EdTech 503 Final Instructional Design Project

V e r t o r i a L a g r o o n

E D T E C H 5 0 3

( S u m m e r 2 0 1 0 )

F i n a l I n s t r u c t i o n a l

D e s i g n P r o j e c t

S u b m i t t e d t o :

D r . J a r e k J a n i o

A u g u s t 2 , 2 0 1 0

Project Title:

Incoming high school freshman solve systems of

equations using elimination.

EDTECH 503 FINAL INSTRUCTIONAL DESIGN PROJECT

Copyright © 2010, Vertoria D. Lagroon 2

TABLE OF CONTENTS

Synthesis Reflection Paper ........................................................................................................ 4

Part 1 Topic ............................................................................................................................... 6

1a Learning Goal .................................................................................................................... 6

1b Audience Description ......................................................................................................... 6

1c Rationale ........................................................................................................................... 6

Part 2 Analysis Report ............................................................................................................... 7

2a Description of the Need ..................................................................................................... 7

2b Description of the Learning Context ................................................................................... 7

Part 3 Planning .........................................................................................................................11

3a Learning Objectives ..........................................................................................................11

3b Objectives Matrix Table ....................................................................................................12

3c ARCS Table ......................................................................................................................13

Part 4 Instructor Guide ..............................................................................................................15

Introduction ...........................................................................................................................15

Activate Attention ...............................................................................................................15

Establish Purpose ..............................................................................................................15

Arouse Interest and Motivation ...........................................................................................15

Preview Learning Activity ...................................................................................................15

Body ......................................................................................................................................16

Activate Prior Knowledge ...................................................................................................16

Present Information and Examples ....................................................................................16

Focus Attention ..................................................................................................................16

Employ Learning Strategies ...............................................................................................16

Guided Practice .................................................................................................................17

Feedback ...........................................................................................................................17

Conclusion ............................................................................................................................18

Summarize and Review .....................................................................................................18

Transfer Learning ...............................................................................................................18

Closure ..............................................................................................................................18

Assessment .......................................................................................................................18

Feedback ...........................................................................................................................18

Part 5 Learner Content ..............................................................................................................19

5a Learning Materials ............................................................................................................19

5b Formative/Summative Assessment Materials ...................................................................20



5c Technology Tool Justification ............................................................................................20

Part 6 Formative Evaluation Plan ..............................................................................................21

6A Expert Review ..................................................................................................................21

6b one-to-one evaluation .......................................................................................................21

6c Small Group Evaluation ....................................................................................................21

6d Field Trial..........................................................................................................................22

Part 7 Formative Evaluation Report ..........................................................................................23

7a Evaluation Survey .............................................................................................................23

7b Expert Review Report .......................................................................................................27

7c Comments on Change ......................................................................................................27

Part 8 AECT Standards Grid .....................................................................................................28

Appendix ...................................................................................................................................34

Appendix A: Needs Analysis Survey ......................................................................................35

Appendix B: Learner Description Survey ...............................................................................41

Appendix C: Lesson Warm-Up Exercises ..............................................................................45

Appendix D: Motivational Script .............................................................................................46

Appendix E: Note-Taking Organizer ......................................................................................47

Appendix F: PowerPoint Packet ............................................................................................49

Appendix G: Guided Practice Worksheets .............................................................................72

Elimination Using Addition Practice ....................................................................................72

Elimination Using Subtraction Practice ...............................................................................74

Elimination Using Multiplication Practice ............................................................................76

Parallel and Coincident Lines with Elimination Practice ......................................................78

Appendix H: Transfer Learning Packet ..................................................................................80

Mobile Service Plans and Providers ...................................................................................80

Application Worksheet .......................................................................................................81

Appendix I: Assessment Quiz ................................................................................................83

Appendix J: Works Cited .......................................................................................................85



SYNTHESIS REFLECTION PAPER

“Something old, something new, something borrowed, something blue!” The

instructional design process is like planning a wedding. Wedding planning entails putting

together several items for several components of the overall wedding. This is much like the

process of instructional design, which has many components that all have to be outlined and

planned. The major events of a wedding include: the engagement, the rehearsal, and the

wedding ceremony. The events correlate with models in the instructional design process. A

wedding planner consults with the bride and critical family members. Important questions will

be asked to gather background information and determine the wants and needs of the bride. This

aligns with the analysis component of instructional design. Wedding planners conduct needs

assessments and plan accordingly. Once the planning is underway, the wedding planner must get

several items together: dresses, tuxedos, decorations, floral arrangements, ministers, the venue,

and much more. An instructional designer must also plan for several items: instructor guide,

learning materials, technology, and assessment tools. The next step is rehearsal. Everything has

been put together, but has to practiced and evaluated to see if any changes must be made before

the big day. In the instructional design process this can be compared to the expert review and

evaluations. The instruction will be rehearsed one-on-one, in a small group setting, with a field

group, and with an expert. The instruction will be modified accordingly. Lastly, the instruction

is implemented. The big day has arrived!

I am currently in the process of planning a wedding and could see the similarities in the

two processes. There are many things included in the processes that are overlooked. I

overlooked all the fine details of instructional design as a classroom teacher. Over the course of

this semester, I learned how detail-oriented the process of designing instruction really was. As a

teacher, new instruction and curriculum is placed in front of me frequently. However, I was

oblivious to the tedious tasks that must be performed in order to design effective instruction.

Examples of components of instructional design that I find challenging as a classroom teacher

include detailed needs assessments, accurate learner descriptions, personally designed learning

materials, expert review, evaluations, and field trials. When I begin each semester, I acquire

very little information about my learners, and information I obtain from them concerning their

needs or backgrounds are not completely accurate. I design quizzes, tests, projects, and other

activities when teaching my classes. However, I rely heavily on my textbook, supplemental

materials, and the fellow mathematics teachers for much of my instruction. Taking the time to

design all of the instruction for my classes would be impossible. As a teacher, I think it would

also be difficult to work with an expert on every single lesson and perform one-to-one, small

group, and field evaluations before teaching every lesson.

Although, I felt that much of the instructional design process would be difficult to

implement as a teacher, there were many components that I felt would help me become a more

effective teacher. As I designed the instruction in the final project, I felt that the instructor guide

was a very useful tool. Classroom teachers have to create lesson plans continually. The

components of the instructor guide as outlined by Smith and Ragan are critical for effective

instruction. Developing lesson plans that include the fifteen parts of instruction catered to the

different types of learning would be extremely beneficial for my learners. While designing the



final design project, I created instruction for a highly procedural lesson. I used an acronym as a

method of employing learning strategies. Prior to the course, I may not have given the lesson

that much thought. However, employing learning strategies during instruction will help me be a

better teacher and my students be more successful.

In the future, I will refer back to the knowledge and skills that I acquired as a result of

this course and apply them in my career as a classroom teacher. I will incorporate the suggested

components of an instructor guide in my lesson plans and future instruction. I will take the time

to plan for ways to employ learning strategies in my lesson, as I feel this is the area in which I

will reap the most benefit as a teacher. Overall, I feel that I learned a lot of valuable information

about instructional design from this course.

Reference

Smith, P.L., & Ragan, T.J. (2005). Instructional Design (3rd ed.). Hoboken, NJ: John Wiley &

Sons



PART 1 TOPIC

1A LEARNING GOAL

The students will find the correct solution to a minimum of 7 out of 10 problems

involving solving systems of equations using the elimination method.

1B AUDIENCE DESCRIPTION

The learners for this instructional design project are ninth graders at McCormick High

School located in McCormick, SC. McCormick High is a secondary school within the

McCormick County School District that instructs grades ninth through twelfth.

1C RATIONALE

The topic for this instructional design project was chosen because a need exists for a

more efficient way to teach Algebra topics to ninth graders. Presently, freshmen are enrolling in

Algebra courses in which they have not mastered the prerequisite skills for. Instruction is needed

that will counteract this dilemma and allow mastery of grade-level content.

The instruction will take on a supplantive approach. The supplantive strategies were

elected primarily because the learning goal falls in the field of mathematics, a scaffolding

subject. “A relatively supplantive, didactic, expository approach, rather than a highly generative,

discovery approach, seems to be best for teaching procedures” (Smith & Ragan, 2005). Also, the

learners possess less prior knowledge and a limited repertoire of learning strategies. According

to Smith and Ragan, it is expected that they will be more successful using the supplantive

approach (2005). The design of this instruction will involve much facilitation and prompting for

the learners.

Strategies for procedural learning will be employed. The learning goal involves a

complex procedure that is used under the broad concept of linear equations; therefore the major

instructional strategy is procedural. Solving a system of linear equations is an algorithm with

definite, ordered steps. Similar to most problems in mathematics, the learning goal includes a

series of steps that the problem-solver should take for increased success. The process requires

learners to use decision points while in route of finding the correct solution. Learners will have

to analyze the mathematical situation during many steps and then determine the appropriate next

step to take.



PART 2 ANALYSIS REPORT

2A DESCRIPTION OF THE NEED

Needs Analysis Survey

A needs analysis survey was developed for potential learners to take in order to assess

prior knowledge and prerequisite skills needed to achieve the learning goal. Certain skills are

needed to establish readiness to receive instruction. For this particular learning goal, those skills

are: graphing linear functions, solving multi-step equations, solving equations for a specific

variable, and evaluating expressions. The needs analysis survey consists of 20 questions

addressing the skills mentioned above. See Appendix A.

