is that the leading coefficient of the trinomial is a number other than one.)

 

Before Phase:  We will review factors and factoring using the distributive property.  Students should have existing knowledge to communicate their thinking about area.  It may be useful for students to complete a mini activity that allows them to investigate factoring trinomials. 

 

During Phase:  Students will use their existing knowledge of area, factors, and factoring using distributive property to explore factoring trinomials.  Our reference suggests that we use the box method, which is similar to the Punnett square in biology, in order to introduce factoring trinomials.  The box method helps students recognize that the sum area within the box method represents the trinomial and its factors are the dimensions of the box.  Additionally, the students can use algebra tiles.    Here, students should use their prior knowledge of prime and composite numbers and GCF to factor the trinomials presented in the textbook.  Students will record their findings, make conjectures, and justify their answers if necessary.  Here, the teacherŐs role is minimal; however, he or she should circulate around the classroom to monitor student progress and thinking.  On the second day, students can model the polynomials using GSP and determine their factors.  These three ways hands-on approaches to factoring will allow students to gain conceptual understanding of factoring trinomials using a method that is most comprehensible to them.

 

After Phase:  Teacher should encourage the class to discuss their conjectures as a whole.  Students should recognize the connection between factors and factoring trinomials.