Mathematics Pacing Guide High School Algebra II/Trigonometry

Mathematics Pacing Guide: High School Advanced Algebra Course

MILWAUKEE PUBLIC SCHOOLS

Mathematics Pacing Guide High School Algebra II/Trigonometry

Math_Pacing Guide Algebra II/Trig_07.27.11_v1

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This Pacing Guide is to be used in conjunction with the Curriculum Guide and the Instructional Design Lesson Plan. The Curriculum Guide addresses the specific standards, essential understandings, misconceptions, instructional practices, and differentiation. The Instructional Design will help with planning lessons using Launch-Explore-Summarize-Apply.

Mathematics Pacing Guide: High School Advanced Algebra Course Time Frame

Common Core State Standards For Mathematics Conceptual Category: Number and Quantity Domain: Quantities* N-Q 1 Cluster: Reason quantitatively and use units to solve problems

Problem Solving with Algebra

Week 1

Conceptual Category: Algebra Domain: Reason with Equations and Inequalities A-REI 3 Cluster: Solve equations and inequalities in one variable


Program Materials Discovering Advanced Algebra Chapter 0: Problem Solving with Algebra Lesson 0.1: Pictures, Graphs, and Diagrams Investigation: Pear Crossing the Arctic Lesson 0.2: Symbolic Representation Investigation: Problems, Problems, Problems Lesson 0.3: Organizing Information Investigation: Who Owns the Zebra?

Formative Assessments Have students journal about the following questions after each investigation: “How did you approach the problem?” “How did you arrive at your conclusion?” “How might you recognize problems for which organizing through units or tables would be a useful technique?”

Summative Assessments

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Common Core State Standards For Mathematics Conceptual Category: Functions Domain: Interpreting Functions F-IF 3 Cluster: Understand to concept of a function and use function notation

Domain: Linear, Quadratic and Exponential Models F-LE 2 Cluster: Construct and compare linear and exponential models and solve problems

Sequences

Weeks 2 and 3

Domain: Building Functions F-BF 2 Cluster: Build a function that models a relationship between two quantities

Program Materials Discovering Advanced Algebra Chapter 1: Sequences Lesson 1.1: Recursively Defined Sequences Investigation: Monitoring Inventory Lesson 1.2: Modeling Growth and Decay Lesson 1.3: A First Look at Limits

Formative Assessments Have students create a graphic organizer to compare and contrast arithmetic and geometric sequences.

Summative Assessments Quiz Chapter 1 Test: Sequences Chapter 1 Constructive Assessment Items: Key Curriculum Resources

Lesson 1.4: Graphing Sequences Investigation: Matching Them Up Lesson 1.5: Loans and Investments Investigation: Life’s Big Expenditures

Possible lesson for students who might need to refresh math skills: Refreshing Your Skills for Chapter 1: Differences and Ratios

Possible Extension Lessons: Exploration: Graphing Sequences Exploration: Refining the Growth Model


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Common Core State Standards For Mathematics Conceptual Category: Statistics and Probability Domain: Interpreting Categorical and Quantitative Data S-ID 1, 2, and 3 Cluster: Summarize, represent, and interpret data on a single count or measurement variable

Program Materials Discovering Advanced Algebra Chapter 2: Describing Data Lesson 2.1: Box Plots Lesson 2.2: Measures of Spread

Describing Data

Weeks 4 and 5

Lesson 2.3: Histograms and Percentile Ranks Investigation: Eating on the Run

Possible lesson for students who might need to refresh math skills:

Formative Assessments Marzano’s Building Academic Vocabulary: Have students create a word wall including terms, descriptions, and visual representations to refer back to throughout the course. Use strategies such as: Talk-A-Mile-A-Minute Charades Pictionary Graphic Organizers I Have, Who Has

Summative Assessments Quiz Chapter 2 Test: Describing Data Chapter 2 Constructive Assessment Items: Key Curriculum Resources

Refreshing Your Skills for Chapter 2: Measures of Central Tendency and Dot Plots Possible Extension Lessons: Exploration: Precision, Accuracy, and Significant Figures Exploration: Census Microdata


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Common Core State Standards For Mathematics Conceptual Category: Number and Quantity Domain: Quantities* N-Q 1 Cluster: Reason quantitatively and use units to solve problems Conceptual Category: Algebra Domain: Seeing Structure in Expressions A-SSE 1a Cluster: Interpret the structure of expressions Domain: Creating Equations* A-CED 1, 2, 3, and 4 Cluster: Create equations that describe numbers or relationships Domain: Reasoning with Equations and Inequalities A-REI 1, 2 Cluster: Solve equations and inequalities in one variable

