Unit Title: Systems of Equations and Inequalities Time Frame: 12 blocks Grading Period: 1 and 2 Unit Number: 3 Curriculum Enduring Understandings (Big Ideas): There are many ways to solve problems, but some are more efficient than others. Solutions need to be evaluated for reasonableness. The student will know: systems include two or more equations/inequalities a solution (or solutions) to a system represents the point (or points) of intersection matrices can be used to represent data from systems there are four different methods to solving systems (substitution, elimination, graphing, and matrices) systems are real world application three variables/unknowns will require three equations a system of inequalities will yield either 0 or infinite solutions equations have equal signs inequality symbols include, >,, and < The student will be able to: write a system of equations from word problems (from three linear equations in three variables) write a system of equations from word problems (from one linear equation and one quadratic) solve systems of three linear equations in three variables using elimination solve systems of three linear equations in three variables using technology with matrices 1
solve systems of three linear equations in three variables using substitution solve systems of of two equations in two variables (1 linear and 1 quadratic) using substitution solve systems of of two equations in two variables (1 linear and 1 quadratic) using elimination determine the reasonableness of solutions to systems of a linear and quadratic in two variables formulate a system of at least two linear inequalities in two variables solve the system of two or more linear inequalities determine possible solutions in the solution set of the system of two or more linear in equalities in two variables write the quadratic function given three specified points write the equation of a parabola using key features (vertex, focus, directrix, axis of symmetry, and direction of opening) determine when to shade and not to shade when working with equations and inequalities Essential Questions: How do we compare real life situations mathematically? How do we know which method is most efficient? What is a solution and what does it represent? How do you know you have the correct solution? Student Understanding (Student Friendly TEKS): Content: I can write systems of three variable linear equations. (taken from 2A.3A) I can write systems of two equations, one linear and one quadratic. (taken from 2A.3A) I can solve systems of equations with three variables with a variety of methods. (taken from 2A.3B) I can solve systems of two equations, one linear and one quadratic. (taken from 2A.3C) 2
I can interpret and determine the reasonableness of a solution to a system of linear and quadratic equations. (taken from 2A.3D) I can write systems of two linear inequalities. (taken from 2A.3E) I can solve systems of two or more linear inequalities. (taken from 2A.3F) I can test points to see if they are solutions to the system of linear inequalities. (taken from 2A.3G) I can write a quadratic function given three points. (taken from 2A.4A) I can write a quadratic function given a variety of characteristics. (taken from 2A.4B) Process: I can apply math to everyday life. (taken from 1A) I can create and use a problem solving plan. (taken from 1B) I can check my answer to see if it makes sense. (taken from 1B) I can solve problems with different stuff. (taken from 1C) I can solve problems with different resources (manipulatives, technology, etc.). (taken from 1C) I can use multiple ways to communicate math ideas. (taken from 1D) I can explain ways to solve math problems. (taken from 1D) I can use different representations to keep information organized when solving problems. (taken from 1E) I can think and talk about the relationships between math ideas. (taken from 1F) I can use math language to explain and defend mathematical ideas in writing or out loud. (taken from 1G) TEKS: Content: (3) Systems of equations and inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutions. The student is expected to: (A) formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations, the first linear and the second quadratic; (B) solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution; (C) solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation; (D) determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables; (E) formulate systems of at least two linear inequalities in two variables; 3
(F) solve systems of two or more linear inequalities in two variables; and (G) determine possible solutions in the solution set of systems of two or more linear inequalities in two variables. (4) Quadratic and square root functions, equations, and inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to: (A) write the quadratic function given three specified points in the plane; (B) write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening; Process: (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the workplace; (B) use a problem solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem solving process and the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; (E) create and use representations to organize, record, and communicate mathematical ideas; (F) analyze mathematical relationships to connect and communicate mathematical ideas; and (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. Targeted College and Career Readiness Standards: IC1, IIB1, IIC1, IIC2, IID1, IID2, VIIB1, VIIB2, VIIC1, VIIC2, VIIIA1, VIIIA2, VIIIA3, VIIIA4, VIIIA5, VIIIB1, VIIIB2, VIIIC1, VIIIC2, VIIIC3, IXA1, IXA2, IXA3, IXB1, IXB2, IXC1, IXC2, IXC3, XA1, XA2, XB1, XB2, XB3 4
Targeted ELPS: 1A, 1C, 1D, 1E, 1F, 1H, 2C, 2E, 2G, 2I, 3D, 3E, 3F, 3G, 3H, 3J, 4C, 4D Academic Vocabulary: matrix Language of Instruction: point of intersection slope solution substitution systems y intercept elimination quadratic linear variable parabola solution set inequalities equations focus directrix axis of symmetry vertex direction of opening 5
Instruction Instructional Resources: Module 5 5 1 5 2 5 3 5 4 Supplement 3A Supplement 3E Technology: Exemplar Lessons: Career Connections/Real Life Application: Research Based Instructional Strategies: Assessment 6
Student self assessment & reflection: Acceptable evidence or artifacts: 7