Hannah Bischoff

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Project Home ETAP 623 Fall 2012

Intent of Project

The intent of this mini-course is to instruct the user on how to factor quadratics using lattice multiplication; thus, allowing them to incorporate this method into their classroom.

Topics that will be addressed:

Introduction to Lattice Multiplication
Factoring ax² + bx + c where a = 1
Factoring ax² + bx + c where a > 1
Factoring the Difference of Perfect Squares

Needs Assessment/Learner Analysis

1. Problem: In previous years, many classrooms have used "FOIL"ing in order to factor polynomials. Unfortunately, some students are unable to grasp this particular method; thus, teachers should have an alternative method that they can show the students. In addition, elementary education is continuously changing, in which they are now using Lattice Multiplication instead of our previous methods. Therefore, teachers must change with their students and mold their processes towards student comprehension.

2. What is to be Learned: Instructors will be introduced to Lattice Multiplication and how it can be used in factoring polynomials. This can serve as either a supplementary method towards factoring polynomials or a new, more outlined method to use. This method could definitely be introduced to help all students including students with disabilities with a more structured approach.

3. The Learners: The learners targeted for this particular mini-course are mainly Secondary Mathematics Teachers who may be teaching this particular topic at some point in their career. In addition, elementary teachers may find this useful for the introduction portion of Lattice Multiplication.

4. Instructional Context: Almost all of the activities in this course will be online and done individually. The instructor will also provide students with worksheets that can allow them to print out and practice similar questions at their leisure.

5. Exploring the Problem and Solution: Students will be provided with guiding questions to determine their understanding and answer keys such that they can perform a self evaluation of their work.

6. Goals: The goal at the end of this mini-course is to provide teachers with the knowledge of factoring polynomials using lattice multiplication in order for them to have the tools needed to incorporate this strategy into their own classroom.

Performance Objectives

At the end of this mini-course, students will be able to:

Accurately perform lattice multiplication for a two digit number
Factor ax² + bx + c where a = 0 using lattice multiplication
Factor ax² + bx + x where a > 0 using lattice multiplication
Factor the Difference of Perfect Squares using lattice multiplication
Decide whether or not they want to teach factoring in this manner

Task Analysis

Course Purpose

The purpose of this course is to provide teachers with an alternate method in introducing how to factor polynomials based off of specific tools students are previously learning.

Learning Outcomes

At the conclusion of this course, students will be able to:

Accurately perform lattice multiplication for a two digit number
Factor ax2 + bx + c where a = 0 using lattice multiplication
Factor ax2 + bx + x where a > 0 using lattice multiplication
Factor the Difference of Perfect Squares using lattice multiplication
Decide whether or not they want to teach factoring in this manner

Prerequisite Skills

Essential Prerequisites

In order to reach outcomes, students must know/learn to:

Understand the basics of lattice multiplication and what the box represents
Define what a polynomial is and be able to recognize examples
Understand different methods of factoring (can be either essential or supportive depending on how you use this course)*
Look at each example as a student in your classroom and identify benefits/drawbacks of this method

Supportive Prerequisites

For easier access to reaching outcomes, students should:

Be open to learning about and using factoring through lattice multiplication in his/her classroom
Understand different methods of factoring*
Be open to reflecting and re-evaluating your own methods in factoring polynomials and the method described here

Curriculum Map

Here is what the course "How To: Factor Polynomials Using Lattice Multiplication" will look like:

Curriculum Map

References

(2008, August 14). Lattice Multiplication. [video file]. Retrieved from http://www.watchknowlearn.org/Video.aspx?VideoID=17808&CategoryID=4625, November 2012.

(2010, May 11). Box Method of Factoring Polynomials. [video]. Retrieved from https://www.youtube.com/watch?v=_Wb_CT-1VN8, November 2012.

CEMSE University of Chicago. Everyday Mathematics Lattice Algorithm for Multiplication. [powerpoint]. Retrieved from http://everydaymath.uchicago.edu/teaching-topics/computation/documents/mult-lattice-ex-2.pdf, November 2012.

Fullerton School District. Factoring Quadratics Part 2. [Document]. Retrieved from http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&cad=rja&ved=0CE8QFjAG&url=http%3A%2F%2Ffsd.k12.ca.us%2Fmenus%2FEdSvcs%2FExCEL%2FExCEL_Lessons%2FAlgebra%2FFactoring_Quadratics_Part2_Algebra.doc&ei=mPDDUIKzKIHV0gH50YGIDg&usg=AFQjCNGRUBNc5d7areJ4YfQkBdSa_XVTJg, November 2012.

Kitt and Leitze. (2000). Using Homemade Algebra Tiles to Develop Algebra and Prealgebra Concepts. Retrieved from http://mathforum.org/kb/servlet/JiveServlet/download/157-1629543-6202516-475281/algebra%20tiles.pdf, November 2012.

Neps and Rollman. (2011). The Life & Times of Chuckles the Rocket Dog: A Companionable Guide to Polynomials & Quadratics. Arbor Center for Teaching, Page 124 - 127. November 2012.

Neps and Rollman. (2011). The Life & Times of Chuckles the Rocket Dog: A Companionable Guide to Polynomials & Quadratics. Arbor Center for Teaching, Page 166 - 167. November 2012.

Roberts, Donna. Factoring by Grouping with a Grid Box. [Website]. Retrieved from http://www.regentsprep.org/Regents/math/algtrig/ATV1/LgroupingBox.htm, November 2012.

West, Lynn. (2011, July). An Introduction to Various Multiplication Strategies. [Document]. Retrieved from http://scimath.unl.edu/MIM/files/MATExamFiles/WestLynn_Final_070411_LA.pdf, November 2012.