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Algebra One, Chapter Two’sSolving EquationsAn Instructional Design PackageCreated by: Jackie HallFall 2012Southwestern College Professional StudiesDr. Jeni McRayTable of Contents Preface……………………………………………………….…Pg. 3Introduction…………………………………………………….Pg. 3Chapter 1: Learning Content Analysis……………………….Pg. 4Chapter 2: Learner Analysis………………………………….Pg. 11Chapter 3: Learning Task Analysis…………….…………….Pg. 17Chapter 4: Assessment Analysis……………………………….Pg. 25Chapter 5: Instructional Strategy Development…….……….Pg. 31References……………………………………………..……….Pg. 36PrefaceThis paper serves as a handbook for teachers who are interested in following the instructional design process. Even though this instructional design package specifically refers to Chapter 2’s “Solving Equations” in the Algebra I course, any teacher for any course can utilize this handbook as a template/guide to create their own package for their own unit. Teachers want to be the best they can be by creating effective instruction, and in the end, making student achievement as high as it can be implementing effective instruction. IntroductionAs a fifth year high school math teacher, I no longer feel like the new kid on the block but still feel that I have a lot of room for growing and becoming a better teacher with each year. There is a lot of research stating the benefits from practicing good instructional design, and I am excited with the outcome of my instructional design package for my Algebra I class. Instructional Design includes a learning context analysis, learner analysis, learning task analysis, learning objectives, an instructional strategy development, and a learner assessment. The first element of the instructional design process is the learning context analysis. Included in the leaning context analysis element is a discrepancy-based needs assessment. CHAPTER 1: LEARNING CONTEXT ANALYSISNeeds AssessmentGoals of Instructional SystemAlgebra I, a math class typically for freshmen in high school, is the foundation for students’ math careers. In order for students to be successful in Geometry, Algebra II, Pre-Calculus/Trigonometry, Calculus and beyond, the students must master the goals set in Algebra I. The school district I am in has an instructional pacing guide that follows the Algebra I textbook to aid teachers in setting common goals. Listed throughout the Prentice Hall Mathematics Algebra I textbook (2004), specifically, students will need to be able to:Master the Tools of Algebra Solve EquationsSolve InequalitiesSolve and Apply ProportionsRead Graphs and Evaluate FunctionsWrite and Graph Linear EquationsSolve Systems of Equations and InequalitiesSimplify Exponents and Exponential FunctionsSimplify Polynomials and FactorSolve and Graph Quadratic EquationsSimplify Radicals and Solve Radical EquationsFurthermore, my school district is in the transition to Common Core Standards (CCS). As we begin this transition, a little from the CCS will be added to the curriculum each year. All the math teachers in the district are to focus on what is being added to our instructional goals this year set by the district. Again, those updated goals will be listed in the district instructional pacing guide. How Well Goals Are Being AchievedOnce goals have been determined to guide where students are going, it is necessary to see how well the students are already reaching these goals. Over the last four years I have observed that, for the most part, the previously stated goals have been reached by my students. I can say this due to their scores on the chapter tests I have administered, and again when I have the students in a later course like Geometry and Algebra II where they continue to use these skills from Algebra I. In addition, the other math teachers and I get together during weekly Professional Learning Committee (PLC) meetings and discuss the vertical alignment between our courses. Higher level math teachers share what skills/concepts they notice are lacking from their current students. However, there are still a percentage of students that are not adequately achieving these goals and therefore the possibility of needing to design and develop new instruction exists. If that is the case, finding an alternate form of instructional delivery is appropriate. These forms include computers, video, manipulatives, and other technological devices.Gap AnalysisAll respectable teachers want 100% of their students to succeed and reach the goals that were set for them at the beginning of instruction. At the same time all realistic teachers know that 100% of students meeting instructional goals every single lesson, chapter, unit, and class is not likely. Regardless, is imperative that teachers take the time to do a gap analysis and look at where the students stand in the present and where they want them to end up in the future. For my instructional goals I am able to look at previous year’s chapter test results and find out what percentage of students met the goals and what percentage did not. Stem and Leaf plots of the students’ grades make this an easy statistic to find. In addition, there are other circumstances where I may be able to look at standardized tests to see what percentages of students are not meeting goals. Explore tests for