Table of Contents



Unit plan:Writing equations of linesinstructor’s manualThis page is left intentionally blankTable of Contents TOC \f \t "Heading 1,2,Heading 2,3,Heading 3,4,Heading 4,5,Heading 5,6,Heading 6,7,Title,1" Plan of Instruction Overview PAGEREF _Toc523004168 \h 7Intended Audience PAGEREF _Toc523004169 \h 7Length PAGEREF _Toc523004170 \h 7Instructional Goal PAGEREF _Toc523004171 \h 7Instructional Sequence PAGEREF _Toc523004172 \h 7Performance Objectives PAGEREF _Toc523004173 \h 8Delivery Approach PAGEREF _Toc523004174 \h 9Materials and Resources PAGEREF _Toc523004175 \h 10Materials Needed: PAGEREF _Toc523004176 \h 10Resources Needed: PAGEREF _Toc523004177 \h 12Individual Lesson Summary PAGEREF _Toc523004178 \h 13How Are Students Assessed? PAGEREF _Toc523004192 \h 15Homework Assignments PAGEREF _Toc523004193 \h 15Exit Tickets PAGEREF _Toc523004194 \h 15Class Participation and Teacher Observation PAGEREF _Toc523004195 \h 15Summative Assessments PAGEREF _Toc523004196 \h 15Lesson Plans PAGEREF _Toc523004197 \h 16Day 1 PAGEREF _Toc523004198 \h 17Intro to Writing Equations of Lines, Including When Given Two Points PAGEREF _Toc523004199 \h 17Day 2 PAGEREF _Toc523004200 \h 26Problem Trail PAGEREF _Toc523004201 \h 26Day 3 PAGEREF _Toc523004202 \h 29Write the Equation of a Line Parallel to a Given Line PAGEREF _Toc523004203 \h 29Day 4 PAGEREF _Toc523004204 \h 34Write the Equation of a Line Parallel to a Given Line (continued) PAGEREF _Toc523004205 \h 34Day 5 PAGEREF _Toc523004206 \h 38Practice Day: Group Work PAGEREF _Toc523004207 \h 38Day 6 PAGEREF _Toc523004208 \h 40Write the Equation of a Line Perpendicular to a Given Line PAGEREF _Toc523004209 \h 40Day 7 PAGEREF _Toc523004210 \h 45Write the Equation of a Line Perpendicular to a Given Line (continued) PAGEREF _Toc523004211 \h 45Day 8 PAGEREF _Toc523004212 \h 49Practice Circuit PAGEREF _Toc523004213 \h 49Day 9 PAGEREF _Toc523004214 \h 52Quiz PAGEREF _Toc523004215 \h 52Day 10 PAGEREF _Toc523004216 \h 54Write Equation of A Line: Advanced Problems PAGEREF _Toc523004217 \h 54Day 11 PAGEREF _Toc523004218 \h 59Practice Day: Group Work PAGEREF _Toc523004219 \h 59Day 12 PAGEREF _Toc523004220 \h 61Test Review PAGEREF _Toc523004221 \h 61Day 13 PAGEREF _Toc523004222 \h 64Unit Test PAGEREF _Toc523004223 \h 64References PAGEREF _Toc523004224 \h 66Appendix PAGEREF _Toc523004225 \h 67Appendix A PAGEREF _Toc523004226 \h 68Appendix B PAGEREF _Toc523004227 \h 69Appendix C PAGEREF _Toc523004228 \h 70Appendix D PAGEREF _Toc523004229 \h 71Appendix E PAGEREF _Toc523004230 \h 72Appendix F PAGEREF _Toc523004231 \h 73Appendix G PAGEREF _Toc523004232 \h 74Appendix H PAGEREF _Toc523004233 \h 75Appendix I PAGEREF _Toc523004234 \h 76Appendix J PAGEREF _Toc523004235 \h 78Appendix K PAGEREF _Toc523004236 \h 79Appendix L PAGEREF _Toc523004237 \h 79Appendix M PAGEREF _Toc523004238 \h 80Appendix N PAGEREF _Toc523004239 \h 80Appendix O PAGEREF _Toc523004240 \h 81Appendix P PAGEREF _Toc523004241 \h 81Appendix Q PAGEREF _Toc523004242 \h 81Appendix R PAGEREF _Toc523004243 \h 82Appendix S PAGEREF _Toc523004244 \h 83Appendix T PAGEREF _Toc523004245 \h 84Appendix U PAGEREF _Toc523004246 \h 85Appendix V PAGEREF _Toc523004247 \h 85Appendix W PAGEREF _Toc523004248 \h 86Appendix X PAGEREF _Toc523004249 \h 88Appendix Y PAGEREF _Toc523004250 \h 90Appendix Z PAGEREF _Toc523004251 \h 92Appendix AA PAGEREF _Toc523004252 \h 95Appendix BB PAGEREF _Toc523004253 \h 95Appendix CC PAGEREF _Toc523004254 \h 95Appendix DD PAGEREF _Toc523004255 \h 96Appendix EE PAGEREF _Toc523004256 \h 97Appendix FF PAGEREF _Toc523004257 \h 98Appendix GG PAGEREF _Toc523004258 \h 99Appendix HH PAGEREF _Toc523004259 \h 101Appendix II PAGEREF _Toc523004260 \h 101Appendix JJ PAGEREF _Toc523004261 \h 101Appendix KK PAGEREF _Toc523004262 \h 102Appendix LL PAGEREF _Toc523004263 \h 102Appendix MM PAGEREF _Toc523004264 \h 103Appendix NN PAGEREF _Toc523004265 \h 105Appendix OO PAGEREF _Toc523004266 \h 106Appendix PP PAGEREF _Toc523004267 \h 106Appendix QQ PAGEREF _Toc523004268 \h 106Appendix RR PAGEREF _Toc523004269 \h 107Appendix SS PAGEREF _Toc523004270 \h 108Appendix TT PAGEREF _Toc523004271 \h 110Appendix UU PAGEREF _Toc523004272 \h 112Appendix VV PAGEREF _Toc523004273 \h 114Appendix WW PAGEREF _Toc523004274 \h 114Appendix XX PAGEREF _Toc523004275 \h 115Appendix YY PAGEREF _Toc523004276 \h 115Appendix ZZ PAGEREF _Toc523004277 \h 115Appendix AAA PAGEREF _Toc523004278 \h 116Appendix BBB PAGEREF _Toc523004279 \h 120Plan of Instruction OverviewIntended AudienceThis unit of instruction is for high school Algebra 1 students at the college prep level. LengthThis unit is designed for thirteen forty-five-minute class meetings. This amount of time includes six traditional lessons, five practice days (circuits, group-work and test review), and two summative assessments (one quiz and one test). Instructional GoalThe students will be able to write the equation of a line in slope-intercept form given various parameters using prior learned concepts (slope formula, solving multi-step equations, solving literal equations, and the relationships of the slopes of parallel and perpendicular lines). Instructional SequenceThis unit builds on the idea that to write the equation of a line in slope-intercept form, a person needs the slope and the y-intercept. The unit begins with relatively simple problems (given slope and y-intercept or given two points), continues to work through parallel and perpendicular lines, and finally covers examples where the line being asked for is parallel or perpendicular to a given line with the same y-intercept as another line. These other lines could be in slope-intercept form, point-slope form or standard form, so knowledge about how to work with those types of equations is crucial, including solving literal equations.Performance Objectives When the slope is explicitly given, students will be able to substitute in to the slope-intercept form of a line 3 out of 3 times.Given two ordered pairs that lie on the line, students will be able to recall the slope formula from memory and use it to calculate the slope of the line 9 out of 10 times.Given an equation in standard form, students will be able to convert it to slope-intercept form 9 out of 10 times.Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that parallel lines have equal slopes 4 out of 5 times.Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that perpendicular lines have opposite reciprocal slopes 4 out of 5 times.Given an equation in point-slope form, students will be able to identify the slope, or convert the equation to slope-intercept form and then identify the slope 4 out of 5 times.When the y-intercept is explicitly given, students will be able to substitute in to the slope-intercept form of a line 3 out of 3 times.Given the equation of a line in slope-intercept, standard or point-slope form, students will be able to recognize y-intercept from slope-intercept form or convert standard form or point-slope form to slope-intercept form 4 out of 5 times.Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Delivery ApproachThe instructional strategies that are used in this unit are lectures, interactive lectures, and student-centered practice. These strategies are the most effective for the audience and content of this unit. Students need to take notes while the teacher presents the new information (lectures). Then students are ready for interactive lectures that involves their participation by way of answering questions, making predictions, and solving examples together as a class or individual. Finally, students are equipped with the skills to complete some independent/group work/stations on the content. This allows the teacher to check-in with all students and assist those who are still struggling with the topic.This unit has lessons and activities that are mainly in the cognitivism learning theory, while a few of the activities can be classified under the behaviorism learning theory. The problem trail, practice circuits, and group work satisfies the learning theory of cognitivism because it includes links to prior knowledge, explanations, summaries of the procedures, and modeling. These instructional strategies support the cognitivism learning theory because they are all ways to process and understand information for recall. This activity is also in the behaviorism category because the stations are only a few types of questions, so the students are repeating the same skill sets, the teacher is circulating and giving students corrective feedback when necessary and they are building fluency with the skills. (Ertmer, 1993)Materials and ResourcesMaterials Needed:Homework Assignments:Review Problems A-Day 1 and answer key (Due on Day 1)Homework-Day 1 and answer keyHomework-Day 2 and answer keyHomework-Day 3 and answer keyHomework-Day 4 and answer keyHomework-Day 5 and answer keyHomework-Day 6 and answer keyHomework-Day 7 and answer keyHomework-Day 8: Quiz Review and answer keyHomework-Day 10 and answer keyHomework-Day 11 and answer keyHomework-Day 12: Test Review and answer keyPowerPoint Presentations:PowerPoint about writing an equation of a line given 2 points or a point and slope: Presentation-Day 1PowerPoint about writing an equation of a line parallel to another line (given in various forms): Presentation-Day 3PowerPoint about writing an equation of a line parallel to another line (given in various forms): Presentation-Day 4PowerPoint about writing an equation of a line perpendicular to another line (given in various forms): Presentation-Day 6PowerPoint about writing an equation of a line perpendicular to another line (given in various forms): Presentation-Day 7PowerPoint about advanced examples of writing equations of lines: Presentation-Day 10PowerPoint: Test Review JeopardyAssessments:Copy of exit ticket: ExitTicket-Day 1 and key (Day 1) Copy of exit ticket: ExitTicket-Day 4 and key (Day 4) Copy of exit ticket: ExitTicket-Day 7 and