Teaching Portfolio for Chelsea Switts



Appendix B – Lesson Plan 1 (Unit Lesson 5)Course: Algebra 1Lesson Title: Word Problems with Constraints - InequalitiesDate: 3/28/2014Source of Lesson: Fellow Mathematics Teacher at the same high schoolConcept/topic/summary of lesson: In this lesson, students will utilize previous knowledge of solving word problems with algebraic equations, but now, the equations will be inequalities due to a given constraint within the problem. The concepts addressed will be converting words into mathematical expressions, identifying constraints, converting the constraint into an inequality, and solving multistep inequalities. Students will start out the lesson with a bell work in which they are introduced to this idea. Next, they are given word problems on whiteboards and are asked to solve in pairs.Background Information: Students will need to know how to solve inequalities and equations, how to find an algebraic expression to represent a real world application, and conceptual knowledge of numerical inequalities.Objectives (Bloom’s taxonomy showed in parenthesis)- Construct an expression from a given word problems (Synthesis)- Identify the constraint placed on the situation that creates an inequality (Comprehension)- Apply concepts of inequalities to real world applications (Application)MaterialsWhiteboards, smart board, dry erase markers, erasers, pencil, solution worksheet, calculatorsState Standards From the Kansas College and Career Ready Math Standards:High School Algebra, Creating Equations, 3. Representing constraints by inequalities and systems of inequalitiesAccommodations/Differentiation:For this activity, students were in mixed ability groups. This allowed students to have the experience of explaining how they think about word problems to each other and justify the steps they took towards solving. SafetyFor this lesson, normal classroom rules are followed, such as no running within the classroom and the noise level must stay at an inside voice level in case of needing to hear an emergency over the intercom. Reading StrategyStudents partner read the word problems given to them on the whiteboards. The word problems used for whole class discussion are introduced through chorus reading.Technology UseA smart board was used at the beginning of the lesson to provide students with a short preview of what they will be learning today. Each student also used calculators.Models of Instruction Used: For the beginning of class, the teacher leads a whole class discussion over the concepts the students will be learning. After this portion, the class is student-centered with them working with partners to accomplish the goal of solving word problems with inequalities. Most of the period is spent like this. However, at the end, there is another whole class discussion in which the teacher facilitates a discussion among students.Integration Within/Across Content AreaAcross: Applications were seen from science, economics, architecture, and engineering. Within: Many algebra I skills for solving equations and graphing on the coordinate plane, were used as well as basic arithmetic and number sense.Lesson Plan (expected time of each activity in parenthesis – following 5E Lesson Plan)ENGAGE (5): Classroom will begin by working on bell work on the smart board. It should connect with the idea of word problems. For example:Find the inequality for the given situations: 1.) There were at least 50 people at the event. 2.) I have no more than 3 gummy bears.To answer these, students work independently for a two minutes. Next, the teacher asks for volunteers and has students come to the smart board to explain to the class how they arrived at their answers. EXPLAIN (15): Next, the teacher will begin a classroom discussion involving solving word problems with a given constraint. The teacher shows a word problem on the smart board. Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile. Katie no more than $10 to spend on a ride. Write an inequality that represent Katie’s situation. How many miles can Katie travel without exceeding her limit?“How could we construct a mathematical expression that represents this part of this word problem?”Underline the portion of the word problem that they need to find the expression representing it. For the above example, underline “$1.75 flat rate in addition to $0.65 per mile.” Then, give students a few minutes to think and try to create this expression.“What are some expressions you came up with for this situation”Write down all of the expressions and have a full class discussion on which one is correct. After the students have picked out the expression, underline the constraint and ask for them to create an inequality like they did in bell work to represent the situation. For the above example, underline “no more than $10.” Allow a few minutes to accomplish this task. Then, ask for all possible inequalities that students came up with for the constraint. Then, the teacher will have a full class discussion over the proper inequality. After the correct inequality is chosen, its time to put it all together.“What if I wanted to combine the expression and inequality to get one inequality that I can solve algebraically? How could I do this?”Discuss the proper way to do this. Then, work through solving the inequality algebraically. After this, since this is a real word application, be sure to address appropriateness of solutions. For example, if one can buy 5.17 shirts without going over his budget of $50, how many shirts can he actually buy? “Can he buy 0.17 of a shirt?”EXPLORE (25): After this, students are partnered with students of mixed ability. There are 12 whiteboards with a different word problem taped on to each one. Each pair grabs a whiteboard, completes the problem, and then has the teacher check the solution. In order for the solution to be accepted, the students must show the inequality that represents the problem, and the answer the arrived at for the problem. If correct, they write their answer on the solution sheet provided by the teacher, and they grab a new whiteboard after erasing. If incorrect, they discuss with the teacher their error and correct it. While students are doing the whiteboard work, the teacher should be walking around the classroom, looking for misconceptions. The teacher is also there to answer questions and to make sure students are equally participating.ELABORATION (6): The teacher will bring the students attention back to her and will begin a full classroom discussion. Things to discuss are what problems caused the most trouble, what common errors students ran into when trying to solve, and what misconceptions were seen while walking around the room.