freshmen, PLAN tests for sophomore, ACT tests for juniors and seniors, and the state math assessment all have breakdowns of the exact concept and how many students met that specific standard. Prioritize gaps according to agreed-upon criteriaOnce the gaps have been identified, it is time to put in a plan of action and decide with which instructional goal to start. It can be tricky to decide where to start if there are several goals set for any given unit. Prioritizing the gaps will help teachers stay organized and get the best results, quickest. Things that need to be considered when prioritizing are the size of the gap, the importance of the goal, the number of the students affected, the consequences of not meeting the goal, and the probability of reducing the gap. At my high school we are lucky to have a data leader that works on compiling data for the math department. Again, during our weekly PLC meetings we look at the data and decide where to start, and the majority of the time we focus on the gap where most of the students are affected. Instruction NeedsUnfortunately no matter how perfect a teacher’s delivery of instruction may become, sometimes students are unsuccessful and may not meet goals for other reasons. It is important that teachers keep this in mind to prevent unnecessary frustration and from wasting valuable time. Besides instruction, low attendance rates, lack of motivation, impossible attitudes, socio-economic demographics, and the need for incentives and feedback are some of the reasons why a student may fall short of the set goals. These performance problems are what make the previously mentioned desirable 100% nearly impossible to obtain. Of course, I will do my best to strengthen my students’ motivation, attitudes, and offer an adequate amount of positive feedback, but some of those factors I cannot control like attendance and socio-economic demographics. Keeping that in mind I may set my goal of where I want my students to be to a 90% success rate versus a 100% success rate. Techniques for Gathering DataGathering data about our students’ progress can be quick or it can be time extensive. The good news for teachers is there are several ways to collect data so it’s nice to just do whatever works best for that specific concept/learning goal. The three needs assessment models described in the book Instructional Design by Smith and Ragan (2005) suggest that data can be acquired through a variety of techniques: analysis of extant data, analysis of subject matter, interviewing, observing, focus groups, and questionnaires and surveys. Furthermore, the Discrepancy model suggests even informal assessments work as well. For example, I may think to myself at the end of the day, “What instructional goals are not being met?” After some reflection I may think, “What are the most important learning gaps I need to work on tomorrow?”For my learning analysis I will use a lot of quick assessments to see where my students are at before the chapter test. I use questioning techniques often. Instead of taking students through a problem step by step, they will take me through the problem step by step. I will call on different students for each step to check for understanding. Likewise, I will use quick checks like Boards, Wipes, and Markers (often referred to as response boards) to get instant feedback on the students’ progression. Furthermore, I end each class period with a closing and sometimes my closing will ask the student, “What topics are still foggy?” or “What is the hardest part of this chapter?” All of these are quick but effective ways to gather data about my students and help me in determining what I need to change, if anything, about my instruction. Learning EnvironmentCharacteristicsThe characteristics of the individuals in the math department at my high school vary. The years of experience range from 5 years to 20 years. One has his master’s, two are in the process of earning their master’s, and three do not have their master’s. All are interested in student achievement, but some are more dedicated to this cause than others. Half of the teachers give up their lunch to monitor lunch tutoring while the other half never spend any outside class time to aid students. Also, most of the teachers see themselves as what Smith and Ragan describe as disseminators of information (2005). However, some incorporate the textbook, activities, and technology while others teach mostly from the textbook with only a little aid from the technological equipment. Technology is heavily available at our school. Currently available for instructional use are Airliners, document cameras, I pads, overhead projectors, projectors, Smart Boards, Smart Response Clickers, CPS clickers, and Laptops. Software available includes Smart Notebook, Prentice Hall Algebra I textbook online resources, Internet, and Exam View. We believe that technology could be used for either the central based portion of instruction or simply for remediation, enrichment, or review. The amount of technology use is up to the discretion of the teacher, and it is not required.Overall though, and most importantly, we all have the same instructional goals which are set by the Wichita Public Schools High School Algebra I Instructional Sequencing Pacing Guide and the Prentice Hall