Needs Analysis Data Report

The results of the needs analysis survey were consistent. Most all survey takers had an

adequate knowledge of evaluating expressions for given variables. However, the learners

performed poorly in the areas of graphing linear functions, solving multi-step equations, and

solving equations for a specific variable. Approximately thirty-one percent of survey takers were

proficient in all prerequisite areas. The results of the needs analysis survey suggest that there is a

need for new instruction.

2B DESCRIPTION OF THE LEARNING CONTEXT

Learning Context

What are the characteristics of the classes and facilities that will use the new instruction?

The instruction for this design project will take place at McCormick High School. The

instruction will occur as a part of five Algebra 1 classes with approximately 12 to 21 students,

taught by a South Carolina certified math teacher. The proposed math teacher to deliver this

instruction has over thirty years teaching experience. This instruction will be merged into the

existing Algebra 1 curriculum, which is adopted from Anderson 5’s curriculum guide.

What hardware is commonly available in the potential learning environments?

Hardware that will be utilized during the delivery of instruction include a SMART

boardTM, LCD projector (Epson EX71 WXGA Multimedia), and a laptop (Dell Latitude E6410).

The following software applications will be used on the laptop: Microsoft Office PowerPoint,

Adobe Reader, Windows Media Player, and Quicktime Movie Player. Students will have access

to a class set of 22 graphing calculators (TI-83+).



What are the characteristics of the school system in which the new instruction will take place?

McCormick High School is a school with the McCormick County School District, whose

mission is to ensure that each student receives a quality education and becomes a productive

citizen by providing an educational environment that utilizes all available resources within our

diverse, rural community surrounded by national forests and lakes. McCormick High School’s

respective mission is teaching and learning through rigor, relevance, and relationships. The

overall goal and expected outcome of this new instruction is to increase the passing rate of the

Algebra 1 end-of-course test (EOC) and High School Assessment Program (HSAP) as well as

strengthen the math department. The new instruction relates to the organizations’ missions in that

it directly corresponds to math instruction and sets to increase learning, which will ultimately

raise standards tests scores. Primary decision makers within the organization include the district

Superintendent, McCormick High School Principal and Assistant Principal, district Director of

Instruction for grades 6th

through 12th

, district Special Needs Coordinator, and the Executive

Director of Finance.

Transfer Context

The learning goal of solving systems of linear equations has many applications or real-

world uses. A specific application that will be relevant for the learners is calculating the best

cell-phone plan or coverage provider. Oftentimes, mobile plans will have a base rate for a

definite amount of minutes and then a rate for every minute beyond your plan’s limit. Equations

can be written to algebraically express the terms of these plans. When these systems of

equations are solved, the solution gives us the point where the price of the plans is the same.

From the solution, one can infer which plan is the better deal or which one gives you the most

minutes for your money. As the learners are statistically great communicators and mobile phone

users, having this skill can potentially save them a lot of money in the future.

FIGURE 1: ILLUSTRATION OF TRANSFER CONTEXT - COMPARING MOBILE PHONE COMPANY

PRICES USING SYSTEMS OF LINEAR EQUATIONS HTTP://2SHORT.NET/RN

http://2short.net/rN



Prices of all types of companies can be compared through solving systems of linear

equations. Learners can transfer context through determining which car rental company to use in

an emergency. Much like the cell phone coverage example, learners can write equations to

express the company’s rates and then find the solution. Other applications include: profit,

motion, and work problems.

Description of the Learners

The learners will be incoming freshmen, ranging from 13 to 15 years of age.

Approximately 88% of the learners are Black, non-Hispanic which is forty-nine percent higher

than the state average. The remaining 12% are White, non-Hispanic which is forty-one percent

below the state average. Sixty-seven percent of the learners are eligible for free or reduced

lunch. This information was provided by the school district.

Learners were given a survey that addressed more socio-economic demographics, such as

household size and highest educational level attained by parents or guardians. The survey was

also used to determine their attitudes towards mathematics and their recent experiences in

mathematic courses. Questions were asked about instructional preferences and how the learners

felt they learned mathematical content best. Statistically, many students do not see the relevance

of Algebra and have encountered negative experience with mathematics. This can be a pre-

cursor for math anxiety, which is “an emotional reaction to mathematics based on a past

unpleasant experience which harms future learning” (Professor Freeman – Western Wyoming

Community College). Studies show that one-half of all students in a developmental mathematics

class suffer forms of this type of anxiety. Two eighth-grade math classes completed the survey

using Google Forms: http://2short.net/rP. See Appendix B.

The results of the survey are as followed. Approximately thirteen percent of the survey

takers had parents that achieved a college degree or higher. The average household size was four

people. According to Professor Freeman’s guide to the math anxiety survey, approximately 47%

of the students surveyed have math anxiety.

88%

12%

Student Ethnicity

Black, non-

Hispanic

White, non-

Hispanic

67%51%

Free or Reduced

Lunch Eligibility

This School

State Average

http://2short.net/rP



Along with the survey discussed above, a sample of the learners was asked to complete a

survey originally designed by Dr. Carolyn Hopper to assess math study skills. The location of

the survey is: http://2short.net/rO.

http://2short.net/rO



PART 3 PLANNING

3A LEARNING OBJECTIVES

1.0 Learners will be able to accurately perform properties used in the elimination method of

solving systems of equations.

1.1 Learners will be able to accurately employ the addition property of equality.

1.2 Learners will be able to accurately employ the multiplication property of equality.

2.0 Learners will be able to accurately use the elimination method to solve systems of equations.

2.1 Learners will be able to add equations correctly.

2.2 Learners will be able to write equations in standard form.

2.3 Learners will be able to multiply equations to get desired coefficients.

2.4 Learners will be able to solve linear equations.

2.5 Learners will be able to evaluate algebraic expressions for a specific value.

2.6 Learners will be able to confirm accuracy of solutions.

2.7 Learners will be able to write solutions as an ordered pair.

3.0 Learners will be able to predict the outcome of the using the elimination method when

solving a system of equations that consist or parallel and coincident lines.

3.1 Learners will be able to compare and contrast parallel and coincident lines.

3.2 Learners will be able to identify conditions within a system of equations that result in

parallel lines.

3.3 Learners will be able to identify conditions within a system of equations that result in

coincident lines.



3B OBJECTIVES MATRIX TABLE

Objective Number

Bloom’s Taxonomy Classification

Strategy to be employed to teach the objective

Type of Learning

1.0 Application Supplantive Conceptual



2.0 Application Supplantive Procedural





2.5 Evaluation Supplantive Procedural

2.6 Evaluation Supplantive Problem-Solving

2.7 Comprehension Supplantive Declarative Knowledge

3.0 Evaluation Generative Problem-Solving

3.1 Analysis Generative Conceptual

3.2 Comprehension Generative Principal

3.3 Comprehension Generative Principal



3C ARCS TABLE

Project Goal Statement: The students will find the correct solution to a minimum of 7 out of 10

problems involving solving systems of equations using the elimination method.

ATTENTION

A.1 Perceptual Arousal

The teacher will attempt to make a call from his/her mobile phone, but will learn from the

operator that his/her phone has been disconnected.

The teacher will explain to the learners that (s)he had been warned by his/her parents not to go

over their service limits or the service would terminated, and the teacher would have to get

his/her own service.

The teacher states how choosing the correct cell phone service provider is a dilemma because

there are so many plans and options to choose from and (s)he doesn’t know how to choose the

best plan for his/her communication habits.

The teacher then tells the learners that after this lesson, they will know how to compare mobile

service plans and ultimately determine the best provider and/or plan for themselves.

A.2 Inquiry Arousal

The teacher will ask learners how they suppose cell phone plans can be compared using math and

content that they previously learned in the unit.

A.3 Variability The teacher will repeatedly explain how (s)he desperately needs the learners’ help in making the

right decision for a cell phone plan.

The teacher will keep students engaged by randomly checking for understanding, random

questioning.

RELEVANCE

R.1 Goal Orientation

The teacher will review prerequisite skills and activate prior knowledge.

The teacher will enhance instruction with activities that align with all learning styles.

R.2 Motive Matching

The teacher will allow students to choose applied problems to solve using systems of equations.

The teacher will allow students to choose which variable to eliminate first.

R.3 Familiarity

The teacher will relate the instruction to the relevant experience of purchasing a mobile service

plan.

The teacher will also relate the instruction to the relevant experience of purchasing a rental car.

CONFIDENCE

C.1Learning Requirements

Objectives and tasks will be chunked into meaningful bits to increase memorization of the new

content.

The teacher will reassure the students that the teacher will be guiding them throughout every step

in the process.



Students will be given significant practice to ensure success.

C.2 Success Opportunities Teacher feedback and suggestions will offered to students during all parts of instruction.

The teacher will allow fast learners to help slower learners.

The teacher will explain how through peer and teacher support, students will be successful.

C.3 Personal Control

Students will be informed of the overall learning goal and how they will be assessed.

Teachers will encourage students to be attentive and participate completely in order to guarantee

success.

SATISFACTION

S.1 Natural Consequences

Teachers will remind students of the passing threshold for achieving the learning goal.

Teachers will remind students that students that do not achieve the learning goal will receive

remedial instruction while successful students progress.

S.2 Positive Consequences After instruction, students will be able to choose the most economical mobile service plan.

Upon successful completion of the learning goal, students will progress to the next unit.

