Katie+Dio


 * QUADRATIC EQUATIONS DIVERSE TEXT SET**


 * Name:** Katie Dio


 * Context for using the text set:** This text set would be used during a unit about Quadratic Equations in a ninth grade Algebra 1 class. This class would have mostly at level students, with some students behind grade level. There is also an Honors section for this class offered in the school, so there are very few students ahead of grade level math within this class. This unit would be introduced after units about solving one step and two step equations, as well as factoring equations. Typically, this unit would be during the third quarter of Algebra 1.


 * Content Standard and Objective:** CCSS.MATH.CONTENT.HSA.REI.B.4 “Solve quadratic equations in one variable.”
 * Students will be able to accurately solve quadratic equations on a chapter exam using the appropriate method of solving with square roots, factoring, completing the square or the quadratic formula with at least 80% accuracy.


 * Reading/Thinking Standard and Objective:** CCSS.ELA-LITERACY.RST.9-10.4 “Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9-10 texts and topics.”
 * Students will demonstrate their understanding of terms such as quadratic equation, quadratic formula, factoring and more through classwork, homework and tests using the meaning of these terms to solve equations and answer understanding questions with at least 80% accuracy on the test.


 * A. Print Resources:**
 * Text #1:** Textbook
 * __Citation__: [|Charles, R. I. (2012).] [|//Algebra 1: common core//] [|(Common core ed.). Boston, Mass.: Pearson.]
 * __Text Summary:__ This textbook is aligned to the Common Core State Standards for Algebra 1. Pearson offers teacher and student support, differentiated worksheets and teacher suggestions and techniques for helping students at level, at risk and ELL students. Chapter nine covers quadratic equations.
 * __Rationale:__ I chose this as the textbook due to the alignment with the Common Core, as well as the resources for students with all different levels of knowledge. The Common Core alignment helps to ensure the questions and topics are at level and challenging.
 * __Use of text:__ I would use this textbook as a guide throughout the unit. This textbook offers an overview of the topic, problems to do and will influence the order that the unit is presented. Some homework assignments may be from the text book. The textbook is a resource for students if they are struggling with a concept or who have matchup gaps or mismatches to get another point of view and more information than is given in class.
 * __Attachment:__ This book is too long to attach.


 * Text #2: Article**
 * __Citation:__ [|Budd, C., & Sangwin, C. (2004). 101 Uses of a Quadratic Equation.] [|//plus//] [|,] [|//1//] [|. Retrieved March 24, 2014, from http://plus.maths.org/content/101-uses-quadratic-equation]
 * __Text Summary:__ This article is in response to the UK questioning the importance of teaching the quadratic formula. The text begins with a brief history of the quadratic formula and its derivation. Then the text continues to explain the uses of the formula with proportions, geometry and the world. It can be a difficult read with a lot of mathematical terms and knowledge as the article continues.
 * __Rationale:__ This text helps to show the context of where this formula that we have memorized and use comes from. It also shows the connection to the natural world. Students who are interested in knowing more about the subject will enjoy this background knowledge and students who struggle to see why any of this unit is useful may also benefit from reading this article.
 * __Use of text:__ I will offer this text as a homework assignment to be discussed the following day towards the beginning of the unit. I will only require that students read the sections about where we begin and the Babylonians to get an understanding of the real life uses and see a derivation of the quadratic formula. I will also offer students the opportunity to read the whole article and part 2 if they are interested, but this is not required for the class as some of these topics have not been explained and may be more confusing than helpful. Students will need to make notes on their copies of the article and include notes to be prepared to discuss one thing they learned, one they are confused about and one thing they are interested in from the article. The emphasis of the assignment is on showing how the quadratic formula was discovered in nature and how this formula is more than just a tool to answer questions.
 * __Attachment:__ See attachment #2 for a copy of this text