Linear Models and Systems

Weeks 6 and 7

Cluster: Solve systems of equations Conceptual Category: Functions Domain: Linear, Quadratic, and Exponential Models F-LE 1a, 1b, 2, and 5 Cluster: Construct and compare linear and exponential models and solve problems Cluster: Interpret expressions for functions in terms of the situation they model. Conceptual Category: Geometry Domain: Expressing Geometric Properties with Equations G-GPE 5 Cluster: Use coordinate geometry to prove simple geometric theorems algebraically

Program Materials Discovering Advanced Algebra Chapter 3: Linear Models and Systems Lesson 3.1: Linear Equations and Arithmetic Sequences Investigation: Match Point Lesson 3.2: Revisiting Slope Lesson 3.3: Fitting a Line to Data Lesson 3.4: The Median-Median Line Investigation: Airline Schedules

Summative Assessments Quiz Chapter 3 Test: Linear Models and Systems Chapter 3 Constructive Assessment Items: Key Curriculum Resources

Lesson 3.5: Prediction and Accuracy Lesson 3.6: Linear Systems Investigation: Population Trends Lesson 3.7: Substitution and Elimination Investigation: What’s Your System Possible lesson for students who might need to refresh math skills:

Conceptual Category: Statistics and Probability Domain: Interpreting Categorical and Quantitative Data S-ID 6a, 6c, and 7 Cluster: Summarize, represent, and interpret data on two categorical and quantitative variables

Refreshing Your Skills for Chapter 3: Linear Relationships

Cluster: Interpret Linear Models

Exploration: Residual Plots and Least Squares


Formative Assessments Use a Quick Write to answer the following prompt: How would you decide which method to use to solve a system of linear equations?

Possible Extension Lessons:

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Common Core State Standards For Mathematics

Functions, Relations, and Transformations

Weeks 8, 9, and 10

Conceptual Category: Algebra Domain: Seeing Structure in Expressions A-SSE 1a, 1b Cluster: Interpret the structure of expressions

Program Materials Discovering Advanced Algebra Chapter 4: Functions, Relations, and Transformations Lesson 4.1: Interpreting Graphs Investigation: Graph a Story

Domain: Creating Equations* A-CED 4 Cluster: Creating equations that describe numbers or relationships

Lesson 4.2: Function Notation Investigation: To Be or Not to Be (a Function)

Domain: Reasoning with Equations and Inequalities A-REI 2, 4b, 10, and 11 Cluster: Understand solving equations as a process of reasoning and explain the reasoning

Lesson 4.3: Lines in Motion

Solve equations and inequalities in one variable

Lesson 4.5: Reflection and the Square Root Family Investigation: Take a Moment to Reflect

Represent and solve equations and inequalities graphically Conceptual Category: Functions Domain: Interpreting Functions F-IF 1, 2, 4, 5, 7a, 7b,and 9 Cluster: Understand the concept of a functions and use function notation Interpret functions that arise in applications in terms of the context Analyze functions using different representations Domain: Building Functions F-BF 3 Cluster: Build new functions from existing functions

Lesson 4.4: Translations and the Quadratic Family Investigation: Make My graph

Formative Assessments

Summative Assessments Quiz Chapter 4 Test: Functions, Relations, and Transformations Chapter 4 Constructive Assessment Items: Key Curriculum Resources

Lesson 4.6: Dilations and the AbsoluteValue Family Lesson 4.7: Transformations and the Circle Family Lesson 4.8: Composition of Functions Possible lesson for students who might need to refresh math skills: Refreshing Your Skills for Chapter 4: Solving Equations Possible Extension Lessons:

Conceptual Category: Geometry Domain: Expressing Geometric Properties with Equations G-GPE 1 Cluster: Translate between the geometric description and the equation for a conic section


Exploration: Rotation as a Composition of Transformations

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Common Core State Standards For Mathematics Conceptual Category: Number and Quantity Domain: The Real Number System N-RN 1, 2 Cluster: Extend the properties of exponents to rational exponents

Conceptual Category: Algebra Domain: Seeing Structure in Expressions A-SSE 1a, 2, 3c Cluster: Interpret the structure of expressions

Exponential, Power, and Logarithmic Functions

Weeks 11, 12, and 13

Write expressions in equivalent forms to solve problems Domain: Creating Equations* A-CED 1, 2, and 4 Cluster: Create equations that describe numbers or relationships Domain: Reasoning with Equations and Inequalities A-REI 1 and 11 Cluster: Understand solving equations as a process of reasoning and explain the reasoning Represent and solve equations and inequalities graphically

