#3788. FOILing

Mathematics, level: Middle
Posted Thu Jun 15 16:28:38 PDT 2006 by Cindy Kor (seakay246@aol.com).
Johnson, Westminster, CA USA
Materials Required: Overhead projector, handouts, markers, transparencies
Activity Time: one 45 class period
Concepts Taught: multiplying polynomials

Lesson Objective: The student will learn a procedure for multiplying two binomial expressions and learn the "FOIL" acronym for the procedure. This objective is not to be stated to the class since it is a "discovery lesson".

Anticipatory Set: 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.

Input Procedures: 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) and problem 6) is the sum of problems 1) and 4). 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.

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.

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.

When multiplying two binomials, multiply the "F"irst terms, then the "O"utside terms, then "I" inside terms, and finally the "L"ast terms.

First terms = x * x = x2
Outside terms = x * 2 = 2x
Inside terms = 3 * x = 3x
Last terms = 3 * 2 = 6

(x + 3)(x + 2) = x2 + 2x + 3x + 6 = x2 +5x + 6

Checking for Understanding: This is done throughout the Input Procedures, by questioning students and observing how they work through the problems.

Guided Practice: Present the following problems and ask students to explain how they would solve each expression, then work through it with them. If they did not choose to use F.O.I.L. after they solve it their way, use F.O.I.L. and compare the answers and the amount of work involved.

( 2 + 2 ) x ( 3 + 2 )
( 7 + 6 ) x ( 8 + 3 )
( 9 - 4) x ( 10 + 2 )
( 11 - 3 ) x ( 7 - 4 )
( x + 4 ) x ( x + 3 )
( x + 6 ) x ( x - 2 )
( x - 5 ) x ( x - 4 )
( x - 4) x ( x + 7 )

Independent Practice: Use the attached work sheet and have students work independently in class (if time allows) or as homework.

Closure: Close before handing out the Independent Practice. F.O.I.L is not some magical process. It is just an acronym to help remember all of the different products you must have when multiplying two binomials. Students should realize all they are really doing is the distributive property of equality. 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.

Assessment: Assessment is through informal observations throughout the lesson, and through the grading of the independent practice.

Re-teach: Use algebra tiles to model the multiplication of two binomials. Show how each part of the product corresponds to a letter of F.O.I.L.

Enrichment/Extension: Challenge students to describe the process for multiplying a binomial and a trinomial, or two trinomials.

Modification(s): As needed according to I.E.P.

Materials: Overhead projector, Algebra tiles (at least one set to demonstrate on overhead projector).

Attachments:

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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 ) =

Answers:

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

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 )

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