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Table of Contents

CHAPTER 1 GENERAL INFORMATION .............................................................................. 1 Overview......................................................................................................................................... 1 Product Overview ........................................................................................................................... 3 CHAPTER 2 PLATO INSTRUCTIONAL STRATEGIES...................................................... 7 Overview......................................................................................................................................... 7 Individualized Instruction ............................................................................................................... 9 Competency-Based Instruction..................................................................................................... 10 The Mastery Model....................................................................................................................... 11 CHAPTER 3 INSTRUCTOR ORIENTATION TO PLATO LEARNING COURSEWARE....................................................................................................................................................... 13 Overview....................................................................................................................................... 13 Implementation of Computer-Based Education............................................................................ 14 Mode ............................................................................................................................................. 16 Troubleshooting ............................................................................................................................ 17 Orienting the Learner.................................................................................................................... 18 Navigating through the Courseware ............................................................................................. 21 CHAPTER 4 LEARNING ACTIVITY AND QUESTION TYPES....................................... 25 Overview....................................................................................................................................... 25 Tutorials ........................................................................................................................................ 26 Applications .................................................................................................................................. 30 Mastery Test.................................................................................................................................. 34 Offline Activities .......................................................................................................................... 35 Question Types ............................................................................................................................. 36 CHAPTER 5 TESTING STRATEGIES................................................................................... 41 CHAPTER 6 LEARNING AIDS............................................................................................... 43 Overview....................................................................................................................................... 43 Notebook....................................................................................................................................... 44 Calculator...................................................................................................................................... 46 Math Entry Tools .......................................................................................................................... 48 Graphing Tool............................................................................................................................... 50 Audio............................................................................................................................................. 51 CHAPTER 7 ALGEBRA 1 SCOPE AND SEQUENCE ......................................................... 53 Overview....................................................................................................................................... 53 Course One Basic Number Ideas .................................................................................................. 54 Course Two Math Sentences ........................................................................................................ 56 Course Three Graphing Basics ..................................................................................................... 58 Course Four Equations and Formulas........................................................................................... 59 Course Five Special Topics .......................................................................................................... 60 Course Six Introduction to Functions ........................................................................................... 62 Course Seven Sets and Numbers .................................................................................................. 63 Course Eight Polynomials and Factoring ..................................................................................... 66 Course Nine Equations and Inequalities ....................................................................................... 68

i

Chapter 1 General Information

Overview

Introduction The Algebra curricula teach learners practical and advanced mathematics

skills and concepts, including basic number ideas, sets, math sentences, rational expressions, graphs, probability, and functions.

Benefits The Algebra curricula help learners to learn important problem-solving skills

and strategies, most of which are drawn from real-life experiences. The curricula does the following: • Provide learners enrolled in algebra courses with either a core or

supplemental instruction. • Prepare learners who need algebra as a prerequisite for their work in

business, economics, computer science, and other areas.

Assumptions This guide is written with the assumption that the instructor and learner are

familiar with a browser, including navigating to a specific Internet address or Uniform Resource Locator (URL).

Continued on next page

1

General Information Overview, Continued

Using this guide This guide provides an overview of the structure and content of the Algebra

curricula. Because you play a key role in ensuring a positive experience for learners, it is important to review all sections of this guide.

Section Description

General Information Introduces the courseware. Read this material as an overview of the product.

PLATO Instructional Strategies

Describes the four companion activities that are part of each Algebra module, including how each is scored and how the score is reported.

Learning Activity Types

Describes the characteristics and scoring of the Tutorials, Mastery Tests, Applications, and Offline Activities used in Algebra.

Testing Strategies Describes the kinds of learner assessment provided at various levels of the curriculum. Consult this section to get acquainted with the PLATO approach to assessment and mastery testing.

Learning Aids Provides basic information for the instructor about PLATO online tools and help features available when working in the courseware.

Instructor Orientation to PLATO Learning Courseware

Suggests how to implement Algebra courseware, discusses the available modes for previewing and for using the courseware, and suggests ways to introduce learners to the courseware.

Scope and Sequence Identifies the modules and courses in Algebra and lists objectives.

Contact us If you need help, please contact PLATO Support using any of the following

methods: • Website: http://platosupport.plato.com/ • Support Request: http://platosupport.plato.com/SupportRequest.asp • Email: [email protected] • Phone: 800-869-2200

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mailto:[email protected]

Product Overview

Introduction The Algebra courseware is divided into the following four levels:

• Algebra 1, Part 1 • Algebra 1, Part 2 • Algebra 2, Part 1 • Algebra 2, Part 2

Algebra curriculum (existing Algebra users only)

If you currently use any of the Algebra curricula, refer to the table below to better understand how the "old" Algebra curricula compare to the "new" Algebra curricula. Tips Refer to the Scope and Sequence chapter of this document for more

information about the learner objectives of each course. Also, refer to the Alignment Migration Information document

(accessed from the documentation.html on the Algebra courseware CD-ROMs or from the user guides>curriculum guides>secondary curriculum guides>mathematics link in PLATO Web Learning Network) for more information about specific courses and modules that existed in the old Algebra courseware and how they align with courses and modules in the new Algebra courseware.

New Curriculum Old Curriculum Courses Algebra 1, Part 1 Pre- 6 courses, 74 modules Algebra 1, Part 2 Beginning 3 courses, 72 modules Algebra 2, Part 1 Intermediate 5 courses, 42 modules Algebra 2, Part 2 Advanced 5 courses, 48 modules


3

Product Overview, Continued

New courseware features

The following features are integrated into PLATO courseware’s design and presentation to benefit learners: • Animated graphics and interactions help illustrate objectives. In the

example below, the correct answer displays after the learner answers incorrectly twice.

• Interactions help students understand concepts and principles that help

them discover connections among concepts. In tutorials, practice and tests, many questions have been redesigned to raise learners' Taxonomy level. Open-ended responses with extensive diagnostic answer analysis and feedback are more widely used than with the previous Algebra courseware. The ability to detect and correct common misconceptions and errors has been greatly improved. And in many cases, question generators have replaced fixed pools of questions, thus greatly reducing item exposure.


4


New courseware features (continued)

• Spiraling curricula give students confidence in their abilities and build on

what they know. • Navigation features are straightforward and easily identified. Users

navigate through PLATO lessons using the Menu button that displays on every page (except the Main Menu page). Students can go directly to any available section by selecting an option on the Main Menu page.

• Online tools, including the Notebook, Calculator, and Graphing Tool help

learners accomplish goals in the courseware. For more information about these tools, see the Learning Aids chapter on page 43.

Main Menu page

Tools
Navigation options

5


New courseware features (continued) • Scaffolded instruction allows learners several opportunities to see whether

they understand an objective before advancing in the course or module. • Large question pools allow extra practice and testing for learners who

need it. Learners can repeat practice, application, and test questions multiple times without seeing the same set of questions.

