A Common Core High School Program by Ron Larson and Laurie Boswell

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1 hmhco.com A Common Core High School Program by Ron Larson and Laurie Boswell Distributed exclusively by Houghton Mifflin Harcourt bigideaslearning.com

2 A New Common Core High School Program By Ron Larson and Laurie Boswell Big Ideas Learning is pleased to present a high school program Big Ideas Math Algebra 1, Geometry, and Algebra 2 that was designed to the Common Core State Standards and uses the Standards for Mathematical Practice as its foundation. With the addition of this program, Big Ideas Learning now has a complete Big Ideas Math Common Core curriculum for Grades 6 through 12. Program Highlights Dynamic Technology for the 21 st -Century Classroom Complete Support for Teachers in Lesson Planning and Lesson Presentation Dynamic Assessment System Research-Based Content and Delivery Rigorous, Focused, and Coherent Curriculum Balanced Approach to Instruction Continuous Preparation for High-Stakes Assessment Embedded RTI, Differentiated Instruction, and ELL Support

3 About the Authors No other authorship team in the industry provides the balance of classroom experience and mathematical expertise that the Big Ideas Math program authors bring to the table. Ron Larson, Ph.D. Ron Larson, Ph.D., is well known as the lead author of a comprehensive program for mathematics that spans middle school, high school, and college courses. He holds the distinction of Professor Emeritus from Penn State Erie, The Behrend College, where he taught for nearly 0 years. He received his Ph.D. in mathematics from the University of Colorado. Dr. Larson s numerous professional activities keep him actively involved in the mathematics education community and allow him to fully understand the needs of students, teachers, supervisors, and administrators. Laurie Boswell, Ed.D. Laurie Boswell, Ed.D., is the Head of School and a mathematics teacher at the Riverside School in Lyndonville, Vermont. Dr. Boswell is a recipient of the Presidential Award for Excellence in Mathematics Teaching and has taught mathematics to students at all levels, from elementary through college. Dr. Boswell is a Tandy Technology Scholar and served on the NCTM Board of Directors from 2002 to She currently serves on the board of NCSM and is a popular national speaker. Dr. Larson and Dr. Boswell began writing together in Since that time, they have authored over three dozen textbooks. In their collaboration, Ron is primarily responsible for the Student Edition while Laurie is primarily responsible for the Teaching Edition. 1

4 Embedded Mathematical Practices Program Philosophy: Rigor and Balance with Embedded Mathematical Practices The Big Ideas Math program balances conceptual understanding with procedural fluency. Real-life applications help turn mathematical learning into an engaging and meaningful way to see and explore the real world. Conceptual Understanding Procedural Fluency Embedded Mathematical Practices Real-Life Applications Embedded Mathematical Practices in grade-level content promote a greater understanding of how mathematical concepts are connected to each other and to real-life scenarios. Mathematical Practices Mathematically proficient students use use appropriate dynamic geometry tools strategically, software including strategically. dynamic geometry software. (MP5) HSG-CO.B.6 USING APPROPRIATE TOOLS STRATEGICALLY To be proficient in math, you need to use appropriate tools strategically, including dynamic geometry software. 2

