Mathematics Pacing Guide High School Algebra · PDF fileMathematics Pacing Guide: High School...

Mathematics Pacing Guide: High School Advanced Algebra Course

Math_Pacing Guide Algebra II/Trig_07.27.11_v1 Page | 1 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 Algebra II/Trigonometry

MILWAUKEE

PUBLIC SCHOOLS



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Common Core State Standards For Mathematics

Program Materials Discovering Advanced Algebra

Formative Assessments

Summative Assessments

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Conceptual Category: Number and Quantity Domain: Quantities* N-Q 1 Cluster: Reason quantitatively and use units to solve problems

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

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?

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?”



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Conceptual Category: Functions Domain: Interpreting Functions F-IF 3 Cluster: Understand to concept of a function and use function notation

Domain: Building Functions F-BF 2 Cluster: Build a function that models a relationship between two quantities Domain: Linear, Quadratic and Exponential Models F-LE 2 Cluster: Construct and compare linear and exponential models and solve problems

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 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

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

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



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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

Chapter 2: Describing Data Lesson 2.1: Box Plots Lesson 2.2: Measures of Spread Lesson 2.3: Histograms and Percentile Ranks Investigation: Eating on the Run Possible lesson for students who might need to refresh math skills:

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

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

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



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Common Core State Standards For Mathematics Program Materials Discovering Advanced Algebra



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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

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 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

Cluster: Interpret Linear Models

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 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:

Refreshing Your Skills for Chapter 3: Linear Relationships Possible Extension Lessons:

Exploration: Residual Plots and Least Squares

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

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



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

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

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

Solve equations and inequalities in one variable

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 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

Chapter 4: Functions, Relations, and Transformations

Lesson 4.1: Interpreting Graphs Investigation: Graph a Story

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

Lesson 4.3: Lines in Motion

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

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

Lesson 4.6: Dilations and the Absolute-Value 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:

Exploration: Rotation as a Composition of Transformations

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



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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

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


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

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

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 Lesson 5.5: Building Inverses of Functions Investigation: The Inverse Lesson 5.6: Logarithmic Functions Possible lesson for students who might need to refresh math skills:

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

Lesson 5.7: Properties of Logarithms

Lesson 5.8: Applications of Logarithms

Exploration: The Number e

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

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



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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

Domain: Reasoning with Equations and Inequalities A-REI 6, 7, 12 Cluster: Solve system of equations

Represent ad solve equations and inequalities graphically

Chapter 6: Matrices and Linear Systems Lesson 6.5: Systems of Inequalities Investigation: Paying for College Lesson 6.6: Linear Programming Investigation: Maximizing Profit Possible lesson for students who might need to refresh math skills:

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

Project: Nutritional Elements p.366

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



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

Chapter 9: Series Lesson 9.1: Arithmetic Series Lesson 9.2: Infinite Geometric Series Lesson 9.3: Partial Sums of Geometric Series Possible lesson for students who might need to refresh math skills:

Refreshing Your Skills for Chapter 9: Arithmetic and Geometric Sequences Possible Extension Lessons:

Exploration: Seeing the Sum of a Series

Quiz Chapter 9 Test: Series Chapter 9 Constructive Assessment Items: Key Curriculum Resources



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Chapters 1 – 6, and 9 Review Semester 1 District Final Exam



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Conceptual Category: Number and Quantity Domain: The Real Number System N-RN 3 Cluster: Use properties of rational and irrational numbers to solve problems Domain: The Complex Number System N-CN 1, 2, 7 Cluster: Perform arithmetic operations with complex numbers

Solve quadratic equations with real coefficients that have complex solutions

Conceptual Category: Algebra 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

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

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

Conceptual Category: Functions Domain: Interpreting Functions F-IF 4, 7a, 7c, 8a, 9 Cluster: Interpret functions that arise in applications in terms of the context


Domain: Building Functions F-BF 3, 4a Cluster: Build new functions from existing functions

Chapter 7: Quadratic and Other Polynomial Functions Lesson 7.1: Polynomial Degree and Finite Differences Lesson 7.2: Equivalent Quadratic Forms Lesson 7.3: Completing the Square Investigation: Complete the Square Lesson 7.4: The Quadratic Formula Investigation: How High Can You Go? Lesson 7.5: Complex Numbers Investigation: Complex Numbers Lesson 7.6: Factoring Polynomials Investigation: The Box Factory Lesson 7.7: Higher-Degree Polynomials Investigation: The Largest Triangle 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

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

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

Quiz Chapter 7 Test: Quadratics and Other Polynomial Functions Chapter 7 Constructive Assessment Items: Key Curriculum Resources



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

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

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

Domain: Reasoning with Equations and Inequalities A-REI 2, 11 Cluster: Understand soling 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 4, 7e Cluster: Interpret functions that arise in applications in terms of the context


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

Chapter 8: Conic Sections and Rational Functions Lesson 8.1: Using the Distance Formula Lesson 8.2: Circles and Ellipses Note: Circles are needed for the CCSS, however, Ellipses are an extension if time permits

Lesson 8.3: Parabolas Investigation: Fold a Parabola Lesson 8.5: The General Quadratic 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

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.

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



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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

Use the rules of probabilities to compute probabilities of compound events in a uniform probability model Domain: Using Probability to Make Decisions S-MD 3 Cluster: Calculate expected values and use them to solve problems

Chapter 10: Probability Lesson 10.1: Randomness and Probability Investigation: Flip a Coin 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

Quiz Chapter 10 Test: Probability Chapter 10 Constructive Assessment Items: Key Curriculum Resources



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Conceptual Category: Statistics and Probability 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

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

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

Chapter 11: Applications of Statistics Lesson 11.1: Experimental Design Investigation: Designing a Study Lesson 11.2: Probability Distribution 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 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

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

Analyze data

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



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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


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

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 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

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

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



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Chapters 7, 8, 10, 11, and 13 Semester 2 District Final Exam

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