Conceptual Category: Functions Domain: Interpreting Functions F-IF 2, 3, 7b, 7e, 8b, and 9 Cluster: Understand the concept of a functions and use function notation

Program Materials Discovering Advanced Algebra Chapter 5: Exponential, Power, and Logarithmic Functions Lesson 5.1: Exponential Functions Lesson 5.2: Properties of Exponents and Power Functions Investigation: Properties of Exponents Lesson 5.3: Rational Exponents and Roots Lesson 5.4: Applications of Exponential and Power Equations

Formative Assessments Use a Quick Write to ensure students understand the concept of inverse functions and can apply that concept to the special case of exponential and logarithmic functions

Summative Assessments Quiz Chapter 5 Test: Exponential, Power, and Logarithmic Functions Chapter 5 Constructive Assessment Items: Key Curriculum Resources

Lesson 5.5: Building Inverses of Functions Investigation: The Inverse Lesson 5.6: Logarithmic Functions

Analyze functions using different representations Domain: Building Functions F-BF 1a, 1b, 2, 3, 4a, 4b, 4c Cluster: Build a function that models a relationship between two quantities


Build new functions from existing functions

Refreshing Your Skills for Chapter 5: Working with Positive Square Roots

Domain: Linear, Quadratic, and Exponential Models F-LE 1a, 1c, 2, 4, and 5 Cluster: Construct and compare linear and exponential models and solve problems Interpret expressions for functions in terms of the situation they model

Conceptual Category: Statistics and Probability

Possible Extension Lessons: Lesson 5.7: Properties of Logarithms Lesson 5.8: Applications of Logarithms Exploration: The Number e

Domain: Interpreting Categorical and Quantitative Data S-ID 6a Cluster: Summarize, represent, and interpret data on two categorical and quantitative variables


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Time Frame

Common Core State Standards For Mathematics Conceptual Category: Algebra Domain: Seeing Structure in Expressions A-SSE 1a Cluster: Interpret the structure of expressions Domain: Creating Equations* A-CE 3 Cluster: Creating equations that describe numbers or relationships

Matrices and Linear Systems

Weeks 14 and 15

Domain: Reasoning with Equations and Inequalities A-REI 6, 7, 12 Cluster: Solve system of equations Represent ad solve equations and inequalities graphically


Program Materials Discovering Advanced Algebra Chapter 6: Matrices and Linear Systems Lesson 6.5: Systems of Inequalities Investigation: Paying for College Lesson 6.6: Linear Programming Investigation: Maximizing Profit


Formative Assessments Project: Nutritional Elements p.366

Summative Assessments Quiz Chapter 6 Test: Matrices and Linear Systems Chapter 6 Constructive Assessment Items: Key Curriculum Resources

Refreshing Your Skills for Chapter 6: Properties of Real Numbers Differentiation: Use Discovering Algebra lessons from Chapter 5 to help build understanding of solving systems of linear equations

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Time Frame

Common Core State Standards For Mathematics Conceptual Category: Algebra

Program Materials Discovering Advanced Algebra Chapter 9: Series

Domain: Seeing Structure in Expressions A-SSE 4 Cluster: Write expressions in equivalent forms to solve problems

Lesson 9.1: Arithmetic Series


Summative Assessments Quiz Chapter 9 Test: Series

Lesson 9.2: Infinite Geometric Series Lesson 9.3: Partial Sums of Geometric Series

Refreshing Your Skills for Chapter 9: Arithmetic and Geometric Sequences

Series

Weeks 16 and 17


Chapter 9 Constructive Assessment Items: Key Curriculum Resources


Possible Extension Lessons: Exploration: Seeing the Sum of a Series

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Common Core State Standards For Mathematics

Program Materials Discovering Advanced Algebra Chapters 1 – 6, and 9 Review


Summative Assessments Semester 1 District Final Exam

Week 18

Time Frame


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Time Frame

Common Core State Standards For Mathematics Conceptual Category: Number and Quantity Domain: The Real Number System N-RN 3 Cluster: Use properties of rational and irrational numbers to solve problems

Quadratic and Other Polynomial Functions

Weeks 19, 20, 21, and 22

Domain: The Complex Number System N-CN 1, 2, 7 Cluster: Perform arithmetic operations with complex numbers

Program Materials Discovering Advanced Algebra Chapter 7: Quadratic and Other Polynomial Functions Lesson 7.1: Polynomial Degree and Finite Differences

Solve quadratic equations with real coefficients that have complex solutions

Lesson 7.2: Equivalent Quadratic Forms

Conceptual Category: Algebra

Lesson 7.3: Completing the Square Investigation: Complete the Square

Domain: Seeing Structures in Expressions A-SSE 1a, 1b, 2, 3a, 3b Cluster: Interpret the structure of expressions Write expressions in equivalent forms to solve problems Domain: Arithmetic with Polynomials and Rational Functions A-APR 2, 3, 4 Cluster: Understand the relationship between zeros and factors of polynomials Use polynomial identities to solve problems

Lesson 7.4: The Quadratic Formula Investigation: How High Can You Go?