key (Day 7) Copy of the quiz for each student and key (Day 9)Copy of exit ticket: ExitTicket-Day 10 and key (Day 10) Copy of the test for each student and key (Day 13)Miscellaneous:Review Problems B-Day 1 and answer keyTape to hang Problem Trail/Stations/Circuit problems around the roomProblem Trail (Stations) and answer key: Stations-Day 2Copies of group work problems-one for each student: Groupwork-Day 5 and one answer keyCircuit: Stations-Day 8 and answer keyCopies of group work problems-one for each student: Groupwork-Day 11 and one answer keyResources Needed:ProjectorComputer with access to Microsoft Office: PowerPointWhiteboard with markers and eraser (for teacher)Individual whiteboards with marker & eraser (paper towel works) for each studentComputer with access to internetWi-FiKhan Academy Video link: Academy Video link: to YouTube Video: to YouTube Video: student will need an internet enabled device to use the Desmos Scientific Calculator. Link: for each student during quiz/test review days and on the quiz/test. (Even though they have been able to use the Desmos Scientific Calculator during class, the temptation for the students to cheat is not worth the risk because they would be typing into their phone.)Ruler for each student. (To complete a couple of the extra credit questions on test.)Individual Lesson Summaryday 1Students are introduced to writing equations of lines in slope-intercept form. The types of problems covered in today’s lesson are when given the slope and the y-intercept and when given two points. There is a lecture where students will take notes, and then complete practice problems. At the end of class, there is an exit ticket for students to complete.day 2Practice Day. Students will complete a “Problem Trail” which is a self-checking circuit activity.Day 3Students will learn strategies about how to write equations of a line that is parallel to a given line (given in various forms) through a given point. There is a lecture where students will take notes, and then complete practice problems.Day 4Students will continue to practice strategies about how to write equations of a line that is parallel to a given line (given in various forms) through a given point. There is a lecture where students will take notes, and then complete practice problems. At the end of class, there is an exit ticket for students to complete.Day 5Practice Day. Students will work in small groups to practice writing equations of parallel and perpendicular lines.Day 6Students will learn strategies about how to write equations of a line that is perpendicular to a given line (given in various forms) through a given point. There is a lecture where students will take notes, and then complete practice problems.Day 7Students will continue to practice strategies about how to write equations of a line that is perpendicular to a given line (given in various forms) through a given point. There is a lecture where students will take notes, and then complete practice problems. At the end of class, there is an exit ticket for students to complete. At the end of class, there is an exit ticket for students to complete.Day 8Practice Day. Students will complete a which is a self-checking circuit activity.Day 9Summative Assessment-Quiz.Day 10Students will practice advanced examples of how to write equations of lines, incorporating parallel and perpendicular lines in addition to having the same y-intercept as another given line (in various forms). There is a lecture where students will take notes, and then complete practice problems. At the end of class, there is an exit ticket for students to complete.Day 11Practice Day. Students will practice advanced examples of writing equations of lines.Day 12Test Review Day. Students will review as a class by playing Jeopardy.day 13Summative Assessment-Unit Test.How Are Students Assessed?Homework AssignmentsStudents will complete nightly homework assignments to cement what is being learned in class. The beginning of class the next day is always focused on reviewing the homework, going over the correct answers and allowing students to ask questions about specific problems/issues they encountered when independently practicing the skills.Exit TicketsAt the end of class on days 1, 4, 8, and 10 students will complete a short formative assessment in the form of an exit ticket for the teacher to asses how the students are doing with the current material.Class Participation and Teacher ObservationEach day, students are assessed through class participation when solving examples or working through circuits or groups work.Summative AssessmentsThis unit includes two summative assessments. The first is a quiz on day 9 and the second is the unit test on day 13.Lesson PlansDay 1Intro to Writing Equations of Lines, Including When Given Two PointsPerformance Objectives: When the slope is explicitly given, students will be able to substitute in to the slope-intercept form of a line 3 out of 3 times.Given two ordered pairs that lie on the line, students will be able to recall the slope formula from memory and use it to calculate the slope of the line 9 out of 10 times. Given an equation in point-slope form, students will be able to identify the slope, or convert the equation to slope-intercept form and then identify the slope 4 out of 5 times.When the y-intercept is explicitly given, students will be able to substitute in to the slope-intercept form of a line3 out of 3 times.Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources and Materials NeededMaterials:Extra copies of the homework due today: Review Problems A-Day 1 (See Appendix A)Answers for the homework due today: Review Problems A-Day 1 (See Appendix B)Copies of review problems: Review Problems B-Day 1 (See Appendix C)Answers for the review problems: Review Problems B-Day 1 (See Appendix D)PowerPoint about writing an equation of a line given 2 points or a point and slope: Presentation-Day 1 (See Appendix E)Exit Ticket: ExitTicket-Day 1 (See Appendix F)Exit Ticket: ExitTicket-Day 1 KEY (See Appendix G)Copies of tonight’s homework assignment: Homework-Day 1 (See Appendix H)Resources: ProjectorComputer with access to Microsoft Office: PowerPointComputer with access to internetKhan Academy Video link: with markers and eraserTime: 45 minutes. Step 1: Pre-Instructional Activities: Check students’ homework (review of calculating slope, and identifying slope from point-slope form, and solving multi-step equations with the variable on one side) and project answers on the board, answer student questions about the homework. Hand-out review problems (more of the same types of problems from the homework with a “push” question at the end, as a preview to what the students will be learning about during the lesson) and have students complete independently. Go over those solutions and answer any questions. The handed-out problems include problems that the slope and the y-intercept are given, and all the student must do it substitute it in to the general form. Step 2: Content Presentation: Students take notes while teacher presents the PowerPoint which includes both the step-by-step procedure how to write the equation of a line (in slope-intercept form) given two points that lie on the line and examples in the pattern of “I do, We do, You do.” The steps are as follows:1) Use the slope formula and the two given points to calculate the slope of the line that passes through them.2) Substitute that slope and one of the ordered pairs into slope intercept form.3) Solve the resulting equation for the y-intercept.4) Write the equation of the line with the slope and y-intercept that you found.Alternatively:1) Use the slope formula and the two given points to calculate the slope of the line that passes through them.2) Substitute that slope and one of the ordered pairs into point-slope form.3) Transform the equation from point-slope form to slope-intercept form. (Solve the resulting equation for the y.)Answers for the problems in the presentation:38624564165600017445938665900Find the slope: Use the slope formula.1.2. Write the equation of a line with the given information: Simply substitute.1. y = 3x – 12. y = 12x + 2Show students both ways; substituting into slope-intercept form and solving for the y intercept and substituting into point-slope form and converting to slope-intercept form; using same set of points so they can see that no matter which method they chose, their final equation in slope-intercept form would be the same.Write the equation of a line given two points.246490-135172003. 24649062948004. 246490176668005. 3426929189920right23854006. After showing the students how to do the problem and doing a few together, examples 1 through 6, show them the video from Khan Academy: Slope-intercept equation from two solutions example. (Academy, 2011) This video is an example of how to write the equation of a line in slope intercept form when given two points. The presenter in the video does a nice job of briefly reviewing a prerequisite skill (slope formula, operations with signed numbers and operations with fractions) before immediately applying the skill within the problem. After the problem is introduced, pause the video and have the students try the problem. After giving them a few minutes to complete it, play the video. At the end of the video, take a poll of the students via the thumbs up/middle/down method. Continue to work through more examples together, at first telling the students which method to use. This is to be sure they are familiar with both ways because they will need flexibility in the future in this unit.As the lesson progresses, allow the students to choose which method they like best. 2941980007.198782-39757008. 