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Mathematics Pacing Guide: High School Algebra Course

Math_Pacing Guide Algebra_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

MILWAUKEE

PUBLIC SCHOOLS



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Common Core State Standards For Mathematics

Program Materials Discovering Algebra

Formative Assessments

Summative Assessments

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Conceptual Category: Number and Quantity Domain: Quantities* N-Q 1, 2, 3 Cluster: Reason Quantitatively and Use Units to Solve Problems.

Chapter 0: Fractions and Fractals Lesson 0.1: The Same Yet Similar Investigation: Connect the Dots Lesson 0.2: More and More Investigation: How Many? Lesson 0.3: Shorter yet Longer Investigation: How Long Is This Fractal? Lesson 0.5: Out of Chaos Investigation: A Chaotic Pattern?

CABS: Fractals and Fractions



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Conceptual Category: Statistics and Probability Domain: Interpreting Categorical and Quantitative

Data S-ID 1, 2, 3, 5, 6a, 6c

Cluster: Summarize, represent and interpret data on a single count or measurement variable

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

Chapter 1: Data Exploration Lesson 1.1: Bar Graphs and Dot Plots Investigation: Picturing Pulse Rates Lesson 1.2: Summarizing Data with Measures of Center Investigation: Making “Cents” of the Center Lesson 1.3: Five-Number Summaries and Box Plots Investigation: Pennies in a Box Lesson 1.4: Histograms and Stem-and-Leaf Plots Investigation: Hand Spans Lesson 1.6: Two-Variable Data Lesson 1.7: Estimating Investigation: Guesstimating Possible Extension Lesson: 1.8: Using Matrices to Organize and Combine Data

CABS: Bob’s Blocks Create an authentic project originating from a research question: Students can articulate a question, a plan to address the question, a process to collect the data, and communicate a summary of the data that defends an answer to the question. To differentiate this project have students who need more directions refer to activity 1.5: Exploring a conjecture

Quiz Chapter 1 Test: Data Exploration Chapter 1 Constructive Assessment Items: Key Curriculum Resources



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Conceptual Category: Number and Quantity Domain: Quantities* N-Q 1, 2, 3 Cluster: Reason quantitatively and use units to solve problems

Conceptual Category: Algebra Domain: Creating Equations* A-CED 1, 2, 3, 4 Cluster: Create equations that describe numbers or relationships Domain: Reasoning with Equations and Inequalities A-REI 1, 2 Cluster: Understand solving equations as a process of reasoning and explain the reasoning

Chapter 2: Proportional Reasoning and Variation Lesson 2.1: Proportions Investigation: Multiply and Conquer Lesson 2.2: Capture-Recapture Investigation: Fish In the Lake Lesson 2.3: Proportions and Measurement System Investigation: Converting Centimeters to Inches Lesson 2.4: Direct Variation Investigation: Ship Canals Lesson 2.5: Inverse Variation Lesson 2.7: Evaluating Expressions Investigation: Number Tricks Lesson 2.8: Undoing Operations Investigation: Just Undo It!

CABS: Jacki’s Homework Question: What is a ratio? What is a proportion? Explain the difference between an equation and an expression.

Quiz Chapter 2 Test: Proportional Reasoning and Variation Chapter 2 Constructive Assessment Items: Key Curriculum Resources



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Conceptual Category: Statistics and Probability Domain: Interpreting Categorical and Quantitative Data S-ID 7, 9 Cluster: Interpret linear models

Conceptual Category: Algebra Domain: Reasoning with equations and inequalities A-REI 3, 10 Cluster: Solve equations and inequalities in one variable

Represent and solve equations and inequalities graphically

Conceptual Category: Functions Domain: Interpreting Functions F-IF 7a, 9 Cluster: Analyze functions using different representations Domain: Building Functions F-B 1a, 2 Cluster: Build a function that models a relationship between two quantities Domain: Linear and Exponential Models F-LEM 1b, 2 Cluster: Construct and compare linear and exponential models and solve problems

Chapter 3: Linear Equations Lesson 3.1: Recursive Sequences Investigation: Recursive Toothpick Patterns Lesson 3.2: Linear Plots Investigation: On the Road Again Lesson 3.3: Time-Distance Relationships Investigation: Walk the Line Lesson 3.4: Linear Equations and the Intercept Form Investigation: Working Out with Equations Lesson 3.5: Linear Equations and Rate of Change Investigation: Wind Chill Lesson 3.6: Solving Equations Using the Balancing Method Investigation: Balancing Pennies Lesson 3.7: Modeling Data Investigation: Tying Knot

CABS: Toothpick Hexagons Students will be able to describe a real world situation through multiple representations: Tables, graphs, symbols written and verbal explanations, models

Quiz Chapter 3 Test: Linear Equations Chapter 3 Constructive Assessment Items: Key Curriculum Resources



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

Domain: Reasoning with Equations and Inequalities A-REI 1, 3 Cluster: Understand solving equations as a process of reasoning and explain the reasoning

