table of contents maryland - walch · application activity . . . . . . . . . . . . . . . . . . . ....
TRANSCRIPT
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
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Table of Contents Marylandacademic support program
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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
© 2007 Walch Publishing Maryland Academic Support Program for Algebra and Data Analysis
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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.
© 2007 Walch Publishing Maryland Academic Support Program for Algebra and Data Analysis
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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
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PART 1 • TEACHER’S GUIDEGraphic Organizers
Marylandacademic support program
Number Line
0
0
Maryland Academic Support Program for Algebra and Data Analysis © 2007 Walch Publishing
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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
Marylandacademic support program
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
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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
Marylandacademic support program
NAME:
ALGEBRAHANDS-ON/REAL-LIFE ACTIVITIES
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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
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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
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Instruction
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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? _____________________________
______________________________________________________________________
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AAccttiivviittyy 22:: AAddddiinngg NNeeggaattiivvee IInntteeggeerrss
This time you will work with the negative tiles. Show the following addition problems with your tiles.
DDrraaww tthhee ttiilleess hheerree:: AAnnsswweerr::
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.
PART 9 • HANDS-ON AND REAL-LIFE ACTIVITIESAlgebra
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© 2007 Walch Publishing Maryland Academic Support Program for Algebra and Data Analysis
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DDrraaww tthhee ttiilleess hheerree:: AAnnsswweerr::
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 ___________________________________________________________________.
PART 9 • HANDS-ON AND REAL-LIFE ACTIVITIESAlgebra
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PART 9 • HANDS-ON AND REAL-LIFE ACTIVITIESAlgebra
Marylandacademic support program
NAME:
IInntteeggeerr MMaatt