198783-95416009. Step 3: Learner Participation: Learners will take notes and then complete examples throughout the presentation. The last few examples, learners may volunteer to write their answers on the board. Step 4: Assessment: Review problems at beginning of class, working examples during the main presentation of content, and tonight’s independent practice (homework assignment). In addition to questions about this content on summative assessments. At the end of the lesson students will complete the Exit Ticket-Day 1: Writing Equations of Lines- Introduction.Step 5: Follow-Through Activities: Problem Trail Activity in the next lesson, as well as including this type of problem as future “Do-Nows” so learners continue to practice. (This lesson is modified from the lesson Writing the Equation of Line Given Two Points by Sarah Weaver from 2012.) (Weaver, 2012)Day 2Problem TrailPerformance Objectives: When the slope is explicitly given, students will be able to substitute in to the slope-intercept form of a line 3 out of 3 times.Given two ordered pairs that lie on the line, students will be able to recall the slope formula from memory and use it to calculate the slope of the line 9 out of 10 times. Given an equation in point-slope form, students will be able to identify the slope, or convert the equation to slope-intercept form and then identify the slope 4 out of 5 times.When the y-intercept is explicitly given, students will be able to substitute in to the slope-intercept form of a line3 out of 3 times.Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources or Materials Needed:Materials: Answers for Homework-Day 1 (Due today) (See Appendix I)Do-Now Video: Presentation-Day 2 (See Appendix J)Problem Trail (Stations) and answer key. Stations-Day 2 (See Appendix K and L)Copies of tonight’s homework: Homework-Day 2 (See Appendix M)Resources: ProjectorComputer with access to internetKhan Academy Video link: with markers and eraserTime: 45 minutes Step 1: Pre-Instructional Activities: Check students’ homework and project answers on the board, answer student questions about the homework. Use the video from Khan Academy: slope intercept from a slope and a point as the “Do-Now.” (Academy, 2011) This video is an example of how to write the equation of a line in slope intercept form when given the slope and a point. At the very beginning of the video, the problem is clearly stated. Allow the students a few minutes to complete the problem. Then play the video and gather feedback from the students about how many completed the problem successfully. Step 2: Content Presentation: n/a. Step 3: Learner Participation: Students will be completing a Problem Trail (station) Activity with assigned partners. Pair or make small heterogeneous groups containing students who are at different levels with the content based on the Exit Ticket from Day 1.Step 4: Assessment: Feedback from students about their success completing the problem from the Khan Academy video. Teacher will circulate amongst the groups and observe how they students are doing. Step 5: Follow-Through Activities: These types of problems will be included as future “Do-Nows” so learners continue to practice. The skills practiced here will continue to be used when learning how to write equations of lines parallel or perpendicular to a given line throughout the remainder of the unit.(The Problem Trail is modified from the lesson Writing the Equation of Line Given Two Points by Sarah Weaver from 2012.) (Weaver, 2012)Day 3Write the Equation of a Line Parallel to a Given LinePerformance Objectives: Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that parallel lines have equal slopes 4 out of 5 times. Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources or Materials Needed: Materials:Answers for the homework due today: Homework-Day 2 (See Appendix N)PowerPoint about writing an equation of a line parallel to another line (given in various forms): Presentation-Day 3 (See Appendix O)Copies of tonight’s homework assignment: Homework-Day 3 (See Appendix P)Resources: ProjectorComputer with access to Microsoft Office: PowerPointWhiteboard with markers and eraserWi-FiEach student will need an internet enabled device to use the Desmos Scientific Calculator. Link: : 45 minutes. Step 1: Pre-Instructional Activities: Students will complete a couple of review problems and then there will be one problem as a preview of today’s lesson. Step 2: Content Presentation: Students take notes while teacher presents the PowerPoint which includes both the step-by-step procedure how to write the equation of a line (in slope-intercept form) parallel to another line (given in various forms) and examples in the pattern of “I do, We do, You do.” The steps are as follows:1) Get slope. Parallel Lines have equal slopes (same number).a. If the line given is in slope-intercept form or point slope form, identify the slope from the equation.b. If line given is in standard form, convert it to slope-intercept form and identify the slope.2) Find the y-intercept. Now that you have the slope of the new line, you need to calculate the exact y-intercept that fits within the specific parameters given.a. If you are given a point that the parallel line passes through, substitute the ordered pair and the slope in to the appropriate places in slope-intercept form and solve for “b” (the y-intercept).b. If you are given another line and are told that the new line has the same y-intercept as it then:i. If in slope-intercept form, simply identify the y-intercept.ii. If in point-slope or standard form, convert to slope-intercept form and then identify the y-intercept.3) Write the equation of your parallel line in slope-intercept form, making sure you are using the slope and y-intercept that you found during these steps.Now it’s time to see these steps in action by working through examples in the presentation together. While the teacher is solving the examples “I do” examples, the teacher should show the students the online scientific calculator from Desmos, which can be found at scientific. (Inc., 2018) The teacher should also explain that this is a tool that can be used during class but isn’t always necessary to use and that on a quiz/test the students will be given a calculator to prevent suspicion of cheating. Most students will be using the Desmos Scientific Calculator on their cell phones, so on a quiz or test they will be typing numbers into their calculator, but that also looks like they could be texting someone for help or asking the internet. There are a variety of types problems students may encounter. As the teacher continues, gauge how the students are doing. If they seem to be understanding, allow them to work through the examples (one at a time) independently, compare their answer with a neighbor, and make any corrections necessary before the teacher models the correct answer on the board (including all supporting work in an organized fashion.)Worked out answers to problems in the PowerPoint Presentation:Do Now3904091-581444000020000240527795240000200001. 2. Examples:5661329848414000020000389613984841400002000020196313713440000200001669781328040000200001. 2. 3. 4. Step 3: Learner Participation: Learners will take notes and then complete examples throughout the presentation. During the middle examples “we do” (if instructor deems appropriate), the students may work on the problems (one at a time) and compare answers with a neighbor. The last few examples, learners may volunteer to write their answers on the board. Step 4: Assessment: Also, review problems at beginning of class, working examples during the main presentation of content, and tonight’s independent practice (homework assignment). In addition to questions about this content on summative assessments. Step 5: Follow-Through Activities: The next two classes will focus on practicing these skills in either whole class practice, independent practice, partner practice, or stations. In addition to including these types of problems as future “Do-Nows” so learners continue to practice. Day 4Write the Equation of a Line Parallel to a Given Line (continued)Performance Objectives: Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that parallel lines have equal slopes 4 out of 5 times. Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources or Materials Needed Materials:Answers for the homework due today: Homework-Day 3 (See Appendix Q)PowerPoint about writing an equation of a line parallel to another line (given in various forms): Presentation-Day 4 (See Appendix R)Copies of exit ticket: ExitTicket-Day 4 (See Appendix S)Key for exit ticket: ExitTicket-Day 4 KEY (See Appendix T)Copies of tonight’s homework assignment: Homework-Day 4 (See Appendix U)Resources: ProjectorComputer with access to Microsoft Office: PowerPointComputer with access to the internetWhiteboard with markers and eraser (for teacher)Individual whiteboard with marker & eraser (paper towel works) for each studentLink to YouTube Video: student will need an internet enabled device to use the Desmos Scientific Calculator. Link: : 45 minutes. Step 1: Pre-Instructional Activities: As students come in, direct them to get a whiteboard, marker and eraser for later in the lesson, this direction could be projected on the board as students come in or the teacher could put the appropriate supplies out on student desks. Review the previous night’s homework by projecting the answers and address any questions the students may have. Step 2: Content Presentation: The YouTube video: Find the equation of a line parallel using slope intercept is a 3-minute single example video. This is going to be the first practice problem for the day. Watch the first 15 seconds or so when the presenter (visible on screen) reads the problem. (McLogan, 2011) Then pause the video and allow students to work out the problem on their own. Give the students a 2-3 minutes to work it out on either the little whiteboard or in their notebook. Instruct students that their final answer must be written on the whiteboard. Once time is up, or most students finish the problem, have them compare their final equation with a neighbor. If there are differences, have them try to find mistakes and work collaboratively to decide which answer is correct. Allow a few minutes for this to happen. Then, have one of the neighbors write their equation from their whiteboard on the whiteboard in the front of the classroom. Finally, tell the students that we are going to watch the video to watch the answer be worked out. Play the video.The PowerPoint presentation has examples of problems to work through. Remind students that they can use their Desmos Scientific Calculator as a tool to help them! Scattered in between the parallel to a given line type questions there are review questions to make sure the students are paying attention, reading/listening to directions. Students will be working the problems in their notebook, and then just like with the video, they will write their final answer on their whiteboard. As the instructor seems appropriate, and time allows, have students compare their answers with a neighbor and analyze each other’s work if they have different answers. Students will take turns writing their answer and all supporting work on the whiteboard at the front of the classroom.Answers to examples in the PowerPoint presentation.5692443859464000020000386433485476400002000020434858547640000200001987825367140000200001. 