Crack that trinomial

Crack that trinomial!

A Wequest for Algebra I students

Designed by

Janet Nelson

Introduction

Your mission is to find a way to “crack” (or factor) a trinomial. You need to find a way to make it a product of 2 binomials, getting rid of the exponent. For example, x² + 5x + 6 is equivalent to (x + 3)(x + 2). This project will help you to learn how to do this.

So how do you factor a trinomial, anyway......?

The task

Your quest begins with the “lingo.” You will start by defining all those unfamiliar math terms. Then you will learn to make factor tables listing the possibilities you may use. After classroom instruction and some practice on your own, you will do some Internet research to find out how others factor trinomials. Then you and your group will prepare a Powerpoint presentation showing one or more ways this can be done.

The process

1. Start with the words. Using your textbook and working with a partner, create a table of vocabulary words in a Word document. Include all the words that appear in bold print in the first eight sections of the chapter. Also include any words from previous chapter that are used often or any others you would like to include. You will use a table with 3 columns. In the first, put the word; in the second, write the definition in your own words; in the third, give an example. If, for example, you are defining “trinomial,” you might include one like the one in the introduction. It doesn’t have to be a complicated example. Some websites are given below that may help you. When you are done, save the file as “lastname_factorwords.” Your partner will save the same file with his/her own name. You will be graded on completeness, accuracy of definition, the examples, appearance, and cooperation.

Resources: Algebra: Structure and Method, Book 1 (McDougal-Littell)

http://library.thinkquest.org/29292/

http://www.learner.org/channel/workshops/algebra/workshop5/index.html - 2

http://www.quia.com/jg/1312.html

http://www.mathwords.com/index_algebra.htm

http://www.math.com/school/subject2/lessons/S2U1L1GL.html

2. With a partner, make factor tables. Create a spreadsheet that contains a list of all the pairs of factors of several different numbers. Choose some that are greater than and a couple that are less than 15. Make another column for the sums of those pairs. One table should look like this:

24		Sum
1	24	25
2	12	14
3	8	39
4	6	10

Make a second table that lists the numbers from 1 to 20 and their squares. It should begin like this:

1	1
2	4
3	9

Save the factor tables as “lastname-factor-table” and the table of squares as “lastname-squares.” Each of you should save the file you created together with your own last name. You will be graded on completeness, accuracy, and appearance.

3. After some classroom instruction and practice, you will work in groups of 4 to research how other people factor trinomials. From your group select one director (committee chair), one recorder (to make notes), and two researchers (using the computers). The director should see that everyone participates and works constructively. Using the websites listed below and any other appropriate ones you find, explore the methods of factoring and select one to present to the class. Make notes on a Word file for use in step 4. Turn in a draft copy of your notes. Your grade will be based on quality of notes, participation by all, and level of cooperation.

Resources: Algebra: Structure and Method, Book 1 (McDougal-Littell)

www.purplemath.com

http://mathforum.org/library/drmath/drmath.high.html

www.coolmath.com/algebra/Algebra1/

www.algebrahelp.com

http://math.usask.ca/emr/menu_alg1.html

www.sosmath.com/algebra/algebra.html

http://library,thinkquest.org/20991/alg/index.html

4. Finally, your group will create a Powerpoint presentation demonstrating how you factor simple trinomials. Prepare it so that it requires no narration, but includes all the instructions needed. Present one of the several methods you may have found in your research. Include some example problems in multiple-choice fashion using non-linear Powerpoint techniques. Show the use of factor tables using examples from step 2. Be sure to use proper terminology (from step 1). You will probably want to make at least 8 slides. Feel free to use interesting transitions and effects if you like. Clarity, accuracy, appearance, and completeness are the grading criteria.

Evaluation

	0	2	4	score
Teamwork	Lack of cooperation; some participated little	Worked fairly well; some did more than others; possibly some goofing off or contention	Worked harmoniously and shared responsibility well.	_____x5
Completeness	Barely satisfies minimum requirements, if that	Most parts nearly complete	Each part satisfies requirements.	_____x6
Accuracy	Many errors in products created	Only a few errors	No errors or omissions	_____x4
Clarity	Products unclear, lacking in detail	Fairly understandable but could be improved	Very clear	_____x7
Appearance	Sloppy or confusing	Fairly good	Great appearance of presentation	_____x3

Conclusion

Now that you can factor trinomials, you are ready to solve quadratic equations – but that is another webquest!

Credits

Clip art and photos from:

http://office.microsoft.com/en-us/clipart/default.aspx?ofcresset=1

Teacher Page

Objective: Students will create a Powerpoint presentation on factoring simple trinomials.

Standards: 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.

The webquest is designed for 9^th grade Algebra 1 students who are experienced in using Microsoft Office applications. This covers the concepts in half of the chapter on factoring trinomials and could easily be expanded to include factoring all kinds of polynomials. In reality there would be two more lessons between steps 2 and 3 covering perfect square trinomials and difference of two squares. Most of the work on the webquest would be done in class, assuming there are about half as many computers as students.

Step 1 – Vocabulary

Step 2 – Factor tables

Step 3 – Internet Research

Step 4 – Powerpoint lesson