Algebra I textbook. We continually collaborate to make these goals obtainable for the students. Existing Curricula For mentioned, the instructional goals are set in the pacing guide and textbook for every teacher to refer to. However, “how” each specific teacher chooses to present the material is up to them. There in no one approach, strategy, theory, or philosophy that must be used when teaching Algebra I. Relevant Technology/Materials ConsiderationsThe technology provided at my school, listed in characteristics of the learning environment, is extremely beneficial to the teacher’s instruction. To discuss technology a little further in this section, it is used at our school but not crucial for the student to learn Algebra I. Students are not dependent on computers, software, and/or videos. Instead, teachers use the hardware to strengthen their instruction. If the students were required to use computers and software programs it would be imperative for the teachers to make sure the resources were available in the learning environment. “Developers should conduct surveys that indicate what hardware is available” if needed (Ragan & Smith, 2005, p. 50).Relevant Classroom/Physical CharacteristicsFortunately, I am at a brand new high school this year that has the best of the best facilities. The classrooms are of normal size with a plethora of technology. Smart boards and white boards are at the front of the class for notes and examples. In my class I like to incorporate several cooperative learning group activities. For the most part all of the activities can take place in my classroom, but if I ever need more space there is an open commons down the hall for students to spread out. Relevant District/System CharacteristicsThe school district I teach in makes their mission known. An abundance of training takes place at new teacher induction meetings, inservice meetings for all teachers, and optional workshops in order for teachers to be introduced to and further trained over the district’s learning goals. Each teacher reviews and keeps and instructional sequence guide at the beginning of each school year. This year the CCS are new to every teacher in the district. The pacing guide also states, “Throughout the year, it is expected that the Standards for Mathematical Practice will be embedded in daily instruction” (Wichita Public Schools, 2012, p. 5). Therefore, any new instructional design must abide by the district’s instructional sequence guide. Relevant Philosophical IssuesFortunately for mathematics, there aren’t a lot of touchy subjects a teacher can come across. You can almost say that all is fair game in math. The philosophy is simple: teach to the districts learning goals however you feel best gets the students there. Then again, this may not be the case in other content areas. But nonetheless, it is important and worth the time to consider any consequences that could arise.CHAPTER 2: LEARNER ANALYSISWhen designing instruction it is extremely critical to analyze the characteristics of the target audience. The knowledge gained from the learner analysis is important in designing effective and interesting lessons for the intended learners. In fact, without keeping the learners in mind even the most brilliant instruction will end up ineffective. The relevant learner characteristics that need to be analyzed are separated into four categories: cognitive, physiological, affective, and social. Smith and Tillman state “Depending upon the instructional task, some characteristics may be more critical than others” (2005, p. 69). Therefore I feel it is unnecessary and sometimes impossible to list every factor and I will focus on the most important factors for my specific audience. With keeping these characteristics in mind, I can plan effective instruction to meet my instructional goals.Cognitive Characteristics Even though my 80 students are all freshmen in Algebra I (except for the two sophomores and the two juniors) they still differ in many ways. For example, their prior knowledge coming in to high school varies drastically. I have students who barely squeaked by Pre-Algebra and students who excelled in Pre-Algebra. I also have students who took Algebra I as eighth graders and that are taking the course again because they failed it the first time or earned an A or a B and simply want to build their Algebra foundation. This causes problems when my high students are bored to death at the beginning of the year adding and subtracting real numbers while my low students still struggle. I have to plan to use my high students more as coaches for the low students. I tell my students if you can teach someone, then that shows me that you truly understand the material. The processing styles of my learners vary as well. I start each school year with a student survey that asks questions about how they prefer to learn and give them choices to choose from including: lecture, notes, video, hands-on, group work, etc. Additionally, I observe characteristics right away that tell me what category of learner the students fall under. Some students take awesome notes while some struggle. Some students are quick to volunteer to get up and use the technology while some students stay to themselves quietly. Some students love group work while others prefer to