2.3.4.386433485476400002000020434858547640000200001987825367140000200005. 6.7.Step 3: Learner Participation: Students will be completing problems independently. Students will also come to board to write their answer to the problem (with all supporting work). Occasionally students may also compare their answers and possibly engage in peer error analysis.Step 4: Assessment: Students will complete an Exit Ticket -Day 4 at the end of the class. Also, review problems at beginning of class, working examples during the main presentation of content, and tonight’s independent practice (homework assignment). In addition to questions about this content on summative assessments. Step 5: Follow-Through Activities: The next class, students will be completing a practice problem activity. Day 5Practice Day: Group WorkPerformance Objectives: Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that parallel lines have equal slopes 4 out of 5 times. Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources or Materials NeededMaterials:Answers for the homework due today: Homework-Day 4 (See Appendix V)Group work problems-one for each student: GroupWork-Day5 (See Appendix W)Key for group work problems: GroupWork-Day5 KEY (See Appendix X)Copies of tonight’s homework: Homework-Day 5 (See Appendix Y)Resources: ProjectorComputerWi-FiEach student will need an internet enabled device to use the Desmos Scientific Calculator. Link: : 45 minutes Step 1: Pre-Instructional Activities: Check students’ homework and project answers on the board, answer student questions about the homework. Step 2: Content Presentation: n/a. Step 3: Learner Participation: Students will be completing problems in assigned small groups. Groups should have 3 or 4 students at varying levels (heterogeneous groups). Each student is responsible for completing all the problems. Remind students that they can use their Desmos Scientific Calculator as a tool to help them!Each student in the group will become the ‘expert’ on two problems, by working out the answer. After all students have become the ‘experts,’ they then will explain their answers and the process to the others in the group.Step 4: Assessment: Teacher will circulate throughout the groups. Formative assessment through teacher observation. Step 5: Follow-Through Activities: These types of problems will be included as future “Do-Nows” so learners continue to practice. The skills practiced here will continue to be used when learning how to write equations of lines parallel or perpendicular to a given line throughout the remainder of the unit.Day 6Write the Equation of a Line Perpendicular to a Given LinePerformance Objectives: Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that perpendicular lines have opposite reciprocal slopes 4 out of 5 times.Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources or Materials Needed Materials: Answers for the homework due today: Homework-Day 5 (See Appendix Z)PowerPoint about writing an equation of a line perpendicular to another line (given in various forms): Presentation-Day 6 (See Appendix AA)Copies of tonight’s homework assignment: Homework-Day 6 (See Appendix BB)Resources:ProjectorComputer with access to Microsoft Office: PowerPointWhiteboard with markers and eraserWi-FiEach student will need an internet enabled device to use the Desmos Scientific Calculator. Link: : 45 minutes.Step 1: Pre-Instructional Activities: Students will complete a couple of review problems and then there will be one problem as a preview of today’s lesson. Step 2: Content Presentation: Students take notes while teacher presents the PowerPoint which includes both the step-by-step procedure how to write the equation of a line (in slope-intercept form) perpendicular to another line (given in various forms) and examples in the pattern of “I do, We do, You do.” The steps are as follows (they are almost identical to the parallel to… steps):1) Get slope. Perpendicular Lines have slopes that are opposite reciprocals. (Change the sign, switch numerator and denominator).a. If the line given is in slope-intercept form or point slope form, identify the slope from the equation. Then take the opposite reciprocal.b. If line given is in standard form, convert it to slope-intercept form and identify the slope. Then take the opposite reciprocal.2) Find the y-intercept. Now that you have the slope of the new line, you need to calculate the exact y-intercept that fits within the specific parameters given.a. If you are given a point that the parallel line passes through, substitute the ordered pair and the slope in to the appropriate places in slope-intercept form and solve for “b” (the y-intercept).b. If you are given another line and are told that the new line has the same y-intercept as it then:i. If in slope-intercept form, simply identify the y-intercept.ii. If in point-slope or standard form, convert to slope-intercept form and then identify the y-intercept.3) Write the equation of your perpendicular line in slope-intercept form, making sure you are using the slope and y-intercept that you found during these steps.Now it’s time to see these steps in action by working through examples in the presentation together. There are a few of each “type” of scenario, so students can see how to solve. As the teacher continues, gauge how the students are doing. Remind students that they can use their Desmos Scientific Calculator as a tool to help them!If they seem to be understanding, allow them to work through the examples (one at a time) independently, compare their answer with a neighbor, and make any corrections necessary before the teacher models the correct answer on the board (including all supporting work in an organized fashion.)Answers to examples in the PowerPoint presentation:386433486802400000569244385946400002000020434858547640000200001987825367140000200001. 2.3.4.5653378854774000020000386433485476400002000020434858547640000200001987825367140000200005. 6.7.8. 21782438509040000200001982868509040000200009. 10. Step 3: Learner Participation: Learners will take notes and then complete examples throughout the presentation. During the middle examples “we do” (if instructor deems appropriate), the students may work on the problems (one at a time) and compare answers with a neighbor. The last few examples, learners may volunteer to write their answers on the board. Step 4: Assessment: Review problems at beginning of class, working examples during the main presentation of content, and tonight’s independent practice (homework assignment). In addition to questions about this content on summative assessments. Step 5: Follow-Through Activities: The next two classes will focus on practicing these skills in either whole class practice, independent practice, partner practice, or stations. In addition to including these types of problems as future “Do-Nows” so learners continue to practice.Day 7Write the Equation of a Line Perpendicular to a Given Line (continued)Performance Objectives: Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that perpendicular lines have opposite reciprocal slopes 4 out of 5 times.Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources or Materials Needed Materials: Answers for the homework due today: Homework-Day 6 (See Appendix CC)PowerPoint about writing an equation of a line perpendicular to another line (given in various forms): Presentation-Day7 (See Appendix DD)Copies of exit ticket: ExitTicket-Day7 (See Appendix EE)Key for exit ticket: ExitTicket-Day7 KEY (See Appendix FF)Copies of tonight’s homework assignment: Homework-Day 7 (See Appendix GG)Resources: ProjectorComputer with access to Microsoft Office: PowerPointComputer with access to the internetWhiteboard with markers and eraser (for teacher)Individual whiteboard with marker & eraser (paper towel works) for each studentWi-FiEach student will need an internet enabled device to use the Desmos Scientific Calculator. Link: to YouTube Video: : 45 minutes. Step 1: Pre-Instructional Activities: As students come in, direct them to get a whiteboard, marker and eraser for later in the lesson, this direction could be projected on the board as students come in or the teacher could put the appropriate supplies out on student desks. Review the previous night’s homework by projecting the answers and address any questions the students may have. Step 2: Content Presentation: The YouTube video: Find the equation of a line perpendicular to a line through a given point is a 5-minute single example video. This is going to be the first practice problem for the day. The video begins with only a point and the equation of a line. There