• Maximum modularity has been built in for alignments and time constraints. Modules are short and focused on one objective making alignments easy and accurate. In addition, because modules are short and focused, learners can complete the module activities within the allotted lab or class time.

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Chapter 2 PLATO Instructional Strategies

Overview

Introduction PLATO curricula use an individualized, competency-based mastery model

that can accommodate a diverse range of learner needs.

Benefits The PLATO approach to learning does the following:

• Encourages learners to study at their own level and move at their own

pace. • Creates a dynamic environment within which to practice and acquire

skills. • Provides precise measurement of the learner's progress. • Promotes individual accountability.

Teaching device Like all PLATO curricula, Algebra consists of individualized activities

suitable to diverse learning situations. These activities include real-life examples and sophisticated graphics and interactions. PLATO curricula require individualized responses to encourage concentration, maintain motivation, and increase proficiency.

Optional audio The Algebra courseware features optional audio. Benefits of optional audio

include the following: • Allows learners with reading difficulties to hear the text and read along. • Sets the pace of the instruction. • Allows learners to hear terminology pronounced and used in context. • Allows learners who do not need or want audio to turn off the option.


7

PLATO Instructional Strategies Overview, Continued

In this chapter This chapter includes the following topics.

Topic See Page Individualized Instruction 9 Competency-Based Instruction 10 The Mastery Model 11

8

Individualized Instruction

Introduction PLATO Learning recognizes that everyone learns at a different rate. With

individualized instruction learners with a clear grasp of a concept can move quickly through the learning activities. However, if a learner is having trouble with a particular concept, he or she can repeat an activity.

Bookmarking If a learner exits a Tutorial or Application activity early, a bookmark is

automatically placed in the section where the learner stopped. When learners restart the activity, they are able to enter the activity where they left off. Note Bookmarking is not available in Mastery Tests.

Feedback PLATO courseware provides immediate feedback when the learner answers a

practice or application question. If the answer is incorrect, PLATO courseware identifies common errors and provides helpful hints to steer learners in the right direction. If a learner answers incorrectly twice, PLATO courseware provides the answer and an explanation or model of the solution before the learner continues.

Learner goals It is common for learners to have different goals, particularly in an

individualized setting. PLATO caters to every learner’s needs. Learning activities are sequential to reinforce skills previously learned. The modules build upon each other; thus, it is strongly recommended that learners take them in order. However, the unique modularity of the courseware allows the instructor to assign individual programs based on specific needs and to accommodate learners who already know a particular skill by letting them bypass the module and move on.

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Competency-Based Instruction

Introduction Competency-based instruction focuses on active learning. Learners

concentrate on fulfilling specific outcomes or objectives. Each objective describes a particular, measurable behavior.

Curriculum design

Competency-based curriculum design always states an objective. For example: Given a linear equation with two variables, learners will be able to: • Determine whether the equation is in slope-intercept form. • Rewrite the equation, if necessary, in slope-intercept form. • Identify the slope from the equation. • Identify the y-intercept from the equation. These objectives allow for an exact way to measure learning.

Objectives The Algebra curricula have objectives at many different levels, ranging from

knowledge acquisition (simple remembering of a fact) to the analysis of ideas and the synthesis of concepts into new knowledge. As learners progress through a curriculum, they build upon previous knowledge.

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The Mastery Model

Introduction Achievement in a traditional instructional setting occurs in varying degrees.

In the mastery model, all learners demonstrate proficiency by mastering the test at 80 %.

Basic principles The mastery model has two basic principles:

• Learners must master all prerequisite objectives. • Learners continue to study the given objective until they have fully

mastered it and are ready to go on to the next module.

Description In mastery-based instruction, achievement is held constant; only instructional

time varies. Learners who do not understand a concept may continue to study a module’s objective on their own without slowing down other learners. Example Some learners may be ready to take the Mastery Test after completing a tutorial, while others may want additional practice before proceeding to the test. Those learners can study the application section of the module and repeat all or part of the tutorial. Other learners may feel they know the material. Those learners may take the Mastery Test first. If they master the test, they progress to the next level.

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Chapter 3 Instructor Orientation to PLATO Learning Courseware

Overview

Introduction This chapter suggests ways to implement Algebra courseware into your

classroom, discusses the available modes for previewing and for using the courseware (including troubleshooting), and suggests how to introduce learners to the courseware.


Topic See Page Implementation 14 Mode 16 Troubleshooting 17 Orienting the Learner 18 Navigating through the Courseware 21

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Implementation of Computer-Based Education

Introduction Effective programs using computer-based education (CBE) involve careful

planning, support for learners, and monitoring individuals’ progress.

How to PLATO courseware is suitable no matter what amount of computer-based

education you want to use in your classroom. • As a primary means of delivering instruction, PLATO provides concept-

learning, practice, application, and testing opportunities. We encourage you to consider use of the curriculum as a primary instructional tool, to leverage your classroom time in a "guide on the side" role. You also may wish to assign pairs of students to work through the tutorial and practice lessons together to engage in peer tutoring. However, tests should be taken individually.

• As a supplement to instruction, PLATO courseware presents alternative instructional activities for specific topics.

• As a complement to instruction, PLATO courseware delivers instructional activities that are difficult to do in other ways. For example, learners can refresh their prerequisite skills using PLATO courseware while trainers teach specific procedures in a class setting.

Instructor roles Your role differs in the following ways for each of the three instructional

approaches: • Primary application changes your role the most. Because PLATO

courseware does much of the initial instruction, the full-time presence of an instructor is not necessary. Teachers build around the courseware.

• Supplemental application changes your role the least. The instructor performs familiar teaching activities using the computer as an alternate resource.

• Complementary application slightly changes your role. The teacher chooses and balances resources. CBE allows the teacher to incorporate the courseware along with the other resources (textbooks, lectures, discussions, independent projects) to deliver instruction.


14

Implementation of Computer-Based Education, Continued

Tips Consider the following as you implement Algebra into your classroom:

• You can use the new algebra curriculum in class or in self-instructional

contexts much as you did the old one. However, the new Investigate section gives you new opportunities to plan large- or small-group collaborative learning activities in addition to the powerful PLATO tutorial instruction.

• If you are using PLATO to implement mastery-model instruction, be sure to set the system to require mastery of each module's test before a learner progresses and limit the number of tries to 2 or 3 without your intervention. You also will find that the time to master each module varies by as much as 6:1 (what one student can master in an hour may take as much as 6 hours for another student to master). Establish a flexible scheduling system that provides extra time for the students who need it.

