COE Algebra Syllabus School Year: 2015-2016 Certificated Teacher: Desired Results Course Title): COE Algebra Credit: x one semester (.5) two semesters (1.0) Prerequisites and/or recommended preparation: Must have already taken Algebra 1, and must have attempted the EOC and not met standards twice. Estimate of hours per week engaged in learning activities: 5 hours of class work per week per 18 week semester Instructional Materials: All learning activity resources and folders are contained within the student online course. Online course is accessed via login and password assigned by student s school (web account) or emailed directly to student upon enrollment, with the login website. This course requires a MathXL account which will be provided by your course instructor. Optional Graphing Calculator (Approximately $50 $100). Many online graphing calculators can do what is required of this course and are free. Course Description: We will be reviewing several units from Algebra 1, which will weave together a variety of concepts, procedures and processes in mathematics. Students will develop the ability to explore and solve mathematical problems, think critically, work cooperatively with others and communicate their ideas clearly as they work through these mathematical concepts and algebraic procedures. Topics for this course include a study of linear, quadratic and exponential functions as well as statistics. The students will compile a Collection of Evidence (COE) and submit it to the state at the end of this course. Enduring Understandings for Course (Performance Objectives): Symbols, such as numbers and variables, can be manipulated using different processes and operations to represent real-life quantities and their relationships. Equations are dynamic tools for problem solving, communicating and expressing ideas and concepts. Functions are used to represent the relationship between unknown quantities. Graphs are visual representations of functions/numerical relationships. Logical reasoning and Problem Solving enable us to approach a problem, explain reasoning and check answers in order to move from simple ideas to complex ones.
Course Learning Goals (including WA State Standards, Common Core Standards, National Standards): UNIT 1-Linear Models Target 2A Understanding Slope as a Rate of Change 1. I can use rate of change to determine if a situation is linear. 2. I can calculate the rate of change in a linear situation (given two points, graph, table, situation etc.). 3. I can explain the meaning of a rate of change in a situation. 4. I can determine the slope of parallel and perpendicular lines. Target 2B Understanding Multiple Forms of Linear Functions 1. I can recall and give examples of the three forms (standard, slope-intercept, point- slope). 2. I can create a graph from any form of a linear equation. 3. I can explain the meaning of the intercepts for a situation. 4. I can write a linear equation in a form of my choice. 5. I can describe how changes in constants affect the graph. 6. I can translate to slope-intercept form. 7. I can use recursive formulas to describe a linear (arithmetic) sequence. A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. A1.4.B Write and graph an equation for a line given the slope and the y- intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. A1.4.B Write and graph an equation for a line given the slope and the y- intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. A1.4.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent. A1.6.D Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions. A1.7.C Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence. Target 2C Understanding Solutions of Linear Equations 1. I can produce a table/graph using a calculator. 2. I can solve linear equations using multiple representations (table, graph, and algebra). 3. I can explain the meaning of an equation in the context of the situation. 4. I can explain the meaning of a solution in the context of the situation. A1.1.A Select and justify functions and equations to model and solve problems. A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. A1.4.A Write and solve linear equations and inequalities in one variable. UNIT 2-Linear Systems Target 3A A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities.
Understanding Solutions Using Tables and Graphs 1. I can write a system of equations to represent a situation. 2. I can produce a table/graph using a calculator. 3. I can use graphs and tables to solve systems of linear equations. 4. I can use graphs and tables to solve inequalities in linear systems. 5. I can explain the meaning of a solution in the context of the situation. A1.1.C Solve problems that can be represented by a system of two linear equations or inequalities. A1.4.D Write and solve systems of two linear equations and inequalities in two variables. A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. Target 3B Understanding Solutions of Linear Systems Using Algebra 1. I can write a system of equations to represent a situation. 2. I can solve systems using substitution. 3. I can solve systems using elimination. 4. I can choose a technique to use to solve a system of linear equations. 5. I can explain the meaning of a solution in the context of the situation. A1.1.C Solve problems that can be represented by a system of two linear equations or inequalities. A1.4.D Write and solve systems of two linear equations and inequalities in two variables. UNIT 3-Data Analysis Target 7A Analyzing Statistics of Single Variable Data 6. I can compare measures of center and spread from one data set to another. 7. I can draw appropriate conclusions from measures of center or spread. 8. I can describe how linear transformations affect the center and spread. Target 7B A1.6.A Use and evaluate the accuracy of summary statistics to describe and compare data sets. A1.6.C Describe how linear transformations affect the center and spread of univariate data. A1.6.B Make valid inferences and draw conclusions based on data. Analyzing Correlation of Linear Data 6. I can describe a correlation using appropriate vocabulary. 7. I can determine whether an argument confuses association with causation. A1.6.E Describe the correlation of data in scatterplots in terms of strong or weak and positive or negative. Target 7C Analyzing Lines of Best Fit 1. I can find the line of best fit with and without technology. 2. I can interpret the meaning of the slope and intercepts for a line of best fit 3. I can make and analyze predictions with lines of best fit. A1.6.D Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions.
