Mathematics Curriculum Document for Middle School Algebra 1

Transcription

1 Unit Title: Equations and Inequalities Time Frame: 16 days Grading Period:1 Unit Number: 1 Curriculum Enduring Understandings (Big Ideas): Simplifying math operations with a standard process helps us communicate and solve real world situations with consistency. Solutions need to be evaluated for reasonableness. Most patterns and relationships can be represented mathematically in a variety of ways The student will know: properties of equality order of operations equations have 1 solution, no solution, or infinite solutions symbols of inequality inequalities represent an unbalanced relationship between two expressions multiplying or dividing an inequality by a negative number will reverse the inequality symbol inequalities have either 0 or infinitely many solutions The student will be able to: solve one variable equations using the distributive property with and without technology solve equations with variables on both sides of the equation with and without technology solve one variable inequalities using the distributive property with and without technology solve inequalities with variables on both sides of the equation with and without technology evaluate reasonableness of solutions solve mathematic and scientific formulas for a specific variable solve literal equations for a specific variable Unit Title: Equations and Inequalities Unit Number: 1 1

2 Essential Questions: Why do we follow a standard process when solving equations and inequalities? Why do some problems have multiple solutions? How do you know if the answer is reasonable? Student Understanding (Student Friendly TEKS): Content: I can solve equations. (taken from 5A) I can solve inequalities. (taken from 5B) I can rewrite formulas for a specific variable. (taken from 12E) 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: (5) Linear functions, equations, and inequalities. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions. The student is expected to: (A) solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides; (B) solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides; and Unit Title: Equations and Inequalities Unit Number: 1 2

3 (12) Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to: (E) solve mathematic and scientific formulas, and other literal equations, for a specified variable. 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: IA1, IB1,IC1, IIA1, IIC1, IIIC1,, IIA1, IVC3, IXA1, IXA2, IXA3,IXC1, IXC2, VIIIA1, VIIIA2, VIIIA3, VIIIA4, VIIIA5 Targeted ELPS: 1A, 1B, 1F, 1H, 2C, 2D, 2I, 3D, 3E, 4F Academic Vocabulary: Literal equation Language of Instruction: coefficient combining like terms common difference consecutive constant distributive property equation equivalent forms Unit Title: Equations and Inequalities Unit Number: 1 3

4 evaluate expression formula graph of an inequality inequality inverse operations order of operations reciprocal sequence simplify solution solution of an inequality solve term variable Instruction Instructional Resources: SpringBoard Algebra 1 Text Activity 1 Investigating Patterns 1.1 Numeric and Graphic Representations of Data 1.2 Writing Expressions Activity 2 Solving Equations 2.1 Writing and Solving Equations 2.2 Equations with Variables on Both Sides 2.3 Solving more Complex Equations 2.4 Equations with No Solutions or Infinitely Many Solutions 2.5 Solving Literal Equations for a Variable Embedded Assessment #1 Patterns and Equations p. 33 Activity 3 Solving Inequalities 3.1 Inequalities and Their Solutions 3.2 Solving Inequalities 3.3 Compound Inequalities (Not in TEKS) Unit Title: Equations and Inequalities Unit Number: 1 4

5 Activity 4 Absolute Value Equations and Inequalities (Not in TEKS) Embedded Assessment 2 Inequalities and Absolute Value (Omit #5) Technology: Exemplar Lessons: Career Connections/Real Life Application: Research Based Instructional Strategies: Assessment Student self assessment & reflection: Acceptable evidence or artifacts: Unit Title: Equations and Inequalities Unit Number: 1 5