• As FASTRACK will not automatically create prescriptions for the new content, an alternative is to allow students to take each module mastery test as a pretest to assure a learner's understanding of the content (regardless of module splits). For more information about FASTRACK, refer to the Algebra Frequently Asked Questions document accessed from the documentation.html on the courseware CD-ROM (PLATO Pathways) or from the user guides>Curriculum Guides>Secondary and adult curriculum guides>Mathematics link (PLATO Web Learning Network).

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Mode

Introduction PLATO Web Learning Network and PLATO Pathways manage the PLATO

courseware and allow you access to the curricula as an administrator or a student.

Administrator mode

Administrator mode allows you to do the following: • Browse through all activities, including tests, without having to answer

the questions. • View the correct answer using the Answer button. • Preview all answer feedback using the Reset button. • Access any part of the Tutorial at any time.

Student mode Student mode allows you and your students to access PLATO lessons as a

student. Student mode is the basic PLATO user mode. Students must complete lesson sections in order, and they must answer questions correctly in order to move forward.

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Troubleshooting

Introduction You can identify each page in the courseware by selecting Tools > Help

About. This menu option displays a unique identifier that allows PLATO Support to better troubleshoot any problems users might have with the courseware. Be prepared to provide this information if you contact PLATO Support by email, phone, or the support site.

Accessing it To access troubleshooting information, follow the steps below.

Step Action 1 Select Help About from the Tools menu.

Result The About This Activity window displays.

Tip When sending an email message to PLATO Support or

using the PLATO Support website, highlight the entire contents of the About This Activity window, right-click (PC users) or Ctrl+mouse-click (Mac users) and choose Copy. Then paste the information into your email message or on the Support website at http://platosupport.plato.com/SupportRequest.asp.

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Orienting the Learner

Introduction Some learners may not be familiar with computer-based education (CBE).

Others may be familiar with courseware, but not with the PLATO courseware.

Checklist Use the following checklist to help orient learners to PLATO courseware.

Task Description Explain how they can proceed at their own pace. Explain how the curriculum relates to each student’s educational

objectives. PLATO will guide them through their studies. Explain how to use the workstation and the mouse.

• Describe how to perform mouse functions such as point, click,

double-click, drag and drop. • Demonstrate how to signon to the PLATO system and begin

the assigned learning activities. Explain how to navigate through a PLATO activity.

• Review the PLATO page and its parts. • Show students how to use the PLATO tools, such as the

Notebook, Graphing Tool, and Calculator. Explain the PLATO activity types and how testing works.

• Explain that there is a Tutorial, Application, Offline Activities,

and a Mastery Test for all modules. Refer to the Learning Activity Types chapter on page 25 for more information.

• Explain that students take tests to ensure their mastery of skills. They can also take these tests as pretests to see if they already know the material.


18

Orienting the Learner, Continued

Checklist (continued)

Task Description Explain how PLATO tracks their progress.

• Describe how the system automatically keeps a record of their

mastery of learning objectives as they go through a curriculum or course.

• Describe the content of their performance reports. (These reports are available to you through PLATO Web Learning Network or PLATO Pathways. Detailed information for the administrator or instructor is provided in the online Help feature and user guide for these products.)

Describe the bookmarking feature. • Explain that if learners exit a Tutorial or Application without

completing it, a bookmark is automatically placed at the beginning of the section where the learner stopped. When learners restart the Tutorial or Application, they will enter at the beginning of that section.


19

Orienting the Learner, Continued

Checklist (continued)

Task Description Define the terminology used below.

Term Definition

Curriculum A study plan composed of courses, modules, and learning activities arranged in a hierarchy.

Course A major topical subdivision of a curriculum. For example, Graphing Basics.

Module A learning activity centered on a terminal objective. For example, Classifying Polynomials.

Mastery Test An activity that evaluates student performance on the terminal objective for the module and reports the student’s score to PLATO Web Learning Network or PLATO Pathways. Only two scores are possible: mastered or not mastered.

Section An instructional segment that covers 1-2 teaching points.

Bookmarking A programming feature that indicates where the student exited a particular section of a PLATO tutorial activity.

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Navigating through the Courseware

Introduction Courseware navigation by activity. There are four different activities in the

courseware: • Tutorial • Application • Mastery Test • Offline Activities

Courseware features

The table below identifies the various features available to learners in Tutorials, Applications, and Mastery Tests. An Offline Activity is an optional two-page printable "homework" exercise. Note All features are not available to learners all of the time in the

courseware.

Option Description Tools Allows learners to access resources (i.e., Notebook,

Graphing Tool, Preferences) to help them throughout the courseware. Refer to the Learning Aids chapter beginning on page 43 for more information on the tools available to learners. Notes The Notebook is not available in Mastery

Tests. The Calculator is not available in the mental math modules (i.e., Basic Number Ideas). Otherwise, all tools are available to learners all of the time.

Refresh Clears and reloads the current page. Objective section (All activities)

Displays the objective and the motivator for the activity.

Study section (Tutorials only)

Instructs learners in the skill and asks scaffolded questions with feedback, but without scoring learners.

Practice section (Tutorials only)

Allows learners to practice skills taught in the Study section. Provides feedback, but does not score learners.

Investigate Allows learners to choose from a gallery of explorations that extend what they studied in the Tutorial. (Tutorials only)


21

Navigating through the Courseware, Continued

Courseware features (continued)

Option Description Application Set (Application only)

Allows learners to practice a set of questions that includes feedback and scoring.

Menu ( ) (Tutorials only)

Allows learners to return to the Main Menu page to access the other sections of the module: Study, Practice, and Investigate.

Progress ( ) (Tutorials only)

Allows learners to see where they are in the Study section and to navigate to subsections of the Tutorial.

Audio ( ) (Tutorials only)

Allows learners to stop and restart audio on and off at any time during the Study section of the Tutorial.

Exit ( ) Exits the activity.

Tutorial The table below describes the progression through a Tutorial.

Note Learners can click the button at any time in a Tutorial. Doing so returns the learner to the previous page. If learners click this button at the beginning of a subsection, they are returned to the beginning of the previous subsection.

Stage Description Result

1 Learners click the Start button.

An example or preview of material from the Tutorial displays.

2 Learners click the

button.

A clearly stated objective for the Tutorial displays.


button.

The Main Menu page displays allowing learners to access the Study section of the Tutorial.

4 Learners click the Study button and then continue to click the Forward arrow.

Learners will be prompted to answer questions and complete interactions until they have completed the Tutorial. (A Congratulations page displays upon completion.)


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Tutorial (continued)

Step Action Result 5 Learner clicks the

button.

A Completion Status reports to PLATO Web Learning Network or PLATO Pathways.

Application The table below identifies a learner's progression through an Application.

Note Learners can click the button in the first two scenes of the Application. Doing so returns the learner to the previous page. Once the questions begin, this button is no longer enabled.