“What problem was hardest for you the construct the expression?”“What problem was the hardest for finding the inequality for the constraint?“What problem was the easiest for you?”“What errors did you find yourself making frequently?”EVALUATE (Incorporated throughout EXPLORE): Students will write answers for word problems on a solution sheet given to them by the teacher. They must get their solutions checked and approved before they can move onto the next word problem.Evaluation MethodsInformal Assessment - Observations during the whiteboard work and throughout the class discussions.Formal Assessment - The solution worksheetAppendix B – Lesson Plan 2 (Unit Lesson 6)Course: Algebra 1Lesson Title: Linear Inequalities Date: 3/31/2014Source of Lesson: Collaboration From Math Department, Learnzillion, and Khan AcademyConcept/topic/summary of lesson: In this lesson, students will learn the concept of linear equalities. They will first define a linear inequality and learn about the solutions to these problems. Next, they will learn how to graph linear inequalities on a coordinate plane. They will be asked to graph a dashed or solid boundary line and shade the appropriate half plane of solutions.Background Information: Students will need to know how to graph lines, how to convert to slope intercept form, and basic knowledge of inequalities in one variable. Objectives (Bloom’s taxonomy showed in parenthesis)- Utilize knowledge of graphing linear equations in order to graph linear inequalities and extend these concepts further to the extra steps that must be taken while graphing linear inequalities (Application)- Identify the half-plane region of solutions and shade appropriate region (Comprehension)MaterialsLaptops, pencil, two worksheets over linear inequalitiesState Standards From the Kansas College and Career Ready Standards:High School Algebra, Reasoning with Equations and Inequalities, 12. Graph the solutions to a linear inequalities as a half plane as well as the solutions to a system of inequalityAccommodations/Differentiation:The difference between the two worksheets allowed for a great deal of differentiation during this lesson. The first worksheet had the boundary lines already in slope-intercept form. This allowed students to focus on the other concepts of graphing linear inequalities. The second worksheet with the graphic organizer really helped students understand the concepts of this lesson. The other worksheet did not have the problems set up in slope-intercept form; thus, graphing was more difficult. For my lower students, their goal to complete two problems instead of all. For my higher students, they needed the challenge so they were required to do the entire worksheet. My middle level students were asked to complete a varying number based off of the typical pace they work.SafetyFor this lesson, normal classroom rules are followed, such as no running within the classroom and the noise level must stay an inside voice level in case of needing to hear an emergency over the intercom. Reading StrategyGraphic Organizer on second worksheet to help students organize concepts and check for understanding.Technology UseSmart board for bell work and laptops for students to watch videosModels of Instruction UsedStudent centered while watching videos. After the students are done watching videos, they have small group discussions over the concepts they just learned. Throughout the process of completing the worksheet, students participate in a collaborative learning environment. Integration Within/Across Content AreaN/ALesson Plan (expected time of each activity in parenthesis – following 5E model)ENGAGE (6): To begin this lesson, have students work on bell work displayed on the smart board that involves graphing lines. For example, convert the following to slope intercept form and graph the line on the coordinate plane. 3x + 4y = 12This will get students to review the idea of graphing lines and converting to slope intercept, which is needed to graph linear inequalities. Allow students 3 minutes to complete this and have students come up to the board, explaining to the other students how the arrived at their line.EXPLORE (10): Students will watch videos over the idea of linear inequalities. One video is on the website Learnzillion and the other is on the website Khan Academy. - Link to Video One: Link to Video Two: These videos present the concept of graphing linear inequalities in two different ways. The first video shows graphing by plugging in values for x, finding y, and plotting that ordered pair. Then, to shade the half plane, students use whether it is less than or greater than inequality symbol to determine whether shading should be done below or above the point. In the second video, they convert to slope-intercept form to find the boundary line. After they graph this line, they used a test point to determine which region to shade. EXPLAIN (15): After watching the videos, students will discuss in groups the ideas they just learned. After this discussion, students will complete a worksheet over graphing in these groups. This worksheet has all of the equations given in slope-intercept form so graphing on this worksheet is easier. Students should have answers checked before they can move onto the next worksheet. During this time, the teacher should be walking around the classroom, checking students’ understanding.ELABORATE (20): Students are given another worksheet after they complete the first one. This worksheet has a graphic organizer on the first side. This helps students put concepts into their own words and to check to see if they understand the ideas they have learned. On the other side, the inequalities are often given so that the boundary line is in standard form. This allows students to choose which method from the videos they want to use. This worksheet can be easily differentiated based off of ability of the students due to extra steps required in converting to slope-intercept form. Students continue to work in groups. Also, the teacher will walk around the room, helping students during this work time as well. EVALUATION (During Lesson): For evaluation, the two worksheets the students are given to complete are used for evaluation.Evaluation MethodsInformal Assessment - Observe as students watched the videos and answered questions. Once they got to the worksheet, observe the work and answered questions over graphing and guided them as neededFormal Assessment - The two worksheets over graphing linear inequalities. ................
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