S.3 Equity Teachers will stress one hundred percent student success as a lesson goal.

High expectations and standards will be held for all students.

Instruction will be given in chunks to ensure success at every benchmark in the instruction.

Keller, J. M. (1987). The systematic process of motivational design. Performance & Instruction, 26 (9/10), 1-8.



PART 4 INSTRUCTOR GUIDE

INTRODUCTION

ACTIVATE ATTENTION

1. Gain the learners’ attention, by first going over the answers to the warm-up. The warm-

up will address skills students must possess prior to instruction. A screenshot of the

warm-up can be found in Appendix C.

2. Announce the title of the lesson and the objectives.

ESTABLISH PURPOSE

1. Announce to the class how they have previously learned that solving equations can help

solve problems in the real world.

2. Further explain how solving more than one equation simultaneously (systems) allows us

to solve even more real world problems.

3. State upon the completion of the lesson, the students will be able to solve a real dilemma

for teenagers by solving systems of equations.

AROUSE INTEREST AND MOTIVATION

Break from the instruction with a dramatic pause and proceed with the motivational script

included in Appendix D.

PREVIEW LEARNING ACTIVITY

As this instruction is highly supplantive, the lesson overview will briefly outline the events in the

instruction. For example, an instructor might say the following:

In this lesson, we will solve systems of equations using the

elimination method, which involves addition, subtraction, and

multiplication. Finally, you will be able to predict the outcome when

solving a systems of equations that consist of parallel and coincident

lines. You will practice every step in the process. At the conclusion

of the lesson, you will compare actual mobile service plans using the

elimination method to solve systems of equations. In a few days you

will have a quiz on this lesson and on the chapter test, you’ll be

tested on your ability to accurately solve systems of equations and

apply your knowledge in real-world situations.



BODY

ACTIVATE PRIOR KNOWLEDGE

Explain to the learners that the elimination method is very similar to the substitution

method that they previously learned in that they have the same goal of getting one

equation that has only one variable. However, in the elimination method the goal will be

achieved by using the skills of adding and subtracting equations.

PRESENT INFORMATION AND EXAMPLES

The content will be presented in an expository sequence, in four components. You will facilitate

a Microsoft PowerPoint presentation using a Smart Board that breaks down instruction into four

segments. See Appendix F. Those segments are: addition, subtraction, multiplication, and

predicting outcomes. Each segment will include a detailed example for you to walk learners

through, followed by an example in which you will merely guide learners through. Segments

will conclude with two examples to be done solely by the learners for the purpose of checking

for understanding. You may choose to begin the first three segments with included video

examples. Between the segments, learners will practice the skills as explained in Guided

Practice.

FOCUS ATTENTION

Learners’ attention will remain focused by constant questioning and note-taking on a provided

graphic organizer. See Appendix E. During the guided examples, ask learners to tell and explain

every step in solving the system. This can be done quickly and efficiently through the use of

index cards or popsicle sticks with students names on them.

1. Get a stack of index cards or popsicle sticks.

2. Write the learners names on the cards or sticks. (One name per card)

It may be necessary to put some students in the stack more than once. This would be a

good idea for learners with shorter attention spans.

3. Simply pull a card or stick and address questions to learners whose name is drawn. The

randomness keeps learners alert. Also, learners will remain focused in order to

successfully complete the graphic organizer. Completion of the graphic organizer could

count for a portion of the daily participation grade.

EMPLOY LEARNING STRATEGIES

As the learning goal is procedural, learners will benefit from a mnemonic device to aid them in

memorizing the main steps in the procedure. There are four main steps to solving a system of

equations using elimination. The acronym LESS will be used as a mnemonic device to help

learners recall the critical steps. Provide learners with a connection between the word “Less”

and the elimination process. “We can remember LESS with the elimination method, because

sometimes it can be less work for us!”



L Like terms aligned (write the system so that like terms are aligned)

E Eliminate one of the variables

S Solve the resulting equation for the remaining variable

S Substitute the value of the variable into one of the original equations and

solve for the other variable.

Give learners the note-taking graphic organizer. See Appendix E. The graphic organizer

will first, stress the mnemonic device mentioned above; then, separate information

concerning eliminating variables using three methods: addition, subtraction, and

multiplication. The worksheet will also include a table to compare and contrast properties

of parallel and coincident lines as related to solving a system of equations.

GUIDED PRACTICE

Practice will occur throughout the instruction at the end of the four major segments. Learners

will have the opportunity to practice the elimination method using addition, subtraction, and

multiplication. Learners will also practice predicting the outcomes of the elimination method:

parallel and coincident lines.

1. At the conclusion of each segment, give learners the respective practice sheets.

See Appendix G for the four practice sheets and answer keys.

2. Allow students to work in appropriate pairs.

3. It is suggested that learners complete at least five practice problems for each segment.

Assign the first five problems and allow early finishers to complete the remaining

problems, while other learners finish.

4. Refer students to their notes during practice and continue to emphasize LESS.

FEEDBACK

1. Provide motivational and informational feedback. Give positive reinforcement and

constructive information.

2. Provide feedback on every step of the LESS procedure. During practice, give learners

information so they can determine if they are right or wrong and why they are right or

wrong before giving them the correct answer.

3. Give learners information on their progress. Explain patterns of errors to learners and

inform them of how close they are to mastering the entire procedure.



CONCLUSION

SUMMARIZE AND REVIEW

1. Review the LESS procedure and briefly summarize the variations in the procedure when

learners have to add, subtract, and multiply.

2. Conclude instruction by presenting the sequence of steps a final time for a simple case

and then build up to a complex case.

3. Stress again common problem areas for learners to be cautious of like distributing the

negative during subtraction.

TRANSFER LEARNING

Allow learners to apply their new knowledge and skills to a real-life situation through comparing

mobile service plans.

1. Provide learners with a listing of current rates for mobile service plans. See Appendix H.

2. Have learners construct systems of equations that align with the given information.

3. Then, have learners solve the systems using the elimination method.

4. Have learners determine the best mobile service plan for you and for themselves.

Learning can also be transferred through similar examples comparing car rental rates and the

optional use of the application instructional video that is included.

CLOSURE

Announce the conclusion of the lesson and thank the learners for their active participation and

attentiveness. Also, thank the learners for helping you choose the most cost efficient mobile

service plan that matches your communication needs. Express to the learners how confident you

are in them that they are now able to be savvy shoppers using Algebra.

ASSESSMENT

Learning will be assessed to determine whether learners have achieved the goal of the

instruction. Learners will be assessed on their ability to apply the procedure when solving a

system of equations. Students will complete a quiz on solving systems of equations using the

elimination method. See Appendix I for assessment quiz and KEY.

FEEDBACK

1. Grade the assessment quiz according to the key and rubric.

2. Return graded quizzes to learners and provide feedback on the percentage correct and

number of objectives successfully mastered.

3. Determine weaknesses and provide remedial instruction in those areas where needed.



PART 5 LEARNER CONTENT

5A LEARNING MATERIALS

The following learning materials will be used for instructional purposes:

Learning Material Purpose

Instructor Guide The Instructor Guide is a set of instructions for

the instructor to follow when delivering the

instruction.

Warm-Up Exercises These exercises are meant to review prerequisite

skills for the instruction and activate prior

knowledge.

Motivational Script The purpose of this script is to provide the

instructor with a guide for arousing interest in the

lesson and motivating learners.

Note-Taking Graphic Organizer The purpose of this graphic organizer is to aid

learners in processing the new information.

Content of this document is meant to help

learners employ effective learning strategies.

Instructional Video 1



The purpose of these videos are to be extra

supplemental material that instructor may choose

to use during the instruction. A password and

user name will be provided to instructors in order

to access the videos.

Note: For the sake of this project, the username is

“idoes1” and the password is “x8e4k”

PowerPoint Packet

PowerPoint Notes

This is the main component of the instruction.

The instructor will facilitate the instruction by

allowing the PowerPoint to be the guide. The

contents of the PowerPoint is direct, supplantive

instruction.

Elimination (Addition) Worksheet and KEY The purpose is to provide learners the opportunity

to practice the skill of using elimination with

addition.

Elimination (Subtraction) Worksheet and

KEY

The purpose is to provide learners the opportunity


subtraction.

Elimination (Multiplication) Worksheet and

KEY



multiplication.

Parallel and Coincident Lines Worksheet

and Key


to practice the skill of predicting parallel and

coincident lines using elimination.

http://my.hrw.com/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=6353/6353.xml



http://db.tt/aExjfL



Transfer Learning Packet The purpose is to allow learners to apply their

new knowledge and skills to a real-life situation

through comparing mobile service plans.

5B FORMATIVE/SUMMATIVE ASSESSMENT MATERIALS

The following materials will be use for assessment purposes:

Assessment Material Purpose

Assessment Quiz and KEY This quiz will serve as a summative assessment

to measure the learning and mastery of the

learning goal. A key is included for instructors

to use to grade the quiz and determine areas of

weakness.

5C TECHNOLOGY TOOL JUSTIFICATION

Technology Tool Purpose

Microsoft PowerPoint This the main component of the instruction is a

PowerPoint Presentation. Microsoft

PowerPoint software is needed to deliver the

instruction. The instructor will facilitate the

instruction by allowing the PowerPoint to be

the guide. The contents of the PowerPoint is

direct, supplantive instruction.