work independently. Some students need hands-on manipulatives while others students can perform a task after hearing it once. In result, I plan a variety of presentation methods and practice activities to make sure every student gets a chance to process the information the way they do best. One processing style that I had never heard of before is the “horizontal learner”. Smith and Tillman state “The horizontal learner is said to learn best when lying down (rather than sitting or standing, presumably)” (2005, p. 63). This now makes perfect sense why one of my students always asks if she can lay down while taking notes or working on practice problems. Physiological CharacteristicsThe students in my Algebra I come in to high school as 14-year-olds. Some turn 15 early in to the year while others will be 14 the entire year if not most of it. As previously mentioned, I have the two sophomores who are 15 turning 16 and the two juniors who are 16 turning 17. For the majority of my students, though, they are at the times in their lives when they are discovering who they are and molding who they will be as young adults. I have to keep this in mind knowing that life issues and emotions may try to interfere with my instructional goals. Making sure that learning continues throughout these interferences is just another part to teaching. The general health of my students is good. There of course will be the occasional cold or stomach flu, but nothing serious where the student will miss an abundance of school. Typically if a student has major health problems they are placed in a tiered Algebra class or have an Individual Education Plan (IEP). My classes are all regular Algebra I courses and I don’t see this often, if at all. Affective Characteristics Affective characteristics are extremely important to the design of my instruction. Being in a public school district, I believe that these characteristics, along with social characteristics, have the biggest effect on whether or not my students meet the set instructional goals. InterestsBefore any learning can take place a teacher must build a relationship with the students. On the same student survey I ask about learning styles I also ask about student interests. I read the surveys after the first day of school so that on the second day of school I can begin to ask individual students about their responses. For instance, I might have students who play sports and ask them how long they have been playing and when their next meet is. Or I may have students who like to sing and tell them that I would love to be able to sing and that I am jealous of their talent. Just these small questions and conversations help me to get to know students on a level other than math. Motivation and Motivation to LearnIt is surprising to see the diverse student motivation levels. Some students come to me ready to learn and all you have to do is tell them what, when, and where. The why and how are not even necessary. Only in a perfect world would this be possible with every student. Some students have no motivation and no motivation to learn whatsoever. I work to make my class fun and upbeat with music, games, videos and activities for students who lack the motivation to be there. Then I always make a point to make every student feel some sort of success with math to let them know how it feels to be successful and hopefully give them the desire to feel successful again. This is usually done when I get around individually to the less motivated students and work with them on a concept until they say something like, “Oh, that’s it?” or they can master the task without any assistance. Social CharacteristicsAnother important factor I like to take in to consideration when analyzing my student characteristics is the social characteristics. Social characteristics include aspects such as feelings toward authority, tendencies toward cooperation, socioeconomic level, race, ethnicity, etc. These characteristics can be very hard to overcome when they affect the learning process in a negative way. The biggest thing I can do at the beginning of the year to prevent any issues with these characteristics is to earn the students trust. I do this by being respectful to every student, and proving that I have a purpose and well thought out plan each and every class period. This relates closely to building relationships with the students and the affective characteristics. I have found that if I can earn a student’s trust, it does not matter the student’s socioeconomic level, race, beliefs or anything doing with social characteristics. Every student out there wants a role model; wants an adult figure they can go to when needed. When this happens, any walls that have been built from previous negative encounters with authority or school are broken down and the student is able to feel they have a fresh start and learning is obtainable. Design ImplicationsAfter conducting a learner analysis it is vital that I include some of the implications that these for mentioned characteristics have for the design of my instruction. I have mentioned some of the implications under each characteristic category throughout the learner analysis including: making sure each student experiences success with math, giving students a survey to learn about their learning