table of contents maryland - walch · application activity . . . . . . . . . . . . . . . . . . . ....

PPaarrtt 11:: TTeeaacchheerr’’ss GGuuiiddeeIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TG1Pacing Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TG5Graphic Organizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TG13Standards Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TG33Pre-/Post-Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TG37Openers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TG55Appendixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TG131

PPaarrtt 22:: AAllggeebbrraa BBaassiiccssPositive and Negative Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Operations with Signed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Multiplying and Dividing Positive and Negative Rational Numbers . . . . . . . . . . . . . 32Algebra Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Algebraic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Unit Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Teaching Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Part 2 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

PPaarrtt 33:: SSoollvviinngg EEqquuaattiioonnss aanndd IInneeqquuaalliittiieessSolving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Solving Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Unit Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178Application Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180Teaching Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183Part 3 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

PPaarrtt 44:: DDaattaa AAnnaallyyssiiss aanndd PPrroobbaabbiilliittyyFrequency Distributions and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191Analyzing Data Using Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . 199Analyzing Data with Respect to Measures of Variation . . . . . . . . . . . . . . . . . . . . . . . 206Applying Data Analysis and Probability Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 216Data Analysis and Probability Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225Part 4 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

PPaarrtt 55:: GGrraapphhiinngg LLiinneeaarr EEqquuaattiioonnssThe Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283Graphing Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315Unit Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335Application Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340Teaching Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341Part 5 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

© 2007 Walch Publishing Maryland Academic Support Program for Algebra and Data Analysis

iii

Table of Contents Marylandacademic support program

Maryland Academic Support Program for Algebra and Data Analysis © 2007 Walch Publishing

iv

PPaarrtt 66:: PPoollyynnoommiiaall OOppeerraattiioonnssAdding and Subtracting Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349Multiplying and Dividing Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367Factoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410Unit Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458Application Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462Teaching Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464Part 6 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465

PPaarrtt 77:: QQuuaaddrraattiicc EEqquuaattiioonnssQuadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473The Quadratic Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511Unit Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532Teaching Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537Part 7 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538

PPaarrtt 88:: HHaannddss--OOnn aanndd RReeaall--LLiiffee AAccttiivviittiieess ffoorr DDaattaa AAnnaallyyssiissData Collection, Surveying, and Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542Data Analysis—Measures of Central Tendency, Variance, . . . . . . . . . . . . . . . . . . . . 553

and Standard DeviationProbability Ratios and Compound Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563Misuse of Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

PPaarrtt 99:: HHaannddss--OOnn aanndd RReeaall--LLiiffee AAccttiivviittiieess ffoorr AAllggeebbrraaAlgebra Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580Solving Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596Graphing Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605Polynomial Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648

PPaarrtt 1100:: TTeesstt--TTaakkiinngg PPrreeppaarraattiioonnTest-Taking Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661Know the Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662Practice Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664Part 10 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739

Table of Contents, continued Marylandacademic support program


TG1

Introduction Marylandacademic support program

PART 1 • TEACHER’S GUIDE

Instruction

The Maryland Academic Support Program (ASP) for Algebra and Data Analysis is a complete,turnkey solution for improving educational performance. Topics are built around accessible corecurriculum ensuring that the ASP is useful for striving students and diverse classrooms.

This program recognizes that many struggling students aren’t reached by traditional “skill-and-drill” or strict test-prep approaches.

The ASP includes components that review, instruct as needed, provide practice, and assessstudents’ skills. Instructional tools and strategies are embedded throughout. The scope and sequenceaddresses the needs of students who require additional support in topics included in Maryland’sCore Learning Goals and the National Council of Teachers of Mathematics Standards.

This 3-ring binder includes:

• Over 120 hours of lessons with reproducible activity sheets

• A section on test-taking strategies and a collection of practice items

• A collection of hands-on and real-life activities for small group work

• A problem-based mathematics teacher’s guide that:

• describes the purpose of the materials and options for using the package

• provides pacing guide options

• recommends an assortment of graphic organizers for instructional strategies

• includes a collection of openers—to begin a class or to make a transition

• references relevant state standards

• supplies a series of appendixes for student reference

Purpose of MaterialsThe Maryland Academic Support Program for Algebra and Data Analysis is a flexible program thathas been organized to fit your students’ needs in credit recovery, evening, or summer school.

Each day’s schedule includes activities beginning with direct instruction and guided practice andmoving on to opportunities for developing and applying new skills and concepts in problem solvingsituations.