Solve equations and inequalities in one variable

Conceptual Category: Functions Domain: Interpreting Functions F-IF 6, 7a Cluster: Interpret functions that arise in applications in terms of the context

Analyze functions using different representations

Domain: Linear, Quadratic, and Exponential Models F-LE 1b, 2, 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, 6c, 7 Cluster: Summarize, represent, and interpret data on two categorical and quantitative variables

Interpret linear models

Chapter 4: Fitting a Line to Data Lesson 4.1: A Formula for Slope Investigation: Points and Slope Lesson 4.2: Writing a Linear Equation to Fit Data Investigation: Beam Strength Lesson 4.3: Point-Slope Form of a Linear Equation Investigation: The Point-Slope Form for Linear Equations Lesson 4.4: Equivalent Algebraic Equations Investigation: Equivalent Equations Lesson 4.5: Writing Point-Slope Equations to Fit Data Investigation: Life Expectancy Lesson 4.6: More on Modeling Lesson 4.7: Applications on Modeling Investigation: What’s My Line? Lesson 4.8: Data Collection and Modeling Activity: The Toyland Bungee Jump

CABS: Equations Have students do a Quick Write to answer the following prompt: “What makes some ways of representing a relationship better or more appropriate than others?”

Quiz Chapter 4 Test: Fitting a Line to Data Chapter 4 Constructive Assessment Items: Key Curriculum Resources



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Conceptual Category: Algebra Domain: Creating Equations* A-CED 1, 3 Cluster: Create equations that describe numbers or relationships Domain: Reasoning with Equations and Inequalities A-REI 3, 5, 6, 11, 12 Cluster: Solve equations and inequalities in one variable

Solve systems of equations


Chapter 5: Systems of Equations and Inequalities Lesson 5.1: Solving Systems of Equations Investigation: Where Will They Meet? Lesson 5.2: Solving Systems of Equations Using Substitution Investigation: All Tied Up Lesson 5.3: Solving Systems of Equations Using Elimination Investigation: Paper Clips and Pennies Lesson 5.5: Inequalities in One Variable Investigation: Toe the Line Lesson 5.6: Graphing Inequalities in Two Variables Lesson 5.7: Systems of Inequalities Possible Extension Lesson: 5.4: Solving Systems of Equations Using Matrices

Constructed Response: The Scale Experiment Canned Hams

Quiz Chapter 5 Test: Systems of Equations and Inequalities Chapter 5 Constructive Assessment Items: Key Curriculum Resources



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Chapters 1 -5 Review Semester 1 District Final Exam



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Conceptual Category: Number and Quantity Domain: The Real Number System N-RN 2 Cluster: Extend the properties of exponents to rational exponents

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

Write expressions in equivalent forms to solve problems Domain: Creating Equations* A-CED 2 Cluster: Create equations that describe numbers or relationships

Conceptual Category: Functions Domain: Interpreting Functions F-IF 5, 7e, 8b, 9 Cluster: Interpret functions that arise in applications in terms of the context

Analyze functions using different representations Domain: Building Functions F-BF 1a, 2 Cluster: Build a function that models a relationship between two quantities Domain: Linear and Exponential Models F-LE 1a, 1c, 2, 3, 5 Cluster: Construct and compare linear and exponential models and solve problems

Interpret expressions for functions in terms of the situation they model

Chapter 6: Exponents and Exponential Models Lesson 6.1: Recursive Routines Investigation: Bugs, Bugs, Everywhere Bugs Lesson 6.2: Exponential Equations Investigation: Growth of the Koch Curve Lesson 6.3: Multiplication and Exponents Investigation: Moving Ahead Lesson 6.4: Scientific Notation for Large Numbers Investigation: Scientific Quandary Lesson 6.5: Looking Back with Exponents Investigation: Division Property of Exponents Lesson 6.6: Zero and Negative Exponents Investigation: More Exponents Lesson 6.7: Fitting Exponential Models to Data Investigation: Radioactive Decay Possible Extension Lesson: Lesson 6.8: Decreasing Exponential Models and Half-Life Activity: Bouncing and Swinging

CABS: Unidel

Quiz Chapter 6 Test: Exponents and Exponential Models Chapter 6 Constructive Assessment Items: Key Curriculum Resources



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Conceptual Category: Functions Domain: Interpreting Functions F-IF 1, 2, 4, 5 Cluster: Understand the concept of a function and use function notation

Interpret functions that arise in applications in terms of the context

Chapter 7: Functions Lesson 7.1: Secret Codes Investigation: TFDSFU DPEFT Lesson 7.2: Functions and Graphs Investigation: Testing for Functions Lesson 7.3: Graphs of Real-World Situations Investigation: Matching Up Lesson 7.4: Function Notation Investigation: A Graphic Message Lesson 7.5: Defining the Absolute-Value Function Investigation: Deviations from the Mean Lesson 7.6: Squares, Squaring, and Parabolas Investigation: Graphing a Parabola