styles and interests, and creating a structured environment with organized lesson plans. However, there are still more design implication that need to be addressed that were not mentioned previously. The pace of my instruction will be not too slow and not too fast. In other words, the pace will be just right. Because my Algebra I is a regular Algebra I class, the students are able to be pushed at some times. But because my students are freshmen at the level that sets the foundation for the rest of their math careers, I choose to go slow sometimes where the content is more important. In addition, it is crucial that I convince the students of the relevancy of the content I am presenting. With math, students continually ask, “Where will I use this in real life? And with technology advancing at a rapid pace, students feel that math is less imperative in their lives. To help this aspect I try to use word problems that relate to specific students’ interest to show them how it relates. I also show videos that show how the math is used in the real world. For instance, I show a video of how rational numbers come in to play when making doughnuts. Most, if not all, my students like doughnuts and enjoy watching this video. Since none of my students learn alike, I incorporate a variety of activities in my classroom to make sure each student gets to participate in an activity where they learn best. Sometimes students learn best in groups. I group students in pairs, groups of 3, 4, and 5 the most. Even the grouping of students takes thought and needs to have a purpose. Sometimes I may pair a high level with a low level student to allow for the low student to get extra help. Other times I may pair students with another student who is at the same level so that they are able to feed off of each other. When we do bigger group activities I may let them chose their own groups so that they are comfortable with each other. Or the next time I may randomly chose with sticks so that the students are working with students they may not be as comfortable with which keeps them a little more focused. Not to mention, this prepares them for the real world. Furthermore, within the groups, I sometimes have roles for each member of the group. I may have a leader, a presenter, an artist, a reporter, etc. This plays to the strengths of each student no matter the learning style. CHAPTER 3: LEARNING TASK ANALYSISAnother part to Instructional Design is the Learning Task Analysis. The learning Task Analysis includes six steps: Writing learning goals, determining types of learning, conducting an information-processing analysis, conducting a prerequisite analysis and determining the type of learning of the prerequisite, writing learning objectives, and writing test specifications. This chapter will take a close look at the first five steps, saving the writing of the test specifications for a later chapter. As I work through the instructional design process I am looking at the entire Algebra I course. However, for this learning task analysis I am going to focus on one unit in the course: Chapter 2’s Solving Equations. This allows me to go in to detail of what I want students to learn and how, specifically, I will design instruction to ensure objectives are met without having to do this for every lesson in every chapter. Learning Task AnalysisLearning Goals“Learning goals are statements of purpose or intention, what learners should be able to do at the conclusion of instruction” (Ragan & Smith, 2005, p. 77). In the mathematics course Algebra I, the students need to be able to solve equations after chapter 2. More specifically, when given an equation with one, two, or multiple steps, the students will be able to determine the order of solution steps and how to correctly implement the steps to solve the equation. With the implementation of the Common Core Standards (CCS), I also have the learning goal of the students will be able to explain the difference between the different steps in solving equations and devise examples of their own. For this learning task analysis I will just refer to Goal #1, solving equations. Types of LearningOnce a learning goal is written, it is necessary to identify the type of learning outcome the goal represents. This is important to help the designer to determine how to analyze the learning goal into its component parts, and later help provide clues as how to teach and assess student learning of the goal. Smith and Ragan discuss the task analysis systems of Bloom, Merrill, and Gagne but go in to more detail on Gagne’s types of learning outcomes (2005). Out of his five large categories, my learning outcome related to my learning goal is the domain intellectual skills. Being able to solve equations is an intellectual skill because the students learn how to respond to class of problems, and not just individual problems. Intellectual skills are also broken in to subcategories: discriminations, concepts, concrete concepts, defined concepts, principles, procedures, and problem solving. When solving equations, students must be able to select from a number of procedural rules and apply those rules in a unique sequence. Therefore, I will focus even more on the subcategory problem solving. Information Processing This step of the learning task