5 .2 Reflections Essential Question How can you reflect a figure in a coordinate plane? Reflecting a Triangle Using a Reflective Device Explorations and guiding Essential Questions encourage conceptual understanding. Work with a partner. Use a straightedge to draw any triangle on paper and label it ABC. a. Use the straightedge to draw a line that does not pass through the triangle and label it m. b. Place a reflective device on line m. c. Use the reflective device to plot the images of the vertices of ABC. Label the images of vertices A, B, and C as A, B, and C, respectively. d. Use a straightedge to draw A B C by connecting the vertices. Identifying Lines of Symmetry A figure in the plane has line symmetry when the figure can be mapped onto itself by a reflection in a line. This line of reflection is a line of symmetry, such as line m at the left. A figure can have more than one line of symmetry. Identifying Lines of Symmetry m OR E nt in math, ook closely attern or How many lines ofrefl symmetry does each hexagon have? ecting a Triangle in a Coordinate Plane Work with a partner. Use dynamic geometry software to draw any triangle and label a. b. c. it ABC. What You Will Learn.2 Lesson a. Reflect ABC in the y-axis to form A B C. b. What is the relationship between the coordinates of the vertices of ABC and those of A B C? Core Vocabul Vocabulary larry SOLUTION c. What do you observe about the side lengths and angle measures of the two triangles? reflection, p. 182 d. Refl Then repeat parts (b) and (c). a.ect ABC in the x-axis to form A B C. b. c. line of reflection, p. 182 Direct instruction lessons Sample allow for procedural fluency C C Points A( 3, 3) and provide the opportunity A A B( 2, 1) to use clear, precise C( 1, ) Segments mathematical language. AB =.12 Perform reflections. Perform glide reflections. Identify lines of symmetry. Solve real-life problems involving reflections. glide reflection, p. 18 line symmetry, p. 185 line of symmetry, p. 185 Performing Reflections Core Concept 3 Reflections A reflection is a transformation that uses a line like a mirror to reflect a figure. The mirror line is called the line of reflection. 2 Monitoring Progress 1 BC =and 5.10Spanish at BigIdeasMath.com Help in English Determine the 1number of lines of3 symmetry 12. B 1 B 13. AC = 2.2 Angles for the figure. m A = m B = m C = A reflection in a line m maps every point P P in the plane to a point P, so that for each point one of the following properties is true: If P is not on m, then m is the, or perpendicular bisector of PP m If P is on m, then P = P. Communicate Your Answer 15. Draw a hexagon with no lines of symmetry. Section.2 Reflections a. In the line n: x = 3 Point P on m a. Point A is 2 units left of line n, so its reflection A is 2 units right of line n at (5, 3). Also, B is 2 units left of line n at (1, 2), and C is 1 unit right of line n at (, 1). 1/8/1 2:38 PM B A 2 m y A C m Real-life applications n provide students with A A B B opportunities to connect C C B classroom lessons toc realistic scenarios.a y 2 B 2 B b. Point A is 2 units above line m, so A is 2 units below line m at (1, 1). Also, B is 1 unit below line m at (5, 0). Because point C is on line m, you know that C = C. A C SOLUTION B b. In the line m: y = 1 SOLUTION You are going to buy books. Your friend is going to buy CDs. Where should you park to minimize the distance you both will walk? Monitoring Progress m Point P not on m Graph ABC with vertices A(1, 3), B(5, 2), and C(2, 1) and its image after the reflection described. 181 Finding a Minimum Distance Reflect B in line m to obtain B. Then AB. Label the intersection of AB draw and m as C. Because AB is the shortest distance between A and B and BC = B C, park at point C to minimize the combined distance, AC + BC, you both have to walk. P Reflecting in Horizontal and Vertical Lines 3. How can you reflect a figure in a coordinate plane? Solving Real-Life Problems P P Monitoring Progress 6 6 x m x Help in English and Spanish at BigIdeasMath.com Graph ABC from Example 1 and its image after a reflection in the given line. 1. x = 2. x = 3 3. y = 2. y = 1 Help in English and Spanish 182 at BigIdeasMath.com Chapter Transformations 3

6 Big Ideas Math Dynamic Technology Dynamic Classroom The Dynamic Classroom is an online interactive version of the Teaching Edition. Teachers can present their lessons and can access all of the online resources available that supplement every section of the Big Ideas Math program at point of use. Dynamic Student Edition ebook App The Dynamic Student Edition ebook App is a complete electronic version of the Student Edition that includes interactive digital resources. This app allows students to navigate through the book, highlight important information, and add notes or bookmarks. With a data or internet connection, students can access embedded, digital enhancements. Dynamic Investigations The Dynamic Investigations in the Big Ideas Math program allow students and teachers to interactively complete the Big Ideas Math explorations.

7 Real-Life STEM Videos Every chapter in the Big Ideas Math program contains a Real-Life STEM Video allowing students to further engage with mathematical concepts. Students learn about the Parthenon, natural disasters, solar power, and more! Dynamic Teaching Tools These tools feature the Interactive Whiteboard Lesson Library. Teachers can present any Big Ideas Math lesson from an interactive whiteboard. Standard whiteboard lessons and customizable templates are included. The Interactive Whiteboard Lessons are compatible with SMART, Promethean, and Mimio technology. Dynamic Assessment System The Dynamic Assessment System allows teachers to track and evaluate their students advancement through the curriculum. Developed exclusively for Big Ideas Math, this technology provides teachers and students an intuitive and state-of-the-art tool to help students effectively learn mathematics. Built for ease of use, the tool is available on a wide range of devices. 5

8 The Big Ideas Math Dynamic Assessment System Homework and Assessment Includes multiple, customizable assignments for each chapter Allows teachers to assign homework and assessments for the entire class or a select group of students Offers progress monitoring assessments for an adaptive testing experience Direct Ties to Remediation Includes direct links to Lesson Tutorial Videos and relevant lesson sections Allows students to access live chat tutors for selected exercises All-In-One Reporting Offers real-time reporting at both the class and student levels Tracks progress through Assignment Performance and Remediation reports 6

9 Assessment Delivery Provides embedded tools for students Includes auto-scored technologyenhanced items such as drag and drop, graphing, point plotting, multiple select and fill in the blank using math expressions Allows teachers to include reminders or notes to students Intuitive Design Operates on a wide range of devices with large and clear icons for visibility Allows for multiple reporting views through toggle options Includes intelligent presets and easy navigation 7