 * Text #3: Online Reference**
 * __Citation:__ [|Quadratic Equations. (n.d.).] [|//Quadratic Equations//] [|. Retrieved March 31, 2014, from http://www.mathsisfun.com/algebra/quadratic-equation.html]
 * __Text Summary:__ This is an online text that introduces quadratic equations, some vocabulary, hidden forms and examples. Then it goes into all of the different methods to solve a quadratic equation, including the derivation of the quadratic formula, factoring and completing the square.
 * __Rationale:__ This text will offer a different explanation of topics from this unit to help students who are looking for more information after class. It can be used by any type of learner as there are some more difficult concepts explained in a nice format and wording.
 * __Use of text:__ I will use this text as a supplement to the lessons for students to go to independently if they would like extra reliable explanation and more examples than the book or I offer.
 * __Attachment:__ See attachment #3 for the link


 * Text #4: Children’s Book**
 * __Citation:__ [|Scieszka, J., & Smith, L. (1995).] [|//Math curse//] [|. New York, N.Y.: Viking.]
 * __Text Summary:__ This text __Math Curse__ is not directly related to quadratic equations, but it tells the story of a boy whose teacher told him that everything is a math problem. He then starts looking at everything in terms of numbers and questions. He starts to see math everywhere.
 * __Rationale:__ I would read this book to my students to show them that math is everywhere. This book helps to show that math is relevant even if students don’t realize they are constantly doing math or equations. Quadratic equations are also present in many everyday things, such as finding areas and physics. This book is in simpler terms, but can help all students start to think about math as a relevant subject, if they aren’t already.
 * __Use of text:__ I would read this book to the class at the beginning of the lesson to help students start thinking mathematically. This will help students start to question the things around them and hopefully get them more excited for the unit.
 * __Attachment:__ This was a print book, so I did not include it here.


 * Text #5: Book**
 * __Citation:__ [|Amdahl, K., & Loats, J. (1995).] [|//Algebra unplugged//] [|. Broomfield, Colo.: Clearwater Pub..]
 * __Text Summary:__ This book attempts to put Algebra in more relatable terms for students who do not necessarily like or understand math. The explanations are a mixture of mathematical and real world terms so students are able to get a better grasp of the topic. It is aimed at people who do not particularly like math. While this will not replace the truly mathematical texts, it will help put the concepts in real world terms as a supplement to instruction.
 * __Rationale:__ I would use this text to help students see beyond the explanations, equations and processes to solve math and see the uses and reasons algebra exists. This aspect of math is sometimes missing in classes as the objectives, standards and lessons need to progress. It is difficult to step back and see what exactly this concept is doing and why it is important. This book can help do that.
 * __Use of text:__ I would have the students read an excerpt of this book about quadratic equations at the beginning of the unit. I would also offer this text to students who would like to read more concepts from this author. It would not have a huge part of the class, more of a resource if students want more context.
 * __Attachment:__ This was a book, so I did not include it here.


 * B. Media Resources**


 * Text #6: Quadratic Formula Song**
 * __Citation:__ [|Songs for the Quadratic Formula. (n.d.).//Songs for the Quadratic Formula//. Retrieved March 24, 2014, from http://www.regentsprep.org/Regents/math/a]
 * __Text Summary:__ This short song is sung to the tune of //Pop Goes the Weasel.// The short lyrics describe the quadratic formula to help aid memorization.
 * __Rationale:__ Memorization of formulas is always difficult for many students. By linking a tune to the formula, this could help students remember the formula. This song will help students with mismatches and matchup gaps in knowledge, as well as students who are musically inclined to help them access music and math at the same time.
 * __Use of text:__ After learning the quadratic formula, I will present the song to the class first on my own and then having the students join in so everyone is introduced to the song. Afterwards, a link to the song will be offered to the students and those who would like to access it again will be able to. This gives students the chance to use the song independently to help them remember the format of the formula.
 * __Attachment:__ See attachment #6 for the website link


