10.2: Factoring Special Cases
This activity is intended to supplement Algebra I, Chapter 9, Lesson 6.
ID: 9604
Time required: 30 minutes
Topic: Quadratic Functions and Equations
- Express a trinomial square of the form \begin{align*}a^2+2ab + b^2\end{align*} as the binomial squared \begin{align*}(a+b)^2\end{align*}.
- Express a difference of squares of the form \begin{align*}x^2 - a^2\end{align*} as \begin{align*}(x - a) \ (x + a)\end{align*} and display as a difference of areas.
Activity Overview
In this activity, students explore geometric proofs for two factoring rules: \begin{align*}a^2 + 2ab + b^2 = (a + b)^2\end{align*} and \begin{align*}x^2 - a^2 = (x - a) (x + a)\end{align*}. Given a set of shapes whose combined areas represent the left-hand expression, they manipulate them to create rectangles whose areas are equal to the right-hand expression.
Teacher Preparation
This activity is appropriate for students in Algebra 1. Prior to beginning this activity, students should be familiar with factoring quadratic expressions. The activity should be followed by practice applying the rules discussed.
- This activity requires students to drag, rotate, and hide objects in CabriJr. If students are not familiar with these functions of the CabriJr, extra time should be taken to explain them.
- To download Cabri Jr. and the calculator files, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=9604 and select Cabri Jr, FACTOR1, FACTOR2, FACTOR3. If you already have Cabri Jr, you will still need to download the calculator files.
Associated Materials
- Student Worksheet: Factoring Special Cases, http://www.ck12.org/flexr/chapter/9619, scroll down to the second activity.
- Cabri Jr.
- FACTOR1, FACTOR2, FACTOR3
Classroom Management
- This activity is designed to be performed by individual students or small groups with teacher assistance. By using the computer software and the questions found in this document, you can lead an interactive class discussion on solving quadratic equations.
- This document guides students through the main ideas of the activity and provides a place for students to record their work. You may wish to have the class record their answers on separate sheets of paper, or just use the questions posed to engage a class discussion.
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