are no directions about what to do with that information. (McLogan, 2012) Write the directions “Write the equation of the line perpendicular through the given line and passing through the given point” on the board, also read these directions aloud. Instruct the students to complete the problem independently. Give the students a 2-3 minutes to work it out on either the little whiteboard or in their notebook. Instruct students that their final answer must be written on the whiteboard. Once time is up, or most students finish the problem, have them compare their final equation with a neighbor. If there are differences, have them try to find mistakes and work collaboratively to decide which answer is correct. Allow a few minutes for this to happen. Then, have one of the neighbors write their equation from their whiteboard on the whiteboard in the front of the classroom. Finally, tell the students that we are going to watch the video to watch the answer be worked out. Play the video.The PowerPoint presentation has examples of problems to work through. Remind students that they can use their Desmos Scientific Calculator as a tool to help them! Scattered in between the perpendicular to a given line type questions (focus topic) there are review questions to make sure the students are paying attention, reading/listening to directions. Students will be working the problems in their notebook, and then just like with the video, they will write their final answer on their whiteboard. As the instructor seems appropriate, and time allows, have students compare their answers with a neighbor and analyze each other’s work if they have different answers. Students will take turns writing their answer and all supporting work on the whiteboard at the front of the classroom.Answers to examples in the PowerPoint presentation.386433486802400000569244385946400002000020434858547640000200001987825367140000200001. 2.3.4.386433485476400002000020434858547640000200001987825367140000200005. 6.7. Step 3: Learner Participation: Students will be completing problems independently. Students will also come to board to write their answer to the problem (with all supporting work). Occasionally students may also compare their answers and possibly engage in peer error analysis.Step 4: Assessment: Student feedback about how successful they were when solving the problem from the video. Students will complete an Exit Ticket-Day 7at the end of the class. Also, review problems at beginning of class, working examples during the main presentation of content, and tonight’s independent practice (homework assignment). In addition to questions about this content on summative assessments. Step 5: Follow-Through Activities: The next class, students will be completing a practice problem activity.Day 8Practice CircuitPerformance Objectives:When the slope is explicitly given, students will be able to substitute in to the slope-intercept form of a line 3 out of 3 times.Given two ordered pairs that lie on the line, students will be able to recall the slope formula from memory and use it to calculate the slope of the line 9 out of 10 times. Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that parallel lines have equal slopes 4 out of 5 times. Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that perpendicular lines have opposite reciprocal slopes 4 out of 5 times.Given an equation in point-slope form, students will be able to identify the slope, or convert the equation to slope-intercept form and then identify the slope 4 out of 5 times.When the y-intercept is explicitly given, students will be able to substitute in to the slope-intercept form of a line 3 out of 3 times.Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources or Materials Needed Materials:Answers for the homework due today: Homework-Day 7 (See Appendix HH)Circuit and answer key: Stations-Day 8 (See Appendices II and JJ)Tape to hang circuit problems around the roomCopies of tonight’s homework: Homework-Day 8: Quiz Review (See Appendix KK)Key for tonight’s homework: Homework-Day 8: Quiz Review KEY (See Appendix LL)Resources: ProjectorComputerCalculator for each studentTime: 45 minutes Step 1: Pre-Instructional Activities: Check students’ homework and project answers on the board, answer student questions about the homework. Step 2: Content Presentation: n/a. Step 3: Learner Participation: Students will be completing a circuit (self-checking stations) with assigned partners. Pair or make small heterogeneous groups containing students who are at different levels with the content based on the Exit Ticket from Day 7. Students can use a regular calculator for this lesson, as it is the day before a quiz/test. To successfully use their tools, a student has to be familiar with how to operate it. Remind students that they can use their calculator as a tool to help them!Step 4: Assessment: Teacher will circulate throughout the groups. Formative assessment through teacher observation. Step 5: Follow-Through Activities: These types of problems will be included as future “Do-Nows” so learners continue to practice. The skills practiced here will continue to be used when learning how to write equations of lines parallel or perpendicular to a given line throughout the remainder of the unit. Day 9QuizPerformance Objectives Covered on Quiz: When the slope is explicitly given, students will be able to substitute in to the slope-intercept form of a line 3 out of 3 times.Given two ordered pairs that lie on the line, students will be able to recall the slope formula from memory and use it to calculate the slope of the line 9 out of 10 times. Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that parallel lines have equal slopes 4 out of 5 times. Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that perpendicular lines have opposite reciprocal slopes 4 out of 5 times.Given an equation in point-slope form, students will be able to identify the slope, or convert the equation to slope-intercept form and then identify the slope 4 out of 5 times.When the y-intercept is explicitly given, students will be able to substitute in to the slope-intercept form of a line3 out of 3 times.Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources or Materials NeededMaterials:Copy of the quiz for each student. (See Appendix MM)Quiz answer key (See Appendix NN)Resources:Calculator for each student. (Even though they have been able to use the Desmos Scientific Calculator during class, the temptation for the students to cheat is not worth the risk because they would be typing into their phone.)Time: 45 minutes Step 1: Pre-Instructional Activities: Take attendance and have students turn in Homework-Day 8: Quiz Review to ensure maximum time is spent on taking the quiz. Step 2: Content Presentation: n/a. Step 3: Learner Participation: Each student takes the quiz independently.Step 4: Assessment: Quiz and the answer key. Step 5: Follow-Through Activities: Go over the answers to the quiz the following class. Day 10Write Equation of A Line: Advanced ProblemsPerformance Objectives: Given an equation in standard form, students will be able to convert it to slope-intercept form 9 out of 10 times.Given an equation in point-slope form, students will be able to identify the slope, or convert the equation to slope-intercept form and then identify the slope 4 out of 5 times.Given the equation of a line in slope-intercept, standard or point-slope form, students will be able to recognize y-intercept from slope-intercept form or convert standard form or point-slope form to slope-intercept form 4 out of 5 times.Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Materials and Resources NeededMaterials: PowerPoint about advanced examples of writing equations of lines: Presentation-Day10 (See Appendix OO)Copies of exit ticket: ExitTicket-Day10 (See Appendix PP)Key for exit ticket: ExitTicket-Day10 KEY (See Appendix QQ)Copies of tonight’s homework assignment: Homework-Day 10 (See Appendix RR)Resources: ProjectorComputer with access to Microsoft Office: PowerPointWhiteboard with markers and eraser (for teacher)Individual whiteboard with marker & eraser (paper towel works) for each studentWi-FiEach student will need an internet enabled device to use the Desmos Scientific Calculator. Link: : 45 minutes. Step 1: Pre-Instructional Activities: As students come in, direct them to get a whiteboard, marker and eraser for later in the lesson, this direction could be projected on the board as students come in or the teacher could put the appropriate supplies out on student desks. Review the previous night’s homework by projecting the answers and address any questions the students may have. Step 2: Content Presentation: The PowerPoint presentation has general instructions about how to go about solving the more complex examples. There are three basic steps, and within each step could be a variety of scenarios, so only the basics are listed.1) Find the slope.2) Find the y-intercept.3) Substitute into slope-intercept form.The presentation continues with several examples of advanced problems to work through. Remind students that they can use their Desmos Scientific Calculator as a tool to help them! Students will be working the problems in their notebook, they will write their final answer on their whiteboard. As the instructor seems appropriate, and time allows, have students compare their answers with a neighbor and analyze each other’s work if they have different answers. Students will take turns writing their answer and all supporting work on the whiteboard at the front of the classroom.213995429895020000Answers to examples in the PowerPoint presentation.1. 211009844550200002.26590419894003.2729551053150200004.255109527050200005. 