Interactive White Board & LCD

Projector

The interactive white board and projector will

enable the instructor to easily present the

instruction to the learners. This technology will

allow the instructor to quickly progress and

return to components of the instruction as

necessary for learners. This technology also

allows instructors to easily annotate the

instruction while in progress.




The purpose of these videos are to be extra

supplemental material that instructor may

choose to use during the instruction. A

username and password will be provided to

instructors in order to access the videos.

Note: For the sake of this project, the username

is “idoes1” and the password is “x8e4k”

TI-83+ Graphing Calculators The calculators will aid learners in making

computations in route of finding the solutions to

systems of equations.






PART 6 FORMATIVE EVALUATION PLAN

6A EXPERT REVIEW

The Subject Matter Expert that evaluated the instructional design was Kelly Coxe, McCormick

County School District Director of Instruction for grades 6th

through 12th

, district technology

coordinator, and former mathematics teacher. Mrs. Coxe proved be perfect for this position, as

she has experience teaching mathematics and overseeing new instruction and technology that is

brought to the district. The evaluation survey, created in Google Documents, and the

instructional materials were made available to Mrs. Coxe in June 2010. Mrs. Coxe completed

the survey and provided feedback in July 2010.

Link to the survey: http://bit.ly/bUykwB

6B ONE-TO-ONE EVALUATION

A small group of three eighth grade students will complete the instructional packet under

conditions similar to the finalized instruction to be implemented. An instructor will facilitate

while the learners progress through the instruction entirely. The students would be asked to

provide comments and suggestions on the delivery of instruction, worksheets, length of time to

complete instruction, and assessment of learning. Learners would individually be asked if there

were any unclear or confusing parts in the instruction. Did the design of the instruction keep

your focus and attention? Were you motivated to achieve the learning goal? Did you see the

importance of learning how to solve systems of equations using elimination? Would you be able

to apply the learning goal to other real-world situations on your own? Did the assessment quiz

align with the instruction? Were you prepared for the assessment quiz upon the completion on

the instruction? Is there anything you would change or add to the learning materials? All

responses would be recorded on the draft materials. Results would be analyzed and learning

materials would be modified appropriately.

6C SMALL GROUP EVALUATION

A small group of 15 students will proceed through portions of the instruction and provide

feedback. The group of students will be comprised of learners that took Algebra 1 the past

school year. There were five Algebra 1 classes during the last school year. The previous teachers

submitted the names of the learners with the highest average, a median average, and the lowest

average from each class last year. The instruction consists of five major components. Those

components are the four instructional segments that break down the procedure of solving

systems of equations and the transfer learning section. Each component of the instruction that

was revised according to the one-to-one evaluation was evaluated by three students: highest,

average, and lowest average learners from a class last year. The instructor would follow the

procedure outlined in the Instructor Guide and use the learning materials to provide instruction to

the sample of learners on solving systems of equations using elimination. The instructional

designer would observe the instruction and record notes on teacher/student interaction, use of

http://bit.ly/bUykwB



time, student motivation, and mastery of the learning goal from practice worksheets. Finally, the

instructor and learners would be asked how they feel about the delivery of the instruction and for

suggestion on improving the instruction. Delivery of instruction and learning materials would be

modified according to the results of the material evaluations.

6D FIELD TRIAL

Two Algebra 1 classes will field the instruction. During this field trial approximately twenty-

four to fifty-six students will receive the revised instruction. The instructor will follow the

modified Instructor Guide and guide learners through the instruction entirely. The instructional

designer will observe the instruction and record notes. Evaluation data will be analyzed along

with results of the assessment quizzes. The instructor and a sample of the students that

participated in the field trial will be interviewed. Questions will be similar to questions from the

one-to-one and group evaluation.



PART 7 FORMATIVE EVALUATION REPORT

7A EVALUATION SURVEY

Solving Systems of Equations using Elimination - Expert Review

The purpose of this survey is to provide valuable feedback on the developing instructional design

project concerning solving systems of equations using elimination.

Learning Goal:

The students will find the correct solution to a minimum of 7 out of 10 problems involving

solving systems of equations using the elimination method.

Please evaluate the following instructional materials prepared by Vertoria Lagroon.

http://db.tt/03HnKn

List of materials:

Instructor Guide - set of instructions to be used by the instructor

Warm-up Exercises - These exercises are meant to review prerequisite skills for the instruction

and activate prior knowledge.

Motivational Script - The purpose of this script is to provide the instructor with a guide for

arousing interest in the lesson and motivating learners.

Note-Taking Graphic Organizer - The purpose of this graphic organizer is to aid learners in

processing the new information. Content of this document is meant to help learners employ

effective learning strategies.

Instructional Videos - The purpose of these videos are to be extra supplemental material that

instructor may choose to use during the instruction. A password and user name will be provided

to instructors in order to access the videos. Note: For the sake of this project, the user name is

"idoes1" and the password is "x8e4k"

PowerPoint Packet & Notes - This is the main component of the instruction. The instructor will

facilitate the instruction by allowing the PowerPoint to be the guide. The contents of the

PowerPoint is direct, supplantive instruction.

Practice Worksheets & KEYs - The purpose is to provide learners the opportunity to practice

the skills needed solve systems of equations using elimination.

Transfer Learning Packet - The purpose is to allow learners to apply their new knowledge and

skills to a real-life situation through comparing mobile service plans.

http://db.tt/03HnKn



Assessment Quiz and KEY - This quiz will serve as a summative assessment to measure the

learning and mastery of the learning goal. A key is included for instructors to use to grade the

quiz and determine areas of weakness.

Thank you for evaluating the materials and providing feedback!

*This survey was created using the template from Cindy Magalio. The survey questions are the

questions Cindy Magalio used in an expert review for an instructional design project.

http://bit.ly/8XRhI5*

The link to the survey is: http://bit.ly/bUykwB

Survey Questions

1. Are the materials and instructions appropriate for the target learners? *

Yes, right on target

Mostly appropriate

No, not at all

Other:

2. Are the materials accurate? *


Mostly accurate

No, not at all

Other:

3. Are the vocabulary and terms appropriate for the students? *


Mostly appropriate

No, not at all

Other:

4. Will the student materials support learner success in completing the learning goal? *

http://bit.ly/8XRhI5*

http://bit.ly/bUykwB



Yes, they will support success

Somewhat

No, not at all

Other:

5. Is the Instructor Guide easy to follow? *

Yes, very helpful

Somewhat

No, not at all

Other:

6. Are the activities in a logical order? *

Yes, well structured

Somewhat

No, not at all

Other:

7. Will the Instructor Guide assist the teacher in leading the students to successful achievement

of the learning goal? *

Yes, very helpful

Somewhat

No, not at all

Other:



8. Which materials are the most valuable for completing the project? Please list. *

9. Is the assessment quiz a good measure of student success? *

Yes

Somewhat

No

Other:

10. Please describe any other issues, comments or suggestions in detail about the materials used?

*



7B EXPERT REVIEW REPORT

The overall results of the survey were positive. The Subject Matter Expert (SME) responded

favorably to all questions. The SME felt that the learning materials and instructions were

appropriate and accurate. The SME responded that the learning materials were arranged in a

logical sequence and would support learner success. The SME also responded highly of the

instructor guide: answering that it was easy to follow and would lead students to achievement of

the learning goal. The SME responded that the most valuable learning materials were the

PowerPoint Notes and Packet and the motivational script. She described how the PowerPoint

Notes were easy to follow from an instructor and student viewpoint. She detailed how the notes

broke the content down into meaningful chunks. The SME responded that the PowerPoint notes

could possibly be used in alternative settings where the facilitator may not be a certified

mathematics teacher. She stated that the motivational script would gain student interest and focus

their attention. The SME responded that instructions concerning the amount of time various

activities should take should be included in the instructor guide, as well as the overall amount

time needed to complete the entire instruction. The SME raised concerns about the amount of

content covered in the instructional design versus the amount of class time, which is fifty

minutes.

7C COMMENTS ON CHANGE

After meeting with the Subject Matter Expert (SME) and analyzing the expert review survey

results, the following changes will be made to improve the instruction. The SME felt that time

guides should be included in the instructor guide to inform the instructor on the amount of time

each activity should take to complete. I will also add a statement that informs the instructor that

the instruction should take 2 class periods to complete, as the district runs on the traditional fifty

minute class schedules. The SME suggested that notes on accommodations be included to aid

instructors in accommodating learners with special needs. The SME suggested explicitly stating

in the instructor guide that assigning less problems for learners with special needs would help

with the time component. Those changes will be made. The SME also felt that the assessment

quiz was a good tool for measuring student success of the learning goal. However, she felt that a

rubric would be better than a key for grading the quiz. The SME determined that learners should

be assessed on every step of the procedure and not just the end result. A rubric will be developed

and added to the instructional design packet so that every step of the procedure can be assessed.

All changes will be made at a later time.



PART 8 AECT STANDARDS GRID

Professional Standards Addressed (AECT)

The following standards, developed by the Association for Educational Communications and Technology

(AECT), and used in the accreditation process established by the National Council for Accreditation of

Teacher Education (NCATE), are addressed to some degree in this course. The numbers of the

standards correspond to the numbers next to the course tasks show on the list of assignments. Not all

standards are addressed explicitly through student work.