 * Text #7: Visual Video of Completing the Square**
 * __Citation:__ [|A Purely Visual Guide to Completing the Square. (n.d.).//TeacherTube//. Retrieved March 24, 2014, from http://www.teachertube.com/viewVideo.php?video_id=113264]
 * __Text Summary:__ This video offers an entirely visual explanation of the process of completing the square. It starts with showing the visual representation of numbers and variables and progresses to show how to complete the square with just the pictures and equations on the screen. The numbers and variables are represented by pieces of paper and the steps to filling out the square are shown.
 * __Rationale:__ I chose this particular video because there are very few words. Instead of an auditory explanation, students can see the process unfold visually. This will help students who are visual learners see how the process works. This will also help students who are ELLs as the only English they would need is the definition of area to follow along to the video. This is also helpful for students who are struggling with the concept or excelling as a class discussion will allow for students of all abilities to listen, learn and contribute.
 * __Use of text:__ I will show this video after explaining the completing the square technique to the class. The video will play through once with no interruptions. During the second viewing, I will pause the video at each step of the equation and ask the students to explain what is happening to ensure everyone is following along with the visual as it’s a little tricky to see in one viewing. After a brief discussion all together about the steps, I will replay the last 40 seconds of the video so students can watch the process again now that they know what is happening.
 * __Attachment:__ I attached the link to the video in attachment #7.


 * C. Online interactive resources**
 * Text #8: Online Question Quiz**
 * __Citation:__ [|Mathopolis Question Database. (n.d.).//Mathopolis Question Database//. Retrieved March 24, 2014, from http://www.mathopolis.com/questions/q.php?id=1084]
 * __Text Summary:__ This website offers an interactive quiz for solving quadratic equations in one variable using all of the various methods. The questions vary in difficulty and are all multiple choice format. Some questions ask students to find the error in the work which is a valuable skill for students to evaluate their own work. The website offers solutions and reasoning as to why the choice is correct or incorrect for every answer so students can see where they are struggling.
 * __Rationale:__ I selected this website because it will help students see how they are doing with the content for themselves. This will also help students see where they are lacking or excelling within the unit. This text is matched to each type of student including those who have matchup gaps, assets and mismatches as the quiz gives each type of student group an idea of their needs through answer explanations and feedback. The questions are also predominantly just the word Solve and then an equation which can help ELLs focus on the topic rather than English.
 * __Use of text:__ I will use this online quiz after all of the methods for solving quadratic equations have been taught as an extra practice before an assessment. The results of this quiz will be printed and turned in as a homework assignment to be used to evaluate where students are lacking and need additional instruction before the class assessment.
 * __Attachment:__ See attachment #8 for the homepage of the website


 * Text #9: Online Quiz**
 * __Citation:__ [|Quiz On Completing The Square. (n.d.).//Quiz on Completing the Square//. Retrieved April 1, 2014, from http://www.proprofs.com/quiz-school/story.php?title=quiz-on-completing-square]
 * __Text Summary:__ This quiz focuses on completing the square to solve quadratic equations. The questions have both equations to solve and thinking questions about the process.
 * __Rationale:__ I chose this quiz because it asks interesting questions about the topic to help students not only solve problems, but think about what each step does. This quiz will help students get extra practice.
 * __Use of text:__ I will use this quiz as a homework assignment after the lessons about completing the square as an assessment of the students’ abilities with this topic.
 * __Attachment:__ See attachment #9 for link
 * D. Instructional Resources**
 * Text #10: Lesson Plan**
 * __Citation:__ [|Longest, M. (n.d.). Chutes and ladders - Quadratic equations review.] [|//Chutes and ladders - Quadratic equations review//] [|. Retrieved April 1, 2014, from http://www.learnnc.org/lp/pages/2981]
 * __Text Summary:__ This lesson plan is for a quadratic equations Chutes and Ladders game. The class is split into groups of four and each player draws a card and rolls a die. Depending on the number on the die, the student will solve the quadratic equation on the card using a certain method. Each student must check the other’s work and at the end of the game the groups hand in their work for the game.
 * __Rationale:__ I chose this lesson plan because it is a fun way for students to review at the end of the unit. Working in groups the students are able to help and learn with one another which helps all learners.
 * __Use of text:__ I will use this text as a review at the end of the unit before the test. I will collect and return each groups work with suggestions for where they are struggling and should review.
 * __Attachment__: See attachment #10 for a copy of the lesson plan.