Stage Description Result 1 Learners click the

Start button. The objective for the Application displays.


button.

A brief one-page review of the Tutorial displays.


button.

An explanation of the Application question sets and scoring displays.


button.

The first question in the question set displays. Note Learner progress information

displays at the bottom of the page with each new question (e.g., Question 2 of 10).

5 Learners select or enter an answer.

Feedback displays. Learners get two chances to answer correctly before the correct answer displays.

6 Learners continue through the question

set using the button.

Once the question set is complete, the score displays. Learners are prompted to request another question set or exit and record their score.

7 Learner clicks the

button to exit the activity.

Completion and the score of the last Application question set reports to PLATO Web Learning Network or PLATO Pathways.


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Mastery Tests The table below identifies the progression through a Mastery Test.

Stage Description Result 1 Learners click the Start

button. The goal for mastering the test displays.

2 Learners click the button.

An explanation of the test and scoring displays. The learner is given the opportunity to proceed with the test when they are ready.

3 Learners click the button.

The first question in the question set displays. Note Learner progress information

displays at the bottom of the page with each new question (e.g., Question 2 of 10).

4 Learners select an answer.

Correct or Incorrect feedback displays. Learners only have one chance to answer each question.

5 Learners continue through the question set

using the button.

The learner's score displays after the last question.

6 The learner clicks the

button on the Score page

Either a Congratulations page displays or a recommendation to review the tutorial and complete the activity again displays.

7 Learner clicks the button to exit the activity.

Completion, mastery status, and a score report to PLATO Web Learning Network or PLATO Pathways.

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Chapter 4 Learning Activity and Question Types

Overview

Introduction Each Algebra course consists of modules containing a number of learning

activities and question types to support a variety of learning styles and needs.

In this chapter This chapter explains the purpose, components, use of, scoring, and reporting

for the following activities.

Topic See Page Tutorials 26 Applications 30 Mastery Tests 34 Offline Activities 35 Question Types 36

25

Tutorials

Description Tutorials include interactive instructional sequences for the various levels of

algebra. Tutorials include the following sections: • Objective • Study • Practice • Investigate

Objective section

The Objective section introduces the skills to be presented in the module and formally states the learning objective.

Study section The Study section of the tutorial presents the skills to the learner. This

section includes text with audio, animation, graphics, interactions, and questions with feedback to provide scaffolded instruction. The example below shows a typical real-life application to illustrate math concepts (e.g., slope).


26

Tutorials, Continued

Practice section The Practice section allows learners to apply what they learned in the Study

section. The practice includes questions with feedback that reinforces the concepts and principles taught in the Study section. Learners are not scored in the Practice section. Learners have two chances to answer correctly before they can access a solution.


27


Investigate section

The Investigate section allows learners to choose from a gallery of explorations that extend what they studied in the Tutorial. The Investigations activities include open-ended learning activities such as free-play use of tools and simulations, interesting topics in applications of math and math history. Algebra 1, Part 1 Investigates

Algebra 1, Part 2 Investigates

Continued on

28

Recommended Investigates, based on the module the learneris in The modules below the learner'slevel are highlighted.

next page


Interactive questions

In Tutorials, students have an opportunity to “learn by doing” without formal assessment. The management system (PLATO Pathways or PLATO Web Learning Network) records completion, but does not record a score. Questions throughout the Tutorial and Practice provide interaction and reinforce concepts and principles.

Practice Each Tutorial ends with a Practice section that allows learners to answer

questions, check their understanding of the skill, and determine which activity to choose next: the Application (more practice) or the Mastery Test. Learners receive feedback but not a score during the Practice section.

Bookmarking If a learner exits a Tutorial activity early, a bookmark is automatically placed

in the section where the learner stopped. When learners restart the Tutorial, they are able to enter where they left off. Example If learners exit a Tutorial during the Study section, the Main menu displays upon re-entry. Learners are able to go to the Study section and use the progress bar to return to first step of the scene they were in when they exited. Note Because PLATO courseware bookmarks at the question set level,

learners may be required to re-answer questions upon re-entry into the Practice section.

29

Applications

Description Application activities are accessible to learners after completion of the

Tutorial. All Applications include the following: • An objective • An on-screen review of the Tutorial • A set of questions with feedback

Objective The objective of every Application is “to practice.”


30

Applications, Continued

Review The Review gives learners the opportunity to recall the skills taught in the

Tutorial. The Application review uses the summary screen from the Tutorial to recall previously learned information.


31


Question set(s) Question sets allow learners to apply skills presented in the Tutorial.

Learners may complete one or more scored question sets to complete the activity, depending upon how much practice they need. Large question pools ensure that learners can complete numerous sets without seeing the same questions.

Scoring Applications are scored. After each set, learners can see the scores of their

last two sets. They then have the option of exiting or doing another set. When a learner exits, the score of the last set becomes part of the student record. Along with the completion status, the score is reported to PLATO Pathways or PLATO Web Learning Network.


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Bookmarking If a learner exits an Application activity early, a bookmark is automatically

placed in the section where the learner stopped. When learners restart the Application activity, they re-enter at the beginning of the section where they exited the Application. Notes If a learner exits an Application in the middle of a question set, the

learner will re-enter the Application at the beginning of the question set and be required to answer all of the questions in that set again.

Learners may see different questions than those questions they saw

before they exited the Application. PLATO courseware draws from a large question pool and generates new question sets each time a learner enters an Application activity.

33

Mastery Test

Description A Mastery Test evaluates performance on the module’s terminal objective

and reports the learner's score to PLATO Pathways or PLATO Web Learning Network.

Questions Each Mastery Test consists of ten questions taken from a large pool of test

questions. Note If a ten-item test could potentially take more than a normal class

period, the Mastery Test has only five items.

Bookmarking Mastery Tests do not have bookmarking capabilities. Therefore, if a learner

exits a Mastery Test early, the test locks, is not mastered, and the learner must re-enter the Tutorial before the Mastery Test will unlock.

Scoring A score of 80% or above demonstrates mastery. The learner must answer at

least eight of ten questions correctly, or four or five questions if the Mastery Test has five items. If the learner misses more than 20% of the questions, he or she is told that mastery of the material has not been achieved at this time. The learner is advised to review the material and must return to the tutorial before he or she is allowed to retake the test. After successful completion of a Mastery Test, a Congratulations page displays. A status of "mastered" or "not mastered" is reported to PLATO Pathways or PLATO Web Learning Network, along with completion status.

34

Offline Activities

Description An offline activity is included in each module of each course. These

activities allow learners to further practice the skills learned in the modules. Offline activities also include open-ended questions for extension and reflection. Each offline activity is two pages in length and must be printed; they cannot be filled out online (electronically).

