Subject: Algebra
1. Topic-
Factoring by Grouping
 
2. Content-
Factoring
Grouping
Problem Solving
 
3. Goals: Aims/Outcomes-
Solve polynomials by factoring.
 
4. Objectives-
1. Factor high-degree polynomials by grouping
2. Determine steps of factoring
3. Choose best factoring method for to factor polynomials
 
5. Materials and Aids-
Factoring puzzle for bell ringer.
 
6. Procedures/Methods-

A. Introduction-

Students will be given 3 polynomials to factor. Two of which they know how to find the GCF, the third has no apparent GCF to factor.
 

B. Development-

4ac+ 6ad + 6bc + 9 bd
1. Tell the students to try and factor 4ac+6ad by itself, and then try to factor 6bc+9bd by itself.
They should factor these as 2a(2c+3d) and 3b(2c+3d)pretty quickly.
2. Write 2a(2c+3d)+3b(2c+3d) on the board. Ask them if this is equivalent to the original polynomial. They should agree. Ask the class if they can find a common factor between 2a(2c+3d) and 3b(2c+3d). Tell them that a factor is not just one term, but can be a binomial or
trinomial. They should be able to point out that 2c+3d is a common factor. Ask them if they could factor this out.
3. Students should be able to see that they can factor out the whole binomial of 2c+3d, making the expression (2c+3d)(2a+3b). If they can't, have them think of 2c+3d as one whole variable,
like X. This would make the expression 2a(X)+3b(X). Factoring out the X, we get X(2a+3b). We know X is(2c+3b), so the factored expression is (2c+3b)(2a+3b)
4. Write the polynomial on the board. Tell the students that the first step is to
group, or put parentheses around the first two and last two terms.
5. The second step they should do is to find the GCF of the first group (in this case, x) This leaves them with x(x+z)+(yx+yz).
6. Some students will find the GCF of the second group to finish the factor. Tell the students that they should try and think of what they can multiply the first binomial by in order to get the second group (in this case, what can they multiply x+z by to get xy+yz, which is y.) Students should find the factored form as (x+z)(x+y)
7. To show why students can't just factor both groups, present the students with the monomial
8. By the GCF method, we get x(y-3)+3(-y+3), which has two different factors.
However, by using the "copy"� step, we get x(y-3) as the factors of the first group. We then ask ourselves, what can we multiply y-3 by to get -3y+9? We get -3, giving us x(y-3)+-3(y-3), which
factors into (x-3)(y-3).
9. Present the students with wy + zx + yx + zw, and ask them to factor it. They will quickly be able to tell that they cannot factor it by grouping. Tell the students that they can change the
order of the polynomial. They will be able to factor this as (w+x)(y+z).
10. After students have successful grasp on the factoring by grouping review all methods by having the students choose the appropriate method based on the polynomial presented.
 

C. Practice-

1.Work sample problems as a class.
2. Work sample problems checking with a partner.
 

D. Independent Practice-

HW in text
 

E. Accommodations (Differentiated Instruction)-

1. A few students are much farther behind than the rest of the class (due to repeated absences), extra help will be provided to these students.
2. All students may use the calculator as needed.
 

F. Checking for understanding-

Informal assessment as students are working on practice problems through questioning.
Formal assessment through a quick quiz and homework.
 

G. Closure-

1. Including factoring by grouping on our factor purple sheet.
2. Summarize steps of factoring.
 

This Lesson Plan is available at (www.teacherjet.com)