Lesson 7.6: Factoring Polynomials Investigation: The Box Factory

Domain: Reasoning with Equations and Inequalities A-REI 1, 4a, 4b, Cluster: Understand solving equations as a process of reasoning and explain the reasoning

Lesson 7.7: Higher-Degree Polynomials Investigation: The Largest Triangle

Domain: Interpreting Functions F-IF 4, 7a, 7c, 8a, 9 Cluster: Interpret functions that arise in applications in terms of the context Analyze functions using different representations Domain: Building Functions F-BF 3, 4a Cluster: Build new functions from existing functions


Summative Assessments Quiz

Have Students Explain: “How are the representations of complex conjugates on the complex plan related?”


Chapter 7 Test: Quadratics and Other Polynomial Functions

Lesson 7.5: Complex Numbers Investigation: Complex Numbers

Domain: Creating Equations* A-CED 1, 2 Cluster: Create equations that describe numbers or relationships

Conceptual Category: Functions

Formative Assessments Have students Create quadratic equations to represent a variety of possible roots in the real and complex number system

Lesson 7.8: More About Finding Solutions Possible lesson for students who might need to refresh math skills: Refreshing Your Skills for Chapter 7: Polynomial Expressions

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Time Frame

Common Core State Standards For Mathematics Conceptual Category: Algebra

Conic Sections and Rational Functions

Weeks 23, 24, and 25

Domain: Seeing Structure in Expressions A-SSE 1a, 1b Cluster: Interpret the structure of expressions

Program Materials Discovering Advanced Algebra Chapter 8: Conic Sections and Rational Functions

Domain: Arithmetic with Polynomials A-APR 6 Cluster: Rewrite rational expressions

Lesson 8.1: Using the Distance Formula

Domain: Creating Equations* A-CED 1, 2 Cluster: Create equations that describe numbers or relationships

Lesson 8.2: Circles and Ellipses Note: Circles are needed for the CCSS, however, Ellipses are an extension if time permits

Domain: Reasoning with Equations and Inequalities A-REI 2, 11 Cluster: Understand soling equations as a process of reasoning and explain the reasoning

Lesson 8.3: Parabolas Investigation: Fold a Parabola

Represent and solve equations and inequalities graphically

Lesson 8.5: The General Quadratic

Formative Assessments Have students journal about their previous understanding of parabolas before beginning work in conic sections and then continue adding to their journal regarding their understanding of a parabola.

Summative Assessments Quiz Chapter 8 Test: Conic Sections and Rational Functions Chapter 8 Constructive Assessment Items: Key Curriculum Resources

Conceptual Category: Functions Domain: Interpreting Functions F-IF 4, 7e Cluster: Interpret functions that arise in applications in terms of the context Analyze functions using different representations Domain: Building Functions F-BF 3 Cluster: Build new functions from existing functions

Conceptual Category: Geometry Domain: Expressing Geometric Properties with Equations G-GPE 1, 2 Cluster: Translate between the geometric description and the equation for a conic section

Lesson 8.6: Introduction to Rational Functions Lesson 8.7: Graphs of Rational Functions Investigation: Predicting Asymptotes and Holes Lesson 8.8: Operations with Rational Expressions Possible lesson for students who might need to refresh math skills: Refreshing Your Skills for Chapter 8: The Distance Formula Possible Extension Lessons: 8.4: Hyperbola Exploration: Constructing the Conic Section


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Time Frame

Common Core State Standards For Mathematics Conceptual Category: Statistics and Probability Domain: Making Inferences and justifying Conclusions S-IC 2 Cluster: Understand and evaluate random processes underlying statistical experiments Domain: Conditional Probability and the Rules of Probability S-CP 1, 2, 3, 4, 5, 6, and 7 Cluster: Understand independence and conditional probability and use them to interpret data

Domain: Using Probability to Make Decisions S-MD 3 Cluster: Calculate expected values and use them to solve problems

Probability

Weeks 26 and 27

Use the rules of probabilities to compute probabilities of compound events in a uniform probability model

Program Materials Discovering Advanced Algebra Chapter 10: Probability


Summative Assessments Quiz

Lesson 10.1: Randomness and Probability Investigation: Flip a Coin

Chapter 10 Test: Probability

Lesson 10.2: Counting Outcomes and Tree Diagrams Investigation: The Multiplication Rule


