Multiplying Polynomials - Part II

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Objective

SWBAT multiply polynomial expressions using the distributive property.

Big Idea

Students will develop an understanding of what it means to multiply polynomial expressions through the use of Algebra Tiles.

Do-Now

10 minutes

Students will complete the Do Now in five minutes. While students are working I will pass back graded exit cards from our last class, and ask them to examine any mistakes that were made.

Students volunteers will then come up to the board to write down their answers. Then, a student will read the objective, "SWBAT multiply polynomials using the distributive property.

I will ask students to summarize what we did during out last class, and to brainstorm how these two lessons could be related.

Guided Practice

25 minutes

We will begin modeling polynomial multiplication with similar examples from our last class, then using FOIL to verify our answers. I will emphasize the rectangular shape of our answer, and the patterns that we see with our exponents. I will also emphasize that all terms are multiplied with each other at some point int the problem.

  1. x(2x + 4)
  2. (x + 3)(x + 2)
  3. (x + 1)(x + 1)
  4. (x + 1)(x - 2)
  5. (x+1)(2x + 1)

Next, we will look at Example One in this presentation. I will use FOIL to multiply the first problem, and ask students to decide if I can multiply the second problem in the same manner. Students will quickly realize that this problem cannot be multiplied with FOIL, because both expressions are not binomials. 

I will show students that we can adapt a similar multiplication pattern to fit this problem by drawing arrows to each term, just as in the FOIL method. I will then ask students if the multiplication patterns we have been using are similar to a property that we have used before. I will then say, we can use a modified distributive property to multiply all polynomials, regardless of the number of terms, as long as each part is multiplied by every term in the other polynomial. 

I will tell students to multiply the number of terms in the problem together before they start in order to verify how many terms the unsimplified answer will have:

  • Monomial*Binomial = 2 terms
  • Monomial*Trinomial = 3 terms
  • Binomial*Binomial = 4 terms
  • Binomial*Trinomial=6 terms
  • Trinomial*Trinomial = 9 terms

We will then work through the five example problems together as a class.

Group Activity: Four in a Row

35 minutes

Students will work in heterogenous groups to complete the Four In A Row activity. The game board should be projected onto the white board. Each group should select a team color dry-erase marker, that they will use to shade circles as they answer questions correctly.

Instructions:

  1. Pairs of students will come up to the front of the room to get one question card before returning to their seats to work on the problem. Students should not write on the cards.
  2. Each group will solve their question, then form a line behind the teacher who will use Page 2 to check their response.
  3.  If their answer is incorrect, students can choose a new card, or return to their seat to correct their mistake. 
  4. If their response is correct, students can shade a circle on the connect four board to represent a chip. The rules of gravity apply in this activity, so students must fill up the board from the bottom up. 
  5. I will encourage students to be competitive and strategize their moves, by "dropping" their chips in the another team's corresponding spot in order to block their win.
  6. The first pair with four in a row wins!

**Instructor Note: These question cards cards should be cut up and shuffled before class begins. The cards should then be placed inside of a large container at the front of the room that is accessible to students. Depending on the class size, one-two copies of this handout should be enough for the entire room to share**

Closing

10 minutes

I will ask a student volunteer to make a connection between FOIL, Distributive Property, and the Algebra Tiles. I will then ask students to predict how many unsimplfied terms would a 4-term polynomial that is multipled by a five term polynomial have in its unsimplified anwer. I will then ask another peer to verify their answer.

Students will then complete an exit card.