Dan's+Look


 * Tim Kirk **
 * April 1, 2011 **


 * Entry 1: Effective Teaching (Instruction and Assessment) **

__Criteria Demonstrated:__ 1(a) Using instructional strategies that make learning meaningful and show positive impact on student learning; 1(b) Using a variety of assessment strategies and data to monitor and improve instruction; 1(d) Designing and/or adapting challenging curriculum that is based on the diverse needs of each student; 1(e) Demonstrating cultural sensitivity in teaching and in relationships with students, families, and community members; 1(f) Integrating technology into instruction and assessment.

// . // |||| The plan is to start the unit with an inquiry-based assignment giving students the opportunity to discover new material by working through word problems in a collaborative setting. After discovering some similarities and differences between the new material (quadratic functions) and what students have already learned (linear functions) definitions will be explored in more detail. Following the state’s performance expectations quadratic functions will be explored in different forms: tabular, graphic, and algebraic. Students will be able to recognize quadratics in all three forms. Next we will learn different strategies for solving quadratics: by graphing, by square roots, factoring, and using the quadratic formula. After learning the different methods, students will be allowed to choose which method works best for them. As far as graphing of these functions is concerned, students will be shown both graphing calculator and long-hand method of solving problems. ||  of Seattle  **Teacher Certification Programs **  ||  **Classroom and Student Characteristics ** **Aligned with the Performance-based Pedagogy Assessment (PPA) **    Complete one //Classroom and Student Characteristics// form for each different group of students you teach. ||   1. Classroom rules and routines that affect the lesson:
 * ** __The Plan:__ **
 * // Title of the Unit: // |||| ** Quadratics ** ||
 * // Grade level // |||| I was teaching ninth grade as my year-long mentored internship. Here is a snapshot of one of my classes.||  **<span style="color: maroon; font-family: 'Arial Narrow',sans-serif; font-size: 18pt; letter-spacing: -1pt;">CityU **<span style="color: maroon; font-family: 'Arial Narrow',sans-serif; font-size: 18pt;">niversity
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Teacher Candidate: || ** Tim Kirk ** || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Date: || April 20, 2010 ||
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Cooperating Teacher: || Karin Stringer || <span style="font-family: Arial,sans-serif; font-size: 10pt;">School / District: || Arlington High School ||
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Grade / Subject: || 9th/Algebra 1 || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Field Supervisor: || Elizabeth Mekelburg ||
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Lesson Title: |||||| Holt Chapter 9-1 ||

Today’s lesson focuses on individual work and self-assessment.

<span style="font-family: Arial,sans-serif; font-size: 10pt;">2. Physical arrangement and grouping patterns that affect the lesson: Desks have been moved to accommodate working individually

Generally, students receive direct instruction from the teacher and then are given time to individually work on practice problems and homework.

<span style="font-family: Arial,sans-serif; font-size: 10pt;">3. Total number of students: 19 4. Females: 12 Males: 7 5. Age range: 14-15 years

<span style="font-family: Arial,sans-serif; font-size: 10pt;">6. Describe the range of abilities in the classroom: More than half have not passed previous WASL tests. One student is talented in math and often seems bored.

<span style="font-family: Arial,sans-serif; font-size: 10pt;">7. Describe the range of socio-economic backgrounds of the students: Roughly 25% Free or reduced lunch throughout the district. <span style="font-family: Arial,sans-serif; font-size: 10pt;">8. Describe the racial/ethnic composition of the classroom, and what is done to make the teaching and learning culturally responsive: Mostly Caucasian. Three students of Hispanic heritage. Two are highly capable, but lack study skills and don’t take school seriously. One is a very good student but has only lived in the US for a short time. She is approaching fluency in English but is not quite there yet. The curriculum offers Spanish online resources.

<span style="font-family: Arial,sans-serif; font-size: 10pt;">9. How many students are Limited English Proficient? One.

<span style="font-family: Arial,sans-serif; font-size: 10pt;">10. Describe the range of native languages and what, if any, modifications are made for Limited English Proficient (LEP) students: One student speaks Spanish as her first language.

