# Mathematics – Algebra 1 Unit 9: Quadratics, Exponentials, and Inverses Fourth Grading Period – Weeks 1 9 (48 days) curriculum overview

 Date 12.07.2018 Size 215 Kb.
M athematics – Algebra 1

Unit 9: Quadratics, Exponentials, and Inverses

Fourth Grading Period – Weeks 1 - 9 (48 days) CURRICULUM OVERVIEW
 Enduring Understandings (Big Ideas) Unit Rationale The student should understand: How to use the quadratic formula The meaning and uses of the exponential function. The meaning and uses of inverse variation. Quadratic and exponential functions are important ways of modeling real-world situations and processes. Students need to become comfortable working with these new types of functions. Essential Questions Guiding Questions How is the quadratic formula useful? How is the exponential function useful? What is inverse variation? √ How do we use the quadratic formula? √How do you write and graph equations for exponential growth and decay functions? √How do you identify the domain and range of an exponential function? √What is the meaning of the exponent in an exponential function? √How do you distinguish between linear, quadratic, and exponential equations? TEKS Standards TEKS Specificity – Intended Outcomes TEKS SEs A.04.A The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations. A.10.A The student is expected to solve quadratic equations using concrete models, tables, graphs, and algebraic methods. A.10.B The student is expected to make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function. A.11.A The student is expected to use patterns to generate the laws of exponents and apply them in problem-solving situations. A.11.C The student is expected to analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods. A.11.B The student is expected to analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods. A.08.AThe student is expected to analyze situations and formulate systems of linear equations in two unknowns to solve problems. A.08.BThe student is expected to solve systems of linear equations using concrete models, graphs, tables, and algebraic methods. A.08.CThe student is expected to interpret and determine the reasonableness of solutions to systems of linear equations. “I CAN” statements highlighted in yellow and italicize should be displayed for students I can: solve quadratic equations using concrete models, tables, graphs, and algebraic methods make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function use patterns to generate the laws of exponents and apply them in problem-solving situations analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods analyze situations and formulate systems of linear equations in two unknowns to solve problems solve systems of linear equations using concrete models, graphs, tables, and algebraic methods

 ELPS 1E – Internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment. 2C – Learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions 2D – Monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed 3D – speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency 3E – Share information in cooperative learning interactions 4F – Use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language. College and Career Readiness Standards I.B.1 Perform computations with real and complex numbers II.A.1 Explain and differentiate between expressions and equations using words such as solve, evaluate and simplify II.B.1 Recognize and use algebraic properties, concepts, procedures, and algorithms to combine, transform and evaluate expressions Evidence of Learning (Summative Assessment) Given an end of unit quiz, students apply the quadratic formula correctly 8 out of 10 times. Given an end of unit quiz, students are able to model exponential functions 8 out of 10 times. Given an end of unit quiz , studentsare able to model inverse variation. Given a variety of problems (different content and context), students will apply a problem solving process 100% of the time.

CURRICULUM GUIDE

 Days 24-26 Semester Review and Final Vocabulary: (Pertinent to the learning – specific) whole number integer rational number irrational number complex number real number roots x-intercepts solutions zeros linear function exponential function y-intercept constant changing rate of change common difference common multiplier inverse variation constant of variation system of equations in two variables substitution linear combination dependent equations independent equations consistent equations inconsistent equations TAKS Vocabulary simplify transform solve factor apply estimate generate graph locate name Resources Agile Mind Topic 23 The Quadratic Formula Topic 24 Modeling with the Exponential Function Topic 25 Modeling with Inverse variation Topic 18 Other Methods of Solving Systems Other Resources Exponential Growth Story Exploring Exponential Growth Activity Exploring Exponential Growth Activity - Key Linear vs. Non-Linear Functions Linear vs Non-Linear Functions - Key Investing \$1000 in a Savings Investing \$1000 in a Savings - Key The Population of the World The Population of the World - Key Strike It Rich! Exploring Exponential Decay-Notes Exploring Exponential Decay Notes - Key Exploring Exponential Decay-Assignment Exploring Exponential Decay Assignment - Key M & M Activity Formulas for Growth and Decay-Notes Formulas for Growth and Decay Notes - Key Formulas for Growth and Decay-Assignment Formulas for Growth and Decay Assignment - Key Exponential Functions - Ups and Downs Page 1 Exponential Functions – Ups and Downs Page 1 - Key Exponential Functions - Ups and Downs Page 2 Exponential Functions – Ups and Downs Page 2 - Key Sketch The Graph Sketch the Graph - Key Function Types-Notes Function Type Notes - Key Function Types Assignment Function Type Assignment - Key Compare Exponential, Linear, Inverse, Quadratics Compare Exponential, Linear, Quadratic Models - Key

 Evidence of Learning Formative Mini Assessments TAKS College-Readiness i.e., Anticipated Skills for SAT/ACT/College Board/Career/Life FMA May 2009  2006 TAKS 9th Grade problem 16 (A.4A) TAKS 2004 Grade 9 (A.4A) SAT Prep James purchased a hybrid golf cart for \$5000 and its value decreases by 20% each year. The value, in dollars, of the golf cart years from the date of purchase is given by the function , where . How many years from the date of purchase will the value of the golf cart be \$3200? A. 1 B. 2 C. 3 D. 4 E. 5

SAISD © 2010-11 – Fourth Grading Period Mathematics Algebra 1 Page of Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.