analysis is where the designer decides what should be included and what should be left out. What need to be included are all the steps it takes to complete the process/task. Smith and Ragan suggest that I convert my goal into a representative “test” question to determine the information-processing steps (2005). Example Test Question: “Correctly solve the equation and show each step used to solve the equation 8(2x – 10) = -160”. Solution Steps: 8(2x) – 8(10) = -16016x – 80 = -160 + 80 + 8016x = -8016x = -8016 16x = -5 This analysis can also be represented graphically on the next page (see Figure 1.1). Figure 1.1 Information-Processing Analysis for Problem Solving Prerequisite AnalysisThe next step in decomposing the task is a prerequisite analysis. The prerequisite analysis will convert the goal and tasks into a hierarchy. I will describe directions to each step and then list the prerequisite skills needed to complete the step if it is needed to continue. Determine if the question is in fact an equation. If yes, then continue on to step 2. If no, then stop. Recognize what characteristics make an equation.Determine if any distribution on either side of the equal sign can be done. If yes, then complete the distribution to the appropriate group of terms and continue on to step 3. If no, continue on to step 3. Recall what situations allow for distribution.Recall how to distribute.Determine if any like terms can be combined on either side of the equation. If yes, then combine the terms and continue on to step 4. If no, continue on to step 4. Recall the definition of like terms and recognize if there are like terms on one side of the equation.Recall how to combine like terms.Determine if any term is added or subtracted to the variable term. If yes, then cancel the term from one side of the equation and incorporate to the other side by using the inverse operation of the term being canceled, then proceed to step 5. If no, then proceed to step 5.Identify which operation is connecting a number term to the variable term.Recognize what the inverse operation would be to cancel the number term. Determine if any term is being multiplied or divided to the variable term. If yes, then cancel the term from one side of the equation and incorporate to the other side by using the inverse operation of the term being canceled, then proceed to step 6. If no, then proceed to step 6. Identify which operation is connecting a number term to the variable term. Recognize what the inverse operation would be to cancel the number term. Determine if the variable is the only remaining term on one side of the equation. If yes, then the equation has been solved. If no, the return to step 2 and continue through the steps again. Recognize if the variable is isolated on its respective side of the equation.Attached is a graphic representation for the prerequisite tasks. See Figure 1.2 on the next page. Learning ObjectivesTo conclude the learning task analysis, learning objectives will be stated. In fact, each major step in the information processing analysis will have at least one terminal objective for the instruction. By the chapter 2 test of Algebra I students will be able to: Solve one step equations by adding, subtracting, multiplying, or dividing with 100% accuracy. (5 out of 5 problems on the chapter test or 12 out of 12 points possible).Solve two step equations with 78% accuracy (or 7 out of 9 points possible on 3 questions from the chapter test).Solve multi-step equations by combining like terms with 80% accuracy (4 out of 5 problems on the chapter test or 10 out of 12 points possible).Solve multi-step equations using the distributive property with 100% accuracy (4 out of 4 problems on the chapter test or 10 out of 10 points possible). Solve multi-step equations with variables on both sides with 80% accuracy (4 out of 5 problems on the chapter test or 11 out of 14 points possible).Solve equations containing fractions with 80% of accuracy (4 out of 5 problems on the chapter test or 9 out of 11 points possible). Identify equations that are identities or have no solution with 100% accuracy. CHAPTER 4: ASSESSMENT ANALYSISSection I: Performance ObjectivesThis section lists the learning objectives again, but takes them a step further by listing each objectives prerequisite skills as well. Based off of my information processing analysis the following objectives will be assessed, the listed prerequisite skills will need to be met, and by the chapter 2 test students will be able to:Solve one step equations by adding, subtracting, multiplying, or dividing with 100% accuracy. (5 out of 5 problems on the chapter test or 12 out of 12 points possible).Recognize what mathematical operation is connecting number to variable.Identify what inverse operation removes number from variable term.Solve two step equations with 78% accuracy (or 7 out of 9 points possible on 3 questions from the chapter test).Identify which number needs to be moved from same side of the equation as variable first, and preform inverse operation.Remove last number from variable using the inverse operation. Solve multi-step equations by combining like terms with 80% accuracy (4 out of 5 problems on the chapter test or 10 out of 12 points possible). Recall the definition of like terms and recognize if there