Location You can print offline activities from the following places:

• PLATO Pathways users

Double-click the documentation.html on the courseware CD-Rom and select the Student Materials and/or Answer Keys links accordingly.

• PLATO Web Learning Network users Click the user guides>Student Materials>Algebra link to access the offline activities and answer keys.

These offline activities also display on the learner's menu within the courseware. Learners can also print these offline activities if they have access to a printer.

Answer keys Answer keys for each offline activity are also included on either the

courseware CD-Rom (PLATO Pathways users) or from the user guides>Student Materials>Algebra link (PLATO Web Learning Network users) for Account or Group Coordinators.

35

Question Types

Introduction The Algebra courseware includes the following types of questions:

• Fill-In • Multiple Choice • Graphing Note Not all question types exist in each Tutorial, Application, or Mastery

Test.

Feedback All of the question types provide immediate feedback once the Learner selects

an answer and clicks the Done button. The table below identifies the type of feedback a learner receives during the Tutorial and Application sections depending on the response they give. Note Even when learners answer correctly, they have the option of selecting

the Answer button to confirm their solution.

Response Feedback Correct the first time Positive feedback (e.g., Great, Yes) and an

option to see more details of the completed problem.

Incorrect the first time Restatement of the rule and prompting to rethink the response.

Incorrect the second time The Answer button displays and must be clicked to see the explanation for the correct answer. Learners cannot move forward until they view the contents of the Answer button.

Note Learners cannot respond to Mastery Test questions multiple times.


36

Question Types, Continued

Feedback (continued)

Below is an example of a learner getting the wrong answer twice. Note the

Answer button is enabled and the learner can see the details of the solution as well as the hint from their first incorrect response.

Continued on ne

In Tutorials, Learners can click the Answer button to receiveinformation about the

more

answer.

xt page

37


Fill-In questions

Fill-In questions require learners to think about what they have learned and compose an answer. The example below illustrates the fill-in field and reference graphic to help learners complete the answer.


38


Multiple Choice questions

Multiple choice questions have three or more answer alternatives from which a learner chooses. Note PLATO courseware contains a few two-choice questions: yes/no,

true/false and infinite/finite (sets). To select an answer, learners click the answer box that contains the correct answer. Learners receive immediate feedback in Tutorials and Mastery Tests. The example below illustrates a four-choice multiple choice in which the learner uses the graph to help determine the correct answer.


39


Graphing questions

Graphing questions prompt learners to plot points for coordinate systems and solutions of linear equations. Here are a few key points your learners should know about Graphing questions: • The DONE button is not active until the learner has selected the required

number of points to answer the question. • When a learner clicks the DONE button, the grid locks. • Learners can drag and drop points to remove (delete) them from the grid. • The Edit button allows users to modify a response after receiving

feedback. The example below illustrates how a learner performs a graphing activity based on the equation given.

Learner feedback displays here once an answer is selected.

40

Chapter 5 Testing Strategies

Introduction Mastery Tests, offered at the beginning of each module, monitor each

learner’s progress and record performance at the module level. Each module contains one Mastery Test. The learner must pass the Mastery Test for each module to achieve a status of completion.

Questions Each Mastery Test consists of ten questions taken from a pool of test

questions. The Mastery Test items come from a large pool of questions so that learners who repeat a test will rarely see an item repeated. A score of 80% or more demonstrates mastery. Note If a ten-item test could potentially take more than a normal class

period, the Mastery Test has only five items.

Feedback Correct or Incorrect feedback appears after every answer and the learner

knows immediately if he or she has answered a question correctly. The learner receives a total score at the end of the test.

Pretesting Taking Mastery Tests as pretests has the following advantages:

• Allows learners to move more quickly through the material. • Provides learners with control over their learning experience. • Allows learners to test out of objectives that they have already mastered.

Posttesting An alternate strategy for learners is to use the Mastery Tests as post-tests

only. Learners first complete a learning activity and then take the Mastery Test. Learners repeat the process until they have mastered all the objectives. While potentially more time-consuming than the pretest sequence, this approach is more appropriate for learners whose skill or knowledge levels are low and who may experience frustration or anxiety with pretests.

41

Chapter 6 Learning Aids

Overview

Introduction PLATO courseware offers a variety of online tools to learners as they work

within the activities.

System requirements

To use Algebra multimedia features, each workstation must have the following: • Headphones or sound speakers • An audio card These are the standard equipment requirements for using the Algebra courseware. The same multimedia rules apply whether you are using speakers or headphones.


Topic See Page Notebook 44 Calculator 46 Math Entry 48 Graphing Tool 50 Audio 51

43

Notebook

Description The Notebook is an online version of a paper notebook. Each learner has one

notebook. Learners can take notes on important points, edit them, and refer quickly to them from within the Algebra courseware to refresh their knowledge of the topic.

Restrictions The Notebook is not available in Mastery Tests.

Availability Each learner has one notebook per curriculum. All of the notes a learner

takes during any Algebra module will exist in the same notebook. These notes are only available to the learner from within the Algebra courseware.

Accessing To access the Notebook, follow the steps below.

Step Action 1 Select Notebook from the Tools menu.

Result The Notebook displays.


44

Notebook, Continued

Accessing (continued)

Step Action 2 Click Close to close the notebook or click Print to print the

contents of the notebook. Note You can print only one page of the Notebook at a time. If

you want to print specific information from the Notebook, you must browse to that page and click the Print button.

45

Calculator

Description The Algebra curriculum includes an online calculator for solving problems. It

supports basic operations in case students do not have access to a hand-held calculator.

Accessing To access the calculator, follow the step below.

Step Action 1 Select Calculator from the Tools menu.

Result The Calculator displays.


46

Calculator, Continued

Functions The table below describes the features of the calculator.

Option Description

Use this button to change the sign of the number (positive or negative).

Use this button to clear the information you most recently entered into the calculator.

Use this button to clear everything you entered into the calculator and start over with the operation.

Use this button to clear any information stored in memory.

Use this button to redisplay information stored in memory.

Use this button to store information in memory.

Use this button to add information to the stored memory.

Use this button for square roots. Press this button after entering the number for which you want to know the square root.

Use this button for percents.

Use this button for reciprocals.

Use this button to view keyboard shortcuts for the calculator buttons.

Use this button to switch between entering information in the calculator or in the courseware. This applies when using keystrokes instead of the number buttons.

Use this button to close the calculator.


47

Math Entry Tools

Description Some questions in the Algebra curriculum require learners to enter fractions,

exponents, radicals, operation signs, and/or inequality signs, and any combination of these. Math Entry tools allow learners to enter the answer as a format identical to how they would write the answer.

Accessing The Math Entry tool buttons (with keyboard equivalents) display as part of

any fill-in questions to assist learners in constructing the answer.