UNIT 4-Exponential Functions Target 8A Understanding Representations of Exponential Functions 1. I can use common ratios to determine if a function or sequence is exponential. 2. I can determine which exponential rule best fits a table or graph. 3. I can sketch the basic shape of a graph of an exponential function. 4. I can use recursive formulas to create exponential (geometric) sequences. 5. I can write recursive formulas to describe exponential (geometric) sequences. A1.1.A Select and justify functions and equations to model and solve problems A1.7.A Sketch the graph for an exponential function of the form y = ab n where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions. A1.7.C Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence. Target 8B Understanding Exponential Expressions 1. I can simplify a same base expression. 2. I can simplify a power of a power expression. 3. I can simplify a power of a product expression. 4. I can simplify the power of a quotient expression. 5. I can simplify expression with a power of zero. 6. I can simplify an expression with a negative exponent. 7. I can simplify an expression using multiple exponential properties Target 8C Understanding Exponential Functions as Models 1. I can write an exponential rule to model a situation. 2. I can describe appropriate domain restrictions for the model. 3. I can solve problems that can be represented by exponential functions. A1.2.C Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions. A1.1.A Select and justify functions and equations to model and solve problems A1.1.E Solve problems that can be represented by exponential functions and equations. A1.7.B Find and approximate solutions to exponential equations.
UNIT 5-Quadratic Equations Target 5A Understanding Graphs of Quadratic Functions A1.3.A Determine whether a relationship is a function and identify the domain and range, roots, and independent and dependent variables. 9. I can determine which quadratic rule best fits a table or graph. 10. I can use a graph to find the x and y intercepts, line of symmetry, and vertex. 11. I can use standard form to find the y intercept, line of symmetry, vertex, and sketch a detailed graph by hand. 12. I can use factored form to find x and y intercepts, line of symmetry, vertex, and sketch a detailed graph by hand. 13. I can use a graph to determine the domain and range. 14. I can describe the effects that changing parameters have on the graph of a quadratic function. A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A1.5.A Represent a quadratic function with a symbolic expression, as a graph, in a table and with a description, and make connections among the representations. A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph and interpret the x-intercepts as solutions to a quadratic equation. Target 5B Understanding Quadratic Expressions 1. I can add/subtract quadratic expressions. 2. I can expand a product of binomials. 3. I can factor simple quadratics (leading coefficient of 1). 4. I can factor complex quadratics (leading coefficient other than 1). 5. I can factor differences of squares. Target 5C Understanding Solutions to Quadratic Problems 4. I can solve quadratic equations using tables and graphs 5. I can solve quadratic equations by factoring. 6. I can solve quadratic equations by using the quadratic formula. 7. I can solve problems that can be represented by quadratic functions. A1.2.E Use algebraic properties to factor and combine like terms in polynomials. A1.5.C Solve quadratic equations that can be factored as (ax + b) (cx + d) where a, b, c, and d are integers. A1.5.C Solve quadratic equations that can be factored as (ax + b) (cx + d) where a, b, c, and d are integers. A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. A1.5.A Represent a quadratic function with a symbolic expression, as a graph, in a table and with a description, and make connections among the representations. A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph and interpret the x- intercepts as solutions to a quadratic equation. A1.1.D Solve problems that can be represented by quadratic functions and equations.