184245-3002510200006.Step 3: Learner Participation: Students will be completing problems independently. Students will also come to board to write their answer to the problem (with all supporting work). Occasionally students may also compare their answers and possibly engage in peer error analysis.Step 4: Assessment: At the end of class students will complete an Exit Ticket-Day 10: Fluency Check. This Fluency Check is used with written permission from the author. Also, review problems at beginning of class, working examples during the main presentation of content, and tonight’s independent practice (homework assignment). In addition to questions about this content on summative assessments. Step 5: Follow-Through Activities: The next class, students will be completing a practice problem activity. Day 11Practice Day: Group WorkPerformance Objectives: Given an equation in standard form, students will be able to convert it to slope-intercept form 9 out of 10 times.Given an equation in point-slope form, students will be able to identify the slope, or convert the equation to slope-intercept form and then identify the slope 4 out of 5 times.Given the equation of a line in slope-intercept, standard or point-slope form, students will be able to recognize y-intercept from slope-intercept form or convert standard form or point-slope form to slope-intercept form 4 out of 5 times.Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources or Materials Needed Materials:Answers for the homework due today: Homework-Day 10 (See Appendix SS)Group work problems-one for each student: GroupWork-Day 11 (See Appendix TT)Key for group work problems: GroupWork-Day 11 KEY (See Appendix UU)Copies of tonight’s homework: Homework-Day 11 (See Appendix VV)Resources: ProjectorComputerWi-FiEach student will need an internet enabled device to use the Desmos Scientific Calculator. Link: : 45 minutes Step 1: Pre-Instructional Activities: Check students’ homework and project answers on the board, answer student questions about the homework. Step 2: Content Presentation: n/a. Step 3: Learner Participation: Students will be completing problems in assigned small groups. Groups should have 3 or 4 students at varying levels (heterogeneous groups). Each student is responsible for completing all the problems. Remind students that they can use their Desmos Scientific Calculator as a tool to help them!Each student in the group will become the ‘expert’ on two problems, by working out the answer. After all students have become the ‘experts,’ they then will explain their answers and the process to the others in the group.Step 4: Assessment: Formative assessment through teacher observation. Step 5: Follow-Through Activities: These types of problems will be included as future “Do-Nows” so learners continue to practice. The skills practiced here will continue to be used when learning how to write equations of lines parallel or perpendicular to a given line throughout the remainder of the unit.Day 12Test ReviewPerformance Objectives:When the slope is explicitly given, students will be able to substitute in to the slope-intercept form of a line 3 out of 3 times.Given two ordered pairs that lie on the line, students will be able to recall the slope formula from memory and use it to calculate the slope of the line 9 out of 10 times.Given an equation in standard form, students will be able to convert it to slope-intercept form 9 out of 10 times.Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that parallel lines have equal slopes 4 out of 5 times.Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that perpendicular lines have opposite reciprocal slopes 4 out of 5 times.Given an equation in point-slope form, students will be able to identify the slope, or convert the equation to slope-intercept form and then identify the slope 4 out of 5 times.When the y-intercept is explicitly given, students will be able to substitute in to the slope-intercept form of a line 3 out of 3 times.Given the equation of a line in slope-intercept, standard or point-slope form, students will be able to recognize y-intercept from slope-intercept form or convert standard form or point-slope form to slope-intercept form 4 out of 5 times.Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources or Materials Needed Materials:Answers for the homework due today: Homework-Day 11 (See Appendix WW)PowerPoint Presentation: Test Review Jeopardy (See Appendix XX)Copies of tonight’s homework: Homework-Day 12: Test Review (See Appendix YY)Key for homework: Homework-Day 12: Test Review (See Appendix ZZ)Resources: ProjectorComputer with access to Microsoft Office: PowerPointWhiteboard with markers and eraser (for teacher)Individual whiteboard with marker & eraser (paper towel works) for each teamCalculator for each studentTime: 45 minutes. Step 1: Pre-Instructional Activities: Check students’ homework and project answers on the board, answer student questions about the homework. Step 2: Content Presentation: n/a. Step 3: Learner Participation: Students will be reviewing for the unit test next class. They will be playing a jeopardy review game. Students must be placed into pre-selected groups with 3 or 4 students in each at varying levels (heterogeneous groups). Each student is responsible for completing all the problems they may be able to steal for points! Students can use a regular calculator for this lesson, as it is the day before a quiz/test. To successfully use their tools, a student has to be familiar with how to operate it. Remind students that they can use their calculator as a tool to help them! Groups must have their final question (it is jeopardy!) written on their group’s whiteboard. (To prevent problems with speed, i.e. who had their hand up first, rang their bell first, etc., we rotate whose turn it is to pick the problem. If the team that chose got the problem wrong, the next team can steal and not miss their turn. Directions are at the beginning of the game.)Step 4: Assessment: Formative assessment through teacher observation. Step 5: Follow-Through Activities: Summative Unit Test next class. Day 13Unit TestPerformance Objectives Covered on Test:When the slope is explicitly given, students will be able to substitute in to the slope-intercept form of a line 3 out of 3 times.Given two ordered pairs that lie on the line, students will be able to recall the slope formula from memory and use it to calculate the slope of the line 9 out of 10 times.Given an equation in standard form, students will be able to convert it to slope-intercept form 9 out of 10 times.Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that parallel lines have equal slopes 4 out of 5 times.Given the equation of a line in slope-intercept, standard, or point-slope form, students will be able to recognize and/or solve for the slope of the line and recall that perpendicular lines have opposite reciprocal slopes 4 out of 5 times.Given an equation in point-slope form, students will be able to identify the slope, or convert the equation to slope-intercept form and then identify the slope 4 out of 5 times.When the y-intercept is explicitly given, students will be able to substitute in to the slope-intercept form of a line 3 out of 3 times.Given the equation of a line in slope-intercept, standard or point-slope form, students will be able to recognize y-intercept from slope-intercept form or convert standard form or point-slope form to slope-intercept form 4 out of 5 times.Given a point that lies on the line and the slope of the line, students will be able to substitute the values appropriately into slope-intercept form and solve the resulting equation for the y-intercept 4 out of 5 times.Given the slope and the y-intercept, students will be able to substitute the values into slope-intercept form of the equation of a line 5 out of 5 times.Resources or Materials NeededMaterials:Copy of the test for each student. (See Appendix AAA)Test answer key (See Appendix BBB)Resources:Calculator for each student. (Even though they have been able to use the Desmos Scientific Calculator during class, the temptation for the students to cheat is not worth the risk because they would be typing into their phone.) Ruler for each student. (To complete a couple of the extra credit questions.)Time: 45 minutes Step 1: Pre-Instructional Activities: Take attendance and have students turn in their homework to ensure maximum time is spent on taking the quiz. Step 2: Content Presentation: n/a. Step 3: Learner Participation: Each student takes the test independently.Step 4: Assessment: Unit Test and the test answer key. Step 5: Follow-Through Activities: Go over the answers to the test the following class. ReferencesAcademy, Khan. (2011, Mar 7). Slope-intercept equation from two solutions example. [Video file]. Retrieved from: , Khan. (2011, Mar 7). Slope intercept from a slope and point. [Video file]. Retrieved from: , P. T. &?Newby, T. (1993). Behaviorism, cognitivism, constructivism: Comparing critical features from an instructional design perspective.?Performance improvement quarterly,?6(4), 50–72Inc., Desmos. (2018). Desmos Scientific Calculator. [Software]. Available from: , Julie. [Common Core Secondary Math]. (2014). Fluent in Math. Fluency Check/Quiz. Equations of Lines. Available from: , Brian. (2011, Dec 13). Find the equation of a line parallel using slope intercept. [Video file]. Retrieved from: , Brian. (2012, Jan 27). Find the line perpendicular to a line through a given point. [Video file]. Retrieved from: Khan VideosWeaver, Sarah (2012, December 22).?Lesson: Writing the Equation of Line Given Two Points. Retrieved from AppendixAppendix AAlgebra 1 CPName:Review Problems A-Day 1Period:_________ Date:__________Solve the following equations for the variable. Show all work!1. 2. What is the slope of the following equations?3. 4. Calculate the slope of the line that passes through the given points. Show all work!5. (7, 12) and (-1, 2)6.(-2, -2) and (5, 7)Appendix B5175885-191135KEY020000KEYAlgebra 1 CPName:Review Problems A-Day 1Period:_________ Date:__________Solve the following equations for the variable. Show all work!1. 