Claudette Tucker

Instructional Unit

Lesson One: 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

Cubes to construct rectangular prisms

Computers with access to the internet and GSP

Grid paper

Paper

Pencil

Textbook

 

Before Phase:  We will discuss area.  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 area such as assembling cubes to determine the area of rectangular prisms or constructing parallelograms of a restricted area. 

 

During Phase:  Students will use their existing knowledge of area to explore factors.  Our reference has provided a number of problems to increase studentsŐ procedural knowledge, but the students will, in groups, construct rectangular prisms using manipulatives/grid paper or parallelograms using GeometerŐs Sketchpad to determine the factors of a specific monomial by depicting a figure with the given area in multiple ways if possible.  Students should be encouraged to use integers.  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.

 

Click here to see how students can model a figure with an area of twelve using GSP.

 

After Phase:  Teacher should encourage the class to discuss their conjectures as a whole.  Students should recognize that the area of certain monomials can be model in more than one way and others are restricted to one visual representation.  Students should also recognize that the dimensions of the rectangular prisms or parallelograms represent factors of the specific area.  Effective teacher questioning will ensure that students gain a deeper understanding of prime and composite numbers and greatest common factor.  It may be useful to introduce these terms on the second day of the lesson or rather whenever student conjectures give way to such terminology.

 

Additional Interactive Activities

http://illuminations.nctm.org/tools/factor/

http://illuminations.nctm.org/ActivityDetail.aspx?id=64