West Haven Public Schools Unit Planning Organizer Subject: Algebra I Grade: 9 Unit 4: Systems of Linear Equations and Inequalities Pacing: 20 Days Essential Question(s): 1) Describe the three types of solutions of a system of linear equations. 2) How would you choose the appropriate method to solve a system of equations? 3) What are the differences in graphing a system of linear equations and a system of linear inequalities? Big Idea(s): 1) No solution represents that there is no set of values that satisfy both equations, so graphically the lines will never intersect. One solution represents that there is exactly one set of values that satisfy both equations, so graphically the lines will intersect at exactly one point. Infinite solutions represents that any set of values will satisfy both equations, so graphically the lines are exactly the same. 2) You would use graphing for solving systems that are easily graphed (when both equations are in slope intercept form). If the point of intersection does not have integers for coordinates, find the exact solution by using a graphing calculator. You would use substitution for solving systems when one variable has a coefficient of 1 or 1 (easiest to solve when one equation is in the slope intercept form or x = ). You would use elimination for solving any system, but usually it is easiest to solve when both are in standard form. 1
3) To graph a system of linear equations, graph the lines and the solution will be the point of intersection (in special case i.e. parallel no solution or equivalent lines infinitely many solutions). However, when graphing a system of inequalities you graph the boundary lines and shade the region above or below the boundary line (depending on inequality sign) and the solution is any ordered pairs in the overlapping shaded region that makes the system true. Common Core State Standards (includes West Haven s Priority Common Core Standards in BOLD and Supporting Standards) A CED 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context... A REI 5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A REI. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A REI 11. Explain why the x coordinates of the points where the graphs of the equations y = f( x) and y = g( x) intersect are the solutions of the equation f( x) = g( x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f( x) and/or g( x) are linear...functions.* A REI 12. Graph the solutions to a linear inequality in two variables as a halfplane (excluding boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables. Mathematical Practices (Practices in BOLD should be focused on in this unit) 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others 4. Model with Mathematics 5. Use appropriate tools strategically.. Attend to precision. 2
7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Unwrapped Concepts and Skills, and Bloom Levels (BL) Concepts(Need to Know) Skills(Able to Do) BL Systems of linear equations x coordinate y coordinate Point of intersection Solution to a system of linear equations Graphing method Substitution method Elimination method Linear inequality System of linear inequalities Solution set to linear inequalities Solve (systems using graphs) Solve (systems using algebraic methods) Explain (why x coordinates of the points of intersection of equations y = f(x) and y = g(x) are the solutions of the equation f(x) = g(x)) Find (solutions) Graph (solutions of a linear inequality as a half plane) Graph (solution set to a system of linear inequalities) 3, 3 2, 4 1, 4 Assessments Common Formative Test A (Followed by Data Team Analysis): Pre Requisite Skills Assessments A, B, C Dipsticks (Informal Progress Monitoring Checks): per teacher discretion Common Formative Test B (Followed by Data Team Analysis): Instructional Planning 7 1 Solving Systems by Graphing 2 Days 7 2 Solving Systems Using Substitution 2 Days 7 3 Solving Systems Using Elimination 2 Days 7 4 Applications of Linear Systems 2 Days Performance Task 1 Day 7 5 Linear Inequalities 2 Days 7 Systems of Linear Inequalities 2 Days 3
Test A (Followed by Data Team Analysis) Buffer (Re Teaching) Test B 1 Day 4 Days 1 Day Suggested Resources/Materials: PHschool.com video tutorials, pearsonsuccessnet.com, smartexchange.com http://sbac.portal.airast.org/wp content/uploads/2013/08/g11_practice Test Scoring Guide 5. 14.14 Final.pdf Algebra I PH Support Workbook Chapter 7 Re teaching, Practice, Enrichment Reading for Problem Solving p. 39 Reading and Math Literacy Masters p. 25 7A: Graphic Organizer p. 2 7B: Reading/Writing Math Symbols p. 27 7C: Reading Comprehension p. 28 7D: Vocabulary Algebra with Pizzazz p.11 19 (systems of linear equations), p. 197 200 (systems of inequalities) Suggested Research based Effective Instructional Strategies: Note taking Homework and Practice Non Linguistic Representation Cooperative Learning 4
Flexible Grouping Cues, Questions, and Advanced Organizers Connect New Concepts to Prior Learning Use of Technology Vocabulary/Word Wall Enrichment/Extension Interdisciplinary Connections System of linear equations Solution of the system of linear equations No Solution Infinitely many solutions Substitution method Elimination method Graphing method Linear inequality Solutions of an inequality System of linear inequalities Solution of a system of linear inequalities x coordinate Investigation: p 34 solving systems using algebra tiles Technology: p 30 31, p 39 matrices and solving systems Technology: Graphing linear inequalities p. 385 Test Taking Strategies: Finding multiple correct answers p. 38 Extra Practice p. 708 SBAC (grade 8) # 1834 SBAC (grade 8) # 184 SBAC (grade 8) # 18 Real World Applications: p. 343 344 24, 25, 39 p. 350 17, 22 24, 45 p. 358 29, 30, 41,45,4 p. 3 15, 1, 18, 19,20,22,24 p. 382 23, 24 p. 374 375 37, 45 p. 37 55 (mixed review), 7 (checkpoint quiz 2) p.382 23, 24, 31 35 p. 383 43, 47, 48 p. 38 Algebra at Work Reading for Problem Solving: p 39 5
y coordinate Point of intersection