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This lesson uses the FOIL method to multiply polynomials




8, 9  

Title – Multiplying Polynomials
By – Erica Rizzo
Primary Subject – Math
Grade Level – 8-9

Class: Algebra I
Unit: Polynomials and Factoring
Lesson: Multiplying Polynomials

PA Academic Standards: 2.5.11.A, 2.5.11.C

      2.5.11A Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems.

    2.5.11C Present mathematical procedures and results clearly, systematically, succinctly, and correctly.

Goal of this Lesson

  • 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.


  • Overhead projector
  • Vis-à-vis markers
  • Transparencies
  • Aluminum foil for all students to have at their desks
  • Teacher notes
  • Copies of homework handout
  • Answer key for homework handout

Clerical/Administrative Tasks

  • Take roll.
  • Report absent students to the office if they are not on the master list.
  • Prepare transparencies for lesson introduction.
  • Prepare teacher notes and examples.
  • Make copies of homework handout.
  • Prepare answer key for homework handout.

Instructional Objectives

  • TSWBAT (the student will be able to) participate in group discussion and respect each other’s opinion.
  • TSWBAT classify a polynomial by degree and by number of terms.
  • TSWBAT multiply polynomials by using the Distributive Property.
  • Given 2 polynomials, TSWBAT multiply using the FOIL pattern.
  • TSWBAT apply polynomials to real-life settings. (If time permits activity)
  • TSWBAT define the basic components of the Distributive Property and FOIL method.

New 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.
      FOIL Method:In the last lesson you learned how to use the distributive property to multiply a single term with every term inside the parenthesis. Now you will learn the foil method for multiplying two binomials.
      When multiplying two binomials, multiply the “F”irst terms, then the “O”utside terms, then then “I” inside terms, and finally the “L”ast terms.

F irst terms = x * x = x 2
O utside terms = x * 2 = 2x
I nside terms = 3 * x = 3x
L ast terms = 3 * 2 = 6



      + 3)(


      + 2) = x


      +2x + 3x + 6 = x


      +5x + 6

Introduction (2-3 min)

  • “Good morning class. Today, we are going to learn how to multiply polynomials.”
    What does everybody have at their desks?
  • Well, are you aware that you can actually multiply polynomials using this?” (holding up the aluminum foil)

Developmental Activities

  • Put up FOIL transparency.
  • Review terms.
  • Review the first problem on the transparency using the Distributive Property.
    “Does everybody remember how we used the Distributive Property in the last chapter?”
  • Show the class what FOIL stands for.
  • Do the first example on the transparency using the FOIL method, step-by-step.
  • Model 3 examples of multiplying binomials using FOIL on the chalkboard, first using the Distributive Property and then using the FOIL method.
  • Put 2 more problems on the chalkboard and ask for 2 volunteers to work the problems at the board while the others do the problems at their seats (I will be monitoring their work as I walk around, troubleshooting any problems)
  • Show the students how to multiply a binomial by a trinomial on the chalkboard, term-by-term (2 examples)


  • 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 homework.


  • Distribute homework handout and give directions.
  • Collect everyone’s aluminum foil and throw it away.
  • If time permits, put trapezoid problem on the board and allow students to work on the problem in groups of two or three as I walk around and monitor progress.

Accommodations/Adaptations for Students with Special Needs

  • Jason has a visual impairment. To accommodate for this, I used a larger font type for items displayed on the overhead projector. I also used large, dark handwriting on the chalkboard.
  • During the lesson, I will directly ask questions to Jason to be sure he is following along with the material.

Reflective Notes

  • “How was my timing?”
  • “Did the students seem to enjoy my introduction or was it too corny?”

E-Mail Erica Rizzo !

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