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.