Evidence of Assessment Performance Tasks: The students will work through a web based math program (MathXL) to master the unit targets based on state standards. Once the work is complete in MathXL, the students will assess their knowledge on individual target quizzes and then an overall Unit test to gauge their understanding of the state standards. Other Evidence (self-assessments, observations, work samples, quizzes, tests and so on): Quizzes/Assessments in MathXL Target quizzes based on state standards Unit assessments based on state standards Weekly blogging on specific teacher-directed topics Types of Learning Activities Indicate from the table below all applicable learning strategies that may be used in the course. Direct Instruction Structured Overview Mini presentation Drill & Practice Demonstrations _X Other (List) Pronto Discussions Virtual Classroom Online Videos Indirect Instruction Problem based Case Studies Inquiry Reflective Practice Project Paper Concept Mapping Other (List) Experiential Learning Virt. Field Trip Experiments X Simulations Games Field Observ. Role playing Model Bldg. Surveys Other (List) Independent Study Essays X_Self paced computer Journals Learning Logs Reports Directed Study Research Projects X Other (List) Target based practice Interactive Web Based Practice Interactive Instruction X Discussion Debates Role Playing Panels Peer Partner Learning Project team Laboratory Groups Think, Pair, Share Cooperative Learning Tutorial Groups Interviewing Conferencing Other (List) Other: Learning Activities
These learning activities are aligned with the successful completion of the course learning goals and progress towards these learning activities will be reported monthly on a progress report. COE Algebra Learning Activities Unit 1: Linear Models Duration: 5 weeks Enduring Understandings: Multiple representations of linear models can be used to solve real world problems Essential Questions: 1) How can we use tables, graphs and equations to model linear patterns. 2) How can we use point-slope form, standard form and slope-intecept form to model real life situations Student Learning Targets: Target 2A: Understanding slope as a rate of change To start the linear model unit students will be finding rate of change to verify that a model is linear. The idea of slope is a topic covered in years past so the extent of the new learning is around finding the slope from many different pieces of information (e.g. two points, a situation, a line, etc.) and explain its meaning in the context of a situation. Target 2B: Understanding multiple forms of linear models Students have experience with slope intercept form in previous courses. This unit extends their understanding to standard and point slope form. Can students fluently go between a graph, table, and equation in any form? This target helps bring to light the pros and cons of each linear form. In each form students will be asked to find intercepts and slope. Additionally, students will be introduced to recursive formulas to express that elementary idea of add 5 to get the next term in linear (arithmetic) sequences. Target 2C: Understanding solutions of linear equations Students have experience using graphs, tables, and algebra to answer questions. This target focuses on using all three techniques to solve problems modeled by linear equations. Moreover, students should understand the meaning of equations and solutions in the context of a situation. Learning Activities:
Unit 2 Target 2A Task #1 Rate of Change and Slope Task #2 The Slope Formula Task #3 Slope of Parallel and Perpendicular Lines Task #4 Target 2A Quiz Unit 2 Target 2B Task #1 Using Intercepts Task #2 Slope Intercept Form Task #3 Point Slope Form Task #4 Arithmetic Sequences Task #5 Target 2B Quiz Unit 2 Target 2C Task #1 Solving One Step Equations Task #2 Solving Two Step Equations Algebra 1A Pacing Guide/Checklist Task #3 Solving Equations with Variables on Both Sides Task #4 Target 2C Quiz Unit 1 COE tasks Unit 2: Systems of Equations Duration: 3 weeks Enduring Understandings: We can represent situations with systems of equations or inequalities. There are multiple ways (graphs, tables, and algebra) that we can solve systems. Essential Questions: 1) How can we represent situations with systems of equations or inequalities? 2) How can we use graphs, tables, and algebraic reasoning to solve systems of equations Student Learning Targets: Target 3A: Understanding Solutions to Linear Systems Using Tables and Graphs Tables and graphs are good tools to solve systems of equalities and inequalities. Students should be able to use technology to create graphs and tables and then find solutions. Extensions could be made to systems where the equations are not linear. That is, with technology we can solve systems of various functions (like quadratic and exponential). Understanding the meaning of the solution is of utmost importance. Target 3B: Understanding Solutions to Linear Systems with Algebra. Using either elimination (also called linear combination) or substitution, students should be able to solve systems of linear equations. With practice they should have good confidence to choose either technique. Understanding the meaning of the solution is of utmost importance. Learning Activities: Unit 3 Target 3A
