LESSON PLAN TOPIC: Multiplying Polynomials     TITLE: FOIL Method

AUTHOR: Cathy Brown

GRADE: 9-12                                                     Integrated Discipline(s): Mathematics

12.6 ALGEBRAIC CONCEPTS

12.6.1 By the end of twelfth grade, students will graph and interpret algebraic relations and inequalities.

12.6.2 By the end of twelfth grade, students will solve problems involving equations and inequalities.

12.6.3 By the end of twelfth grade, students will solve problems involving systems of two equations, and systems of two or more inequalities.

12.6.4 By the end of twelfth grade, students will solve problems using patterns and functions.

OBJECTIVES: Students will be able to:

1. participate in group discussion and respect each other’s opinion.
2. classify a polynomial by degree and by number of terms.
3. multiply polynomials by using the Distributive Property.
4. given 2 polynomials, multiply using the FOIL pattern.
5. apply polynomials to real-life settings. (If time permits activity)
6. define the basic components of the Distributive Property and FOIL method.

• Informally assess students’ progress and help troubleshoot problems during the lesson.
• Informally assess students by asking them what to do next when solving examples on the chalkboard.
• Formally assess students when grading the independent practice.

MATERIALS:

• Overhead projector, Vis-à-vis markers, Transparencies for all students to have at their desks
• Copies of independent practice to hand out

 

PROCEDURES: Students will learn how to multiply polynomials using the Distributive Properties and the FOIL method. They will also learn how to use polynomial multiplication in real-life settings.

The attached problems are posted on the board when students arrive and are to be done as a "warm up". After a few minutes have students volunteer to come to the board and show how they solved each problem.

Vocabulary

Polynomial: A term or sum of terms which has non-negative integer exponents only.
Binomial: A polynomial with two terms.
Coefficient: The number in front of the variable.

Activities

1. Review the anticipatory set. Hopefully some students solved the addition in the parenthesis and then multiplied, while others distributed the multiplication over the addition expression. If these two different methods were not used by students then ask the class if they can think of alternative methods than the ones shown and try to lead them to a comparison of these two methods.

Ask the class if they notice anything about problems 5) and 6) as compared to the first four. The objective is to lead them to the observation that problem 5) is the sum of problems 2) and 3)

2) 3 x ( 2 + 3 ) =

3) 9 x ( 2 + 3 ) =

5) ( 2 + 3 ) x ( 3 + 9) =

1) 2 x ( 3 + 7 ) =

4) 7 x ( 3 + 7 ) =

6) ( 3 + 7 ) x ( 2 + 7 ) =

Write out these equalities and show how one expression is being "distributed" over the other, much like the distributive property may have been used in the first four problems.

2. Review problems 7) and 8) again and show how the distributive property could have been used to solve them if it was not already used by the students who demonstrated their work.

7) ( 4 + 8 ) x ( 3 + 6 ) =

8) ( 5 + 6 ) x ( 8 + 3 ) =

Ask students how they might use this to simplify an expression like ( x + 7 ) x ( x + 3). Note to the students that here they do not have the option of performing the addition within the parenthesis before multiplying, so they will have to use another method. Guide them through the process to arrive at x² + 3x + 7x + 21. Before combining like terms, show them how these four terms relate to the acronym F.O.I.L.

3. Put up FOIL transparency.

4. Review terms.

5. Do the first example on the transparency using the FOIL method, step-by-step.

• Clear, concise instructions

• Use of visuals

• Modeling of expectations

• Repeating of instructions

• Model a variety of problem solving strategies.

• Assist students to develop criteria for choosing a strategy

• Apply reading comprehension strategies to problem solving (i.e. deciding what the main idea is and what information is extraneous to the problem).

• Use simpler problems of the same type to model methods.

• Encourage students to represent problem in pictorial or other visual form before attempting solution.

• Focus students' understanding of algebraic symbols as representing real numbers or operations.

• Permit extended time for problem solving, including pre-solution stage trial and error.

• Teach prediction and estimation skills.

• Consider the use of pictorial flow charts to plan strategies before setting up equations.

• Other modifications as needed by IEP in consultation with the special education teacher

What are the steps for "FOIL"? Ask for volunteers for F, O, I, L---and reinforce how to use the method. Why do we use FOIL?

Possible ANSWERS to Why use--- When we multiplied expressions that were all numbers, often it was easier or less work to do the addition first and then multiply the sums. In those situations we did not use the distributive property (or F.O.I.L) at all and there was no need to. But when dealing with binomials we cannot perform the addition first so we must distribute and F.O.I.L. helps us remember how.

Title - Multiplying Polynomials, By - Erica Rizzo at and Title - Multiplying Binomials with F.O.I.L, By - Noel Chang at http://www.lessonplanspage.com/MathMultiplyingPolynomialsFOILMethod89.htm

Ideas for helping students with special needs in mathematics at http://www.bced.gov.bc.ca/specialed/landbdif/42.ht

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Warm Up Problems

Solve each of the following expressions, showing your work:

1) 2 x ( 3 + 7 ) =

2) 3 x ( 2 + 3 ) =

3) 9 x ( 2 + 3 ) =

4) 7 x ( 3 + 7 ) =

5) ( 2 + 3 ) x ( 3 + 9) =

6) ( 3 + 7 ) x ( 2 + 7 ) =

7) ( 4 + 8 ) x ( 3 + 6 ) =

8) ( 5 + 6 ) x ( 8 + 3 ) =

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Independent Practice

Simplify each of the following expressions:

1) ( 8 + 6 ) x ( 11 - 3)

2) ( 7 + 2 ) x ( 13 + 3 )

3) ( 9 - 2 ) x ( 13 - 7 )

4) ( 5 - 7 ) x ( 7 + 6 )

5) ( x + 5 ) x ( x + 2 )

6) ( x + 5 ) x ( x - 7 )

7) ( x - 3 ) x ( x + 8 )

8) ( x - 11 ) x ( x - 2)

9) ( 2x - 6 ) x ( x + 5 )

10) ( x + 3 ) x ( 3x - 5 )

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Warm Up Problems Answers:

1) 20
2) 15
3) 45
4) 70
5) 60
6) 90
7) 108
8) 121

Independent Practice Answers:

1) 112
2) 144
3) 42
4) -26
5) x² + 7x + 10
6) x² - 2x - 35
7) x² + 5x - 24
8) x² - 13x + 22
9) 2x² + 4x - 30
10) 3x² + 4x – 15