Learners can click the ? button to learn more about using the tool.

Using Math Entry tools

Learners select the button that corresponds with the placement of the entry they want to make (e.g., base, exponent, numerator, denominator).


48

Math Entry Tools, Continued

Functions The table below describes the various math entry tools.

Tip For more information about these functions, click the button near

the math entry tool.

Option Description Shortcut Key Add + Subtract - Multiply * Less Than < Greater Than > Less Than or Equal To <= Greater Than or Equal To >= Backspace Backspace Help NA

Base Space, →

Exponent ^

Fraction /, Spacebar

Square Root @

Clears entries in the text field NA

49

Graphing Tool

Description The Graphing Tool allows learners to see a visual representation of an

equation on a graph.

Accessing To access the Graphing Tool, follow the steps below.

Step Action 1 Select Graphing Tool from the Tools menu.

Result The Graphing Tool displays

2 Learners solve for y by entering an equation in the text field. 3 Learners click the DONE button.

Result The graph of the equation displays.

4 Learners can click the DEL button for any equation they want to delete (remove from the graph).

5 Click the Close button to close the Graphing Tool.

Learners can modify the range of the x- and y- coordinates here.

Learners can enter multiple equations and compare the results by selecting a different color for each graph.

50

Audio

Description The Algebra courseware allows learners to listen to the words that display for

each scene within the Study section of Tutorial.

Benefits Benefits of optional audio include the following:

• Allows learners with reading difficulties hear the text and read along. • Sets the pace of the instruction. • Allows learners to hear terminology pronounced and used in context.

Audio states While the audio plays, the audio controls display like this:

• Learners can click the Audio button to stop the audio.

When the audio stops, the audio controls display like this:

• Learners can click the Forward arrow to continue. • Learners can click the Replay button to replay the audio for the scene.

Replay

51

Chapter 7 PLATO Algebra 1 Scope and Sequence

Overview

Introduction This chapter identifies the instructional scope and sequence of the PLATO

Algebra 1 curriculum.

Factors The average time required for a learner to complete and assignment depends

on the learner's reading rate, a learner's experience with computers and PLATO courseware, the difficulty level of the content, and finally the number of activities included in the learner's assignment. Students may take anywhere from a few seconds to answer a simple practice or test item to several minutes to answer a more complex item. You can use the following estimated time guideline for each activity of a module realizing that some will take longer than others and some less: • Tutorials—20 minutes • Applications—15-20 minutes • Mastery Tests—15 minutes • Offline Activities—20 minutes


Topic See Page Course One Basic Number Ideas 54 Course Two Math Sentences 56 Course Three Graphing Basics 58 Course Four Equations and Formulas 59 Course Five Special Topics 60 Course Six Introduction to Functions 62 Course Seven Sets and Numbers 63 Course Eight Polynomials and Factoring 66 Course Nine Equations and Inequalities 68

53

Course One Basic Number Ideas

Description The table below identifies the modules and their objectives included in

Course One Basic Number Ideas. * Denotes a new module as of the October 2002 release.

Module Objective

Odd and Even Numbers Given a whole number, learners will determine whether the number is odd or even.

Prime and Composite Numbers

Given a whole number, learners will determine whether the number is prime or composite.

Exponents: Exponential Form

Given a series of self-multiplications, learners will write the product in exponential form.

Exponents: Expanded Form

Given a whole number taken to a power, learners will write the product in exponential form.

Exponents: Product Rule Given the multiplication of numbers with the same base, learners will apply the product rule of exponents.

Exponents: Power Rule Given a number in exponential form taken to a power, learners will apply the power rule of exponents.

The Additive Inverse of Integers

Given an integer, learners will identify the opposite or additive inverse.

Adding Integers Given an addition problem with integers, learners will find the sum.

Subtracting Integers Given a subtraction problem with integers, learners will find the difference.

Multiplying Integers Given a multiplication problem with integers, learners will find the product.

Dividing Integers Given a division problem with integers, learners will find the quotient.


54

Course One Basic Number Ideas, Continued

Description (continued)

Module Objective Square Roots of Perfect Squares

Given a perfect square, learners will identify the square root.

Square Roots of Imperfect Squares

Given a whole number that is not a perfect square, learners will identify the integer boundaries of the root.

Multiplying Common Fractions

Given two fractions, learners will find the product.

Adding and Subtracting Fractions

Given two fractions with like or unlike denominators, learners will find the sum or the difference.

Adding and Subtracting Mixed Numbers

Given two mixed numbers, learners will find the sum or the difference.

Dividing Fractions Given a division problem with two fractions, learners will find the quotient.

Multiplying and Dividing Mixed Numbers

Given a multiplication or division problem with mixed numbers, learners will find the product or quotient.

Using Basic Number Ideas

Given a real-world problem that involves the basic operations with integers or fractions, learners will find the solution.

*Mental Math with Whole Numbers and Decimals

Given whole numbers or decimals to add, subtract, multiply, or divide, learners will perform the calculations mentally using mental math strategies.

*Mental Math with Fractions and Percents

Given fractions to add, subtract, multiply, or divide or given whole numbers to find percentages of, learners will find the answer using mental math strategies.

55

Course Two Math Sentences


Course Two Math Sentences. * Denotes a new module as of the October 2002 release.

Module Objective

*Order of Operations Given a mathematical problem involving integers, the basic operations, and powers, learners will find the answer by following the order of operations.

Expressions in 1 Variable

Given an expression in one variable and a value for the variable, learners will evaluate the expression.

Expressions in 2 or More Variables

Given an expression in more than one variable and values for the variables, learners will evaluate the expression.

Determining the Truth Value of a Statement

Given an equation with variables, learners will identify values that make the statement true.

Adding Monomials Given two or more monomials, learners will find the sum.

Subtracting Monomials Given a subtraction problem with two monomials, learners will find the difference.

Multiplying Monomials Given two or more monomials, learners will find the product.

Dividing Monomials Given a division problem with two monomials, learners will find the quotient.

Adding Binomials and Monomials

Given an addition problem with monomials and binomials, learners will find the sum.

Subtracting Binomials and Monomials

Given a subtraction problem with monomials and binomials, learners will find the difference.


56

Course Two Math Sentences, Continued


Module Objective Multiplying Binomials and Monomials

Given monomials and binomials, learners will find the product.

Dividing Binomials and Monomials

Given the division of a binomial by a monomial, learners will find the quotient.

Linear Equations in 1 Variable: Solving by Inspection

Given a linear equation in one variable, learners will find the solution by inspection.

Linear Equations in 1 Variable: Isolating the Variable

Given a linear equation in one variable, learners will find the solution by isolating the variable.

Linear Inequalities in 1 Variable, Part 1

Given a linear inequality that can be solved by adding or subtracting values to isolate the variable, learners will find the solution.