Assignments meeting standard in whole or part

Standard 1: DESIGN

1.1 Instructional Systems Design (ISD) X ID Projects 1 & 2

1.1.1 Analyzing X ID Projects 1

1.1.2 Designing X ID Projects 1 & 2

1.1.3 Developing X ID Projects 1 & 2

1.1.4 Implementing X ID Project 2

1.1.5 Evaluating X Selected Discussion Forums; ID Project 2

1.2 Message Design

1.3 Instructional Strategies X ID Project 2

1.4 Learner Characteristics X ID Project 1

Standard 2: DEVELOPMENT

2.0 (includes 2.0.1 to 2.0.8) X ID Project 02

2.1 Print Technologies X Reading Quiz; ID Projects 1 & 2

2.2 Audiovisual Technologies

2.3 Computer-Based Technologies X (all assignments)

2.4 Integrated Technologies

Standard 3: UTILIZATION

3.0 (includes 3.0.1 & 3.0.2)

3.1 Media Utilization X (all assignments)

3.2 Diffusion of Innovations

3.3 Implementation and Institutionalization X

ID Project 2

3.4 Policies and Regulations

Standard 4: MANAGEMENT

4.0 (includes 4.0.1 & 4.0.3)

4.1 Project Management

4.2 Resource Management

4.3 Delivery System Management

4.4 Information Management

Standard 5: EVALUATION

5.1 Problem Analysis X

5.2 Criterion-Referenced Measurement X ID Project 2

5.3 Formative and Summative Evaluation X ID Project 2

5.4 Long-Range Planning



COURSE GOALS & OBJECTIVES The overall goal for the course is for each student to consider and use the systematic process of instructional design to create an instructional product. To

achieve this goal, students will engage in activities that promote reflective practice, emphasize realistic contexts, and employ a number of communications

technologies. Following the course, students will be able to:

1. Discuss the historical development of the practice of instructional design with

regard to factors that led to its development and the rationale for its use

2. Describe at least two reasons why instructional design models are useful

3. Identify at least six instructional design models and classify them according

to their use

4. Compare and contrast the major elements of three theories of learning as they relate to instructional design

5. Define “instructional design.”

6. Define the word “systematic” as it relates to instructional design

7. Define “learning” and synthesize its definition with the practice of

instructional design

8. Relate the design of instruction to the term “educational (or “instructional”)

technology”

9. Describe the major components of the instructional design process and the

functions of models in the design process

10. Provide a succinct summary of various learning contexts (declarative knowledge, conceptual, declarative, principle, problem-solving, cognitive, attitudinal, and psychomotor)

11. Build an instructional design product that integrates major aspects of the

systematic process and make this available on the web.

a. Describe the rationale for and processes associated with needs,

learner, context, goal, and task analyses

i. Create and conduct various aspects of a front-end analysis

ii. Identify methods and materials for communicating subject

matter that are contextually relevant



b. Describe the rationale for and processes associated with creating

design documents (objectives, motivation, etc.)

i. Construct clear instructional goals and objectives

ii. Develop a motivational design for a specific instructional task

iii. Develop assessments that accurately measure performance

objectives c. Select and implement instructional strategies for selected learning

tasks

i. Select appropriate media tools that support instructional design decisions

d. Describe the rationale and processes associated with the formative evaluation of instructional products

i. Create a plan for formative evaluation

12. Identify and use technology resources to enable and empower learners with

diverse backgrounds, characteristics, and abilities.

13. Apply state and national content standards to the development of

instructional products

14. Meet selected professional standards developed by the Association for

Educational Communications and Technology

15. Use various technological tools for instructional and professional communication



AECT STANDARDS (Applicable to EDTECH 503) 1.0 Design

1.1 Instructional Systems Design

1.1.a Utilize and implement design principles which specify optimal conditions for learning.

1.1.b Identify a variety of instructional systems design models and apply at least one model.

1.1.1 Analyzing

1.1.1.a Write appropriate objectives for specific content and outcome levels.

1.1.1.b Analyze instructional tasks, content, and context.

1.1.2 Designing

1.1.2.a Create a plan for a topic of a content area (e.g., a thematic unit, a text chapter, an interdisciplinary unit) to demonstrate application of the principles of macro-level design.

1.1.2.b Create instructional plans (micro-level design) that address the needs of all learners, including appropriate accommodations for learners with special needs.

1.1.2.d Incorporate contemporary instructional technology processes in the development of interactive lessons that promote student learning.

1.1.3 Developing

1.1.3.a Produce instructional materials which require the use of multiple media (e.g., computers, video, projection).

1.1.3.b Demonstrate personal skill development with at least one: computer authoring application, video tool, or electronic communication application.

1.1.4 Implementing

1.1.4.a Use instructional plans and materials which they have produced in contextualized instructional settings (e.g., practica, field experiences, training) that address the needs of all learners, including appropriate accommodations for learners with special needs.

1.1.5 Evaluating

1.1.5.a Utilize a variety of assessment measures to determine the adequacy of learning and instruction.

1.1.5.b Demonstrate the use of formative and summative evaluation within practice and contextualized field experiences.

1.1.5.c Demonstrate congruency among goals/objectives, instructional strategies, and assessment measures.

1.3 Instructional Strategies

1.3.a Select instructional strategies appropriate for a variety of learner characteristics and learning situations.

1.3.b Identify at least one instructional model and demonstrate appropriate contextualized application within practice and field experiences.

1.3.c Analyze their selection of instructional strategies and/or models as influenced by the learning situation, nature of the specific content, and type of learner objective.

1.3.d Select motivational strategies appropriate for the target learners, task, and learning situation.

1.4 Learner Characteristics



1.4.a Identify a broad range of observed and hypothetical learner characteristics for their particular area(s) of preparation.

1.4.b Describe and/or document specific learner characteristics which influence the selection of instructional strategies.

1.4.c Describe and/or document specific learner characteristics which influence the implementation of instructional strategies.

2.0 Development

2.0.1 Select appropriate media to produce effective learning environments using technology resources.

2.0.2 Use appropriate analog and digital productivity tools to develop instructional and professional products.

2.0.3 Apply instructional design principles to select appropriate technological tools for the development of instructional and professional products.

2.0.4 Apply appropriate learning and psychological theories to the selection of appropriate technological tools and to the development of instructional and professional products.

2.0.5 Apply appropriate evaluation strategies and techniques for assessing effectiveness of instructional and professional products.

2.0.6 Use the results of evaluation methods and techniques to revise and update instructional and professional products.

2.0.7 Contribute to a professional portfolio by developing and selecting a variety of productions for inclusion in the portfolio.

2.1 Print Technologies

2.1.3 Use presentation application software to produce presentations and supplementary materials for instructional and professional purposes.

2.1.4 Produce instructional and professional products using various aspects of integrated application programs.

2.3 Computer-Based Technologies

2.3.2 Design, produce, and use digital information with computer-based technologies.

3.0 Utilization

3.1 Media Utilization

3.1.1 Identify key factors in selecting and using technologies appropriate for learning situations specified in the instructional design process.

3.1.2 Use educational communications and instructional technology (SMETS) resources in a variety of learning contexts.

3.3 Implementation and Institutionalization

3.3.1 Use appropriate instructional materials and strategies in various learning contexts.

3.3.2 Identify and apply techniques for integrating SMETS innovations in various learning contexts.

3.3.3 Identify strategies to maintain use after initial adoption.



4.0 Management

(none specifically addressed in 503)

5.0 Evaluation

5.1 Problem Analysis

5.1.1 Identify and apply problem analysis skills in appropriate school media and educational technology (SMET) contexts (e.g., conduct needs assessments, identify and define problems, identify constraints, identify resources, define learner characteristics, define goals and objectives in instructional systems design, media development and utilization, program management, and evaluation).

5.2 Criterion-referenced Measurement

5.2.1 Develop and apply criterion-referenced measures in a variety of SMET contexts.

5.3 Formative and Summative Evaluation

5.3.1 Develop and apply formative and summative evaluation strategies in a variety of SMET contexts.

SMET = School Media & Educational Technologies



APPENDIX



APPENDIX A: NEEDS ANALYSIS SURVEY

The following assessment consists of 20 questions. Please take your time and carefully answer

all questions to the best of your ability. Your responses on this assessment will be very

beneficial to your math teachers and school. This assessment is designed to last no longer than

one hour and thirty minutes. Thank you for your cooperation.

Match each term on the left with a definition on the right.

12Solve each equation.

5.

6.

7.

8.

Solve each equation for y.

9.

10.

1. linear equation

2. slope

3. ordered pair

4. solution of an equation

A. A pair of numbers (x, y) that represent the coordinates of a point.

B. The y-value of the point at which the graph of an equation crosses the y-axis.

C. The value of the variable that makes an equation true.

D. The ratio of the vertical change to the horizontal change for a nonvertical line.

E. An equation whose graph is a straight line .



11.

12.

Evaluate each expression for the given value of the variable.

13. for

14. for

15. for

16.

for

Graph each function.

17.

18.



19.

20.



Needs Analysis Survey – Key

Match each term on the left with a definition on the right.

12Solve each equation.

5.

6.

7.

8.

Solve each equation for y.

9.

10.

11.

1. linear equation E

2. slope D

3. ordered pair A

4. solution of an equation C

A. A pair of numbers (x, y) that represent the coordinates of a point.

B. The y-value of the point at which the graph of an equation crosses the y-axis.

C. The value of the variable that makes an equation true.

D. The ratio of the vertical change to the horizontal change for a nonvertical line.

E. An equation whose graph is a straight line .



12.

Evaluate each expression for the given value of the variable.

