Adding and Subtracting Polynomials

The purpose of today's Do-Now is to refresh students' memory of integers and the distributive property. Both of these concepts are important in today’s lesson. Students will work on the Do-Now silently for 3 minutes. While students are working, I will pass out Algebra tiles and Promethean clickers to all students.

Next, I will reveal the answer to all four Do-Dow problems. Then, I will call on two different students to explain how they solved Number 1 and Number 4. I will ask students focus to listen for their reasoning, to try to hear how each student solved the problems without using paper. After these presentations, I will ask the whole class to compare and contrast the reasoning of these two peers.

Next, I will ask a volunteer to read the objective, "SWBAT identify polynomials. SWBAT add and subtract polynomials."

Students have never heard the word polynomial prior to today's class. I will use their unfamiliarity with the word to help them make some predictions about its meaning:

• Who has heard the word polynomial before?
• What is the prefix in the word polynomial?
• What does the prefix poly mean?
• Do we know any other words that have “poly” in them?

I will add to the student's list of words that contain "poly" with words and short definitions of the following terms:

• polyclinic
• polydactyl
• polysyllabic
• polymorphous

Lastly, I will ask students to use this list and our conversation to make an inference with respect to possible meanings of of the mathematical word, polynomial.

For today's Guided Practice, students will follow along with this presentation using a graphic organizer. Below, I highlight some of the points of emphasis:

Slide Three: I will ensure students know the definition of sum, difference, and term. After showing examples and non-examples, I will invite students to create their own example of polynomials and non-polynomials.

Slide Four: A volunteer will name each objectWe will focus on the prefix in each word. As a whole class, we will create a definition of each word (monomial, binomial, trinomial) using what we know about the prefix. I will then invite students to create their own examples to write on their papers.

Slide Seven: I will tell students that the skinny yellow tile represents x. As a class we will develop the significance of the other blocks.

Next, I will discuss the definition of additive inverse with my students. Using tiles, I will demonstrate that 1 – 1 = 0 because it makes an additive inverse (zero pair). I will scaffold examples until students are adding binomial and trinomial zero pairs.

Once this is done, I will write (x^2 + x) on the board, and then place the corresponding model on the integer mat. I will ask the students what the sum is of the two terms. 

I will then ask the group to prove that x^2+x not equal to 3x or 3x^2 using Algebra Tiles.

Students will then complete the following problems with a partner using the tiles:

(4x - 5) + (3x + 6)       

(3x² – 2x + 3) - (x² + 7x + 7)

(5x² - x - 7) + (2x² + 3x + 4)                            

(5x + 9y) - (4x + 2y)

In groups of 2 or 3, students will complete a polynomial puzzle using the skills they have learned today. I will explain directions to the class using Slide 16, and then have two students (one volunteer, one non-volunteer) repeat the directions back to the class.

After 20 minutes we will reconvene as a whole group, and students will round-robin correct answer pairs aloud to the class.

Students who finish the puzzle early will transition to this crossword activity, from this website.

Please enjoy this video which shows my students working on both activities.