Claudette Tucker
Instructional Unit
Lesson Five: Special Factors
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
Before Phase: We will review factor trinomials. Students should have existing knowledge to communicate their mathematical thinking. 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 perfect square trinomials. 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 need some guidance on how to determine if a trinomial is a perfect square trinomial. It may suffice to ask oneÕs self the following questions:
¬ Is the first term a perfect square?
¬ Is the last term a perfect square?
¬ Is the middle term twice the product of quantities squared to obtain the first and last perfect square terms?
(A response of no implies that the trinomial is not a perfect square.)
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. Students can model the special 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.
Click here to see a perfect square trinomial was modeled using GSP.
After Phase: Teacher should encourage the class to discuss their conjectures as a whole and any other apparent differences between factoring perfect square trinomials and non perfect square trinomials. Students should recognize the connection between factors and factoring trinomials.