Claudette Tucker

Instructional Unit

Lesson Two: Factoring using the Distributive Property

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

Pentominoes

Algebra tiles

Paper

Pencil

Computers with access to GSP

 

Before Phase:  We will review factors.  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 factors. 

 

During Phase:  Students will use their existing knowledge of area to explore factoring using the distributive property.  Our reference suggests that we use pentominoes in order to introduce factoring using the distributive property.  The pentominoes helps students recognize that an area of a specific square unit can be decomposed into smaller square unit such as the idea behind factoring.  Students will learn more about factoring using algebra tiles.  It may be useful for the teacher to provide some background information on algebra tiles and model a problem, but if a strong community of mathematical learners has been established, then students may be inclined to factor with algebra tiles without assistance from the teacher.  Here, students should use their prior knowledge of prime and composite numbers and GCF to factor the polynomials.  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.  This will allow students to gain conceptual understanding of factoring using distributive property.

 

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