<span style="font-family: Arial,sans-serif; font-size: 10pt;">11. How many special education and gifted/talented students are in the class and what accommodations, if any, are made for them? None <span style="font-family: Arial,sans-serif; font-size: 10pt;">12. How many 504 students are there? None What accommodations are made for these students? <span style="font-family: Arial,sans-serif; font-size: 10pt;"> None. <span style="background: #e0e0e0; margin-left: .25in; mso-layout-grid-align: none; mso-list: l3 level1 lfo1; punctuation-wrap: simple; tab-stops: list .25in 37.5pt; text-autospace: none; text-indent: -19.5pt; vertical-align: baseline;"><span style="font-family: Arial,sans-serif; font-size: 10pt;">13. <span style="font-family: Arial,sans-serif; font-size: 10pt;">Are there additional considerations about the classroom/students for which you need to adapt your teaching (e.g., religious beliefs, family situations, sexual orientation)? One student’s mother is a math teacher in the district. <span style="mso-layout-grid-align: none; punctuation-wrap: simple; text-autospace: none; vertical-align: baseline;"><span style="font-family: "Times","serif";">Traditionally this has been my toughest class. Since semester many difficult students have left. Now this is the smallest and quietest class and they are getting more work done. <span style="mso-layout-grid-align: none; punctuation-wrap: simple; text-autospace: none; vertical-align: baseline;"><span style="font-family: "Times","serif";">


 * // Subject areas: // |||| Math, Reading, Writing, Art and Music ||
 * // Length of unit: // |||| This unit of study will take place for about three weeks.
 * Math: **Story problems, practice problems, warm-ups for review of rudimentary skills.
 * Reading: ** Reading Strategies, Story problems.
 * Writing: ** Students create own story problems, power points or posters. Friday reflection journal writing.
 * Art: ** Students use posters and power points to be visually creative.
 * Music **: YouTube song “Quadratic Formula” ||
 * // Basic mapping: // |||| ** Day 1 – Inquiry-based Activity **
 * Day 2 – Reading Strategies and Vocabulary **
 * Day 3 – Identifying Quadratic Functions **
 * Day 4 – Characteristics of Quadratic Functions **
 * Day 5 – Quiz and Friday Reflections **
 * Day 6 – Graphing Quadratic Functions **
 * Day 7 – Solving Quadratic Functions using Square Root **
 * Day 8 – Solving Quadratic Formula by Factoring **
 * Day 9 – Quadratic Formula **
 * Day 10 – Quiz and Friday Reflections **
 * Day 11 – Review of methods for Solving Quadratic Equations **
 * Day 12 – Activity of Student Choice **
 * Day 13 – Activity of Student Choice **
 * Day 14 – Review and Poster Presentation **
 * Day 15 – Test and Friday Reflections ** ||
 * ** __The Rationale:__ **
 * ** __The Rationale:__ **

