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Lesson Plan 1:  Algebra I, Grade 9

Course:  Algebra I, 9th grade.

Topic:  Factoring Polynomials having common factors.

Content of Lesson:

        Prerequisite Knowledge

        VocabularyOld:  Factor, product, polynomial, monomial.

                      New: Common factor, greatest common factor

                       Concepts:   Old: Distribute law.  

                      New: Factoring polynomials that have common factors is the  inverse  process of  multiplying by a monomial.

    Method of Presentation: Teacher-pupil discussion.

    Time Schedule: 10 min. - "Brainbooster"-sponge activity.

                          15 min. - present new material.

                          15 min. - supervised study.

                            5 min. - close lesson.

    Assignment: Read pp. 244-245,p. 245,1-29 all odd numbers.

Objectives:

   a.  Pupils will be able to demonstrate that factoring polynomials having common factors is the inverse process of multiplying a polynomial by a monomial. 

   b.  Pupils will be able to find the greatest common factor.

Procedure

Review:  What is a product?  What is a factor?  Tell me the factors of 36, 19xy, a^2b.   When is the greatest common factor used?  Why is it an important concept?

Given the problem: 4a x (3a - 4b) what are the factors?  How do we find the products?  What is the product?

Can we write this problem another way?  4a(3a-4b) = 12a^2-16ab.  What gives us the right to do the problem this way?  (dist.  law).  What is the distributive law?

Give examples:  2a(m + sn), 3x(2x-1), a^2(a^2 + b^2).

a(x+y+z)=ax+ay+az.  What law is used here?  When multiplying a polynomial by a monomial, what may be said about the product?  What relationship does a have in the expression?

In 2ax+2ay = what is the common factor?  Where do you think we would put the common factor?  What do we do to each term in the product?  Just as division is the inverse of multiplication, what can we say about the relationship between factoring polynomials and the process of multiplying a polynomial by a monomial is? 

For each example listed below, What is the common factor?  Where do you put it?  What do you do to each term in the product?

                6m+6n=6(m+n). 

                4a+12a=4a(a+3).

                6xy-3x

Give:  4a+12a =4a(a+3).  Could you write 4a^2+12a=4(a^2+3a)?  Why?  What is 4a called?  What is the greatest common factor in these problems?  Where does it go?  What do you do to each term in product?

        6xy-3x^2 = 3x(2y-x)              2zr-2zR = 2z(r-R)   2a+4ab+2ac=2a(1+2b+c).

Closure:  Ask various students to summarize what they learned.

Evaluation:  Student responses to questions, observation during guided practice.  Homework assignment, and tomorrow's Brainbooster.