are like terms on one side of the equation.Correctly combine like terms. Solve multi-step equations using the distributive property with 100% accuracy (4 out of 4 problems on the chapter test or 10 out of 10 points possible). Recall what situations allow for distribution and use the distributive property.Solve multi-step equations with variables on both sides with 80% accuracy (4 out of 5 problems on the chapter test or 11 out of 14 points possible).Identify variables on both sides of the equation. Correctly move variables to one side of the equation using inverse operations.Correctly move number terms to the opposite side of the equation using inverse operations. Solve equations containing fractions with 80% of accuracy (4 out of 5 problems on the chapter test or 9 out of 11 points possible). Recall the definition of least common denominator. Identify the least common denominator of all the fractions listed. Correctly simplify equation by multiplying the entire equation by the least common denominator. Identify equations that are identities or have no solution with 100% accuracy. Identify solution as either Identity or No Solution when the variable term disappears and the resulting statement is either true or false. Section II: Assessment ToolsListed below is the entry skills assessment/pretest used to determine what the students know prior to the instruction unit, chapter 2. In some cases, an instructor may give both an entry skills assessment and then a pretest, but in my case I will use the entry skills test in combination with the pretest. Pre/Post Assessment:Algebra I Chapter 2Name: _______________________Section 1: Multiple ChoiceIn this section there are ten multiple choice questions. Choose the best answer for each question. Each question is worth 2 points. (Total 20 points) ____1.14 = t + 7a.11b.7c.3d.21____2.a.b.–14c.40d.–40_____3.x = 27a.65b.13c.81d.72____4.11 = –d + 15a.11b.–4c.4d.6____5.a.–4b.–16c.15d.–5___6.37 – 18 + 8w = 67a.–6b.4c.7d.6_____ 7. a.18b.1.8c.–9d.9____8.3(y + 6) = 30a.5b.16c.4d.–16____9.a.–31b.c.–50d.–3____10.a.3b.0c.–9d.–10Section 2: Short AnswerIn this section there are ten short answer questions. Solve each equation and show all work. Partial credit will be given for correct work. Each question is worth 3 points. (Total 30 points)1. 1.2. 2.3.3.4. 4.5. 5.6. 6.7. 7.8. 8.9. 9.10. 10.Assessment/Objectives TableThe table uses the points indicated in the initial objective outline (1-7) to indicate terminal objectives and (1A, 1B, 2A, etc.) to indicate subordinate objectives. Test SectionsObjectives TestedSubordinate ObjectivesSection 1(20 points) 1, 2, 3, 4, 5, 61 A and B2 A and B3 A and B4 A5 A, B and CSection 2(30 points) 1, 3, 4, 5, 6, 71 A and B3 A and B4 A5 A, B and C6 A, B and C7 ACHAPTER 5: INSTRUCTIONAL STATEGY DEVELOPMENTThroughout the Instructional Design process I have focused on the Algebra I course. At times I focused more on Chapter 2 in Algebra I to show specific examples. For the Instructional Strategy Development, I am going to focus on one concept in Chapter 2, “Solving 1-step Equations”, which is covered in sections 2.1 and 2.2. Focusing on one concept allows me to break down each “event of instruction” in as much detail as possible (Ragan & Smith, 2005, p. 129). My procedure learning lesson’s events of instruction will consist of the learning task, review of learning task, introduction, body, conclusion, and assessments with all the events’ elements included.Learning TaskThe procedure for this lesson is to solve one-step equations. In the end, the objective for the lesson is for students to be able to solve one-step equations. Review of Learning Task Within this lesson I hope to do a few things. First, I want the students to know the importance of this chapter in Algebra I and catch their attention and arouse their interest. Next, I want to teach them “how” to solve a one-step equation and “why” it works. Last, I want to give the students an opportunity to practice and with immediate feedback give the students the confidence to continue and/or fix their mistakes. With all of this said and done, the learning objective should be obtainable. IntroductionDeploy Attention/Establish Purpose/Arouse Interest and MotivationJust like I tell me students at the beginning of the year, if you start class off on the right foot by being on time you typically have a good rest of the class, same goes for the start of a lesson. If you get the students from the beginning and “hook” them in, you typically have a good/successful rest of the lesson. Therefore, it is extremely important to activate attention, establish instructional purpose, and arouse interest. I activate attention by showing the students one of the hardest equations they will solve by the end of the chapter. For example, ?