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Factoring POLYNOMIALS. Ryann Kramer EDU 521.02 Prof. R. Moroney Summer 2010. Introduction.
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FactoringPOLYNOMIALS Ryann Kramer EDU 521.02 Prof. R. Moroney Summer 2010
Introduction • Factoring is an important, yet difficult concept to grasp and is a building block to many other units in mathematics. This unit is aimed for students to be able to understand the concept of how to factor polynomials. It goes over important strategies that are extremely helpful and beneficial for solving polynomials. Some important strategies that will be covered are using the greatest common factor, difference of two squares, trinomials, trinomial squares, and factoring by grouping. These strategies will also be helpful when solving equations.
Context of the Project • Subject: Mathematics - Algebra • Grade Level: 9th • Team Teaching or Collaboration: No • Class Size: 25 students • Students with Special Needs: 1 Student with ADHD and one student that has visual impairment. • Students’ Experience with Technology: Internet, Emailing, Texting, Ipods • Class Access to Technology: There is a SMART board, there are a few computers with Internet access in the back of the room, the computer lab in the library, and a personal computer at home • Where do the two detailed lessons fit into my unit? The first one is at the beginning and the second one after the first one.
Aim of the Project • The aim of this unit is to have students be able to understand how to factor polynomials. Throughout the unit, students will learn different strategies that they will use to help them to factor different polynomials and solve many questions. The worksheets, projects and activities will help to assist them to prepare for the exam at the end of the unit. • The students will demonstrate the knowledge they learn by watching videos, making PowerPoint presentations, and working in groups to solve problems. Students will be given many problems that will be completed for homework as well. At the end of the unit, students will take an exam in order to test their knowledge about everything we covered in class.
Justification • I am using technology in my unit in order to make learning algebra more interactive and enjoyable for the students. I think incorporating technology such as using SMART Notebook and having the students use PowerPoint to make presentations about material we are covering will make the lessons fun for the students and it will make some of concepts more fun to learn and understand. Sometimes incorporating technology is a nice change of pace in the classroom. Technology supports my curriculum because the students will be using technology for help with solving problems and they will be using it for homework problems and reviewing material.
Materials • Pens and/or pencils • Notebook • Computer with Internet access • PowerPoint software • SMART board • SMART Notebook software • Algebraic tiles • worksheets
NYS Standards NYS LearningStandards for Mathematics, Science, and Technology Standard 1: Analysis, Inquiry, and Design Students will use mathematical analysis, scientific inquiry, and engineering designs, as appropriate, to pose questions, seek answers, and develop solutions.
NYS Standards NYS Standards for Mathematics, Science, and Technology Standard 3: Mathematics Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
NYS Standards NYS LearningStandards for Mathematics, Science, and Technology Standard 7: Interdisciplinary Problem Solving Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real-life problems and make informed decisions.
NYS Standards New York State English Language Arts Standard # 4: Language for Social Interaction Students will use oral and written language for effective social communication with a wide variety of people. As readers and listeners, they will use the social communications of others to enrich their understanding of people and their views.
NETS for Students • 1.Creativity and Innovation Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students: • a. apply existing knowledge to generate new ideas, products, or processes. • b. create original works as a means of personal or group expression. • c. use models and simulations to explore complex systems and issues. • d. identify trends and forecast possibilities.
NETS for Students • 2.Communication and Collaboration Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others. Students: • a. interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments and media. • b. communicate information and ideas effectively to multiple audiences using a variety of media and formats. • c. develop cultural understanding and global awareness by engaging with learners of other cultures. • d. contribute to project teams to produce original works or solve problems.
NETS for Students Continued • 4.Critical Thinking, Problem Solving, and Decision Making Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. Students: • a. identify and define authentic problems and significant questions for investigation. • b. plan and manage activities to develop a solution or complete a project. • c. collect and analyze data to identify solutions and/or make informed decisions. • d. use multiple processes and diverse perspectives to explore alternative solutions.
Essential Question • What strategies can we use to find the factors of polynomials?
Lesson Plan #1 • Topic: Factoring using the greatest common factor. • Motivational Activity: Students will answer a word problem to find the GCF between two numbers. Once they do that, students will create their own problem and give it to a partner to have them solve it. • Objective: The main objective of this lesson is to have students learn how to factor using the greatest common factor. Students will make PowerPoint presentations and be provided with worksheets with numerous problems to be completed at school and at home for homework. Students will also play a matching game and this game will assess the students to see which students understand the material and which students are struggling.
Lesson Plan #2 • Topic: Factoring using the method of Factoring by Grouping. • Motivational Activity: Students will use algebraic tiles to help them to visualize the concept of factoring by grouping. • Objective: After learning to factor polynomials using the method of factoring by grouping, students will work in groups to complete the problems in the worksheet. Each group will be assigned one problem to present to the class using SMART Notebook and students will show how they solved the problem.
Lesson Plans Lesson #3: Factoring Using the Difference of 2 Squares • Students will split into groups and watch videos about how to factor the difference of 2 squares. After watching the video, each group will present the information they got out of the video and the steps that are necessary to solve problems. Lesson #4: Trinomials • Students will use an Internet Hotlist to read about trinomials and then students will work in pairs to answer all of the questions from both math pages.
Lesson Plans Continued Lesson #5: Factoring Trinomial Squares • Students will read about trinomial squares and in their notebooks they will summarize what trinomial squares are and the steps to solving a trinomial square. Lesson #6: Solving Equations by Factoring • Students will use all of what they learned about factoring polynomials to help them to solve equations by factoring. They should write down all of the rules and steps that they learned for each different strategy on one page and use that as a reference to help them to solve equations. Review for ExamEXAM
2 Different Forms of Technology • In the first lesson, I incorporated a PowerPoint activity in which students will work in groups to create a presentation about factoring using the greatest common factor. • In the second lesson, I had the students watch a video from YouTube. I also had the students work in groups to solve a problem and then use SMART Notebook to show the class how they solved the problem. • Assistive technology for students that are visually impaired can be full page magnifiers. Students can also use the JAWS for Windows Screen Reading Software which lets students work with many applications. Another assistive technology would be an EasyRead which is soft ware that you can download to Internet Explorer that allows you to view different web pages at any size you want. • Assistive technology for students with ADHD can be computer based educational software. That can helps students to keep their focus.