Given a linear inequality that can be solved by multiplying or dividing both sides to isolate the variable, learners will find the solution.

More Difficult Linear Inequalities in 1 Variable

Given a linear inequality in one variable that can be solved by adding, subtracting, multiplying, or dividing values to isolate the variable, learners will find the solution.

Special Quadratic Equations, Part 1

Given quadratic equations of the type x^2 = b^2, learners will find the solution.

Special Quadratic Equations, Part 2

Given quadratic equations of the type x^2 + bx = 0, learners will find the solution.

Using Linear Equations to Solve Problems

Given real-world problems, learners will represent the problem using linear equations and find the solution.

Using Quadratic Equations to Solve Problems

Given real-world problems, learners will represent the problem using quadratic equations and find the solution.

57

Course Three Graphing Basics


Course Two Graphing Basics.

Module Objective Coordinate Plane Given a point on a coordinate plane, learners will

identify its coordinates. Identifying Points on a Coordinate Plane

Given coordinates of a point, learners will plot the point on a coordinate plane.

Ordered Pairs as Solutions to a Linear Equation

Given a linear equation in two variables and a coordinate pair, learners will determine whether the pair represents a solution of the equation.

Graphing Linear Equations in 2 Variables

Given a linear equation in two variables, learners will determine whether a given point lies on the graph of the equation and use points to draw the line that represents the equation.

Solving and Graphing Systems of Equations

Given a system of linear equations in two variables, learners will find the solution by graphing the system.

Solving Problems with Systems of Linear Equations

Given real-world problems that can by represented by a system of linear equations, learners will find the solution.

58

Course Four Equations and Formulas


Course Two Equations and Formulas. * Denotes a new module as of the October 2002 release.

Module Objective

*Literal Equations Given a real-world situation, learners will write a literal equation that represents it.

*Adapting and Using Formulas

Given a formula that represents a real-world situation, learners will adapt the formula and use it to solve problems.

59

Course Five Special Topics


Course Five Special Topics. * Denotes a new module as of the October 2002 release.

Module Objective

Visualizing Percents Less than 1%

Given a visual representation of a percent less than 1%, learners will represent the quantity as a percent.

Converting Percents Less Than 1% to Decimals

Given a percent that is less than 1%, learners will convert the percent to a decimal.

Converting a Decimal to a Fraction of a Percent

Given a number less than 0.01, learners will convert it to a percent.

Finding the Amount With Percents Less than 1%

Given a percent that is less than 1% and a whole, learners will find the amount.

Visualizing Percents Greater than 100%

Given a visual representation of a percent greater than 100%, learners will represent the quantity as a percent.

Converting Percents Greater than 100% to Decimals

Given a percent that is greater than 100%, learners will convert the percent to a decimal.

Converting a Number Greater than 1 to a Percent

Given a number greater than 1, learners will convert it to a percent.

Mean, Median, and Mode

Given a set of data, learners will find the mean, median, and/or mode.

Probability and Possible Outcomes

Given a description of a chance experiment, learners will determine the number of ways an event can occur and the total number of possible outcomes.

Probability of an Event

Given a description of a chance experiment, learners will determine the probability a given event will occur.

Solving Problems With Percents

Given a real-world problem that involves percents, learners will find the answer by calculating the whole, amount, or percent.


60

Course Five Special Topics, Continued


Module Objective Solving Problems With Mean, Median, and Mode

Given a real-world problem that involves sets of data, learners will solve the problem by calculating the mean, median, or mode.

Solving Problems With Probability

Given a real-world problem that involves chance, learners will solve the problem by calculating the probability a given event will occur.

*Estimation Basics Given a set of real-world data, learners will estimate a calculation by rounding appropriate values up or down.

*Estimation by Clustering

Given a set of real-world data, learners will estimate a calculation by clustering some or all of the data.

*Scaling and Proportion, Part 1

Given representational diagrams and scale drawings, learners will distinguish each from the other and identify appropriate ratios for scale drawings.

*Scaling and Proportion, Part 2

Given a scale drawing, learners will determine the actual size of an object or dimension.

61

Course Six Introduction to Functions


Course Six Introduction to Functions. * Denotes a new module as of the October 2002 release.

Module Objective

*Patterns and Sequences

Given visual and numerical patterns, learners will predict what comes next in a sequence.

*Functions Given appropriate information about a function, learners will identify the rule that describes how input and output data are related and use the rule to generate data.

*Describing Functions with Equations, Tables, and Graphs

Given one or two representations of a function (context, graph, table, equation), learners will identify other representations of the same function.

*Linear Patterns Given a table, equation, or graph of a function, learners will determine whether the function it represents is linear.

*Graphs, Slopes and y-Intercepts

Given the graph of a linear function, learners will find the slope and y-intercept.

*Equations, Graphs, Slopes, and y-Intercepts

Given the equation of a linear function, learners will use their knowledge of slope and y-intercept to identify the graph; given the graph, they will identify the equation.

*Interpreting Graphs to Solve Problems

Given the graph of a linear function, learners will interpret the graph to solve a real-world problem.

62

Course Seven Sets and Numbers


Course Seven Sets and Numbers.

Module Objective Additive Inverse of an Integer

Given an integer, learners will find the additive inverse.

Integer Sum Given two or more integers, learners will find the sum.

Integer Difference Given subtraction problems involving two or more integers, learners will find the difference by adding the opposite.

Integer Product Given a multiplication problem involving integers, learners will find the product.

Integer Quotient Given a division problem involving integers, learners will find the quotient.

Adding Fractions Given two or more fractions with like or unlike denominators, learners will find their sum.

Subtracting Fractions Given two or more fractions with like or unlike denominators, learners will find their sum.

Multiplicative Inverse of a Fraction

Given a fraction, learners will find the multiplicative inverse.

Product of Fractions Given two or more fractions, learners will find the product.

Quotient of Fractions Given two fractions, learners will find the quotient. Basic Set Concepts: Elements in a Set

Given a set and its elements, learners will describe the set by listing the elements.

Basic Set Concepts: Finite or Infinite

Given a description of a set, learners will determine whether the set is finite or infinite.


63

Course Seven Sets and Numbers, Continued


Module Objective Basic Set Concepts: Subsets

Given a description of a set, learners will identify and describe subsets.

Basic Set Concepts: Roster and Set-builder Forms

Given a description of a set, learners will represent the set using roster and set-builder forms.

Union of Sets Given two sets, learners will find the union of the sets.

Intersection of Sets Given two sets, learners will find the intersection of the sets.

Positive and Negative Exponents

Given an expression with a positive or negative integer exponent, learners will identify an equivalent expression.

Integer Exponents and the Product Rule

Given the multiplication of terms with like bases and with integer exponents, learners will apply the product rule for exponents.