Lesson 10.3: Mutually Exclusive Events and Venn Diagrams

Possible lesson for students who might need to refresh math skills: Refreshing Your Skills for Chapter 10: Basic Probability Possible Extension Lessons: Lesson 10.4: Random Variables and Expected Values Exploration: Geometric Probability Exploration: The Law of Large Numbers


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Time Frame

Common Core State Standards For Mathematics Conceptual Category: Statistics and Probability

Program Materials Discovering Advanced Algebra Chapter 11: Applications of Statistics

Domain: Interpreting Categorical and Quantitative Data S-ID 4, 5, 6, 8, and 9 Cluster: Summarize, represent, and interpret data on a single count or measurement variable

Lesson 11.1: Experimental Design Investigation: Designing a Study

Summarize, represent, and interpret data on two categorical and quantitative variables

Lesson 11.2: Probability Distribution

Applications of Statistics

Weeks 28, 29, 30 and 31

Interpret linear models Domain: Making Inferences and Justifying Conclusions S-IC 1, 3, 4, 5, and 6 Cluster: Understand and evaluate random processes underlying statistical experiments Make inferences and justify conclusions from sample surveys, experiments and observational studies Domain: Using Probability to make decisions S-MD 1, 2, 3, 4, and 7 Cluster: Calculate expected value and use them to solve problems Use probability to evaluate outcomes of decisions

Lesson 11.3: Normal Distribution Lesson 11.4: z-Values and Confidence Intervals Investigation: Keeping Score Lesson 11.5: Bivariate Data and Correlation Investigation: Looking for Connections

Formative Assessments Projects: Simpson’s Paradox p.633 Correlation vs. Causation p.663 Have students conduct a Statistical Study:  Formulate a question  Design an experiment  Collect data



Summative Assessments Quiz Chapter 11 Test: Applications of Statistics Chapter 11 Constructive Assessment Items: Key Curriculum Resources

Analyze data

Lesson 11.6: The Least Square Line Possible lesson for students who might need to refresh math skills: Refreshing Your Skills for Chapter 11: Statistics Possible Extension Lessons: Exploration: Normally Distributed Data Exploration: Prediction Intervals Exploration: Nonlinear Regression


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Common Core State Standards For Mathematics Conceptual Category: Algebra Domain: Creating Equations* A-CED 2 Cluster: Create equations that describe numbers or relationships

Conceptual Category: Functions Domain: Interpreting Functions F-IF 4, 5, 7e Cluster: Interpret functions that arise in applications in terms of the context Analyze functions using different representations

Trigonometric Functions

Weeks 32, 33, 34, and 35

Domain: Building Functions F-BF 1b, 3 Cluster: Build a function that models a relationship between two quantities Build new functions from existing functions Domain: Trigonometric Functions F-TF 1, 2, 3, 4, 5, 6, 7, 8 Cluster: Extend the domain of trigonometric functions using the unit circle Model periodic phenomena with trigonometric functions Prove and apply trigonometric identities

Conceptual Category: Geometry Domain: Similarity, Right Triangle, and Trigonometry G-SRT 5 Cluster: Find arc lengths and areas of sectors of circles

Program Materials Discovering Advanced Algebra Chapter 13: Trigonometric Functions Lesson 13.1: Defining the Circular Function Investigation: Paddle Wheel Lesson 13.2: Radian Measure Investigation: A Radian Protractor Lesson 13.3: Graphing Trigonometric Functions

Formative Assessments Students will be able to model situations in which they collect data, choose an appropriate function family, and a function from that family to model the situation and then justify their reasoning

Summative Assessments Quiz Chapter 13 Test: Trigonometric Functions Chapter 13 Constructive Assessment Items: Key Curriculum Resources

Lesson 13.4: Inverse of Trigonometric Functions Lesson 13.5: Modeling with Trigonometric Equations Lesson 13.6: Fundamental Trigonometric Identities Investigation: Pythagorean Identities Possible lesson for students who might need to refresh math skills: Lesson 12.1: Right Triangle Trigonometry Refreshing Your Skills for Chapter 13: Geometry of the Circle Possible Extension Lessons: Exploration: Circular Functions Lesson 13.7: Combining Trigonometric Functions


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Mathematics Pacing Guide: High School Advanced Algebra Course Common Core State Standards For Mathematics

Program Materials Discovering Advanced Algebra Chapters 7, 8, 10, 11, and 13


Summative Assessments Semester 2 District Final Exam

Week 36

Time Frame


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