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  This lesson provided by:  
Author:Leah Drauch
System: Cullman County
School: West Point Middle School

  General Lesson Information  
Lesson Plan ID: 4152


Factoring Fanatic


This activity is designed to give students practice in "finding" the correct factors to use when attempting to factor a trinomial. The students are provided with a Tic-Tac sheet to help them discover the relationship or pattern between two numbers. Students then use their discovery to fill in a second Tic Tac sheet. At this point students have uncovered the mystery of how to locate the appropriate factors in a given trinomial. They can now factor any trinomial placed in front of them!

 Associated Standards and Objectives 
Content Standard(s):
MA2015 (9-12) Algebra
8. Use the structure of an expression to identify ways to rewrite it. [A-SSE2]
Example: See x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).
MA2015 (9-12) Algebra
9. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [A-SSE3]
a. Factor a quadratic expression to reveal the zeros of the function it defines. [A-SSE3a]
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. [A-SSE3b]
c. Determine a quadratic equation when given its graph or roots. (Alabama)
d. Use the properties of exponents to transform expressions for exponential functions. [A-SSE3c]
Example: The expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Local/National Standards:


Primary Learning Objective(s):

Students will be able to factor complex trinomials.

Additional Learning Objective(s):


 Preparation Information 

Total Duration:

61 to 90 Minutes

Materials and Resources:

Tic-Tac-But No Toe handouts, practice worksheet (see attachments)

Technology Resources Needed:

Computer, Power Point software, (presentation attached), LCD projector or other large-group computer projection device. If the software is not available, handouts are also attached. Transparencies can be made from the handouts.


Students will need to have the following prerequisite skills. Factor out the GCF from polynomials. Factor the "Special Products" (Difference of Squares and Binomial Squares)

1.)Explain to students that they will learn to factor any trinomial using one basic method. This will eliminate the need for the traditional "trial and error" method of factoring more complex trinomials. This lesson allows teachers to complete the teaching of factoring in about 3 days.

2.)Use the PowerPoint presentation to display the first slide "Tic-Tac-But No Toe" (or give each student handout 1). Instruct students to find the relationship that the numbers in Quadrant I and IV (the two on the right) have with the numbers in Quadrant II and III (on the left). This relationship is the common factoring relationship --the numbers multiply to give me the top number and add to give me the bottom number. Make sure they answer and understand the observations at the bottom of the slide.

3.)Next, display the second "Tic-Tac-But No Toe" sheet (the one missing 2 numbers)(handout 2). Ask the students to complete the Tic-Tac with the correct numbers following the observations they made on the previous sheet. Answer any questions that the students have.

4.)The rules for the correct placement of numbers is the next slide in the PowerPoint presentation (or on handout 3). Have students copy these in their notes. Students will now be prepared to do some examples. Make sure they understand that for each problem, they will need to draw a Tic-Tac. The students must have an understanding of the placement of numbers, or this method will not work!

5.)Once students understand how to put numbers in Quadrants II and III, they are ready to find out how the Tic-Tac work will relate to their factored answer. This is demonstrated on the next slide of the PowerPoint presentation (or handout 4). Make sure students understand the process of interpreting the answers from the Tic-Tac. Answer any questions the students have.

6.)Students are now ready to try the examples on the next PowerPoint slides (or handout 5). Note that the examples go from simple trinomials to the more complex. Students will need to be reminded that any GCF needs to be factored out prior to placing numbers in the Tic-Tac. This will eliminate many large numbers. Ask students to do some of the examples on the board or overhead and have them explain their steps. This serves as an assessment of their understanding.

7.)Students will need to be reminded of the objectives of the lesson at the completion. Give all students some practice in several types of trinomials. Spend two days with students actually factoring trinomials for experience. Practice worksheets are attached as handout 6.

8.)Credit should be given to Ms. Stephanie McCullough, who presented the original idea for this lesson at the NCTM Regional Conference in Biloxi in October 2002. Students really like this method. I hope you find it worthwhile. I do have the algebraic proof provided by Ms. McCullough if anyone is interested.

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Assessment Strategies

Students may be tested on this concept alone or as a unit on factoring. It should also be tested with its prerequisite skills. Daily assessment can occur through interaction with the students during class time and also through homework.


Many students have trouble with the traditional "trial and error" method of factoring more complex trinomials. This lesson eliminates the need for the old methods that are frustrating to both students and teachers. The lesson can be extended into the realms of solving quadratic equations.


Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior

Be sure to check the student's IEP for specific accommodations.
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