13. for 2

14. for 0

15. for -4

16.

for 2

Graph each function.

17.

18.



19.

20.



APPENDIX B: LEARNER DESCRIPTION SURVEY

Please complete this survey to the best of your ability as accurately as possible. The information obtained will be used

solely with the intent of providing you with improved instruction. There are no right or wrong answers. All information

provided will be kept confidential.

* Required

1. How many people live in your household? * (How many people live with you?)

2. What is the highest level of education your parents or guardians have received? * Check the one that best applies.

some high school

high school diploma or G.E.D.

some college

college degree

graduate degree

doctorate degree

3. I cringe when I have to go to math class. * Rate whether you agree or disagree.

1 2 3 4 5

Disagree

Agree

4. I am uneasy about going to the board in math class. * Rate whether you agree or disagree.

1 2 3 4 5

Disagree

Agree

5. I am afraid to ask questions in math class. * Rate whether you agree or disagree.

1 2 3 4 5

Disagree

Agree



6. I am always worried about being called on in math class. * Rate whether you agree or disagree.

1 2 3 4 5

Disagree

Agree

7. I understand math now, but I worry that it's going to get really difficult soon. * Rate whether you agree or disagree.

1 2 3 4 5

Disagree

Agree

8. I tend to zone out in math class. * Rate whether you agree or disagree.

1 2 3 4 5

Disagree

Agree

9. I fear math tests more than any other kind. * Rate whether you agree or disagree.

1 2 3 4 5

Disagree

Agree

10. I don't know how to study for math tests. * Rate whether you agree or disagree.

1 2 3 4 5

Disagree

Agree

11. It's clear to me in math class, but when I go home it's like I was never there. * Rate whether you agree or disagree.

1 2 3 4 5

Disagree

Agree

12. I'm afraid I won't be able to keep up with the rest of the class. * Rate whether you agree or disagree.

1 2 3 4 5

Disagree

Agree



13. If I have to learn how to do something, I learn best when I watch someone show me how. * Choose the best answer.

Most of the time

Sometimes

Rarely

14. I would rather tell how something works than write how it works. * Choose the best answer.

Most of the time

Sometimes

Rarely

15. If I had to remember a list of items, I would remember it best if I said them over and over to myself. * Choose the best

answer.

Most of the time

Sometimes

Rarely

16. When trying to concentrate, I have a difficult time when there is a lot of clutter in the room. * Choose the best answer.

Most of the time

Sometimes

Rarely

17. When learning, I prefer information to be written on the board along with visual aids and assigned readings. * Choose

the best answer.

Most of the time

Sometimes

Rarely



18. I prefer teachers who assign hands-on activities. * Choose the best answer.

Most of the time

Sometimes

Rarely

19. I can remember more about a subject through the lecture method with information, explanations, and discussion. *

Choose the best answer.

Most of the time

Sometimes

Rarely

20. I do math by counting on my fingers. * Choose the best answer.

Most of the time

Sometimes

Rarely



APPENDIX C: LESSON WARM-UP EXERCISES



APPENDIX D: MOTIVATIONAL SCRIPT

Note: Script does not have to be followed exactly. A cell phone prop is needed. This can be an

actual cell phone or a toy.

Teacher

Says:

Excuse me, class. I need to make a very important phone call before we begin

the lesson.

Teacher takes out his or her cell phone and makes several attempts to make a phone call.

Teacher appears to get frustrated that phone is not working. Teacher then gives a facial

expression that gives students the notion that (s)he has finally discovered the solution to the cell

phone problem.

Teacher

Says:

(Sadly) Oh no! I just remembered that I didn’t pay my phone bill and my

service has been disconnected. I have been having an issue of going over my

monthly minutes and text messages allowance. I ran my bill through the roof

and can’t afford to pay it off right now.

Teacher perks up as if (s)he has just had an epiphany – gets a bright idea.

Teacher

Says:

(happily) After I pay this bill off, I am going to switch plans or service

providers. I need to find a plan that fits my communication needs, but also

inexpensive.

Teacher

Says:

But how will I ever determine which plan is right for my communication habits

and budget, with so many plans out there to choose from?

The teacher seems to ponder the answer to the question. At the point, the teacher may even take

suggestions from students.

Teacher

Says:

In today’s lesson we will learn how to use systems of equations to compare

mobile service plans and decide which plan is the best deal available. I really

need your help on this!



APPENDIX E: NOTE-TAKING ORGANIZER

Lesson 6 – 3: Solving Systems by Elimination

Note-Taking Organizer

Instructions: Complete this handout during the lesson. Refer back to this handout while

completing assignments and studying.

L

E

S

S

Notes and Examples

Addition Subtraction Multiplication (first)



Parallel & Coincident Lines with the Elimination Method

Instructions: Write information about parallel and coincident lines as they relate to the

elimination method in the respective circles. Write information that is similar between the two in

the center. Refer back to this handout while completing assignments and studying.

Parallel Coincident



APPENDIX F: POWERPOINT PACKET

Slide 1

Solving Systems of Equations

Using Elimination

Slide 2

Warm Up

Simplify each expression.

1. 3x + 2y – 5x – 2y

2. 5(x – y) + 2x + 5y

3. 4y + 6x – 3(y + 2x)

4. 2y – 4x – 2(4y – 2x)

–2x

7x

y

–6y

Write the least common multiple.

5.

7.

6.

8.

3 and 6

6 and 8

4 and 10

2 and 5

6

24

20

10

Have this slide displayed on the board at the beginning of class. Gain the learners’ attention, by first going over the answers to the warm-up. The warm-up will address skills students must possess prior to instruction.

Slide 3

Solve systems of linear equations using the elimination method.

Compare, contrast, and predict parallel and coincident lines using the elimination method.

Objectives

Announce the title of the lesson: “Solving Systems of Equations Using Elimination” and the objectives.



Slide 4

Announce to the class how they have previously learned that solving equations can help solve problems in the real world. Further explain how solving more than one equation simultaneously (systems) allows us to solve even more real world problems. State upon the completion of the lesson, the students will be able to solve a real dilemma for teenagers by solving systems of equations. Break from the instruction with a dramatic pause and proceed with the motivational script included in Appendix D

Slide 5

Hand out the graphic organizer that is to be completed by the learners during instruction. Learners’ attention will remain focused by constant questioning and note-taking on the provided graphic organizer. See Appendix E SAY: In this lesson, we will solve systems of equations using the elimination method, which involves addition, subtraction, and multiplication. Finally, you will be able to predict the outcome when solving a systems of equations that consist of parallel and coincident lines. You will practice every step in the process. At the conclusion of the lesson, you will compare actual mobile service plans using the elimination method to solve systems of equations. In a few days you will have a quiz on this lesson and on the chapter test, you’ll be tested on your ability to accurately solve systems of equations and apply your knowledge in real-world situations.



Slide 6

SAY: Another method for solving

systems of equations is

elimination. Like substitution, the goal of elimination is to get

one equation that has only one variable. To do this by

elimination, you add the two equations in the system

together. Remember that an equation

stays balanced if you add equal amounts to both sides. So, if 5x

+ 2y = 1, you can add 5x + 2y to one side of an equation and

1 to the other side and the

balance is maintained.

Since –2y and 2y have opposite

coefficients, the y-term is eliminated. The result is one

equation that has only one variable: 6x = –18.

When you use the elimination method to solve a system of

linear equations, align all like terms in the equations. Then

determine whether any like

terms can be eliminated because they have opposite



coefficients.

Slide 7

Solving Systems of Equations by Elimination

LESS


EEliminate one of the variables

S

Solve the resulting equation for the remaining variable

SSubstitute the value of the variable into one of the original equations and solve for the other variable

SAY: There are four main steps to solving a system of equations using elimination. The acronym LESS will be used as a mnemonic device to help you recall the critical steps. “We can remember LESS with the elimination method, because sometimes it can be less work for us!” READ SLIDE

Slide 8

ELIMINATION USING

ADDITION

Segment 1



Slide 9

You may play optional video at this time by clicking on the hyperlink.

Slide 10

Direct Instruction Example

3x – 4y = 10

x + 4y = –2Solve by elimination.

Step 1 3x – 4y = 10 Write the system so that like terms are aligned.

Add the equations to eliminate the y-terms.

4x = 8 Simplify and solve for x.

x + 4y = –2

4x + 0 = 8Step 2

Divide both sides by 4.4x = 8

4 4

x = 2

Walk learners through example in great detail.

Slide 11

Direct Instruction Example Continued

Step 3 x + 4y = –2 Write one of the original equations.

2 + 4y = –2 Substitute 2 for x.–2 –2

4y = –4

4y –4

4 4y = –1

Step 4 (2, –1)

Subtract 2 from both sides.

Divide both sides by 4.

Write the solution as an ordered pair.




Slide 12

Instructor Guided Example

y + 3x = –2

2y – 3x = 14Solve by elimination.

Write the system so that like terms are aligned.

Step 1 2y – 3x = 14

y + 3x = –2

Add the equations to eliminate the x-terms.Step 2 3y + 0 = 12

3y = 12 Simplify and solve for y.

Divide both sides by 3.

y = 4

During the guided examples, ask learners to tell and explain every step in solving the system.

Slide 13

Step 3 y + 3x = –2

Instructor Guided Example Continued

Write one of the original equations.

