ࡱ>  Qbjbj ;dattF*jf$FFFFFFFH{KFQjjFiF!!!!!!F!!F!!!!n@C 7A FF0FALhL@CCLJDh!!TVFF !FLt }:  Course NameAlgebra II HonorsCourse Number1200340Module TitleModule 01 Linear SystemsTime Frame9 daysDeveloped ByAlgebra II Curriculum Revision TeamIdentify Desired Results (Stage 1)Content StandardsMA.912.A.3.10 Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line. Moderate MA.912.A.3.3 Solve literal equations for a specified variable. Moderate MA.912.A.3.14 Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods. Moderate MA.912.A.3.15 Solve real-world problems involving systems of linear equations and inequalities in two and three variables. High MA.912.A.3.6 Solve and graph the solutions of absolute value equations and inequalities with one variable. Moderate UnderstandingsEssential QuestionsEnduring UnderstandingOverarchingTopicalSolutions to linear systems can be no solution, one solution or infinitely many solutions. We can use graphs to demonstrate a constant rate of change for linear equations. There are several approaches to solving various systems. How do you use mathematics to compare two or three linear situations? How do you use mathematics to represent situations with a constant rate of change? What are the benefits of knowing how to manipulate formulas? How do you use mathematics to represent situations that require a range of solutions?  FORMTEXT      Related MisconceptionsThe method for solving the inequalities is the exact same as solving regular equalities. Zero slope and no/undefined slope mean the same thing. When solving absolute value equations or inequalities you can drop the absolute value symbols and solve as before.Knowledge Students will knowSkills Students will be able toThe formulas for the equation of a line including, slope-intercept, point-slope form and standard form. The various methods to isolate a variable in a literal equation. The key components, slope and x- & y-intercepts, of a line. Recognize parallel and perpendicular lines. The methods of solving systems of equations using graphing, substitution, and elimination. The definition and concepts of absolute value and inequalities.Graph linear equations and identify key points such as x- and y-intercepts and slope. Isolate a variable in a literal equation. Find the equation in various forms (standard, slope-intercept, point-slope) of a line given key pieces of information such as slope, y-or x-intercept, one or two points. Write the equation of a parallel and perpendicular line given a line and a point. Recognize the equations of parallel and perpendicular lines. Solve a system of equations in 2 or 3 variables. Solve equations and inequalities containing absolute value. Assessment Evidence (Stage 2)Performance Task Description Senior Tyler Smith budgets $1100 for a 4 day trip to Orlando. He expects to pay $600 on travel and lodging. The price per ticket for theme parks is $60 and he expects to pay an average of $20 per meal. If T represents the number of tickets and M represents the number of meals, then give an inequality to represent the feasible options. Using the inequality above, solve the inequality for M. If he eats at least one meal per day and visits a minimum of 3 parks, write two inequalities one for the number of meals he can eat and one for the number of parks he can visit. Using the three inequalities graph the feasible region (T is the independent variable and M is the dependent variable). Are the maximum numbers of meals and tickets reasonable? Is it possible/reasonable to visit 6 parks and eat 5 meals? What is the best scenario (number of tickets, number of meals) for Tyler? Explain your suggestion. GoalTo create travel suggestions for a high school senior to visit Orlando over 4 days on a budget of $1100.RoleTo create a travel package for the customer within their budget.AudienceThe customer visiting Orlando on a fixed budget.SituationThe customer has $1100 to spend on a 4 day trip to Orlando and wants to visit multiple parks which cost $60 and has appropriate spending money for meals which cost $20 on average. Product/Performance and PurposeTravel package which would include the maximum number of parks and meals that are possible within the budget.StandardsSolve real-world problems involving systems of linear equations and inequalities in two and three variables. Solve literal equations for a specified variable. Solve and graph the solutions of absolute value equations and inequalities with one variable.Other EvidenceSystems of three equations and absolute