Authors Shannon Mccaw Beth Armstrong matt mccaw sarah schuhl michelle terry scott VAlwAy

Transcription

1 Authors Shannon Mccaw Beth Armstrong matt mccaw sarah schuhl michelle terry scott VAlwAy Oregon Focus On Lines and Angles i

2 cover photograph Copyright 2008 by SM c Curriculum LLC. All rights reserved. Printed in China. This publication is protected by copyright. No part of this publication should be reproduced or transmitted in any form or by any means without prior written consent of the publisher. This includes, but is not limited to, electronic reproduction, storage in a retrieval system, photocopying, recording or broadcasting for distance learning. For information regarding permission(s), write to: Permissions Department. ISBN: ii Oregon Focus On Lines and Angles

3 Series Author ABOUT THE AUTHORS Shannon McCaw is a classroom teacher and consultant. She has taught mathematics in the Newberg and Parkrose School Districts. She has been trained in Professional Learning Communities, Differentiated Instruction and Critical Friends. Shannon currently works with math teachers from over 40 districts around the State of Oregon. Her expertise lies in Oregon standards, curriculum alignment and assessment practices. Shannon has a Masters of Arts in Secondary Math Education from Colorado College. Contributing Authors Beth Armstrong has been an elementary school teacher in the Beaverton School District. She has received training in Talented and Gifted Instruction. She recently completed her Masters in Curriculum and Instruction from Washington State University. Matt McCaw has been a classroom teacher and special education case-manager in the Newberg, Centennial and Parkrose School Districts in Oregon. Matt has been trained in Differentiated Instruction, Professional Learning Communities, Critical Friends Groups and Understanding Poverty. He currently teaches math at Parkrose High School. Matt has a Masters of Special Education from Western Oregon University. Sarah Schuhl has been a classroom teacher in Union, Lake Oswego and Centennial School Districts in Oregon. She has been trained in Assessment for Learning, Professional Learning Communities, Advanced Placement and Instructional Coaching. She currently serves as the Math Instructional Coach at Centennial High School. Sarah has a Masters of Science in Teaching Mathematics from Portland State University. Michelle Terry has been a classroom teacher in the Estacada and Newberg School Districts in Oregon. Michelle has received training in Professional Learning Communities, Critical Friends, and ELL Instructional Strategies. Michelle has an Interdisciplinary Masters from Western Oregon University. She currently fills the role of a Teacher on Special Assignment with a focus on math curriculum and instruction at Newberg High School. Scott Valway has been a classroom teacher in the Tigard-Tualatin, Newberg and Parkrose School Districts in Oregon. Scott has been trained in Differentiated Instruction, Professional Learning Communities, Critical Friends, Discovering Algebra, and Pre-Advanced Placement. Scott has a Masters of Science in Teaching from Oregon State University. He currently teaches math at Parkrose High School. Oregon Focus On Lines and Angles iii

4 oregon Core standards The complete set of Oregon Core Standards can be found at This book focuses on the highlighted core standards shown below. Grade 8 It is essential that these standards be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations. 8.1 Algebra: Analyze and represent linear functions, and solve linear equations and systems of linear equations Translate among contextual, verbal, tabular, graphical, and algebraic representations of linear functions Determine the slope of a line and understand that it is a constant rate of change Identify and interpret the properties (i.e. slope, intercepts, continuity, and discreteness) of linear relationships as they are shown in the different representations and recognize proportional relationships (y/x = k or y = kx ) as a special case Use linear functions and equations to represent, analyze and solve problems, and to make predictions and inferences Relate systems of two linear equations in two variables and their solutions to pairs of lines that are intersecting, parallel, or the same line Use informal strategies (e.g., graphs or tables) to solve problems involving systems of linear equations in two variables. 8.2 Data Analysis and Algebra: Analyze and summarize data sets Organize and display data (e.g., histograms, box-and-whisker plots, scatter plots) to pose and answer questions; and justify the reasonableness of the choice of display Use measures of center and spread to summarize and compare data sets Interpret and analyze displays of data and descriptive statistics Compare descriptive statistics and evaluate how changes in data affect those statistics Describe the strengths and limitations of a particular statistical measure, and justify or critique its use in a given situation Use sample data to make predictions regarding a population Identify claims based on statistical data and evaluate the reasonableness of those claims Use data to estimate the likelihood of future events and evaluate the reasonableness of predictions. 8.3 Geometry and Measurement: Analyze two- and three-dimensional spaces and figures by using distance and angle Use properties of parallel lines, transversals, and angles to find missing sides and angles, and to solve problems including determining similarity or congruence of triangles Use models to show that the sum of the angles of any triangle is 180 degrees and apply this fact to find unknown angles Use models and logical arguments to show that the sum of the angles of any quadrilateral is 360 degrees, and apply this fact to find unknown angles Use models to explore the validity of the Pythagorean Theorem, and use it to find missing lengths Apply the Pythagorean Theorem to find distances in a variety of 2- and 3-dimensional contexts, including distances on coordinate graphs Use models and referents to explore and estimate square roots. Reprinted with permission from the Oregon Department of Education. All rights reserved. iv Oregon Focus On Lines and Angles

