## Algebra II

I.

**Section 5.5: Completing the Square.**

__Topic__:II.

__Objectives/Standards__:a) Given the class lesson on completing the square TSWBAT accurately solve 19 of the 22 guided practice problems on solving quadratic equations by completing the square. (Standards 2.8.11.B, A2.1.3.1.1, 2.8.A2.B)

b) Given the lesson and guided practice problems on completing the square TSWBAT correctly complete 10 of the 12 homework problems on solving quadratic equations by completing the square. (Standards 2.8.11.B, A2.1.3.1.1, 2.8.A2.B)

III.

__Teaching Procedures__(5 min.)1.

**Introduction:**

A.

__Anticipatory Set:__I will start out class with a nice discovery learning exercise where the students will understand why this section is called completing the square. I will have some home-made algebra tiles that I will work with on the projector. I will explain how they work, and I will write the pictures and dimensions on the white board. Then we will work through some examples which they will copy down in their notebooks to develop the formula. There is a table that we will be filling in on the PowerPoint presentation, in which the information comes from manipulating the algebra tiles. This will be a good geometrical approach that will give the students something to visualize as they work on the problems. Basically through these examples, the students will tell me how many 1-by-1 tiles we need to literally and geometrically complete the square. The goal of this will be for the students to discover the formula and pattern we use for completing the square.

(25 min) 2.

**Development**

To begin the development section of the lesson I will show the students the rule for completing the square they just developed and then I will ask them how we could also solve these problems algebraically based on the factoring rules we discovered in the previous lesson. The students will recognize that when we are completing the square we are setting up a Perfect Square Trinomial. I will show the students this in the general case and then I will direct their attention to the side board where we have the criteria for a Perfect Square Trinomial written. This will help the students understand why this works algebraically and it will build off of their prior knowledge.

Next, we will work through a simple example in which we find the value of that makes a PST. I will call on different students to walk the class through this step by step. After that we will solve an example dealing with a quadratic equation when the coefficient of is . Upon completion of the problem I will ask my students how we could check this solution two ways. One way will involve a graphing calculator which I will show on the overhead projector. Using the graphing calculator we will plug in the original equation, graph it, and then find the zeros.

After that, we will solve a quadratic equation when the leading coefficient is not . This particular example will result in taking the square root of a negative number which will serve as a good review from the previous lesson. The answers will be complex numbers. Then we will work through a word problem that uses a quadratic equation to model distance. I will lead into this example by making up some crazy story about one of the students who thinks he is a race car driver but keeps hitting cows when he flies around a certain curve. This will add some humor to the lesson and capture their attention.

Next we will work through another real life example that deals with creating the dimensions of a garden. After that we will look at how we can use completing the square to manipulate a quadratic into intercept form which will tell us where the minimum or maximum occurs. Next, we will work with a specific example that will relate in the real world sense for businesses that desire to find their maximum of something.

(5 min) 3.

**Guided & Independent Practice:**

A. We will talk through the 22 Guided Practice problems as a class. Questioning will be key and I will even have students come up to show their work on the board and talk through a problem if time allows.

B. For 1-3 I will have them work with their partners. 4-22 we will do together as a class.

(5 min) 4.

**Closure:**

A. I will ask the students to explain to me how completing the square works geometrically. Then I will ask the class to tell me the formula we use for this and how completing the square relates to a Perfect Square Trinomial.

**IV. Materials:**

McDougal Little (2001), Algebra II • Whiteboard and Markers • Projector and Laptop

**V. Modifications:**

A. For the Learning Support students the interactive style of the lesson will allow me to gauge their progress more immediately.

B. For the Nonreaders/ Struggling Readers all of the work completed by myself on the board will help them to feel more comfortable in following along with the lesson.

C. For the Emotional Support students the opportunity to work with partners and the positive feedback I will provide will hopefully improve their emotional state.

D. For the English Language Learners the visual depiction and reinforcement of key vocab at the beginning and end of lesson will offer a great base knowledge.

**VI. Evaluations:**

1. Formative- Evaluation of the students will occur as I gain feedback and input from them through each step of the lesson progression. Questioning will be key and as I circulate through the classroom and have students go up to the board to show and explain their work I will have a solid understanding of how my class is processing the information.

2. Summative- The summative evaluation will be done through a unit test that includes concepts they demonstrated here.

**VII. Reflection**

1. Did the students seem to be actively engaged in the lesson? How well did they do on the guided and independent problems?

2. How well did I manage this classroom? What changes would I make to this lesson and to my teaching if I were given the opportunity to teach it again?