Lesson Plan

Factoring Using Geometric Representations (Algebra Tiles)

by Carlos Montaño

Introduction Standards Objectives Activities Assessment Results Resources

Introduction
In this lesson, students are introduced to factoring quadratics through Geometric Representations with the use of Algebra Tiles. Students will use their knowledge to construct Geometric Representations of quadratic expressions.

Subject: Mathematics
Topic: Factoring Quadratics
Grade Level: Eight to Twelve
Student Lesson name and URL: Factoring with Algebra Tiles: http://ctap295.ctaponline.org/~cmontano/student/index.html

Standards Addressed
          Grades Eight to Twelve
          Algebra I

11.0 Students apply basic factoring techniques to second- and simple third-degree
        polynomials. These techniques include finding a common factor for all terms
        in a polynomial, recognizing the difference of two squares, and recognizing
        perfect squares of binomials.

14.0 Students solve a quadratic equation by factoring or completing the square.

Instructional Objectives

Objective 1: Using Algebra Tiles, students will sketch a model of the solution for factoring a quadratic expression.

Objective 2: After students factor the quadratic expressions they will input the information into a Table in Excel.

Objective 3: Using Algebra Tiles, students will make as many rectangular arrangements to represent each quadratic expression.

Objective 4: Students will write an quadratic expression for the area of a rectangle.

Student Activities
Introductory Activities
1. The teacher introduces Algebra tiles to the students using the introduction page from Suzanne Alejandre's site http://forum.swarthmore.edu/alejandre/algfac.html). This will give the students a visual representation of Algebra Tiles and how they represent algebraic expressions. It give them a little background on Algebra and Geometry and how they are tied together.

2. Guide the students through Activity 1 in Suzanne Alejandre's site (http://forum.swarthmore.edu/alejandre/algfac1.html).

3. Guide the students through Activity 2 in Suzanne Alejandre's site (http://forum.swarthmore.edu/alejandre/algfac2.html).

4. Guide the students through Activity 3 in Suzanne Alejandre's site (http://forum.swarthmore.edu/alejandre/algfac3.html).

5. Guide the students through Activity 4 in Suzanne Alejandre's site (http://forum.swarthmore.edu/alejandre/algfac4.html).

Enabling Activity(ies)
1. Students complete a table on Excel Spreadsheet that lets them identify the different parts of the quadratics given. The students construct a Geometric representation of the rectangle for the given quadratic expression using the draw feature. Once they have completed the table, they can print out their results (Factoring with Algebra Tiles Table.xls).

2. Students print out a worksheet from Microsoft Word in which they will work on creating geometric representations of quadratic expressions. (Factoring Using Geometric Representations)

Culminating Activity
1. Students are asked to construct ten different rectangles using Algebra Tiles then write the dimensions and area as a sum.

Assessment
Insert your grading rubric for the culminating activity or a link to your rubric or test document file.

Results
After implementing your lesson (sometime between January & March), insert a chart of your pre-test, post-test, and culminating assessment data.

Web Resources & Supplementary Materials

Introductory Activity
1. http://forum.swarthmore.edu/alejandre/algfac.html

2. http://forum.swarthmore.edu/alejandre/algfac1.html

3. http://forum.swarthmore.edu/alejandre/algfac2.html

4. http://forum.swarthmore.edu/alejandre/algfac3.html

5. http://forum.swarthmore.edu/alejandre/algfac4.html

Enabling Activity
Factoring with Algebra Tiles Table.xls

Culminating Activity
http://www.math.com/students/calculators/source/quadratic.htm

De Anza Jr. High School
824 Blair Ave. Calexico, CA 92231
Carlos Montaño: cmontano@calexico.k12.ca.us
Last Revised: 8/04/2000