 * Which texts/tasks selected for each type of learners:** (indicate by listing the # of each resource selected for that population)


 * Students with Matchup Assets: #1,2,4,7,8,10
 * Students with Matchup Gaps: #1,2,3,4,5,6,7,8,9,10
 * Students with Mismatches: #1,2,3,4,5,6,7,8,9,10
 * Non-native English speakers: #1,4,7,8,10


 * Using these texts together in the classroom:**

This collection of texts would be used throughout the unit about quadratic equations. I would not use every text explicitly within the class as some are intended to be extra resources to aid lessons. I would use many to help get students excited about the lesson and to aid understanding. The children’s book would be used to introduce the unit and show students that math and numbers can be found in many everyday situations. I would also show the video about completing the square after teaching that concept. The song about the quadratic formula would be utilized after students have some practice using the formula to aid memorization. Some of the readings would be homework assignments, like the text about uses of the quadratic formula and the online quiz. Some of the texts I would present, others would be for homework with a discussion after and some would be independent resources given for students to access for their own understanding. I would hope that giving texts and resources that help to aid students with matchup assets, gaps and mismatches would help everyone understand the material more. I would also hope that these texts that access the musical, lingual, visual, mathematical, intrapersonal and interpersonal intelligences would help a broader range than just the verbal/linguistic intelligence usually accessed during lectures.


 * Attachments:**
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= = = Chutes and ladders - Quadratic equations review = This lesson is designed as a review lesson for solving quadratic equations. Students will play the game "Chutes and Ladders," modified for quadratic equations, as they review for the test.
 * 1) 10 []
 * A lesson plan for grades 9–12 Mathematics**
 * BY [|MICHELLE LONGEST]  **

Learning outcomes
By the end of the lesson, the students will have reviewed how to solve quadratic equations using the four methods that we have studied in this unit: graphing, completing the square, quadratic formula, and factoring.

TIME REQUIRED FOR LESSON
60 minutes

MATERIALS/RESOURCES

 * “Chutes and Ladders” game boards (I used similar game boards that I found at the dollar store.)
 * 1 die for each group
 * 1 pack of cards with 1 quadratic equation on each card for each group
 * 4 game disks per group for moving along the board

Pre-activities
Prior to this lesson, students will have spent a couple of weeks learning the different ways to solve a quadratic equation.

This lesson is designed as a review day.

Activities
Quadratic “Chutes and Ladders”
 * 1) 1. The students will be divided into groups of four.
 * 2) 2. Each group will be given a game board, 1 die, 1 pack of quadratic equation cards, and 4 disks to move along the board.
 * 3) 3. Project the directions for playing this review game. The directions will read as follows:
 * 1) 1. Draw a card.
 * 2) 2. Roll the die.
 * 3) 3. If you roll a 1 or a 6, then solve your quadratic equation by completing the square.
 * 4) 4. If you roll a 2 or a 5, then solve your quadratic equation by using the quadratic formula.
 * 5) 5. If you roll a 3, then solve your quadratic equation by graphing.
 * 6) 6. If you roll a 4, then solve your quadratic equation by factoring if possible. If not, then solve it another way.
 * 7) 7. If you solve your equation correctly, then you may move on the board the number of spaces that corresponds to your roll of the die.
 * 8) 8. If you answer the question incorrectly, then the person to your left has the opportunity to answer your question and move your roll of the die.
 * 9) 9. The first person to reach the end of the board first wins the game!
 * 10) 10. Good luck!!

Assessment

 * Students will double check each other’s answers in order to make sure that their opponents have successfully completed their questions in order to move along the board.
 * At the end of the period, students will turn in their solutions, including work shown, for the questions on the cards that were used for the game.

COMMENTS
This lesson can be used as a review for any topic by creating new cards. For example, the game could be used for solving systems of equations by graphing, multiplication/elimination, substitution, matrices, or Cramer’s Rule. Also, the game could be adapted to fit whatever amount of time you wanted.

[|High School: Algebra]

 * § Reasoning with Equations & Inequalities
 * § ALG.REI.4Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. Solve...