Natalie's+Blog+Lesson+Plan

This lesson will be taught to three sections of Academic Algebra III/Trigonometry classes, each of which contains 24-26 students. Students in these classes are either in 11th or 12th grade. Most of the seniors have passed the 11th grade PSSA test (Pennsylvania State Standardized Assessment) by this point (although some had to recently complete retests). Most of the students in the class have good algebra skills; however, their ability and motivation to work through problems on their own is limited. They want to be “told” what to do and are not used to school environments that are more constructivist. Through this activity, I hope that students will begin to take a more active role in their learning and feel responsible for what they get out of the lesson. Two of the students (out of the three classes) have IEPs and are classified as gifted. Two other students are classified as having learning disabilities. = = = Goals and Objectives =  ·  To accurately describe and summarize the role of each variable in a quadratic equation, //y = a(x – h)2 + k//, and how it affects the corresponding graph  ·  To describe graphs of quadratic equations based on their concavity, domain, range, increasing and decreasing intervals, x- and y-intercepts, and vertex  ·  To sketch the graph of a quadratic equation  ·  To use blogging to post reflections about quadratic equations and images of parabolas created using online graphing tools  ·  To use blogging to analyze graphs of quadratic equations using appropriate mathematics vocabulary = Materials  = ·  Graphing calculators ·  Colored pencils ·  Laptops and access to the following websites: o  http://www.shodor.org/interactivate/activities/DataFlyer/?version=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc. o  http://webgraphing.com/graphing_basic.jsp o  http://mrstaahs.wordpress.com/ Procedures and Activities **Opening / Anticipatory Set**: To begin this lesson we will review graphing //linear// equations and how each variable in the equation affects the graph. I will show students the following website http://www.shodor.org/interactivate/activities/DataFlyer/?version=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc. and how it can be used to see the role of each variable in the corresponding graph. I will allow students to access the website themselves and manipulate the graph so that they become comfortable with the way the equations are entered and how to manipulate the graph. We will discuss some vocabulary words, such as //slope//, //intercepts//, //domain// and //range//, and //increasing// and //decreasing//, as they relate to the linear graph, and I will also show them how the websites can aid in their understanding of the vocabulary by showing them illustrations of how the terms are present in the graph. **Lesson**: I will present students with an “investigation sheet” about graphing //quadratic// equations in which they will use interactive graphing websites, http://www.shodor.org/interactivate/activities/DataFlyer/?version=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc. and http://webgraphing.com/graphing_basic.jsp, and their calculators to graph parabolas and create tables of values. I will have students work in pairs to complete the investigation, which allows them to analyze how each variable affects the graph of a quadratic equation. I will also have students define and describe in their own words the following terms: //concavity//; //x//- and //y//-//intercepts//, //domain//, //range//, //vertex//, and //increasing// and //decreasing// //intervals//. Students should have definitions that relate directly to the graphs they create. In order to guide students in their definitions, I will direct them to the following sites: http://webgraphing.com/graphing_basic.jsp, http://www.analyzemath.com/quadratics/quadratics.htm , http://www.coolmath.com/algebra/Algebra2/04QuadraticsReview/03_graphing.htm. I will also encourage them to find their own helpful websites that they can share with the class. After students are comfortable with the vocabulary and properties of quadratic equations and graphs, I will have them complete an assignment where they visit my blog and post comments on a quadratic equation and corresponding graph that I have posted for them. They will then create their own equation and graph and post it to the site for others to comment see and analyze. We will discuss as a class how to post the image and corresponding equation to the site by saving each as a jpeg or gif file from the website. Students will then be responsible for commenting on/analyzing at least one other student’s graph according to its properties. **Part A**: **Blog Comment** **5 points**: correct description of one aspect of the graph (or two aspects if you choose to describe concavity) including correct mathematics vocabulary, use of appropriate variables, and a connection between the equation and the graph **3 points**: adequate description of graph that does not incorporate math vocabulary or does not make the connection between the equation and the graph **1 point**: adequate description of graph that uses incorrect vocabulary or variables or makes an incorrect connection between the equation and the graph **Part B**: **Equation Creation and Blog Posting** **5 points**: posts graph and equation correctly to the blog; chooses an equation that has values for //a//, //h//, and //k// other than 0 or 1. **3 points**: posts graph and equation correctly to the blog; chooses an equation that uses a value of 1 or 0 for either //a//, //h//, or //k// **1 point**: neglects to post equation and graph together; chooses an equation that uses a value of 1 or 0 for more than one of the variables //a//, //h//, or //k// **Part C**: **Blog Comment on Another Student’s Graph** **5 points**: correct description of two aspects of the graph (excluding concavity) including correct mathematics vocabulary, use of appropriate variables, and a connection between the equation and the graph **3 points**: adequate descriptions of graph that do not incorporate math vocabulary or do not make the connection between the equation and the graph **OR** correct description about only one aspect of the graph **1 point**: adequate description of graph that uses incorrect vocabulary or variables or makes an incorrect connection between the equation and the graph - Below is the blogging part of the assignment as it appears on my blog: http://mrstaahs.wordpress.com/2009/01/27/blogging-lesson-plan-graphing-quadratics/
 * Formal Lesson Plan: Analyzing Graphs of Quadratic Equations**
 * Class Description **
 * Blogging Component of Lesson Plan Evaluation Rubric **

[|Blogging Lesson Plan - Graphing Quadratics]
Based on what you’ve learned about quadratic equations, consider the equation below and its corresponding graph.

//

Graph created at http://webgraphing.com/graphing_basic.jsp // // (Although there aren’t arrows at the ends of the parabola, assume that it extends indefinitelydownward on either side) // **__ Part A __****. Respond to this post by commenting on at least one of the following: ** 1) Concavity (If you choose to comment on concavity, you must also comment on one of the other topics below)   2) Increasing and Decreasing Intervals 3) Intercepts: (how to find them on the graph **and** how to find them algebraically using the equation)   4) Vertex: (how to find it on the graph **and** how to find it using the equation) 5) The domain and range of the graph   6) The role of the “a” value in the graph’s appearance. **__ Part B __****. Create your own quadratic graph and equation and post it to the blog. ** **__ Part C __****. Respond to another classmate’s graph by commenting on two of the six components from Part A. Reference the equation and the graph as you commment. Note: You may NOT use concavity as one of your two components. **

Helpful graphing links if you are still having trouble: http://www.shodor.org/interactivate/activities/DataFlyer/?version=1.5.0_06&browser=MSIE&vendor=Sun_Microsystems_Inc. http://webgraphing.com/graphing_basic.jsp