Oregon Focus On Data Analysis i

AuthorsShannon Mccaw

Beth Armstrong • mAtt mccAw • sArAh schuhl • michelle terry • scott VAlwAy

ii Oregon Focus On Data Analysis

Copyright ©2008 by SMc Curriculum LLC. All rights reserved. Printed in China. Th is 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. Th is 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: 978-1-935033-09-7

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Oregon Focus On Data Analysis iii

ABOUT THE AUTHORSABOUT THE AUTHORSABOUT THE AUTHORS Series Author Series Author Series Author

Contributing Authors Contributing Authors Contributing Authors

Beth Armstrong has been an elementary school teacher in the Beaverton School District. She has received training in Talented and Gift ed Instruction. She recently completed her Masters in Curriculum and Instruction from Washington 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 fi lls 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 Diff erentiated 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.

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.

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, Diff erentiated 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.

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 Diff erentiated 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.

iv Oregon Focus On Data Analysis

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 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.8.1.1 Translate among contextual, verbal, tabular, graphical, and algebraic representations of linear functions. 8.1.2 Determine the slope of a line and understand that it is a constant rate of change.

8.1.3Identify 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.

8.1.4 Use linear functions and equations to represent, analyze and solve problems, and to make predictions and inferences.

8.1.5 Relate systems of two linear equations in two variables and their solutions to pairs of lines that are intersecting, parallel, or the same line.

8.1.6 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.

8.2.1 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.

8.2.2 Use measures of center and spread to summarize and compare data sets. 8.2.3 Interpret and analyze displays of data and descriptive statistics. 8.2.4 Compare descriptive statistics and evaluate how changes in data affect those statistics.

8.2.5 Describe the strengths and limitations of a particular statistical measure, and justify or critique its use in a given situation.

8.2.6 Use sample data to make predictions regarding a population. 8.2.7 Identify claims based on statistical data and evaluate the reasonableness of those claims.8.2.8 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.

8.3.1 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.

8.3.2 Use models to show that the sum of the angles of any triangle is 180 degrees and apply this fact to find unknown angles.

8.3.3 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

8.3.4 Use models to explore the validity of the Pythagorean Theorem, and use it to find missing lengths.

8.3.5 Apply the Pythagorean Theorem to find distances in a variety of 2- and 3-dimensional contexts, including distances on coordinate graphs.

8.3.6 Use models and referents to explore and estimate square roots.

Reprinted with permission from the Oregon Department of Education. All rights reserved.

Oregon Focus On Data Analysis v

OregOn FOcus On Data analysis

cOntents in BrieFHow To Use YoUr MaTH Book ------------------------------------------------------ viii

LeTTer FroM THe aUTHors ----------------------------------------------------------- x

BLock 1 raTios, ProPorTions and PercenTs ---------------------------------------- 1

BLock 2 MeasUres oF cenTer ------------------------------------------------------- 35

BLock 3 daTa disPLaYs -------------------------------------------------------------- 83

BLock 4 Two-variaBLe daTa -------------------------------------------------------- 128

acknowLedgeMenTs ---------------------------------------------------------------- 165

engLisH/sPanisH gLossarY ---------------------------------------------------------- 166

seLecTed answers ------------------------------------------------------------------ 191

index ------------------------------------------------------------------------------- 198

ProBLeM-soLving ------------------------------------------------------------------- 201

sYMBoLs ----------------------------------------------------------------------------- 203

oregon sTaTe assessMenT ForMULa sHeeT ----------------------------------------- 204

vi Oregon Focus On Data Analysis

Block 1 ~ rAtios, ProPortions And Percents

Block 2 ~ meAsures of center

Lesson 1 raTios and raTes - ---------------------------------------------------- 3Lesson 2 ProPorTions ----------------------------------------------------------- 8

Explore! Proportions and Cross ProductsLesson 3 PercenTages ---------------------------------------------------------- 13Lesson 4 creaTing and anaLYzing Bar graPHs -------------------------------- 18Lesson 5 creaTing and anaLYzing Pie cHarTs --------------------------------- 23

Explore! Easy As Piereview BLock 1 ~ raTios, ProPorTions and PercenTs ------------------------ 29

Lesson 6 MeasUres oF cenTer -------------------------------------------------- 37 Explore! Mr. Booker’s Class

Lesson 7 Using THe Mean To Find daTa ---------------------------------------- 42Lesson 8 coMPLeTing daTa seTs - ----------------------------------------------- 47

Explore! Frog DataLesson 9 eFFecTs oF cHanging daTa ------------------------------------------- 52

Explore! Ch-Ch-Ch-ChangesLesson 10 eFFecTs oF oUTLiers on daTa ----------------------------------------- 57

Explore! Outliers and DataLesson 11 sTrengTHs and LiMiTaTions oF daTa ----------------------------------- 62

Explore! Comparing Cell Phone CompaniesLesson 12 Five-nUMBer sUMMaries oF daTa ------------------------------------- 66Lesson 13 Finding oUTLiers ------------------------------------------------------ 72review BLock 2 ~ MeasUres oF cenTer --------------------------------------- 77

Oregon Focus On Data Analysis vii

Block 3 ~ dAtA disPlAys

Block 4 ~ two-VAriABle dAtA

Lesson 14 HisTograMs ----------------------------------------------------------- 85Lesson 15 anaLYzing HisTograMs ------------------------------------------------ 92

Explore! Predicting from HistogramsLesson 16 sTeM-and-LeaF PLoTs ------------------------------------------------- 98

Explore! Making a Stem-and-Leaf PlotLesson 17 anaLYzing sTeM-and-LeaF PLoTs -------------------------------------- 104Lesson 18 Box-and-wHisker PLoTs ----------------------------------------------- 109Lesson 19 anaLYzing Box-and-wHisker PLoTs ----------------------------------- 115

Explore! Visualizing Skewreview BLock 3 ~ daTa disPLaYs ---------------------------------------------- 122

Lesson 20 scaTTer PLoTs and correLaTion -------------------------------------- 130Lesson 21 PredicTing wiTH Lines oF BesT FiT ------------------------------------- 134

Explore! Finding a Good FitLesson 22 Q-PoinTs and Lines oF BesT FiT --------------------------------------- 139

Explore! The WaveLesson 23 PredicTing wiTH BesT FiT eQUaTions ---------------------------------- 145Lesson 24 cHoosing aPProPriaTe daTa disPLaYs --------------------------------- 149Lesson 25 Using daTa and graPHs To PersUade --------------------------------- 153

Explore! Eliminating Biasreview BLock 4 ~ Two-variaBLe daTa ---------------------------------------- 159

viii Oregon Focus On Data Analysis

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. Th e defi nition can be found with the word. You can also fi nd the defi nition 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 diff erent types of problems. Look for the word example and the green line.

helPful hints

Blue Boxes

Th is 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.

Oregon Focus On Data Analysis ix

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

x Oregon Focus On Data Analysis

Letter FroM the Authors

Dear Student,

Th is textbook was specifi cally 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 Focus on Fractions and Decimals Focus on Ratios, Rates and Percents Focus on Introductory Algebra

Stage 2 Focus on Rational Numbers and Equations Focus on Proportionality Focus on Surface Area and Volume

Stage 3 Focus on Linear Equations Focus on Data Analysis Focus on Lines and Angles

When you successfully fi nish 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 eff ort 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 fi nd information about places and events from all across the state of Oregon. We hope you enjoy learning about your state. You may even fi nd something about the city or town you live in!

Sincerely,

Shannon McCaw

Sarah Schuhl

Matt McCawBeth Armstrong

Scott ValwayMichelle Terry