// Washington State education goals, Algebra I standards and Performance Expectations // |||| ** Washington State Algebra I Standards involved in Unit ** A1.1.A Select and justify functions and equations to model and solve problems. Students can analyze the rate of change of a function represented with a table or graph to determine if the function is linear. Students also analyze common ratios to determine if the function is exponential. After selecting a function to model a situation, students describe appropriate domain restrictions. They use the function to solve the problem and interpret the solution in the context of the original situation. A1.1.D Solve problems that can be represented by quadratic functions and equations. Examples: • Find the solutions to the simultaneous equations y = x + 2 and y = x2. • If you throw a ball straight up (with initial height of 4 feet) at 10 feet per second, how long will it take to fall back to the starting point? The function h(t) = -16t2 + v0t + h0 describes the height, h in feet, of an object after t seconds, with initial velocity v0 and initial height h0. A1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. • As constants such as a, b, and c in the equation y = ax2 + bx + c; A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A1.3.C Evaluate f(x) at a (i.e., f(a)) and solve for x in the equation f(x) = b.  A1.5.A Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations. Example: • Kendre and Tyra built a tennis ball cannon that launches tennis balls straight up in the air at an initial velocity of 50 feet per second. The mouth of the cannon is 2 feet off the ground. The function h(t) = -16t2 + 50t + 2 describes the height, h, in feet, of the ball t seconds after the launch. Make a table from the function. Then use the table to sketch a graph of the height of the tennis ball as a function of time into the launch. Give a verbal description of the graph. How high was the ball after 1 second? When does it reach this height again? A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation. A1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. Algebra 1 A1.8. Core Processes: Reasoning, problem solving, and communication Students formalize the development of reasoning in Algebra 1 as they use algebra and the properties of number systems to develop valid mathematical arguments, make and prove conjectures, and find counterexamples to refute false statements, using correct mathematical language, terms, and symbols in all situations. They extend the problem-solving practices developed in earlier grades and apply them to more challenging problems, including problems related to mathematical and applied situations. Students formalize a coherent problem-solving process in which they analyze the situation to determine the question(s) to be answered, synthesize given information, and identify implicit and explicit assumptions that have been made. They examine their solution(s) to determine reasonableness, accuracy, and meaning in the context of the original problem. The mathematical thinking, reasoning, and problem solving processes students learn in high school mathematics can be used throughout their lives as they deal with a world in which an increasing amount of information is presented in quantitative ways and more and more occupations and fields of study rely on mathematics. ** Performance Expectations: ** Students are expected to: A1.8.A Analyze a problem situation and represent it mathematically. A1.8.B Select and apply strategies to solve problems. A1.8.C Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem. A1.8.D Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems. A1.8.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics. A1.8.F Summarize mathematical ideas with precision and efficiency for a given audience and purpose. A1.8.G Synthesize information to draw conclusions, and evaluate the arguments and conclusions of others. A1.8.H Use inductive reasoning about algebra and the properties of numbers to make conjectures, and use deductive reasoning to prove or disprove conjectures. ** Washington State Alg1 Performance Expectations ** A1.8.A Analyze a problem situation and represent it mathematically A1.8.B Select and apply strategies to solve problems A1.8.C Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem. A1.8.D Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems. A1.8.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics. A1.8.F Summarize mathematical ideas with precision and efficiency for a given audience. A1.8.G Synthesize information to draw conclusions, and evaluate the arguments and conclusions of others. A1.8.H Use inductive reasoning about algebra and the properties of numbers to make conjectures, and use deductive reasoning to prove or disprove conjectures. || <span style="margin-left: 5.95pt; mso-layout-grid-align: none; mso-pagination: none; text-autospace: none; text-indent: -5.95pt;"> || Here is the portion of Arlington High School’s SIP as regards mathematics. Goals include raising the HSPE pass rate to 58% to meet AYP, increased collaboration between teachers, greater emphasis on interventions especially early on when Freshmen are taking Algebra I. ||
 * // The plan is data-driven. // |||| Student performance in the district is available to all teachers. Available date include grades, test scores (WASL/HSPE), and behavioral issues over the course of the students’ career. At the beginning of the year a test was given as a pre-assessment for all algebra students across the district to get a baseline understanding of student math skills. Common assessments are given to all 20 algebra classes across the district to make monitoring progress easier. ||
 * // Explain how the plan is research-based or based or best practice(s). // |||| Collaborative inquiry-based activity allows students to solve problems with minimal instruction and according to Linda Hammond Darling is a more effective strategy. Reading Strategies for comparing and contrasting different functions and Modeling problems and practice are included in Classroom Instruction that works by Robert J. Marzano. Allowing students to create posters/power points for presentation to the class allow for student voice and collaborative learning by ‘Jigsaw’ meth as illustrated by Harvey F. Silver et al in The Strategic Teacher.
 * // The plan is appropriate to the learning context and accommodations for special needs students. // |||| All objectives taught are taken directly from the Washington state Algebra I standards and performance expectations. Since these are new standards and these students have switched from having grade-level expectations to curriculum-based standards, there has been a bit of a learning curve for some students. A percentage of the freshman population has been assigned to ‘Looping Algebra’ and are given an extra year to complete the Algebra course. ||
 * // The plan is tied to the School Improvement Plan. // |||| [[image:file:///C:/Users/DAVISK~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif width="576" height="476"]]
 * // Explain what/how multicultural applications are included. // |||| Students are asked to make their own story problem involving their own experiences. Spanish resources are also available for native speakers. ||
 * // Student Voice. // |||| Students take notes everyday on the learning objectives and are asked to put them in their own words. Friday Reflections give students another way to express what they learn in mathematics in their own words. Students are given a choice about what the topic of their project is. Students create posters and are encouraged to be creative while sharing their ideas with the class. ||
 * // Students use technologies to enhance their learning. // |||| This is the first unit where the graphing calculator becomes and essential tool for the students. In order to demonstrate how to use the calculator I utilize the virtual calculator on the smart board. Projects are submitted with power point or word onto the wiki page or glogster page for students to share their work beyond the classroom. ||
 * // Opportunities provided to invite collaboration with students, families, colleagues, and community stakeholders // |||| The algebra team meets every morning to discuss strategies, successes and obstacles. District-wide intervention team meets every month. Parents are invited to conferences and curriculum open house. Postcards are sent home to highlight positive behavior. ||
 * Friday Reflection Questions: **
 * How are quadratic functions different from linear functions?
 * What sorts of applications use quadratics?
 * What are some of the different ways to solve quadratic equations?
 * How is the rate of change different for these functions as compared to linear?
 * How can we recognize quadratics in a table, a graph, and an equation?
 * How can we recognize quadratics in a table, a graph, and an equation?