(4x – 12) + 10x = -5x + 31 incorporates 5 steps and is one of the more difficult equations of the chapter. I do this to intimidate them just a little bit (but in a good way). Then, I show them the type of equation they will solve today in sections 2.1/2.2: x – 8 = 2. I believe showing them the where they will be by the end of the chapter and then show them what they are starting with gives them a sense of confidence and a goal/purpose in mind. To establish instructional purpose even more, I explain to my students that solving equations is something they will use for the rest of their math career in Geometry, Algebra II, Pre- Calculus/Trigonometry, Calculus, etc. I try to arouse their interest as well by stressing the importance of this chapter and concept by stating that it is one of the three most important chapters in all of Algebra I, along with chapter 6 and 9. Last, I give the students a real world example of how they solve equations every day but now will be able to do it in a mathematically correct and easy way. For instance, you go shopping and have $100 to spend. You buy a shirt for $35, how much money do you have left to spend on other items? All students can relate to this because every student wears clothing and most students like to buy new clothing. Preview the LessonThe lesson will include the following explanations: What is an equationWhat is an inverse operationHow to apply an inverse operationHow to solve a one-step equation BodyRecall Prior KnowledgeAs we begin the lesson I tell the students they will need to be able to apply some concepts we learned in the previous chapter, chapter 1. For solving one-step equations, the students need to recall how to add integers and multiply integers. The good news for the students is that while they were learning these concepts in chapter 1 they were not allowed to use a calculator, and now that they are in chapter 2 they can use a calculator. Process InformationThe students then must learn when they are being asked to solve a one-step equation. When they see a variable with either a coefficient or a constant on one side of an equal sign, while the other side has number term, then they know to solve a one-step equation. Focus AttentionOnce the students know “when” they are to solve a one-step equation, they need to know “how”. This is when I tell them about inverse operations. Inverse operations “undo” the operation given in the equation. I ask the students questions like “How do we undo addition?” From this they learn what inverse operations are, and when to use them. Employ Learning StrategiesWith solving one-step equations the students need to get used to explaining their work and showing their work. We practice saying what inverse operation needs to happen, and that we do it to BOTH sides of the equation. Then, we show the work. For example, with x – 8 = 2, the students will practice saying, “ADD 8 to BOTH sides of the equation”. They then physically write “plus 8” underneath the numbers on both sides of the equation. This repetitive practice of saying, hearing, and seeing help them learn the procedure to solving one-step equations. PracticeTo practice a task as quick as solving one-step equations, we utilize boards, wipes, and markers (otherwise known as response boards). I give the students an equation to solve and on their boards, they write the equation, show the inverse operation, and then their final answers. They individually show me as soon as they are finished.Evaluate Feedback Once the boards are shown to me, I tell them whether they are correct or not. If they are not correct, I give them a hint to fix their answers. If after the hint they still don’t have it correct, I show them what needs to be fixed. After about 7 or 8 of these practice problems, they get used to the concept. ConclusionSummarizeTo summarize this section, I have the students “close” for the day in their spiral notebooks that are designated for this Algebra I class. The closing will ask the students “How do you know which mathematical operation (+, -, x, ÷) to use when solving an equation?” The students take time to reflect and answer the question in their spiral notebooks. They can either write it out in words or show an example. TransferStudents will eventually transfer the concept of solving one-step equations to word problems. They will have to read a real world scenario and then set-up the equation on their own. We may not necessarily do this on the same day we learn the concept but it will come sooner than later. Re-motivate At the end of the class period I take the time to reiterate how important solving one-step equations will be in math and that showing their work now will help them not only now, but in the future when the equations become tougher. It is extremely helpful to ensure the students can recall the task of the day when I recap what we did and re-state the learning task. AssessmentsAssess Performance/Evaluate Feedback Since this section is at the very beginning of the chapter I believe it is important to quiz the students on this concept and then test them at the end of the unit. The quiz allows for another opportunity to evaluate feedback. Students can either verify that they know how to solve-one step equations, or get help before the chapter 2 test. Once the chapter 2 test is taken, the students get the tests back to see comments or mistakes made on the assessment. ReferencesBellman, A. E., Bragg, S. C., & Handlin, W. G. (2004). Prentice Hall Mathematics Algebra 1. Upper Saddle River, NJ: Pearson Education, Inc.Smith, P. L. & Ragan, T. J. (2005). Instructional Design. Hoboken, NJ: John Wiley & Sons, Inc.Wichita Public Schools (2012). High School Algebra 1 Instructional Sequence Pacing Guide. Wichita, KS. ................
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