2. What is the slope of the following equations?3. 4. Calculate the slope of the line that passes through the given points. Show all work!5. (7, 12) and (-1, 2)6.(-2, -2) and (5, 7)Appendix CAlgebra 1 CPName:Review Problems B-Day 1Period:_________ Date:__________Solve the following equations for the variable. Show all work!1. 2. What is the slope of the following equations?3. 4. Calculate the slope of the line that passes through the given points. Show all work!5. (1, 1) and (-1, 1)6.(-3, -5) and (4, -8)7.What is the equation of the line that passes through the point (4, 1) and has a slope of ? THINK!5141851-5839KEY020000KEYAppendix DAlgebra 1 CPName:Review Problems B-Day 1Period:_________ Date:__________Solve the following equations for the variable. Show all work!1. 2. What is the slope of the following equations?3. 4. Calculate the slope of the line that passes through the given points. Show all work!5. (1, 1) and (-1, 1)6.(-3, -5) and (4, -8)7.What is the equation of the line that passes through the point (4, 1) and has a slope of ? THINK! 345127144716500Appendix EAppendix FAlgebra 1 CPName __________________Writing Equations of Lines-IntroductionPeriod _____ Date ________Exit TicketDirections: Write the slope-intercept form of the equation of the line described. SHOW ALL WORK AND WRITE ANSWER ON ANSWER LINE!!!!1) slope of -52 and has a y-intercept of 12.1) __________________2) passing through the points (-9, 13) and (-15, 5).2) __________________-762001847850Circle the description that best matches how you feel about the current topics.I understand!I’m getting the hang of it.No idea!Sunny skiesPartly cloudy skiesStormy SkiesAppendix G4819650-419100KEY020000KEYAlgebra 1 CPName __________________Writing Equations of Lines-IntroductionPeriod _____ Date ________Exit TicketDirections: Write the slope-intercept form of the equation of the line described. SHOW ALL WORK AND WRITE ANSWER ON ANSWER LINE!!!!447630773734RUBRIC: 1 Point - Slope Intercept Form2 Points – Slope2 Points – y-intercept00RUBRIC: 1 Point - Slope Intercept Form2 Points – Slope2 Points – y-intercept1) slope of -52 and has a y-intercept of 12.y = mx + b488214316995300given slope, m = -52given y-intercept, b = 121) __________________2) passing through the points (-9, 13) and (-15, 5).Calculate the slope using the slope formula.38862008743954000020000Solve for b. Use slope-intercept form:Using point slope form:4732345268369RUBRIC: 1 Point - Slope Intercept Form4 Points – Slope4 Points – y-intercept00RUBRIC: 1 Point - Slope Intercept Form4 Points – Slope4 Points – y-intercept4899181167053002) ________________-501651996540Circle the description that best matches how you feel about the current topics.I understand!I’m getting the hang of it.No idea! 4277516288985RUBRIC: 1 Point - Answered00RUBRIC: 1 Point - AnsweredSunny skiesPartly cloudy skiesStormy Skies Appendix HAlgebra 1 CPHomework-Day 1Name:Writing the Equation of Line from Two PointsPeriod:_________ Date:__________Write the slope intercept form of the equation of the line that passes through the given points.Show all work!1. (2, 0) and (-2, 6)2.(3, -2) and (-6, 4)3.(5, 3) and (4, -3)4.(2, -3) and (-3, 7)5.(12, 2) and (7, 2)6.(1, 1) and (7, 4)7.(-8, -4) and (4, 2)8.(-1, 0) and (0, -3)Appendix I5107305-10160KEY020000KEYAlgebra 1 CPHomework-Day 1Name:Writing the Equation of Line from Two PointsPeriod:_________ Date:__________Write the slope intercept form of the equation of the line that passes through the given points.Show all work!1. (2, 0) and (-2, 6)2.(3, -2) and (-6, 4)Calculate the slope using the slope formula.Calculate the slope using the slope formula.38862008743954000020000right147728Substitute slope and the first point into point-slope form and then convert to slope-intercept form.00Substitute slope and the first point into point-slope form and then convert to slope-intercept form.Solve for b. Use slope-intercept form: 47642442981600 105235612700003.(5, 3) and (4, -3)4.(2, -3) and (-3, 7)397519512110500230117187761005.(12, 2) and (7, 2)6.(1, 1) and (7, 4)-4924425103949500 255204888020000507591492610200007.(-8, -4) and (4, 2)8.(-1, 0) and (0, -3)14109801427233020000427696278472800Appendix JAppendix KEnhancedMetaFilefalse\f 0Appendix LEnhancedMetaFilefalse\f 0 \* MERGEFORMATAppendix MEnhancedMetaFilefalse\f 0 \* MERGEFORMATAppendix NEnhancedMetaFilefalse\f 0Appendix OEnhancedMetaFilefalse\f 0Appendix PEnhancedMetaFilefalse\f 0 \* MERGEFORMATAppendix QEnhancedMetaFilefalse\f 0Appendix REnhancedMetaFilefalse\f 0Appendix SAlgebra 1 CPName __________________Writing Equations of Parallel LinesPeriod _____ Date ________Exit TicketDirections: Write the slope-intercept form of the equation of the line described. SHOW ALL WORK AND WRITE ANSWER ON ANSWER LINE!!!!1) slope of 13 and passing through the point (0, -5)1) __________________2) Parallel to the line y-3=-54(x+2) and passes through the point (8, -7)2) __________________-762001847850Circle the description that best matches how you feel about the current topics.I understand!I’m getting the hang of it.No idea!Sunny skiesPartly cloudy skiesStormy SkiesAppendix T4819650-419100KEY020000KEYAlgebra 1 CPName __________________Writing Equations of Parallel LinesPeriod _____ Date ________Exit TicketDirections: Write the slope-intercept form of the equation of the line described. SHOW ALL WORK AND WRITE ANSWER ON ANSWER LINE!!!!4552950224317RUBRIC: 1 Point - Slope Intercept Form2 Points – Slope2 Points – y-intercept00RUBRIC: 1 Point - Slope Intercept Form2 Points – Slope2 Points – y-intercept1) slope of 13 and passing through the point (0, -5)y = mx + bgiven slope, m = 1/3given y-intercept as an ordered pair. The b value is the y value of the ordered pair. b = -54920035715624000020000512445010604540000200001) __________________2) Parallel to the line y-3=-54(x+2) and passes through the point (8, -7)Parallel lines have the same slope. The line that is given is in point-slope form and the slope is -54Use the point the new line passes through as x and y appropriately in your equation with the slope.right417520RUBRIC: 1 Point - Slope Intercept Form4 Points – Slope4 Points – y-intercept00RUBRIC: 1 Point - Slope Intercept Form4 Points – Slope4 Points – y-intercept4924425190944540000200002) ________________-762001847850Circle the description that best matches how you feel about the current topics.I understand!I’m getting the hang of it.No idea!right271780RUBRIC: 1 Point - Answered00RUBRIC: 1 Point - AnsweredSunny skiesPartly cloudy skiesStormy SkiesAppendix UEnhancedMetaFilefalse\f 0Appendix VEnhancedMetaFilefalse\f 0Appendix WAlgebra 1 CPName ____________________________Writing Equations of LinePeriod _________ Date ______________Group Work - Day 5Directions: Each member of the group will become an expert on 2 problems. Those are the problems the expert will explain how to solve to the rest of the group.NOTE: ALL STUDENTS RESPONSIBLE FOR UNDERSTANDING ALL PROBLEMS!!!Write the slope-intercept equation of the line parallel to the given line through the given point:1) Parallel to y = x + 4, through (2, 2)2) Parallel to y+3 = 43(x-5), through (-9, -2)3) Through (2, -4), parallel to y = 3x + 24) Through (10, -1), parallel to y = -25 + 35) Parallel to 6x + y = 5, through (4, 4)6) Through (-5, 5), parallel to 3x + y = 37) Parallel to y – 9 = -12(x + 4), through (-8, 3)8) Parallel to x = 0, through (4, 3)Appendix X4286250-459105KEY020000KEYAlgebra 1 CPName ____________________________Writing Equations of LinePeriod _________ Date ______________Group Work - Day 5Directions: Each member of the group will become an expert on 2 problems. Those are the problems the expert will explain how to solve to the rest of the group.NOTE: ALL STUDENTS RESPONSIBLE FOR UNDERSTANDING ALL PROBLEMS!!!Write the slope-intercept equation of the line parallel to the given line through the given point:1) Parallel to y = x + 4, through (2, 2)2) Parallel to y+3 = 43(x-5), through (-9, -2)3) Through (2, -4), parallel to y = 3x + 24) Through (10, -1), parallel to y = -25 + 35) Parallel to 6x + y = 5, through (4, 4)6) Through (-5, 5), parallel to 3x + y = 37) Parallel to y – 9 = -12(x + 4), through (-8, 3)8) Parallel to x = 0, through (4, 3)Appendix YAlgebra 1 CPName __________________________Writing Equations of Parallel LinesPeriod _______ Date ______________Homework-Day 5A given line has a slope of - ?. (ie, m = -?)What would the slope of a line parallel to this line be and why?A given line has a slope of 7. (ie, m = 7)What would the slope of a line parallel to this line be and why?A given line has a slope of -13. (ie, m = -13)What would the slope of a line parallel to this line be and why?Write the equation of the line that passes through (-1, 3) and is parallel to the line y = -x + 1.Write the equation of the line that passes through (4, -8) and is parallel to the line y = -2x - 13.Write the equation of the line that passes through (0, 19) and is parallel to the line y = x + 33.Write the equation of the line that passes through (-6, 0) and is parallel to the line y = 5x - 43.Write the equation of the line that passes through (-4, 8) and is parallel to the line that passes through (2, 1) and (-2, -1).Write the equation of the line that passes through (-1, 8) and is parallel to the line that passes through (5, -1) and (2, -5).Write the equation of the line that passes through (-1, -3) and is parallel to the line that passes through (10, 3) and (7, -1).Appendix Z4371975-461010KEY020000KEYAlgebra 1 CPName __________________________Writing Equations of Parallel LinesPeriod _______ Date ______________Homework-Day 5A given line has a slope of - ?. (ie, m = -?)What would the slope of a line parallel to this line be and why?The slope of a line parallel would be -5/6 because parallel lines have equal slopes.A given line has a slope of 7. (ie, m = 7)What would the slope of a line parallel to this line be and why?The slope of a line parallel would be 7 because parallel lines have