FL State Adoption Bid # 3707 Teacher Edition Eureka Math Precalculus Module 2 Special thanks go to the GordRn A. Cain Center and to the Department of Mathematics at Louisiana State University for their support in the development of Eureka Math. For a free Eureka Math Teacher Resource Pack, Parent Tip Sheets, and more please visit www.Eureka.tools Published by Great Minds®. Copyright © 2018Great Minds® . No part of this work may be reproduced, sold, or commercialized, in whole or in part, without written permission from Great Minds® . Noncommercial use is licensed pursuant to a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 license; for more information, go to http://greatminds.org/copyright. Great Minds and Eureka Math are registered trademarks of Great Minds®. Printed in the U.S.A. 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Cain Center for STEM Literacy at Louisiana State University William Kelly, Treasurer, Co-Founder and CEO at ReelDx Jason Griffiths, Secretary, Director of Programs at the National Academy of Advanced Teacher Education Pascal Forgione, Former Executive Director of the Center on K-12 Assessment and Performance Management at ETS Lorraine Griffith, Title I Reading Specialist at West Buncombe Elementary School in Asheville, North Carolina Bill Honig, President of the Consortium on Reading Excellence (CORE) Richard Kessler, Executive Dean of Mannes College the New School for Music Chi Kim, Former Superintendent, Ross School District Karen LeFever, Executive Vice President and Chief Development Officer at ChanceLight Behavioral Health and Education Maria Neira, Former Vice President, New York State United Teachers This page intentionally left blank ^dKZzK&&hEd/KE^ DĂƚŚĞŵĂƚŝĐƐƵƌƌŝĐƵůƵŵ WZ>h>h^EsEdKW/^ͻDKh>Ϯ Table of Contents1 sĞĐƚŽƌƐĂŶĚDĂƚƌŝĐĞƐ Module Overview .................................................................................................................................................. 3 Topic A: Networks and Matrices.......................................................................................................................... 15 Lesson 1: Introduction to Networks ....................................................................................................... 16 Lesson 2: Networks and Matrix Arithmetic ............................................................................................ 33 Lesson 3: Matrix Arithmetic in Its Own Right ......................................................................................... 46 Topic B: Linear Transformations of Planes and Space ......................................................................................... 64 Lesson 4: Linear Transformations Review .............................................................................................. 66 Lesson 5: Coordinates of Points in Space ............................................................................................... 81 Lesson 6: Linear Transformations as Matrices ..................................................................................... 106 Lesson 7: Linear Transformations Applied to Cubes ............................................................................ 122 Lessons 8–9: Composition of Linear Transformations ......................................................................... 138 Lesson 10: Matrix Multiplication Is Not Commutative ......................................................................... 167 Lesson 11: Matrix Addition Is Commutative ........................................................................................ 177 Lesson 12: Matrix Multiplication Is Distributive and Associative ......................................................... 187 Lesson 13: Using Matrix Operations for Encryption ............................................................................. 199 Mid-Module Assessment and Rubric ................................................................................................................ 215 Topics A through B (assessment 1 day, return 1 day, remediation or further applications 2 days) Topic C: Systems of Linear Equations.. ............................................................................................................... 239 Lesson 14: Solving Equations Involving Linear Transformations of the Coordinate Plane .................. 241 Lesson 15: Solving Equations Involving Linear Transformations of the Coordinate Space .................. 255 Lesson 16: Solving General Systems of Linear Equations ..................................................................... 270 Topic D: Vectors in Plane and Space .................................................................................................................. 282 Lesson 17: Vectors in the Coordinate Plane ......................................................................................... 285 1Each lesson is ONE day, and ONE day is considered a 45-minute period. DŽĚƵůĞϮ: Vectors and Matrices 1 ©201ϴ Great Minds ®. eureka-math.org A STORY OF FUNCTIONS DŽĚƵůĞKǀĞƌǀŝĞǁ DϮ PRECALCULUS AND ADVANCED TOPICS Lesson 18: Vectors and Translation Maps ............................................................................................ 303 Lesson 19: Directed Line Segments and Vectors .................................................................................. 326 Lesson 20: Vectors and Stone Bridges .................................................................................................. 344 Lesson 21: Vectors and the Equation of a Line ..................................................................................... 362 Lesson 22: Linear Transformations of Lines ......................................................................................... 376 Lessons 23–24: Why Are Vectors Useful? ............................................................................................ 389 Topic E: First-Person Video Games—Projection Matrices ................................................................................. 416 Lesson 25: First-Person Computer Games............................................................................................ 418 Lesson 26: Projecting a 3-D Object onto a 2-D Plane ........................................................................... 436 Lesson 27: Designing Your Own Game ................................................................................................. 448 End-of-Module Assessment and Rubric ............................................................................................................ 462 Topics C through E (assessment 1 day, return 1 day, remediation or further applications 3 days) 2 DŽĚƵůĞϮ: Vectors and Matrices ©201ϴ Great Minds ®. eureka-math.org A STORY OF FUNCTIONS DŽĚƵůĞKǀĞƌǀŝĞǁ DϮ PRECALCULUS AND ADVANCED TOPICS Precalculus and Advanced Topics ͻ Module 2 sĞĐƚŽƌƐĂŶĚDĂƚƌŝĐĞƐ OVERVIEW In Module 1, students learned that throughout the 1800s, mathematicians encountered a number of disparate situations that seemed to call for displaying information via tables and performing arithmetic operations on those tables. One such context arose in Module 1, where students saw the utility of representing