Integer Exponents and the Quotient Rule

Given the division of terms with like bases and integer exponents, learners will apply the quotient rule for exponents.

Integer Exponents and the Power Rule, Part 1

Given a base number and exponent, raised to another power, learners will apply the power rule for exponents.

Integer Exponents and the Power Rule, Part 2

Given the product of two or more numbers written in exponential form and raised to a power, learners will apply the power rule of exponents.

Square Roots of Integers

Given a positive integer, learners will find the square roots; given a positive integer under a radical sign, learners will find the value.

Multiplication Rule for Radicals

Given the multiplication of two radicals, learners will apply the multiplication rule to find the product.

Division Rule for Radicals

Given the division of two radicals, learners will apply the division rule for radicals to find the quotient.


64

Course Seven Sets and Numbers, Continued


Module Objective Simplifying Radicals, Part 1

Given an expression involving radicals, learners will write the expression in simplest form using the multiplication or division rules for radicals.

Simplifying Radicals, Part 2

Given an expression that involves adding or subtracting radicals, learners will rewrite the expression in simplest form.

Review: Fractions and Sets

Given a mixture of problems involving fractions or involving sets, learners will find the answers using the concepts and principles taught in this course.

Review: Exponents and Radicals

Given a mixture of problems involving exponents and radicals, learners will find the answers using the concepts and principles taught in this course.

65

Course Eight Polynomials and Factoring


Course Eight Polynomials and Factoring.

Module Objective Classifying Polynomials

Given a polynomial, learners will classify it as a monomial, binomial, or other polynomial.

Additive Inverse of a Monomial

Given a monomial, learners will find the additive inverse.

Monomial Sum Given two or more monomials, learners will find their sum.

Monomial Difference

Given two monomials, learners will find the difference.

Monomial Product Given two or more monomials, learners will find the product.

Monomial Quotient Given a division problem involving monomials, learners will find the quotient.

Binomial Sum Given two binomials, learners will find their sum. Additive Inverse of a Binomial

Given a binomial, learners will find the additive inverse.

Binomial Difference

Given a subtraction problem involving binomials, learners will find the difference.

Value of a Polynomial

Given a polynomial expression and values for the variables, learners will find the value of the polynomial.

Polynomial Sum Given an addition problem involving polynomials, learners will find the sum.

Polynomial Difference

Given a subtraction problem involving polynomials, learners will find the difference.

Product of a Monomial and Polynomial

Given a multiplication problem involving monomials and polynomials, learners will find the product.


66

Course Eight Polynomials and Factoring, Continued


Module Objective Simplifying Polynomial Expressions

Given an expression that includes products, sums, and differences of polynomials, learners will write the expression in simplest terms.

Product of Polynomials Given two polynomial expressions in several variables, learners will find the product.

Quotient of a Monomial and Polynomial

Given the division of a polynomial by a monomial, learners will find the quotient.

Quotient of a Binomial and Polynomial

Given the division of a polynomial by a binomial, learners will find the quotient.

Greatest Common Factor of Monomials

Given two or more monomials, learners will find the greatest common factor.

Monomial Factors of Polynomials

Given a polynomial, learners will factor the expression by finding the greatest monomial factor of its terms.

Binomial Factors of Polynomials, Part 1

Given a polynomial with terms that have been regrouped for factoring, learners will complete the factoring using the distributive property.

Binomial Factors of Polynomials, Part 2

Given a polynomial, learners will factor the expression by regrouping terms and factoring sums and differences of terms using the distributive property.

Factoring the Difference of 2 Squares

Given an algebraic expression that can be written as the difference of two squares, learners will factor the expression using this pattern: a^2 - b^2 = (a+b)(a-b).

Factoring Perfect Square Trinomials

Given a trinomial that is a perfect square trinomial, learners will recognize the pattern and factor the trinomial as a binomial squared.

Factoring Trinomials, Part 1 Given a trinomial of the form x^2 + bx + c, learners will find the binomial factors by using what they know about multiplying binomials.

Factoring Trinomials, Part 2 Given a trinomial of the form ax^2 + bx + c, learners will find the binomial factors by using what they know about multiplying binomials.

Review: Polynomials and Factoring

Given a mixture of problems involving polynomials and factoring, learners will find the answers using the concepts and principles taught in this course.

67

Course Nine Equations and Inequalities


Course Nine Equations and Inequalities. * Denotes a new module as of the October 2002 release.

Module Objective

Simple Equations in 1 Variable: Using Inspection

Given an equation in one variable, learners will solve the equation by inspection.

Simple Equations in 1 Variable: Isolating the Variable

Given an equation in one variable of the type x + b = c, learners will solve the equation by isolating the variable.

More Difficult Linear Equations in 1 Variable

Given an equation in one variable of the type ax + b = c, learners will solve the equation by isolating the variable.

Absolute Value of a Number

Given a number, learners will find its absolute value.

Equations with Absolute Values

Given an equation in one variable that involves absolute value, learners will find the solution set.

Graphing a Solution Set on a Number Line

Given a solution set or a simple inequality in one variable, learners will graph the solution set on a number line.

Solving and Graphing Equations in 1 Variable

Given an equation in one variable that involves absolute value or an inequality in one variable, learners will find and graph the solution set.

Solving Problems with Linear Equations in 1 Variable

Given a word problem, learners will solve the problem by setting up and solving a linear equation in one variable.


68

Course Nine Equations and Inequalities, Continued


Module Objective Linear Inequalities in 1 Variable, Part 1

Given a linear inequality in one variable that can be solved by adding or subtracting a constant to both sides, learners will solve the inequality and graph the solution.


Given a linear inequality in one variable that can be solved multiplying or dividing both sides by the same quantity, learners will solve the inequality and graph the solution.


Given a linear inequality that requires multiple steps to isolate the variable, learners will solve the inequality and graph the solution.

Solving Simple Quadratic Equations

Given a quadratic of the form ax^2 + bx = 0, learners will find the solution set by factoring and using the zero product rule.

Solving Quadratic Equations by Factoring, Part 1

Given a quadratic equation of the form x^2 - a^2 = 0, learners will find the solution by factoring and using the zero product rule.


Given a quadratic equation that involves a perfect square trinomial, learners will solve the equation by factoring and using the zero product rule.


Given a quadratic equation that involves a factorable trinomial, learners will solve the equation by finding the binomial factors and using the zero product rule.

Quadratic Formula Given a quadratic equation, learners will solve the equation by using the quadratic formula.

Solving Problems With the Quadratic Equations

Given a real-world problem, learners solve the problem by setting up and solving a quadratic equation.

Review: Equations and Inequalities

Given a mixture of problems involving equations and inequalities, learners will find the answers using the concepts and principles taught in this course.

69

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