The 120-hour program includes all the major topics in the Maryland Core Learning Goals forAlgebra and Data Analysis. These include:

• Functions and Algebra

• Data Analysis and Probability

Problem solving, reasoning and proof, communication, connections, and representation areinfused throughout.


TG3

Structure of UnitsNearly all of the instructional units in Parts 2 through 7 have some common features.

In each class session, you will present a topic. Some topics may be a review for students. Othertopics may be completely new to them. After some instruction, you will provide students withpractice activities to try. Students will have a chance to talk about how they completed their work.There are additional materials to use if you are confident that students are ready to extend theirlearning. If students need more practice or further explanation, you can provide them with that, too!

11.. TThhee GGooaall SSttaatteemmeenntt

Each unit begins with a brief objective of what students should know, understand, or be able do atthe end of the unit.

22.. WWoorrddss ttoo KKnnooww

Vocabulary terms are provided as background information for instruction or to review key conceptsthat are addressed in the unit.

33.. DDiirreecctt IInnssttrruuccttiioonn

This section is a guide for a teacher-led activity to review and/or instruct students on a specific skillor topic (activities are 15 to 45 minutes in length). Instructional strategies include lecture, modeling,discussion, group facilitation, and more. The activities may include the use of one or more of thegraphic organizers found in the Teacher’s Guide. This section frequently refers to presentinginformation on the board or via an overhead projector, and includes diagrams and sample problemsto be presented to the class in this manner.

44.. SSttuuddeenntt AAccttiivviittyy SShheeeettss

Each unit includes three or more lesson tasks and activities to support students’ achievement oflearning objectives. These sheets are written for the student. They can be used in any combination ofteacher-led instruction, cooperative learning, or independent application of knowledge.

55.. AAsssseessssmmeennttss

Each unit includes a review assessment to document the extent to which students’ grasped theconcepts and skills addressed during instruction.

PART 1 • TEACHER’S GUIDEIntroduction

Marylandacademic support program


TG21

PART 1 • TEACHER’S GUIDEGraphic Organizers


Number Line

0

0


TG46

11.. Look at the pattern below.

2x + 4, 2x + 1, 2x – 2, . . .

If the pattern continues, what will be the seventh term?

aa.. 2x + 11 cc.. 2x + 14

bb.. 2x – 11 dd.. 2x – 14

22.. The table below shows a linear relationship between x and y.

Which of the following graphs shows this relationship?

aa.. cc..

bb.. dd..

PART 1 • TEACHER’S GUIDEPost-Assessment


NAME:

Assessment

x –3 –1 1 3 5

y 2 1 0 –1 –2

yy

5

–5

xx–5 5

yy

5

–5

xx–5 5

yy

5

–5

xx–5 5

yy

5

–5

xx–5 5


TG107

52. Nine DonkeysNine donkeys in a large pen are having a hard time getting along. Can you draw two squares so thateach donkey has its own pen?

PART 1 • TEACHER’S GUIDEOpeners


NAME:

ALGEBRAHANDS-ON/REAL-LIFE ACTIVITIES


579

IntroductionThis section contains a collection of hands-on and real-life activities to complement the direct instructionand guided practice exercises provided elsewhere in the ASP. These instructional experiences may beused to introduce a new concept or skill, or as opportunities for practice and application.

The pacing guide offers suggestions for the scheduling of these activities.

Algebra Marylandacademic support program

PART 9 • HANDS-ON AND REAL-LIFE ACTIVITIES

Instruction

IInnssttrruuccttiioonn aanndd GGuuiiddeedd PPrraaccttiiccee TTooppiicc HHaannddss--OOnn//RReeaall--LLiiffee AAccttiivviittiieess PPaaggee NNuummbbeerrss

