Student Name: Leslie Daughtry Date: 10/11/13

SEU Course: EDUC 4334

Topic: Converting Vertex Form to Standard Form

Grade Level: 11th Grade

Subject: Algebra 2

Objectives

Behavioral objective(s):

•  TEKS/College Career Readiness Standards

o  §111.39. Algebra I, Adopted 2012 (One Credit): C. (6)Quadratic functions and equations. The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations. The student is expected to: (B)write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)2+ k), and rewrite the equation from vertex form to standard form (f(x) = ax2+ bx + c).

o  Specifically in this lesson, the student will be able to rewrite the equation from vertex form to standard form.

Purpose

This lesson ties into the work the students have previously worked on (the students have worked with equations in vertex form previously, specifically graphing transformations of equations in vertex form) as well as what they will be working on. They previously learned how to graph an equation in vertex form and now they will learn what the standard form is and how to expand an equation in vertex form into standard form. One main purpose in the world at large is to be able to figure out where something is at or will be at a certain time.

Materials

For the students / For the teacher
Pencil, paper, and calculator / Dry erase board and markers (I used four different color markers to represent each letter of FOIL) and a worksheet for each student

Procedures/Activities

Introduction/Anticipatory Set/Engagement and Exploration: (< 5 min)
I will have a couple of vocabulary words (vertex and vertex form) they have seen before, which relates to this lesson and previous lessons, already written on the board before they arrive to class. (Side note: I will also have an agenda written on the board breaking down the main points of what we will be doing and covering throughout the class. I briefly went over the agenda at the beginning.) I will write what the students come up with for the definitions or examples on the board later in the introduction. I will have a few potentially new words (FOIL, mnemonics, expand, binomial, like terms, distribute, standard form) the students will need to know for this lesson written on the board as well. I will begin the introduction by explaining that these words written on the board relate to the ideas and concepts they will be learning during this lesson. I will state that we will be rewriting vertex form into standard form now that they have previously learned how to graph an equation from vertex form. (In actuality I began by introducing the topic for the lesson being covered and then I briefly went over the agenda for the day. After that I introduced the vocabulary words written on the board.) I have the students briefly explain to me what the definitions/examples of what vertex and vertex form are (the vocabulary words they have previously been introduced to), filling in any points that they do not cover (I kept probing for the answers). I will explain that sometimes words in math can take on different meanings than words in English, which we will discover specifically with the word, expand (I did not explain this). I will end by telling them that learning math is like learning a new language and must be practiced both inside and outside of school. (I did not explain this).
Note (Dr. David):
The text I am using is vocabulary words from previous lessons and vocabulary words that apply to this current lesson.
I am teaching the students the vocabulary by having a series of questions and answers, asking the students what they know about the word or equation and what they do not know. I will write the main points we come up with on the board. This will be similar to a chalk talk.
I am using the vocabulary text in order to monitor for sense to determine the level students are on as far as the general concept and meaning of the words and to clear up any contradictions or misunderstandings.
Model:
1.  I will start off by writing an equation written in vertex form on the board that will need to be expanded into standard form using the FOIL techniques (y=-8(x+6)^2-9). I will then define what the equation for a standard form is (y=ax^2+bx+c, I will give an example using numbers as well, y=5x^2-3x+3)[1]. Next, I will ask the class if anyone has ever heard of the word mnemonic (a word meaning memory device. The word is derived from Mnemosyne, the Greek goddess of memory and the mother of the nine Muses of Greek mythology)[2] before and what it means. I will then clarify the meaning if needed and list a few examples that I have encountered in my life and specifically in math (“PEMDAS,” which represents the order of operations and “ROYGBIV,” which represents the order of the colors of the rainbow). I will ask the students to give me examples of mnemonics they have learned in the past. Once I have done this, I will introduce the FOIL (first, outer, inner, last) mnemonic and how this relates to this lesson. I will then proceed in asking the students to define what the word expand means in the English language (become or make larger or more extensive) and then I will explain what the definition is relating to mathematics. I will fill in a brief definition on the board with an example. I will ask students if they can explain or provide an example of what binominals (two terms) and like terms (terms that have the same variables (x and y) and powers (^a). The coefficients do not need to match.)[3] are along with what it means to distribute (distribute means to give shares of (something) or deal out[4]) a number. I will write an example and the definition of each (going by the information the students give me if it is correct) underneath the vocabulary words written on the board. Once the students fully understand what all the words/ideas mean I will continue to have them help me work out the problem I have written on the board (y=-8(x+6)^2-9)by keeping in mind the order of operations, (PEMDAS) using the FOIL process (x+6)(x+6)= x^2+6x+6x+36), distributing (-8x^2-48x-48x-288), and combining like terms to get the equation in standard form (y=-8x^2-96x-279). I covered everything I wrote down in my model; However, I did not follow this exact order nor did I write down the definition to every vocabulary word I had written on the board. I first wrote out what the standard form equation is and an example of an equation in standard form. I then told the students we would be using FOIL, which I stated is a type of mnemonic, to convert an equation from vertex form to standard form. I asked them if they were familiar with FOIL and since most of the students gave me blank stares and others said they did not really remember, I decided to stick with my original