Task #1 Solving Systems by Graphing Task #2 Solving Linear Inequalities Task #3 Solving Systems of Linear Inequalities Task #4 Target 3A Quiz Unit 3 Target 3B Task #1 Solving Systems by Substitution Task #2 Solving Systems by Elimination Task #3 Solving Application Problems Task #4 Target 3B Quiz Unit 2 COE Tasks Unit 3: Analyzing Data Duration: 3 weeks Enduring Understandings: We can analyze arguments and people s conclusions. Is there a relationship between the variables and can you make a conclusion and defend that the conclusion is reasonable or accurate. Essential Questions: 1) How can we use statistical measure to analyze arguments 2) How can we link relationships between variables to create and defend a conclusion Student Learning Targets: Target 7A: Analyzing Statistics of Single Variable Data We will compare measures of centers from two different data sets to make conclusions We will also describe how transformations affect the center and spread. Target 7B: Analyzing Correlation of Linear Data We will focus on the difference between association and causation. Target 7C: Understanding Lines of Best Fit We will be able to create a line of best fit with and without technology and use the line of best fit to make and analyze predictions. Learning Activities: Unit 7 Target 7A Task #1 Organizing and Describing Data Task #2 Target 7A Quiz Unit 1 Target 7B Task #1 Describing Correlation Task #2 Target 7B Quiz Unit 1 Target 7C Task #1 Lines of Best Fit Task #2 Target 7C Quiz
Unit 3 COE tasks Unit 4: Exponential Models Duration: 3 weeks Enduring Understandings: Exponential models make up the 2 nd most important model for us in Algebra (the other being linear models). Repeated multiplication by a constant ratio can model many areas of life. We can view these models in many ways: graphs, tables, as well as explicit and recursive rules. Essential Questions: 1) How can we use graphs, tables, recursive and explicit formulas to model exponential situations? 2) How can we use exponential graphs, tables, and formula to find solutions to situations modeled by exponential functions? Student Learning Targets: Target 8A: Understanding Representations of Exponential Functions We will look at graphs, tables, and rules for exponential functions. Explicit rules like f(x) = 5 3 x are commonplace. Moreover, recursive rules like a n+1 = a n 3 where a 0 = 5 will be used. Target 8B: Understanding Exponential Expressions Students must understand and be able to use the properties of exponents. Understanding and simplifying basic exponential expressions is key. Target 8C: Understanding Exponential Functions as Models We will find rules to model situations and determine appropriate domain restrictions. Furthermore, we will solve problems in situations by using tables and graphs. Learning Activities: Unit 8 Target 8A Task #1 Geometric Sequences Task #2 Exponential Functions Task #3 Target 8A Quiz Unit 5 Target 8B Task #1 Integer Exponents Task #2 Multiplication Properties of Exponents Task #3 Division Properties of Exponents Task #4 Target 5B Quiz Unit 8 Target 8C Task #1 Exponential Growth and Decay Task #2 Target Quiz 8C Unit 4 COE tasks Unit 5: Quadratic Models Duration: 6 weeks
Essential Understandings: Some data are best modeled by quadratic functions. Let's study two of the quadratic forms (standard and factored) as we look at how we can model situations. Essential Questions: 1) How can we model real life situations with standard and factored form? Student Learning Targets: Target 5A: Understanding Graphs of Quadratic Functions Graphs of quadratic functions can be easily understood by their symmetry. The characteristic line of symmetry and vertex help define one of the most basic non linear functions. We will look at both standard and factored form of equations and how they relate to graphs. This target helps set the stage for student understanding of equivalency of quadratic expressions in factored or expanded form. Target 5B: Understanding Quadratic Expressions Factoring and expanding quadratic expressions two essential tools for understanding quadratic models are the focus for this target. After seeing graphs of quadratics in factored and standard form, students are ready to understand equivalency at a deeper level. Furthermore, the connection between factored form and zeros of a quadratic is of utmost importance for mathematical connections. Target 5C: Understanding Solutions to Quadratic Problems Quadratic equations can be solved using multiple strategies. We will focus on the use of graphs, tables, factoring, and the quadratic formula. Additionally, we will solve quadratic equations that come from situations. Learning Activities: Unit 5 Target 5A Task #1 Identifying Quadratic Functions Task #2 Characteristics of Quadratics Task #3 Graphing Quadratic Functions Task #4 Transforming Quadratic Functions Task #6 Target 5A Quiz Unit 5 Target 5B Task #1 Polynomials Task #2 Adding and Subtracting Polynomials Task #3 Multiplying Polynomials Task #4 Factoring GCF Task #5 Factoring Leading Coefficient a=1 Task #6 Factoring Leading Coefficient a>1 Task #7 Factoring Special Products Task #8 Target 5B Quiz Unit 5 Target 5C Task #1 Solving Quadratics by Graphing Task #2 Solving Quadratics by Factoring Task #3 Solving Quadratics using Quadratics Formula
Task #4 Target 8C Quiz Unit 5 COE tasks