· Computer/Internet Use · Projector Use · Power Point · Glogster · Virtual Calculator · Wiki site · Blog · Smart Board and Notebook · Online curriculum including homework help and video tutorials ||  ||
 * Instructor Resources: **
 * Holt Algebra I textbook and online curriculum
 * Postcards for parents
 * Internet Access for blog updates
 * Copy machine and printer
 * Teacher created assessments
 * Pencils
 * Classroom set of Mac notebooks available from computer lab.
 * Chart Paper
 * Butcher Paper
 * Magic marker
 * Notebook
 * Integration of technology: **
 * ** __Rationale:__ **
 * 1(a) Using instructional strategies that make learning meaningful and show positive impact on student learning;**

Collaborative inquiry-based activity allows students to solve problems with minimal instruction and according to Linda Hammond Darling is a more effective strategy. Reading Strategies for comparing and contrasting different functions and Modeling problems and practice are included in Classroom Instruction that works by Robert J. Marzano. Allowing students to create posters/power points for presentation to the class allow for student voice and collaborative learning by ‘Jigsaw’ meth as illustrated by Harvey F. Silver et al in The Strategic Teacher.

<span style="font-family: "Times","serif";">


 * 1(b) Using a variety of assessment strategies and data to monitor and improve instruction;**

Warm-ups, Exit Slips, Quizzes, Test, Poster/Project, Practice Problems


 * 1(d) Designing and/or adapting challenging curriculum that is based on the diverse needs of each student**;

Students are shown multiple ways to solve quadratic equations. Tabular, Graphic and Algebraic. Depending on their learning style, they can choose the method they prefer to solve these problems. For the projects, students are given a choice between science and business applications to appeal to their interests.


 * 1(e) Demonstrating cultural sensitivity in teaching and in relationships with students, families, and community members; **

Students are encouraged to write their own story problems to illustrate practical uses of quadratics. Anything subject to gravity can be a subject for quadratic functions. Any sport involving a ball or projectile could be a subject. The Holt curriculum also offers online support in Spanish, including the entire textbook translated with Spanish/English glossary.


 * 1(f) Integrating technology into instruction and assessment.**

Students have online access to the textbook and moodle for communication. Grades are posted every other week for 24/7 online access including missing assignments. Assignments are available on wiki site for absent students to access. Teachers keep in touch with parents online as well as via phone conversations. If students choose they can submit power point presentations and via the wiki or glogster which offers a richer, multimedia platform for student work. ||

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