10 Continuous Preparation for High-Stakes Testing Each chapter of the Big Ideas Math program utilizes question types frequently found on standardized tests. The balanced approach to instruction also helps students develop the habits of mind required to be successful on high-stakes tests. Exercises The Exercises in the Big Ideas Math program provide students with opportunities to use multiple approaches to solve problems. Dynamic Assessment System This tool allows teachers to provide customizable homework directly related to the Big Ideas Math program. Assignments are automatically scored and students have access to immediate remediation on homework questions. Explorations The Explorations that begin each section require students to use higherlevel thinking to work through each problem and to explain their reasoning in the solution. Cumulative Assessments Each chapter in the Big Ideas Math program includes a Cumulative Assessment. The questions in each assessment were carefully chosen to represent problem types and reasoning patterns frequently found on standardized tests. Quizzes and Tests The Quizzes and Tests in the Big Ideas Math program assess the concepts students learned in each lesson. Online Test Practice Self-grading tests are available online, allowing students to receive immediate feedback on their progress. Performance Tasks Each chapter of the Big Ideas Math program contains a Performance Task in the Assessment Book and an online Performance Task that correlates to the STEM video of the chapter. Each Performance Task allows students to work with multiple standards. Alternative Assessments Alternative Assessments provide teachers with the opportunity to assess students on the same content in a variety of ways. 3. HOW DO YOU SEE IT? The function y = A(x) represents the attendance at a high school x weeks after a flu outbreak. The graph of the function is shown. Number of students Attendance A Week a. What happens to the school s attendance after the flu outbreak? b. Estimate A(13) and explain its meaning. c. Use the graph to estimate the solution(s) of the equation A(x) = 00. Explain the meaning of the solution(s). d. What was the least attendance? When did that occur? e. How many students do you think are enrolled at this high school? Explain your reasoning. 29. MAKING AN ARGUMENT Your friend claims the uneven parallel bars in gymnastics are not really parallel. She says one is higher than the other, so they cannot be in the same plane. Is she correct? Explain. 0. ERROR ANALYSIS You deposit $250 in an account that pays 1.25% annual interest. Describe and correct the error in finding the balance after 3 years when the interest is compounded quarterly A = 250 ( 1 + ) 3 A = $

11 Print Components Student Edition The Student Edition was designed using the Universal Design for Learning Guidelines (CAST 2011) and features carefully chosen images that increase student engagement and enhance the mathematical content. Teaching Edition The Teaching Edition provides teachers with complete support for every Big Ideas Math lesson. Master Educator Laurie Boswell incorporates instructional insights and recommendations in Laurie s Notes. Student Journal This consumable workbook serves as a valuable resource where students can solve extra practice problems, take notes, and internalize new concepts by expressing their findings in their own words. Resources by Chapter Start Thinking Warm Up Cumulative Review Warm Up Extra Practice (Practice A and B) Enrichment and Extension Puzzle Time Family Communication Letters Available in English and Spanish All print components are also available online. Assessment Book Performance Tasks Prerequisite Skills Tests with Item Analysis Cumulative Tests Mid-Chapter Quizzes Chapter Tests Alternative Assessments with Scoring Rubrics Pre-Course Test with Item Analysis Post-Course Test with Item Analysis 9

12 Chapter 1 Chapter 2 Chapter 3 Chapter Chapter 5 Chapter 6 Solving Linear Equations Solving Linear Inequalities Graphing Linear Functions Writing Linear Functions Solving Systems of Linear Equations Exponential Functions and Sequences Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Polynomial Equations and Factoring Graphing Quadratic Functions Solving Quadratic Equations Radical Functions and Equations Data Analysis and Displays Chapter 1 Chapter 2 Chapter 3 Chapter Chapter 5 Chapter 6 Basics of Geometry Reasoning and Proofs Parallel and Perpendicular Lines Transformations Congruent Triangles Relationships Within Triangles Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Quadrilaterals and Other Polygons Similarity Right Triangles and Trigonometry Circles Circumference, Area, and Volume Probability Chapter 1 Chapter 2 Chapter 3 Chapter Chapter 5 Linear Functions Quadratic Functions Quadratic Equations and Complex Numbers Polynomial Functions Rational Exponents and Radical Functions Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Exponential and Logarithmic Functions Rational Functions Sequences and Series Trigonometric Ratios and Functions Probability Data Analysis and Statistics Visit bigideaslearning.com for more information about the Big Ideas Math High School program. Distributed exclusively by Houghton Mifflin Harcourt bigideaslearning.com To obtain pricing information or to place an order, please contact your Houghton Mifflin Harcourt Account Executive or call Connect with us: BigIdeasLearning Big Ideas Math and Big Ideas Learning are registered trademarks of Larson Texts, Inc. Mimio is a registered trademark of Mimio, LLC. SMART is a registered trademark of SMART Technologies ULC in the U.S. and/or other countries. Promethean is a registered trademark of Promethean Limited. Houghton Mifflin Harcourt is a trademark of Houghton Mifflin Harcourt. Houghton Mifflin Harcourt. All rights reserved. Printed in the U.S.A. 10/15 MS15866 hmhco.com hmhco.com/bigideasmath