value inequalities.Learning Plan (Stage 3)Where are your students headed? Where have they been? How will you make sure the students know where they are going?Students should be able: Solve equations including absolute value and inequalities in one variable. Graph a linear equation and an inequality. In the future students will: Isolate a variable in a literal equation. Find the equation in various forms (standard, slope-intercept, point-slope) of a line given key pieces of information such as slope, y-or x-intercept, one or two points. Write the equation of a parallel and perpendicular line given a line and a point. Recognize the equations of parallel and perpendicular lines. Solve a system of equations in 2 or 3 variables. Solve equations and inequalities containing absolute value. How will you hook students at the beginning of the unit?Introduce the performance task at the beginning of the unit.What events will help students experience and explore the big idea and questions in the unit? How will you equip them with needed skills and knowledge?The Springboard MIU Choices and Ottos Toy Factory CPM Unit 5 are the 2 exploration activities needed for success on the performance task. In these activities the students will be exposed to a real world situation that require the development of inequalities, graphing inequalities, finding a feasible region and making conclusions from the feasible region. How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work?Ask questions that require students to write about the connections between graphical and algebraic solutions to systems of equations. How solving literal equations can be applied in other subjects such as science. Students will use self and peer assessment to revise their work. How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?Students will share their work within a group or to the whole class.How will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit?Differentiated activities including hands on and visual and oral presentations of content.How will you organize and sequence the learning activities to optimize the engagement and achievement of ALL students?Present information in a logical, step-by-step fashion. (Teacher as a guide) Move from basic skills to more advanced topics.What FCAT benchmark(s) align most appropriately with the material in this unit? How can you connect, review, and assess this benchmark in a sensible manner?MA.A.3.4.2 Selects and justifies alternative strategies, such as using properties of numbers, including inverse, identity, distributive, associative, and transitive, that allow operational shortcuts for computational procedures in real-world or mathematical problems. MA.C.3.4.2 Using a rectangular coordinate system (graph), applies and algebraically verifies properties of two- and three-dimensional figures including distance, midpoint, slope, parallelism, and perpendicularity. MA.D.1.4.1 Describes, analyzes, and generalizes relationships, patterns, and functions using words, symbols, variables, tables, and graphs. MA.D.2.4.2 Uses systems of equations and inequalities to solve real-world problems graphically, algebraically, and with matrices. Daily exemplars, warm ups and assessments can be used to review, assess and connect the benchmarks. Module 01 BenchmarksCPM ResourcesSpringBoard ResourcesAdditional ResourcesMA.912.A.3.10 Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line.CPM Math 1 Algebra I Skill Builders Linear Equation EF-3, EF-13 Linear Inequalities LS-15 Slope Intercept EF-113 Standard EF-113 Dependent variable EF-37, EF-50 Independent Variable EF-37, EF- 46 Domain EF-46 Range EF-50 Graphing EF-36 Sketch a graph EF-12 Intercepts EF-14 X-intercepts EF-30 Y-intercepts EF-29 Point if Intersection EF-18 Activity 1.2MA.912.A.3.3 Solve literal equations for a specified variable.Literal Equation EF-28, EF-104 HYPERLINK "http://www.edhelper.com" www.edhelper.com MA.912.A.3.14 Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods.Inequalities LS-9-13, 22,35,150 Graphing LS-16 Linear LS-15 Systems LS-23 Activities 1.1 and 1.2 HYPERLINK "http://www.kutasoftware.com/Alg2Worksheets/Systems%20of%20Equations%20Word%20Problems.pdf" http://www.kutasoftware.com/Alg2Worksheets/Systems%20of%20Equations%20Word%20Problems.pdf MA.912.A.3.15 Solve real-world problems involving systems of linear equations and inequalities in two and three variables.Sharpening Pencils Lab EF-20 Systems of Equations BB-17 Two variables Three variables LS-93, 106, 141,154Activities 1.1 and 