equal slopes.A given line has a slope of -13. (ie, m = -13)What would the slope of a line parallel to this line be and why?The slope of a line parallel would be -13 because parallel lines have equal slopes.Write the equation of the line that passes through (-1, 3) and is parallel to the line y = -x + 1.Write the equation of the line that passes through (4, -8) and is parallel to the line y = -2x - 13.Write the equation of the line that passes through (0, 19) and is parallel to the line y = x + 33.Write the equation of the line that passes through (-6, 0) and is parallel to the line y = 5x - 43.Write the equation of the line that passes through (-4, 8) and is parallel to the line that passes through (2, 1) and (-2, -1).Write the equation of the line that passes through (-1, 8) and is parallel to the line that passes through (5, -1) and (2, -5).Write the equation of the line that passes through (-1, -3) and is parallel to the line that passes through (10, 3) and (7, -1).Appendix AAEnhancedMetaFilefalse\f 0Appendix BBEnhancedMetaFilefalse\f 0Appendix CCEnhancedMetaFilefalse\f 0Appendix DDEnhancedMetaFilefalse\f 0Appendix EEAlgebra 1 CPName __________________Writing Equations of Perpendicular LinesPeriod _____ Date ________Exit TicketDirections: Write the slope-intercept form of the equation of the line described. SHOW ALL WORK AND WRITE ANSWER ON ANSWER LINE!!!!1) through the points (-6, -5) and (4, 5)1) __________________2) passes through the point (-4, 10) and perpendicular to the line 2x-y=-9 2) __________________-762001847850Circle the description that best matches how you feel about the current topics.I understand!I’m getting the hang of it.No idea!Sunny skiesPartly cloudy skiesStormy SkiesAppendix FF4991100-459740KEY020000KEYAlgebra 1 CPName __________________Writing Equations of Perpendicular LinesPeriod _____ Date ________Exit TicketDirections: Write the slope-intercept form of the equation of the line described. SHOW ALL WORK AND WRITE ANSWER ON ANSWER LINE!!!!4552950122082RUBRIC: 1 Point - Slope Intercept Form4 Points – Slope4 Points – y-intercept00RUBRIC: 1 Point - Slope Intercept Form4 Points – Slope4 Points – y-intercept1) through the points (-6, -5) and (4, 5)Calculate the slope using the slope formula.Solve for b. Use slope-intercept form:Using point slope form:4828540938530001) __________________2) passes through the point (-4, 10) and perpendicular to the line 2x-y=-9 right10160002) __________________right6985RUBRIC: see 100RUBRIC: see 1-762001847850Circle the description that best matches how you feel about the current topics.I understand!I’m getting the hang of it.No idea!Sunny skiesPartly cloudy skiesStormy Skiesright119513RUBRIC: 1 Point - Answered00RUBRIC: 1 Point - AnsweredAppendix GGAlgebra 1 CPWriting Equations of Lines: Parallel and Perpendicular LinesName ______________________________Homework - Day 7Period ________ Date_________________Write the equation in slope intercept form of the line parallel and line perpendicular to given line through given point.Show ALL work! Parallel Perpendicular1) y = 4x + 7 (─2, ─9) ____________________ __________________2) 2x ─ 5y = 10 (3, ─7) _____________________ __________________3) 3x + 4y = 16 (12, ─5)_____________________ ___________________Write the equation of a line (a) parallel to and (b) perpendicular to .4) A (3, ─6) B (7, 2)5) A (2, 5) B (6, ─7) _________________________(a) ________________________ ________________________(b) ________________________6) A (8, 1) B (0, ─1) 7) A (7, 9) B (1, 5)_________________________(a) ________________________ ________________________(b) ________________________State if the lines are Parallel, Perpendicular, or Neither. 8) 6x ─ 12y = 24 9) 4x + y = 510) ─2x + 7y = 14 4x + 2y = 8 3x +12y = ─6 4x = 14y Appendix HHEnhancedMetaFilefalse\f 0Appendix IIEnhancedMetaFilefalse\f 0Appendix JJEnhancedMetaFilefalse\f 0Appendix KKEnhancedMetaFilefalse\f 0Appendix LLEnhancedMetaFilefalse\f 0Appendix MMAlgebra 1 CP 1718Name: ____________________________________QUIZ: Writing EquationsDate: ___________________Period: ___________I. Write the Slope-Intercept Form of the equation of each line described. Show all work. 1.…..a line that contains with slope 1.______________________2.….a line that contains and (8-Points)2.______________________(10-Points)3..…a line that is parallel to the graph of and whose y- intercept is 8.3.______________________(8-Points)4.....a line that contains and is parallel to the graph of 4.______________________(10-Points)5..…the line that is perpendicular to the graph of and passes through .5.______________________ (10-Points)6….the line that is perpendicular to the graph of and has the same y-intercept as the graph of 6. ______________________(10-Points)II. REVIEW7.....a line that contains and is horizontal7. ______________________(8-Points)8. the x-intercept and y-intercept of the graph of (6-Points) 8. x- int ; y- int 9. Name the point on the line and the slope of the graph of the equation shown below. (6-Points) 9. m = ___________point Appendix NNEnhancedMetaFilefalse\f 0 \* MERGEFORMATAppendix OOEnhancedMetaFilefalse\f 0Appendix PPEnhancedMetaFilefalse\f 0Appendix QQEnhancedMetaFilefalse\f 0Appendix RRAlgebra 1 CPName ___________________Writing Equations of Lines-AdvancedPeriod ______ Date ________Directions: Write the equation of the line described in slope-intercept form. Show all work!1. Parallel to y = 43x – 2, same y-intercept as -7x + 3y = -182. Parallel to 7x + 5y = 15, same y-intercept as y - 2 = 49(x + 27)3. Perpendicular to y = 43x – 2, same y-intercept as -4x + 3y = -184. Perpendicular to 7x + 5y = 15, same y-intercept as y - 2 = 49(x + 27)Appendix SS4848225-459105KEY020000KEYAlgebra 1 CPName ___________________Writing Equations of Lines-AdvancedPeriod ______ Date ________Directions: Write the equation of the line described in slope-intercept form. Show all work!1. Parallel to y = 43x – 2, same y-intercept as -7x + 3y = -1845434256610352. Parallel to 7x + 5y = 15, same y-intercept as y - 2 = 49(x + 27)454342537782503. Perpendicular to y = 43x – 2, same y-intercept as -4x + 3y = -18452437579946504. Perpendicular to 7x + 5y = 15, same y-intercept as y - 2 = 49(x + 27)44100753803650Appendix TTAlgebra 1 CPName ____________________________Writing Equations of LinePeriod _________ Date ______________Group Work - Day 11Directions: Each member of the group will become an expert on 2 problems. Those are the problems the expert will explain how to solve to the rest of the group.NOTE: ALL STUDENTS RESPONSIBLE FOR UNDERSTANDING ALL PROBLEMS!!!Write the equation of the line described in slope-intercept form.1.Through the points (-3, 7) and (6, -8)2.Parallel to , with same y-intercept as y = -2x - 63.Perpendicular to y = 3, through (9, -12)4.Perpendicular to , with same y-intercept as 5.Parallel to , with same y-intercept as 6.Parallel to x = -9, through (1, 3)7.Parallel to , through the point (-12, -23)8.Perpendicular to , through the point (-8, 6)Appendix UU4244454-461730KEY020000KEYAlgebra 1 CPName ____________________________Writing Equations of LinePeriod _________ Date ______________Group Work - Day 11Directions: Each member of the group will become an expert on 2 problems. Those are the problems the expert will explain how to solve to the rest of the group.NOTE: ALL STUDENTS RESPONSIBLE FOR UNDERSTANDING ALL PROBLEMS!!!Write the equation of the line described in slope-intercept form.1.Through the points (-3, 7) and (6, -8)45441702665072.Parallel to , with same y-intercept as y = -2x - 6448056026860003.Perpendicular to y = 3, through (9, -12)4467225181165004.Perpendicular to , with same y-intercept as 449646356735005.Parallel to , with same y-intercept as 4464657785274006.Parallel to x = -9, through (1, 3)4481802136608007.Parallel to , through the point (-12, -23)4527854602615008.Perpendicular to , through the point (-8, 6)452826761774500Appendix VVEnhancedMetaFilefalse\f 0Appendix WWEnhancedMetaFilefalse\f 0Appendix XXEnhancedMetaFilefalse\f 0Appendix YYEnhancedMetaFilefalse\f 0Appendix ZZEnhancedMetaFilefalse\f 0Appendix AAAAlgebra CP 1718 Name: ______________________________________________UNIT 4 TEST: Writing Equations of LinesDate: __________________________Period: ______________I. Write the equation of each line described in SLOPE-INTERCEPT FORM. Show all work. 1. Has a slope of and passes through the point (0, -2)1._________________________2.Is a horizontal line and passes through the point 2._________________________3.The line through the points 3. __________________________Has a x-intercept of and y-intercept of 4.4._________________________5. Contains and is perpendicular to the graph of . 5._________________________6. The line that is parallel to the graph of and contains the point . 6. __________________________ Is parallel to the graph of and contains 7. ________________________8.The line that is perpendicular to the graph of and has thesame y-intercept as the graph of 8. __________________________II. Miscellaneous Questions9. An equation in Point-Slope form of the line that contains the points 9. ______________________10. What is the slope of the line containing?10._______________ Are the lines with the given slopes PARALLEL, PERPENDICULAR, or NEITHER.a. 11a. ____________________b. 11b. ____________________c. 11c. ____________________12. Write the SLOPE-INTERCEPT FORM of the equation of the line graphed below. Show all work.2476491206500 12._________________________BONUS ****BONUS*****************EXTRA CREDIT***************BONUS****Graph using ANY appropriate method. Do NOT change the scale!!!1.2. 38671501501243271819956Transform each equation into STANDARD-FORM. Show all work.3. 4. 3. ___________________________ 4. ___________________________ 5. If , then _______ (Please, show some supporting work) (A) 4 (B) 8 (C) (D) 5._____________Appendix BBBEnhancedMetaFilefalse\f 0 \* MERGEFORMAT ................
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