AAllggeebbrraa BBaassiiccss

Negative and Positive Numbers Integer Tiles 580–586

Operations with Signed Numbers Subtracting with Integer Tiles 587–591

Algebra Concepts Discovering Algebra Tiles 592–595

SSoollvviinngg EEqquuaattiioonnss aanndd IInneeqquuaalliittiieess

Solving Equations My First CarEnergy Savings

596–601

Solving Inequalities Inequalities 602–604

GGrraapphhiinngg LLiinneeaarr EEqquuaattiioonnss

The Coordinate Plane The Language of a Cartesian Coordinate System

605–608

Graphing Linear Equations Patterns and Slope-Intercept 609–615

Slope Slope as RateRising Tuition

616–628

PPoollyynnoommiiaall OOppeerraattiioonnss

Adding and Subtracting Algebraic Expressions

Alternative Fuels 629–631

Multiplying and Dividing Algebraic Expressions

Multiplying with Algebra Tiles 632–637

Factoring Factoring Trinomials with Algebra Tiles

Perfect Square Trinomials

638–647

QQuuaaddrraattiicc EEqquuaattiioonnss

Quadratic Equations Pizza by the InchHow Cold Is It?Miles per Gallon

648–659


580

Negative and Positive Numbers: Integer TilesCCoonntteexxtt

hands-on manipulatives

MMaatthh TTooppiicc

integers

OOvveerrvviieeww

Teams (pairs of students) will use positive and negative integer tiles to perform addition andsubtraction and to discover some properties of integers. Students will draw the tile operations ontheir worksheets and summarize their findings.

OObbjjeeccttiivveess

Students will

• discover the properties for adding and subtracting integers

• understand the concept of additive inverse

MMaatteerriiaallss

• groups of 20 tiles that are two different colors or that are marked with + and – symbols

• integer mats (on page 586)

TTeeaacchhiinngg NNootteess

AAccttiivviittyy 11

• Pass out integer mats and positive and negative tiles for each pair of students. If tiles are notmarked with + and – symbols, choose one color to represent negative numbers and one torepresent positive numbers.

• You may wish to model the activity, or you may have each pair work at its own pace.

• The purpose of Activity 1 is to discover that adding a positive to a positive equals a positive.

AAccttiivviittyy 22

• Follow the same procedure as Activity 1, only this time students should discover that a negativeadded to a negative is always a negative.

PART 9 • HANDS-ON AND REAL-LIFE ACTIVITIESAlgebra


Instruction


583

Negative and Positive Numbers: Integer TilesAAccttiivviittyy 11:: AAddddiinngg IInntteeggeerrss

You will use positive and negative integer tiles to discover some properties of adding and subtracting. Each positive tile has a value of 1. To show the number positive 3, you would place 3 positive tiles on the mat.

= 3

To show negative integers you will use the negative tiles. Each negative tile has a value of negative 1. To show the number negative 4, you would place 4 negative tiles on the integer mat.

= –4

Try the following additions with the tiles and the integer mat.

DDrraaww tthhee ttiilleess hheerree:: AAnnsswweerr::

11.. 3 + 5 ________

22.. 4 + 2 ________

33.. 1 + 7 ________

44.. In every example above, what type of numbers were you adding? ______________________

55.. Did you ever use a negative tile? ___________

66.. What rule can you develop for adding positive integers? _____________________________

______________________________________________________________________



NAME:


584

AAccttiivviittyy 22:: AAddddiinngg NNeeggaattiivvee IInntteeggeerrss

This time you will work with the negative tiles. Show the following addition problems with your tiles.


77.. –3 + –2 ________

88.. –4 + –3 ________

99.. –1 + –5 ________

1100.. In every example, what type of numbers were you adding? ___________________________

1111.. Did you ever use a positive tile? ___________

1122.. What rule can you develop for adding negative integers? ____________________________

______________________________________________________________________

AAccttiivviittyy 33:: TThhee ZZeerroo PPaaiirr

When two tiles of unlike signs are combined, they form a zero pair. That is, their value = zero.

EExxaammppllee::

When you put the two together, they form a zero pair and cancel each other out.

When you combine positive and negative tiles, find how many form zero pairs and remove themfrom the mat. The tiles that remain show the answer.

Show the following additions with the tiles. Remove all zero pairs and find the answer.



NAME:


585


1133.. –3 + 5 ________

1144.. –5 + 2 ________

1155.. –6 + 3 ________

1166.. 4 + –1 ________

1177.. –4 + 4 ________

1188.. In every example, what types of numbers were you adding? __________________________

1199.. What did you notice happening each time you added the integers with different signs?

______________________________________________________________________

______________________________________________________________________

2200.. What rule(s) could you develop for adding positive and negative integers?

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

SSuummmmaattiioonn::

A positive + a positive = _____________________________

A negative + a negative = _____________________________

A negative + a positive can be ______________, ______________, or ______________

because ___________________________________________________________________.



NAME:


586



NAME:

IInntteeggeerr MMaatt

table of contents maryland - walch · application activity . . . . . . . . . . . . . . . . . . . ....

Documents