Adding and Subtracting Polynomials
Lesson 3 of 9
Objective: SWBAT identify and classify polynomials. SWBAT add and subtract polynomials using Algebra tiles
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:
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.
Guided Notes + Practice
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)
Partner Activity: Puzzle
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.
Please enjoy this video which shows my students working on both activities.