plan of describing the FOIL process first (I also asked a few students before class if they had learned FOIL and some had not learned that technique while others were a little rusty with the concept). Next, I asked the students if they had heard of and/or knew what a mnemonic was and, when they said no, I explained to them what it means and why FOIL is considered a mnemonic. We talked about other examples of mnemonics and then I began introducing the FOIL process. I used different color markers to represent each letter of FOIL and help students see visually what happens during this process. I used a few examples where two binomials were being multiplied and used the colored markers and my hands to help the students better understand that, when multiplying two binomials, you must distribute each term in the first binomial to each term in the second. Instead of asking the students to explain all of the vocabulary words on the board, I worked through the FOIL process and when the words came up I asked the students to explain what the words meant and I added to their answers when needed. After I showed them the FOIL process, I worked out one of the problems on their worksheet and I had them, as a class, tell me how to solve the problem by first making the connection that they could start expanding the problem by using the FOIL process for one part of the equation. I then helped guide them through the rest of the process. I had them compare their answer to the standard form equation written on the board to reinforce what the standard form looks like and what their answer should look like.
Check for Understanding/Explanation:
Some of the questions I will use:
“Can you explain to me what a vertex is and how it is represented?”
“What is the equation for the vertex form of a parabola?”
“What is the equation for the standard form of a parabola?”
“Can any of you tell me, what is a mnemonic? What is an example of a mnemonic you have heard before?”
“What does the mnemonic FOIL stand for?”
“What is the purpose for using the mnemonic FOIL?”
“Why do you focus on the exponent first when you convert the vertex form of an equation to standard form?”
“What does the word, expand, mean? What does the word expand mean in mathematical terms?”
“What is a binomial? What is an example of a binomial?”
“When we expand a binomial what are we doing?”
“What are like terms? What is an example of like terms?”
“What happens when you distribute a number?”
(I asked these questions, but I worded the questions a little different).
Nonverbal behaviors I will observe:
I will pay attention to the facial expressions the students give me and whether or not they look confused. I will also note how willing they are to answer questions. I will pay attention to their eye contact and how quiet they are as well. (I also paid attention to whom all was participating and who was trying to avoid being called on).
Challenges:
The students may not be able to explain what certain vocabulary words mean because they do not understand the full meaning. I could give them the definition instead of continuing to ask them what a word means if they clearly do not seem to understand it fully. The students may also find it hard to understand what is happening when you use FOIL and they may make mistake doing this process because of their misunderstanding. I will explain that you must distribute each term in order to multiply binomials. In other words, you must multiply each term in the one binomial with the other two terms in the other binomial. It may help to cover up one of the terms in the first binomial and use the same distribution process they have learned before. Then they must not forget about the other term in the first binomial and do the same distribution process, and then add these two answers together combining like terms. I may work out two problems during the “model” if I do not feel as if they understand the process. The students also may forget about order of operations. I will explain that you must first focus on the exponent by multiplying the binomials together. Then you can focus on the parentheses and distribute the term outside the parentheses to the terms inside the parentheses because of PEMDAS (mnemonic for the order of operations). (These challenges occurred and I addressed them in the manor I stated above. One other challenge that I was caught a little off guard with was when a girl was confused about whether to add or subtract a number during the FOIL process. I explained that you are adding all the terms together but because you are multiplying a positive and a negative number you would be left adding a negative number or in other words subtracting the number. She was able to understand better when I wrote all the steps out on the board again and explained it more to her.)
Guided Practice/Exploration:
We will work together to solve one of their homework problems (y= -(x+9)^2-5). I will be looking for the equation in standard form with all like terms together (simplified form). I will also be looking for all work to be shown. (We worked more than one of the homework problems together. The students asked how to solve specifically number 9 in their worksheet because this problem had an extra number and step that needed to occur. We solved this problem as a class. I explained that the problem consisted of more distribution.)
Check for Understanding/Explanation:
I will make sure the students show all of their work when converting the equation into standard form.
Questions:
“Why do you have to multiply the two binomials together first?”
“Why did you add those terms together?”
“Why did you multiply those terms together?”
“How can you simplify this equation?”
(I asked questions along these lines but most mostly my questions consisted of me asking them to explain the steps they were taking when solving each problem.)
Independent Practice/Elaboration:
The students will take out an extra sheet of paper and work with the person next to them, solving at least one of the questions from the worksheet given (#3).[5] They will be using the “claim-support-question” routine. I will explain that they write on their paper their claim of what the answer is, support of why that is the answer, and anything that makes them potentially question that answer (not necessarily in that order). I will explain that this will be their “exit ticket” and that I will have one of the groups come up and share their claim, support, and question and leave it up to the rest of the class to either question or support this. I expect to see all work shown on their paper (“exit ticket”). I expect to see students asking questions and working on the problems with no distractions. I will then choose a group to come up and share.