1.2MA.912.A.3.6 Solve and graph the solutions of absolute value equations and inequalities with one variable.Absolute value LS-3, LS-13Activity 1.3 DayGoals / Objectives / OutcomesActivitiesAssessment1Diagnostic: Assess student on the following Algebra I topics: -Solving -Graphing -Slopes & Intercepts -Factoring -Inequalities -Order of OperationsStudent: CW: Assessment Game Introduction to Performance Task HW: EF 3-9 Questions: How does the slope of the line relate to the graph of the line? What is the difference between the graph of an equation and the graph of an inequality? What is the relationship between the slopes of parallel and perpendicular lines? What is the relationship between the slopes of horizontal and vertical lines? Current: Review various Algebra I concepts.Teacher: Facilitate Assessment Game Review Outcome of Assessment Game Assessment Game Directions This activity consists of a game where assessments are placed at each of 6 stations (or more with a group larger than 24). Participants are expected to answer the questions. Answers are placed on colored paper (keyed to each station) and turned in before moving to a new station. The color coding is used to identify which station the answers come from. This is a timed activity where each group has the same amount of time at each station to work on the questions. Suggested time is 7 minutes per station. The winner of the game is the group with the most correct answers. An important part of this activity is the debriefing of the game. The purpose of the game is to inform assess the students prior knowledge. Point out the scoring grid and how to keep track of each groups score. It may be helpful to have each group write their names on a piece of paper and put that paper on the front table. As each timed session finishes the group puts their answer sheet (answers down) on their paper in the front. Then while the participants work at their new station, the teacher grades and records the results of the previous round. Exemplars: Low: Graph the line y = 3x -5. Moderate: Where does the line 2y+ 3x =12 cross the x-axis? Where does it cross the y-axis? High: Write equations for three different lines with a slope of 4 and explain the relationship between the lines. Graph the lines and compare their graphs.Misconceptions: Student Reflection: What station was the most difficult for you? What did you learn today?2Diagnostic: Write the equation of a line in slope-intercept form given the graph of a line.Student: CW: Cornell notes/ toolkit and practice problems. HW: Worksheet #1-16  HYPERLINK "https://webmail.duvalschools.org/exchweb/bin/redir.asp?URL=http://www.kutasoftware.com/FreeWorksheets/Writing%2520Linear%2520Equations.pdf" \t "_blank" http://www.kutasoftware.com/FreeWorksheets/Writing%20Linear%20Equations.pdfQuestions: What is the slope formula, slope-intercept formula, standard formula, point-slope formula? Write the standard form of an equation?Current: Write the equation of a line in standard form, slope-intercept form or point-slope form given various information. Teacher: Direct instruction and questioning. Cover increasing, decreasing , horizontal, and vertical description of a line. Cornell notes/toolkit Demonstrate the proper use of Cornell notes Exemplars: Low: Use the point-slope formula to write the equation of a line containing the point (-3, 1) and has a slope of 1/3. Moderate: Determine the equation of the line that contains the points (4, -2) and (-1, 13). High: Suppose a manufacturer of graphing calculators has determined that 10,000 calculators per week would be sold at a price of $95. At a price of $90 it was estimated that 12,000 would be sold. Determine a linear function to predict a number of calculators to be sold at a given price. Misconceptions: Students may use point slope formula instead of the slope intercept to graph linear equation. Zero slope and no/undefined slope mean the same thing. Student Reflection: What is the point-slope formula? Describe the steps to find the equation of a line given two points.3Diagnostic: Write the equation of a line and identify the slope and y-intercept. Calculate the slope and describe the line: (-2,13) and (-2, 7) (3,-7) and (0.,-5) Student: CW: Cornell notes/toolkit and worksheet #17-24  HYPERLINK "https://webmail.duvalschools.org/exchweb/bin/redir.asp?URL=http://www.kutasoftware.com/FreeWorksheets/Writing%2520Linear%2520Equations.pdf" \t "_blank" http://www.kutasoftware.com/FreeWorksheets/Writing%20Linear%20Equations.pdf HW: Milepost #11 Questions: How do you recognize parallel and perpendicular lines? How do you determine lines are parallel or perpendicular? Current: Determine the equation of a line parallel or perpendicular to a given line through a given point. Teacher: Direct instruction and questioning. Allow students to use graph paper and scale the x- and y-axes. The teacher will also ensure that students are making accurate sketches (labeling the axes, and plotting key points). The teacher will circulate to each group and ask questions during the class work time. The teacher will also ask questions as the groups present their solutions. Exemplars: Low: Are the lines y=1/2x +3and y= 2x -7 parallel, perpendicular or neither? Moderate: Are the lines 2x + 3y = 2 and 2x + 3y = -4 parallel, perpendicular or neither? High: Are the vertices (0, 0), (4, 2) and (3, 4) the vertices of a right triangle? Explain why.Misconceptions: Remember to change the sign for the perpendicular lines.Student Reflection: Explain how to determine if lines parallel and perpendicular. What is the slope of any line parallel to the x-axis?4Diagnostic: Given the equation 6x + 2y = 14, rewrite the equation in slope intercept form. Are the following equations parallel, perpendicular or neither? 4x +6y = 12 y - 4 = 2/3 (x +3)Student: CPM & www.regentsprep.org CW: EF-28, 104, FCAT Math & Science Reference Sheet (Solve for different variables) HW: Milepost 7 Questions: What is your first step in isolating a variable? How does the order of operations apply? Have you thought of all possibilities?Current: Solve literal equations.Teacher: Review vocabulary Explain the value of isolating a variable. Use all Algebra to demonstrate solving for variables other than x (i.e physics, or chemistry equations) Assign a samplings of formulas on the FCAT Math & Science Reference Sheet to solve for different variables (Supplies copies of reference sheets) Literal Equations Lesson on Website  HYPERLINK "http://www.regentsprep.org/Regents/math/ALGEBRA/AE4/litless.htm" http://www.regentsprep.org/Regents/math/ALGEBRA/AE4/litless.htm Exemplars: Low: Solve for R: S = s(R + r). Moderate The surface area of a kite can be calculated by S= (wh1 wh2). Solve the equation for w. List the steps you took. High Sam says that the following equations are two ways to write the SAME formula. Decide whether or not you agree with Sam. Explain how you made your decision. The two equation are: s = n/(n+1) and s/(s-1) = n. Misconceptions: Practical use across content area is not recognized.Student Reflection:5Diagnostic: Graph the following equations on the same axes. y= -3/2 x + 1 y x 3 Substitute the answer into the equations. What do you notice? Student: CW: BB- 17,27, 66, 95, Milepost #4 HW  HYPERLINK "http://www.kutasoftware.com/Alg2Worksheets/Systems%20of%20Two%20Equations.pdf" http://www.kutasoftware.com/Alg2Worksheets/Systems%20of%20Two%20Equations.pdf Link includes worksheets & answer keyQuestions: Why is an equation written in the form Ax +By=C called a linear equation? How many times do two linear equations intersect? Current: Use substitution and elimination to solve systems of equations. Graph systems of equations to determine the solution. Teacher: Review substitution and elimination with student Assign BB-17 a & b during class. Supplies graph paper & rulersExemplars: Low Solve 7x y =98 3x -5y =10 Moderate Solve the following system:  EMBED Equation.3  High Gloves R' Us was having a great day at their warehouse. Before lunch they had sold a total of 82 pairs of gloves and sales were brisk. At the end of the day Dan, the owner, realized he just had the biggest day in Gloves R' Us history with a total of 127 pairs of gloves sold. As he was heading back to restock for the next day, he asked his new employee, Mittsy, how many of each (cloth and rubber) they had sold. Poor Mittsy, being new, did not know that she was supposed to keep them separate. All she knew was that the rubber gloves were $8.95 each, the cloth gloves were $6.95 each and the total sales for the day $1070.65. Help Mittsy keep her job by finding out how many of each type of glove was sold so Dan, the glove man, can restock. Misconceptions: The Solutions found algebraically are not related to the graphsStudent Reflection: FX 116How is a solution of two equations in two variables represented? What do you find when you are solving a system of equations? Create a real-world situation can be solved by using the systems of equations. How do you verify that your solution is correct?Student: Midterm Assessment (Mini Assessment 30 minutes- Day 1-5) CW LS 93, 106,154, Milepost 21(selected problems) HW  HYPERLINK "http://www.kutasoftware.com/Alg2Worksheets/Systems%20of%20Three%20Equations%20Elimination.pdf" http://www.kutasoftware.com/Alg2Worksheets/Systems%20of%20Three%20Equations%20Elimination.pdf  HYPERLINK "http://www.kutasoftware.com/Alg2Worksheets/Systems%20of%20Three%20Equations%20Substitution.pdf" http://www.kutasoftware.com/Alg2Worksheets/Systems%20of%20Three%20Equations%20Substitution.pdf Link includes worksheets & answer keyQuestions: Is there a systematic approach to solving systems of two equations? Three equations? Identify the differences in solving two systems of equations versus three. Current: Solve systems of three equations Teacher: The teacher will also ensure that students are following a systematic approach to solving three variable systems. The teacher will circulate and ask questions during the class work time. The teacher will also ask questions as the groups present their solutions. Exemplars: Low Solve  Moderate: Solve 8x -2y +6z =9 4x +5y =3 -4x +7y =21 High A group of students are busy studying for their Algebra final. They spent three evenings studying and of course they got hungry. Each day they sent out to the same place for food. Monday evening they purchased 5 hot dogs, 2 hamburgers and 4 orders of fries at a total cost of $23.00 before tax. Tuesday evening they purchased 2 hot dogs, 4 hamburgers and 3 orders of fries at a total cost of $22.50 before tax. Wednesday evening they purchased 3 hot dogs, 3 hamburgers and 5 orders of fries at a total cost of $24.00 before tax. How much does each item cost before tax (hot dog, hamburger and fries)? A complete answer will include a definition of the variables, the system of equations to be solved, an organized algebraic approach to solving the problem and the answer written in sentence form.Misconceptions:Student Reflection: Milepost #21 Problem #87Diagnostic: Graph the following equations: y = 2x +1 y( 2x + 1 Which of the following points satisfies y( 2x + 1? ( 3, -2) ( 0, 9) Student: SpringBoard Choices Pages 5-9 #1-11 Introduction to Performance Task (Rubics) HW : Systems of Inequalities  HYPERLINK "http://www.kutasoftware.com/Alg2Worksheets/Systems%20of%20Inequalities.pdf" http://www.kutasoftware.com/Alg2Worksheets/Systems%20of%20Inequalities.pdf Link includes worksheets & answer keyQuestions: Current: Create a system of inequalities from a set of data, represent the system graphically, and determine its domain. Teacher: The teacher may want to create a warm-up to ensure understanding of graphing and solving linear equations and the use of Function notation. Separate the students in groups of four. Identify the four team members roles ( i.e. Team Leader, Reporter/Recorder, Time Keeper, Supply Person). Administer ground rules for group work. Cover graphing equations that apply to feasible regions After reading the introduction to Choices: Allow the students to summarize or paraphrase the process. Apply to real life connection (i.e. shopping for school clothes). The teacher will circulate to each group and ask questions during the class work time. The teacher will question the groups as they present their solutions. Exemplars: Low:Three cans of soda and two bags of chips cost $2.72 and two cans of soda and four bags of chips cost $3.92. What is the cost of each item? A complete response will include an equation(s) and your work clearly shown Moderate: Identify the inequalities that describe this region?  High: Gloves R' Us was having a great day at their warehouse. Before lunch they had sold a total of 82 pairs of gloves and sales were brisk. At the end of the day Dan, the owner, realized he just had the biggest day in Gloves R' Us history with a total of 127 pairs of gloves sold. As he was heading back to restock for the next day, he asked his new employee, Mittsy, how many of each (cloth and rubber) they had sold. Poor Mittsy, being new, did not know that she was supposed to keep them separate. All she knew was that the rubber gloves were $8.95 each, the cloth gloves were $6.95 each and the total sales for the day $1070.65. Help Mittsy keep her job by finding out how many of each type of glove was sold so Dan, the glove man, can restock. Misconceptions:Student Reflection: LS 1058Diagnostic: Use substitution and elimination to solve systems of equations. Graph systems of equations to determine the solution. 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