CABS: Susan’s Code Given data from a problem situation, students should be able to: Choose a family of

functions that sensibly models the situation

Find parameters for a function to approximately match the data

Use the resulting function to solve the problem

Interpret and reflect on their solution in the context of the problem

Quiz Chapter 7 Test: Functions Chapter 7 Constructive Assessment Items: Key Curriculum Resources



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Conceptual Category: Algebra Domain: Seeing Structure in Expressions A-SSE 1b Cluster: Interpret the structure of expressions Domain: Arithmetic with Polynomials and Rational Expressions A-APR 1 Cluster: Perform arithmetic operations on polynomials

Conceptual Category: Functions Domain: Interpreting Functions F-IF 7b Cluster: Analyze functions using different representations Domain: Building Functions F-BF 3 Cluster: Build new functions from existing functions

Conceptual Category: Geometry Domain: Congruence G-CO 2, 5 Cluster: Experiment with transformations in the plane

Chapter 8: Transformations Lesson 8.1: Translating Points Investigation: Figures in Motion Lesson 8.2: Translating Graphs Investigation: Translation of Functions Lesson 8.3: Reflecting Points and Graphs Investigation: Flipping Graphs Lesson 8.4: Stretching and Shrinking Graphs Investigation: Changing the Shape of a Graph Lesson 8.6: Introduction to Rational Functions Investigation: I’m Trying to Be Rational Possible Extension Lessons: 8.5: Using Transformations to Model Data Activity: Roll, Walk, or Sum 8.7: Transformations with Matrices Investigation: Matrix Transformations

CABS: My Initials CR: Triangle PBJ Create an image and perform all transformations and have students explain the meaning and relationship of the transformations to the original image

Quiz Chapter 8 Test: Transformations Chapter 8 Constructive Assessment Items: Key Curriculum Resources



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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

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

Write expressions in equivalent forms 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, 11 Cluster: Understand solving equations as a process of reasoning and explaining the reasoning

Solve equations and inequalities in one variable


Conceptual Category: Functions Domain: Interpreting Functions F-IF 1, 2, 7a, 7c, 8a, 9 Cluster: Understand the concept of a function and use function notation

Analyze functions using different representations

Chapter 9: Quadratic Models Lesson 9.1: Solving Quadratic Equations Investigation: Rocket Science Lesson 9.2: Finding the Roots and the Vertex Investigation: Making the Most of It Lesson 9.3: From Vertex to General Form Investigation: Sneaky Squares Lesson 9.4: Factored Form Investigation: Getting to the Root of the Matter Lesson 9.6: Completing the Square Investigation: Searching for Solutions Lesson 9.7: The Quadratic Formula Investigation: Deriving the Quadratic Formula Lesson 9.8: Cubic Functions Investigation: Rooting for Factors Possible Extension Lessons: 9.5: Projectile Motion Activity: Jump or Roll

CABS: Mary’s Dots Sally’s Doorbells

Quiz Chapter 9 Test: Quadratic Models Chapter 9 Constructive Assessment Items: Key Curriculum Resources



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Conceptual Category: Statistics and Probability Domain: Conditional Probability and the Rules of Probability S-CP 1, 2, 3, 5, 6 Cluster: Understand independence and conditional probability and use them to interpret data

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

Chapter 10: Probability Lesson 10.1: Relative Frequency Graphs Lesson 10.2: Probability Outcomes and Trials Investigation: Candy Colors Lesson 10.3: Random Outcomes Investigation: Calculator Coin Toss Lesson 10.4: Counting Techniques Investigation: Prizes Lesson 10.5: Multiple-Stage Experiments Investigation: Pinball Pupils Lesson 10.6: Expected Value

CABS: Free Throws

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



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Conceptual Category: Geometry Domain: Similarity, Right Triangles, and Trigonometry G-SRT 6, 8 Cluster: Define trigonometric ratios and solve problems involving right triangles Domain: Expressing Geometric Properties with Equations G-GPE 5, 7 Cluster: Use coordinates to prove simple geometric theorems algebraically

Chapter 11: Introduction to Geometry Lesson 11.1: Parallel and Perpendicular Investigation: Slopes Lesson 11.2: Finding the Midpoint Investigation: In the Middle Lesson 11.3: Squares, Right Triangles, and Areas Investigation: What’s My Area? Lesson 11.4: The Pythagorean Theorem Investigation: The Sides of a Right Triangle Lesson 11.5: Operations with Roots Investigation: Radicals Lesson 11.6: A Distance Formula Investigation: Amusement Park Lesson 11.7: Similar Triangles and Trigonometric Functions Investigation: Ratio, Ratio, Ratio Lesson 11.8: Trigonometry

CABS: Tommy’s Deck

Quiz Chapter 11 Test: Introduction to Geometry Chapter 11 Constructive Assessment Items: Key Curriculum Resources



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Chapters 6-11 Review Semester 2 District Final Exam

mathematics pacing guide high school · pdf filemathematics pacing guide high school algebra...

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