5 OregOn FOcus On Lines and angles contents in BrieF How To Use YoUr MaTH Book LeTTer FroM THe authors BLock 1 angle Pairs BLock 2 TriangLes and QUadriLaTeraLs BLock 3 THe PYTHagorean THeoreM acknowledgements english/spanish glossary selected answers index ProBLeM-soLving symbols oregon state assessment ForMULa sheet viii x Oregon Focus On Lines and Angles v

6 Block 1 ~ Angle Pairs Lesson 1 MeasUring and naming angles Lesson 2 classifying angles Explore! Classify an Angle Lesson 3 complementary and supplementary angles Explore! Complementary vs Supplementary Lesson 4 vertical angles Explore! The Vertical Angle Relationship Lesson 5 alternate exterior and interior angles Explore! Alternate Exterior and Alternate Interior Lesson 6 corresponding and same-side interior angles Explore! More Angle Pairs review BLock 1 ~ angle Pairs Block 2 ~ triangles and Quadrilaterals Lesson 7 classifying TriangLes Explore! Naming By Sides Lesson 8 angle sum of a TriangLe Explore! Add Them Up Lesson 9 special TriangLes Explore! What Makes Me Special? Lesson 10 congruent and similar TriangLes Lesson 11 ParaLLeL Lines and similar TriangLes Explore! Parallel Similarity Lesson 12 angle sum of a QUadriLaTeraL Explore! Four Corners Lesson 13 special QUadriLaTeraLs review BLock 2 ~ TriangLes and QUadriLaTeraLs vi Oregon Focus On Lines and Angles

7 Block 3 ~ the Pythagorean theorem Lesson 14 PerFecT squares Explore! Squares That Are Perfect Lesson 15 estimating square roots Explore! Calculate It! Lesson 16 THe PYTHagorean THeoreM Explore! A Rule for Right Triangles Lesson 17 converse of THe PYTHagorean THeoreM Explore! Make It Right Lesson 18 applying THe PYTHagorean THeoreM Explore! 3D PT Lesson 19 distance on THe coordinate PLane Explore! Perimeter on the Coordinate Plane Lesson 20 THe distance ForMULa review BLock 3 ~ THe PYTHagorean THeoreM Oregon Focus On Lines and Angles vii

8 how to use Your MAth BooK Your math book has features that will help you be successful in this course. Use this guide to help you understand how to use this book. lesson target VocABulAry Each new vocabulary word is printed in red. The definition can be found with the word. You can also find the definition of the word in the glossary which is in the back of this book. explore! Some lessons have explore! activities which allow you to discover mathematical concepts. Look for these activities in the Table of Contents and in lessons next to the purple line. examples Examples are useful because they remind you how to work through different types of problems. Look for the word example and the green line. helpful hints Blue Boxes This calculator icon will appear in Lessons and Exercises where a calculator is needed. Your teacher may want you to use your calculator at other times, too. If you are unsure, make sure to ask if it is the right time to use it. viii Oregon Focus On Lines and Angles

9 exercises The exercises are a place for you to find practice problems to determine if you understand the lesson s target. You can find selected answers in the back of this book so you can check your progress. review The review provides a set of problems for you to practice concepts you have already learned in this book. The review follows the exercises in each lesson. There is also a review section at the end of each Block. tic-tac-toe ActiVities Each Block has a Tic-Tac-Toe board at the beginning with activities that extend beyond the Oregon Core Standards. The Tic-Tac-Toe activities described on the board can be found throughout each Block in yellow boxes. career Focus At the end of each Block, you will find an autobiography of an Oregon resident. Each person explains what they like about their job and how math is used in their career. oregon Focus on math StaGe 3 Oregon Focus On Lines and Angles ix

10 Letter FroM the Authors Dear Student, This textbook was specifically designed for you. As a student learning math in Oregon, you are responsible for learning three areas of mathematics each year. Each year you will take a state assessment that tests your skills in these areas. Stage 1 Stage 2 Stage 3 Focus on Fractions and Decimals Focus on Ratios, Rates and Percents Focus on Introductory Algebra Focus on Rational Numbers and Equations Focus on Proportionality Focus on Surface Area and Volume Focus on Linear Equations Focus on Data Analysis Focus on Lines and Angles When you successfully finish these areas, you will be ready to enter Algebra I. For the graduating class of 2014 and beyond, you will need 3 credits of mathematics in high school that are at the Algebra I level and above. It is important that you give your best effort in math class as everyone can be good at math if they try. If you have questions, ask your teacher, a friend or a parent. Do not be shy; nearly everyone struggles with math sometimes. In these books you will find information about places and events from all across the state of Oregon. We hope you enjoy learning about your state. You may even find something about the city or town you live in! Sincerely, Shannon McCaw Matt McCaw Beth Armstrong Sarah Schuhl Scott Valway Michelle Terry x Oregon Focus On Lines and Angles