Authors Shannon Mccaw Beth Armstrong matt mccaw sarah schuhl michelle terry scott VAlwAy Oregon Focus On Introductory Algebra i
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: 978-1-935033-02-8 3 4 5 6 7 8 9 10 ii Oregon Focus On Introductory Algebra
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 Introductory Algebra iii
oregon Core standards The complete set of Oregon Core Standards can be found at www.ode.state.or.us/go/math. This book focuses on the highlighted core standards shown below. Grade 6 It is essential that these standards be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations. 6.1 Number and Operations: develop an understanding of and fluency with multiplication and division of fractions and decimals. 6.1.1 Select and use appropriate strategies to estimate fraction and decimal products and quotients. 6.1.2 Use and analyze a variety of strategies, including models, for solving problems with multiplication and division of fractions. 6.1.3 Use and analyze a variety of strategies, including models, for solving problems with multiplication and division of decimals. 6.1.4 Develop fluency with efficient procedures for multiplying and dividing fractions and decimals and justify why the procedures work. 6.1.5 Apply the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions and justify why they work. 6.1.6 Apply the properties of operations to simplify calculations. 6.1.7 Use the relationship between common decimals and fractions to solve problems including problems involving measurement. 6.2 Number and Operations and Probability: Connect ratio, rate, and percent to multiplication and division. 6.2.1 Develop, analyze, and apply the meaning of ratio, rate, and percent to solve problems. 6.2.2 Determine decimal and percent equivalents for common fractions, including approximations. 6.2.3 Understand the meaning of probability and represent probabilities as ratios, decimals, and percents. 6.2.4 Determine simple probabilities, both experimental and theoretical. 6.2.5 Develop the concept of π as the ratio of the circumference of a circle to its diameter. 6.3 Algebra: Write, interpret, and use mathematical expressions and equations. 6.3.1 Use order of operations to simplify expressions that may include exponents and grouping symbols. 6.3.2 Develop the meanings and uses of variables. 6.3.3 Write, evaluate, and use expressions and formulas to solve problems. 6.3.4 Identify and represent equivalent expressions (e.g., different ways to see a pattern). 6.3.5 Represent, analyze, and determine relationships and patterns using tables, graphs, words and when possible, symbols. 6.3.6 Recognize that the solutions of an equation are the values of the variables that make the equation true. 6.3.7 Solve one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. Reprinted with permission from the Oregon Department of Education. All rights reserved. iv Oregon Focus On Introductory Algebra
OregOn FOcus On IntrOductOry AlgebrA contents In brief How To Use YoUr MaTH Book ------------------------------------------------------ LeTTer FroM THe authors ----------------------------------------------------------- BLock 1 order of operations ------------------------------------------------------ 1 BLock 2 algebraic expressions ---------------------------------------------------- 27 BLock 3 solving equations --------------------------------------------------------- 67 BLock 4 FUncTions ------------------------------------------------------------------ 108 acknowledgements ---------------------------------------------------------------- 140 english/spanish glossary ---------------------------------------------------------- 141 selected answers ------------------------------------------------------------------ 166 index ------------------------------------------------------------------------------- 169 problem-solving------------------------------------------------------------------- 171 symbols ----------------------------------------------------------------------------- 173 oregon state assessment ForMULa sheet ----------------------------------------- 174 viii x Oregon Focus On Introductory Algebra v
Block 1 ~ order of operations Lesson 1 THe FoUr operations ------------------------------------------------- 3 Lesson 2 powers and exponents ----------------------------------------------- 6 Explore! Folding Paper Lesson 3 order of operations with powers ----------------------------------- 11 Lesson 4 order of operations with grouping symbols ----------------------- 14 Explore! Fact Puzzle Lesson 5 number properties --------------------------------------------------- 18 Explore! Discovering Properties review BLock 1 ~ order of operations -------------------------------------- 23 Block 2 ~ AlgeBrAic expressions Lesson 6 variables and expressions ------------------------------------------- 29 Explore! Translate Those Words Lesson 7 evaluating expressions ---------------------------------------------- 33 Lesson 8 evaluating geometric ForMULas ------------------------------------ 38 Explore! Using Formulas Lesson 9 evaluating More ForMULas ------------------------------------------ 43 Explore! Earning Interest Lesson 10 simplifying algebraic expressions ----------------------------------- 49 Lesson 11 THe distributive property -------------------------------------------- 53 Explore! Shopping Spree Lesson 12 Using THe distributive property with variables --------------------- 58 Explore! Equivalent Expressions review BLock 2 ~ algebraic expressions ------------------------------------ 62 vi Oregon Focus On Introductory Algebra
Block 3 ~ solving equations Lesson 13 equations and solutions --------------------------------------------- 69 Lesson 14 solving equations Using MenTaL MaTH ------------------------------ 73 Explore! Record-Setting Lesson 15 solving addition equations ------------------------------------------ 77 Explore! Introduction to Equation Mats Lesson 16 solving subtraction equations -------------------------------------- 81 Lesson 17 solving MULTipLicaTion and division equations ---------------------- 84 Explore! Multiplication Equations Lesson 18 Mixed one-step equations ------------------------------------------- 89 Explore! Inverse Operations Lesson 19 ForMULas and equation-solving ------------------------------------- 93 Lesson 20 solving Two-sTep equations ----------------------------------------- 97 Explore! Equation Mats for Two-Step Equations review BLock 3 ~ solving equations ----------------------------------------- 102 Block 4 ~ functions Lesson 21 THe coordinate plane ----------------------------------------------- 110 Explore! Buried Treasure Lesson 22 input-output TaBLes ------------------------------------------------- 114 Lesson 23 writing FUncTion rules ---------------------------------------------- 119 Explore! Function Rules Lesson 24 graphing Linear FUncTions ------------------------------------------ 125 Explore! Function Fun Lesson 25 patterns and FUncTions ---------------------------------------------- 130 review BLock 4 ~ FUncTions -------------------------------------------------- 135 Oregon Focus On Introductory Algebra vii
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 Introductory Algebra
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 1 Oregon Focus On Introductory Algebra ix
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 Introductory Algebra