4 + 3x = –2 Substitute 4 for y.Subtract 4 from both sides.–4 –4

3x = –6

Divide both sides by 3.3x = –63 3

x = –2Write the solution as an

ordered pair.Step 4 (–2, 4)


Slide 14

Check for Understanding Example 1

x – y = 2

3x + y = 14Solve by elimination.

Write the system so that like terms are aligned.

Step 1 3x + y = 14

x - y = 2

Add the equations to eliminate the y-terms.Step 2 4x + 0 = 16

4x = 16 Simplify and solve for x.

Divide both sides by 4.x = 4

Example to be done solely by the learners for the purpose of checking for understanding.



Slide 15

Step 3 x – y = 2

Check For Understanding Example Continued


4 - y = 2 Substitute 4 for x.Subtract 4 from both sides.–4 –4

-y = –2

Divide both sides by -1.-y = –2-1 -1

y = 2Write the solution as an

ordered pair.Step 4 (4, 2)


Slide 16


x + 6y = 8

-x – 2y = 0Solve by elimination.


Slide 17

Distribute worksheet found in Appendix G Allow students to work in appropriate pairs. It is suggested that learners complete at least five practice problems for each segment. Assign the first five problems and allow early finishers to complete the remaining problems, while other learners finish. Refer students to their notes during practice and continue to emphasize LESS. Provide motivational and informational



feedback. Give positive reinforcement and constructive information. Provide feedback on every step of the LESS procedure. During practice, give learners information so they can determine if they are right or wrong and why they are right or wrong before giving them the correct answer. Give learners information on their progress. Explain patterns of errors to learners and inform them of how close they are to mastering the entire procedure.

Slide 18

ELIMINATION USING

SUBTRACTION

Segment 2

Slide 19




Slide 20

2x + y = –5

2x – 5y = 13Solve by elimination.


Add the opposite of each term in the second equation.

Step 1–(2x – 5y = 13)

2x + y = –5

2x + y = –5

–2x + 5y = –13

Eliminate the x term.

Simplify and solve for y.

0 + 6y = –18Step 2

6y = –18

y = –3


Slide 21



Step 3 2x + y = –5

2x + (–3) = –5Substitute –3 for y.

Add 3 to both sides.2x – 3 = –5

+3 +3

2x = –2 Simplify and solve for x.

x = –1


Step 4 (–1, –3)


Slide 22

Remember to check by substituting your answer into both original equations.

Remember!

READ SLIDE



Slide 23


3x + 3y = 15

–2x + 3y = –5Solve by elimination.

3x + 3y = 15

–(–2x + 3y = –5)

Step 1

3x + 3y = 15+ 2x – 3y = +5


Eliminate the y term.

Simplify and solve for x.

5x + 0 = 20

5x = 20

x = 4

Step 2


Slide 24



Substitute 4 for x.


Step 3 3x + 3y = 15

3(4) + 3y = 15

12 + 3y = 15

–12 –123y = 3

y = 1



(4, 1)Step 4


Slide 25


3x + y = 1

5x + y = 3Solve by elimination.

3x + y = 1

–(5x + y = 3)

Step 1

3x + y = 1+ -5x –y = -3


Eliminate the y term.


-2x + 0 = -2

-2x = -2

x = 1

Step 2




Slide 26

Check for Understanding Example 1 Continued


Substitute 1 for x.


Step 3 3x + y = 1

3(1) + y = 1

3 + y = 1

–3 –3y = -2

y = -2



(1, -2)Step 4


Slide 27


x + 4y = 1

x – 2y = -5

Solve by elimination.


Slide 28

Distribute worksheet found in Appendix G Allow students to work in appropriate pairs. It is suggested that learners complete at least five practice problems for each segment. Assign the first five problems and allow early finishers to complete the remaining problems, while other learners finish. Refer students to their notes during practice and continue to emphasize LESS.



Slide 29

ELIMINATION USING

MULTIPLICATION

Segment 3

Slide 30


Slide 31

In some cases, you will first need to multiply one or both of the equations by a number so that one variable has opposite coefficients. This will be the new Step 1.

READ SLIDE



Slide 32

x + 2y = 11

–3x + y = –5

Solve the system by elimination.


Multiply each term in the second equation by –2 to get opposite y-coefficients.

x + 2y = 11Step 1

–2(–3x + y = –5)

x + 2y = 11

+(6x –2y = +10) Add the new equation to the first equation.7x + 0 = 21

Step 2 7x = 21

x = 3



Slide 33



Step 3 x + 2y = 11

Substitute 3 for x. 3 + 2y = 11

Subtract 3 from each side.–3 –3

2y = 8

y = 4



Step 4 (3, 4)


Slide 34

–5x + 2y = 32

2x + 3y = 10



Step 1 2(–5x + 2y = 32)

5(2x + 3y = 10)

Multiply the first equation by 2 and the second equation by 5 to get opposite x-coefficients –10x + 4y = 64

+(10x + 15y = 50) Add the new equations.

Simplify and solve for y. 19y = 114

y = 6

Step 2




Slide 35



Step 3 2x + 3y = 10

Substitute 6 for y. 2x + 3(6) = 10

Subtract 18 from both sides.–18 –18

2x = –8

2x + 18 = 10

x = –4 Simplify and solve for x.

Step 4 Write the solution as an ordered pair.

(–4, 6)


Slide 36

Check For Understanding Example 1


3x + 2y = 6

–x + y = –2

Step 1 3x + 2y = 6

3(–x + y = –2)

3x + 2y = 6

+(–3x + 3y = –6)

0 + 5y = 0

Multiply each term in the second equation by 3 to get opposite x-coefficients.

Add the new equation to the first equation.

Simplify and solve for y.5y = 0

y = 0

Step 2


Slide 37

Check For Understanding Example 1 Continued


Step 3 –x + y = –2

Substitute 0 for y. –x + 3(0) = –2

–x + 0 = –2

–x = –2



(2, 0)

x = 2




Slide 38

Check For Understanding Example 2


2x + 5y = 26

–3x – 4y = –25

Step 1 3(2x + 5y = 26)

+(2)(–3x – 4y = –25)

Multiply the first equation by 3 and the second equation by 2 to get opposite x-coefficients 6x + 15y = 78

+(–6x – 8y = –50) Add the new equations.

Simplify and solve for y. y = 4

0 + 7y = 28Step 2


Slide 39

Check For Understanding Example 2 Continued


Step 3 2x + 5y = 26

Substitute 4 for y. 2x + 5(4) = 26



(3, 4)

x = 3

2x + 20 = 26–20 –20

2X = 6



Slide 40

Distribute worksheet found in Appendix G Allow students to work in appropriate pairs. It is suggested that learners complete at least five practice problems for each segment. Assign the first five problems and allow early finishers to complete the remaining problems, while other learners finish. Refer students to their notes during practice and continue to emphasize LESS.



Slide 41

PARALLEL AND COINCIDENT

LINES

Segment 4

Slide 42

Parallel Coincident

If computations eliminate all variables and produce an identity, the two lines

of the system are coincident.

If computations eliminate all variables and produce a contradiction, the two

lines of the system are parallel.

All variables are eliminated.

An ordered pair solution is not possible.

READ SLIDE

Slide 43

2x - y = 1

4x - 2y = 4

Solve the system by elimination. Determine whether lines are parallel or coincident.


Multiply each term in the first equation by –2 to get opposite coefficients.

4x - 2y = 4Step 1

–2(2x - y = 1)

4x - 2y = 4

+(-4x +2y = -2) Add the new equation to the first equation.0 + 0 = 2

Step 2 0 = 2

The lines are parallel.

Contradiction




Slide 44

4x + 8y = 8

3x + 6y = 6



Step 1 3(4x + 8y = 8)

-4(3x + 6y = 6)

Multiply the first equation by 3 and the second equation by -4 to get opposite coefficients 12x + 24y = 24

+(-12x - 24y = -24) Add the new equations.

Identity.0 = 0

The lines are coincident.

Step 2


Slide 45 Check For Understanding Example 1


-3x – 4y =2

-9x – 12y = 6

Step 1 -9x - 12y = 6

-3(–3x - 4y = 2)

-9x - 12y = 6

+(9x + 12y = –6)

0 + 0 = 0

Multiply each term in the first equation by -3 to get opposite coefficients.

Add the new equation to the first equation.

Identity.0 = 0

The lines are coincident.

Step 2


Slide 46 Check For Understanding Example 2


3x + y = -1

12x + 4y =6

Step 1 (12x + 4y = 6)

+(-4)(3x + y = –1)

Multiply the first equation by -4 to get opposite coefficients

12x + 4y = -1

+(–12x – 4y = 4) Add the new equations.

Contradiction.The lines are parallel.

0 + 0 = 3Step 2




Slide 47

Distribute worksheet found in Appendix G Allow students to work in appropriate pairs. It is suggested that learners complete at least five practice problems for each segment. Assign the first five problems and allow early finishers to complete the remaining problems, while other learners finish. Refer students to their notes during practice and continue to emphasize LESS. Provide motivational and informational feedback. Give positive reinforcement and constructive information. Provide feedback on every step of the LESS procedure. During practice, give learners information so they can determine if they are right or wrong and why they are right or wrong before giving them the correct answer. Give learners information on their progress. Explain patterns of errors to learners and inform them of how close they are to mastering the entire procedure.



Slide 48

SUMMARIZE AND REVIEW

Review the LESS procedure and briefly summarize the variations in the procedure when learners have to add, subtract, and multiply. Conclude instruction by presenting the sequence of steps a final time for a simple case and then build up to a complex case. Stress again common problem areas for learners to be cautious of like distributing the negative during subtraction.

