Claudette Tucker
Instructional Unit
Lesson Two: Factoring Trinomials
x2 + bx + c
Key Principles and 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
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 teacherÕs 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.
Using the GSP, the students can model the trinomial and then determine its factor. Click here to see how this can be done.
After Phase: Teacher should encourage the class to discuss their conjectures as a whole. Students should recognize the connection between factors and factoring trinomials.