Slide 49

Solving Systems of Equations by Elimination

LESS


EEliminate one of the variables

S

Solve the resulting equation for the remaining variable

SSubstitute the value of the variable into one of the original equations and solve for the other variable

READ SLIDE

Slide 50

READ SLIDE



Slide 51

Remember to correctly distribute the negative when using elimination by subtraction.

Remember!

READ SLIDE

Slide 52

In some cases, you will first need to multiply one or both of the equations by a number so that one variable has opposite coefficients.

READ SLIDE

Slide 53

Remember to check by substituting your answer into both original equations.

Remember!

READ SLIDE



Slide 54

Parallel Coincident

If computations eliminate all variables and produce an identity, the two lines

of the system are coincident.

If computations eliminate all variables and produce a contradiction, the two

lines of the system are parallel.

All variables are eliminated.

An ordered pair solution is not possible.

READ SLIDE

Slide 55

TRANSFER LEARNING

Allow learners to apply their new knowledge and skills to a real-life situation through comparing mobile service plans. Provide learners with a listing of current rates for mobile service plans. See Appendix H. Have learners construct systems of equations that align with the given information. Then, have learners solve the systems using the elimination method. Have learners determine the best mobile service plan for you and for themselves. Learning can also be transferred through similar examples comparing car rental rates and the optional use of the application instructional video that is included.



Slide 56

Distribute Transfer Learning materials to learners.

Slide 57

CLOSURE

Announce the conclusion of the lesson and thank the learners for their active participation and attentiveness. Also, thank the learners for helping you choose the most cost efficient mobile service plan that matches your communication needs. Express to the learners how confident you are in them that they are now able to be savvy shoppers using Algebra.

Slide 58

ASSESSMENT

Learning will be assessed to determine whether learners have achieved the goal of the instruction. Learners will be assessed on their ability to apply the procedure when solving a system of equations. Students will complete a quiz on solving systems of equations using the elimination method. See Appendix I for assessment quiz and KEY.



Slide 59

Distribute Assessment Quizzes and giver learners sufficient time to complete the quiz. Grade the assessment quiz according to the key and rubric. Return graded quizzes to learners and provide feedback on the percentage correct and number of objectives successfully mastered. Determine weaknesses and provide remedial instruction in those areas where needed.



APPENDIX G: GUIDED PRACTICE WORKSHEETS

ELIMINATION USING ADDITION PRACTICE

Solve each system by elimination.

1.

2.

3.

4.

5.

6.

7.



Elimination Using Addition Practice ~ KEY


2.

3.

(2, 4) (3, 4) (2, -3)

5.

6.

(-9, 1) (3, -1) (-1, -6)

7.

(1/3, ¼)



ELIMINATION USING SUBTRACTION PRACTICE


2.

3.

5.

6.

7.



Elimination Using Subtraction Practice ~ KEY


2.

3.

(3, -1) (6, -2) (2, 4)

5.

6.

(-6, 18) (6, 4) (-1, 2)

7.

(-1, 1)



ELIMINATION USING MULTIPLICATION PRACTICE


2.

3.

5.

6.

7.



Elimination Using Multiplication Practice ~ KEY


2.

3.

(2, 5) (-8, -1) (7, -4)

5.

6.

(4, -6) (- ½, 3) (-4, -1)

7.

(-1/5, -2)



PARALLEL AND COINCIDENT LINES WITH ELIMINATION PRACTICE

Predict whether the system represents parallel or coincident lines. Justify your prediction by

solving the system using elimination.

2.

3.

5. –

6.



Parallel and Coincident Lines with Elimination Practice ~ KEY

Predict whether the system represents parallel or coincident lines. Justify your prediction by

solving the system using elimination.

2.

3.

Parallel coincident parallel

5. –

6.

Coincident parallel coincident

coincident



APPENDIX H: TRANSFER LEARNING PACKET

MOBILE SERVICE PLANS AND PROVIDERS

Verizon Wireless Nationwide Single-Line Plans

Anytime Minutes Talk & Text Per-Minute Rate After Allowance

450 $59.99 $0.45

900 $79.99 $0.40

Unlimited $89.99 -

Alltel Wireless Nationwide Single-Line Plans

Anytime Minutes Talk Per-Minute Rate After Allowance

900 $59.99 $0.40

Sprint Wireless Nationwide Single-Line Plans

Anytime Minutes Talk, Data, & Text Per-Minute Rate After Allowance

450 $69.99 $0.45

900 $89.99 $0.40

Unlimited $99.99 -

AT&T Wireless Nationwide Single-Line Plans

Anytime Minutes Talk Per-Minute Rate After Allowance

450 $39.99 $0.45

900 $59.99 $0.40

Unlimited $69.99 -



APPLICATION WORKSHEET

Instructions: Use the information on the previous sheet to write equations according to the

directions below. Create systems of equations that align with the rate plans and solve them

using the elimination method. Record answers in the provided table.

Example: Compare AT&T 450 and AT&T 900

AT&T 450 → y = 39.99 + .45x → .45x – y = -39.99

(400, 219.99)

AT&T 900 → y = 59.99 + .40x → .40x – y = -59.99

You can conclude that the prices of these plans would be the same if the customer uses 400

minutes over the allowance. That price would be $219.99

1. Compare Verizon 450 and Sprint 450 5. Compare Verizon 900 and Sprint 900

2. Compare Verizon 450 and AT&T 450 6. Compare Verizon 900 and AT&T 900

3. Compare Verizon 900 and Verizon Unlimited 7. Compare Sprint 900 and Sprint Unlimited

4. Compare AT&T 900 and AT&T Unlimited

8. Your teacher talks an average of 1050 minutes per month and sends texts and emails

through his or her phone. According to your data, which plan would be best for him or her?

Justify your answer. Which plan would be best for you? Justify your answer.

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________

Minutes Over Allowance Price

Example: 400 $219.99

1.

2.

3.

4.

5.

6.

7.



Application Worksheet ~ KEY

Instructions: Use the information on the previous sheet to write equations according to the

directions below. Create systems of equations that align with the rate plans and solve them

using the elimination method. Record answers in the provided table.

Example: Compare AT&T 450 and AT&T 900

AT&T 450 → y = 39.99 + .45x → .45x – y = -39.99

(400, 219.99)

AT&T 900 → y = 59.99 + .40x → .40x – y = -59.99

You can conclude that the prices of these plans would be the same if the customer uses 400

minutes over the allowance. That price would be $219.99

1. Compare Verizon 450 and Sprint 450 5. Compare Verizon 900 and Sprint 900

Parallel Parallel

2. Compare Verizon 450 and AT&T 450 6. Compare Verizon 900 and AT&T 900

Parallel Parallel

3. Compare Verizon 900 and Verizon Unlimited 7. Compare Sprint 900 and Sprint Unlimited

(25, 89.99) (25, 99.99)

4. Compare AT&T 900 and AT&T Unlimited

(25, 69.99)

8. Your teacher talks an average of 1050 minutes per month and sends texts and emails

through his or her phone. According to your data, which plan would be best for him or her?

Justify your answer. Which plan would be best for you? Justify your answer.

The teacher talks 1050 minutes, which is 150 minutes over the 900-minute limit. Since

150 is over the 25-minute mark, an unlimited plan would be best for the teacher.

Because the teacher uses text and data services, the Sprint Unlimited plan is the best

deal. (Answers will vary)

Minutes Over Allowance Price

Example: 400 $219.99

1. Parallel

2. Parallel

3. 25 $89.99

4. 25 $69.99

5. Parallel

6. Parallel

7. 25 $99.99



APPENDIX I: ASSESSMENT QUIZ

Instructions: Solve the systems of equations using the elimination method.

2.

3.

5.

6.

Solve the systems of equations using the elimination method and determine whether the system

implies a pair of parallel or coincident lines.

9.

10.



Assessment Quiz ~ KEY

Instructions: Solve the systems of equations using the elimination method.

2.

3.

(2,2) (0, -6) (0, 0)

5.

6.

(-3, 1) (-2, 2) (-4, 3)

(1, 1)

Solve the systems of equations using the elimination method and determine whether the system

implies a pair of parallel or coincident lines.

9.

10.

Parallel Coincident Coincident



APPENDIX J: WORKS CITED

Coffman, J. L. (n.d.). Solving Systems Algebraically. Retrieved June 30, 2010, from Joseph L.

Coffman: http://www.jcoffman.com/Algebra2/ch3_2.htm

Ellis, W., & Burzynski, D. (2009, June 1). Systems of Linear Equations: Elimination by Addition.

Retrieved June 30, 2010, from Connexions: http://cnx.org/content/m21986/latest/

Freedman, E. (2010). Do You Have Math Anxiety? Retrieved June 25, 2010, from Professor

Freedman's Math Help: http://www.mathpower.com/anxtest.htm

Holt McDougal: Holt, Rinehart and Winston. (2007). Holt Online Learning Materials.

Hopper, D. C. (2010). Math Study Skills Self-Survey. Retrieved June 25, 2010, from

Purplemath: http://www.purplemath.com/stdysrvy.htm

Smith, P. L., & Ragan, T. J. (2005). Instructional Desgin, 3rd Edition. Hoboken, NJ: John Wiley

& Sons, Inc.

EdTech 503 Final Instructional Design Project

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