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MyCar
Geoffrey Burr
TEP 118
Instructional Unit
Table of Contents
Introduction 3-7
Sources Cited 8
Lesson 1-1
Unit Overview 9-10
Lesson 1-2
What are the issues of Buying a Car? 11-13
Lesson 1-3
Research day in the library 14
Lesson 1-4
Drill Groups Report Back 15-16
Lesson 1-5
Ratios and Proportions 17
Lesson 1-6
Working with the Interest and Percent: The Cost of Financing the Vehicle 18
Lesson 1-7
Mean, Median, and Mode 19-20
Lesson 2-1
Role Playing Sceneries and the Cost of Maintaining an Automobile 21-22
Lesson 2-2
Rates of Change 23-24
Lesson 2-3
Conversions using the Metric System 25
Lesson 2-4
Calculating Depreciation/Scatter Plots 26-27
Final Evaluation 28
Introduction
Motivation for the Unit
This quarter I have been student teaching in Scripps Ranch high school in a pre-algebra level mathematics class. From my experiences, I have seen that the typical structure of a unit is for the students to be taught the information right out of one chapter in a book, section by section. The emphasis is usually on showing how to do certain problems while teaching various concepts. Usually the skills are taught first, students are drilled, and they are shown how what they learned can be applied to one or more themes in the real world. Usually this application is a theme that is used for only one problem as an example in a chapter. The chapter is designed showing the mechanics of how to do simple arithmetic and algebra. Most of the lessons involve independent drill and practice where students spend most of their time working out the mechanical aspects of the math.
My experience working with high-school students in pre-algebra has been that they are not motivated like the students in subjects like calculus, geometry, or trigonometry. Many of the students want to know how the math they are using is going to help them, and that gets in the way of their motivation. The students in the other classes ask as well, but they do not let that get in the way of their work. These students have usually seen the material for many years prior to coming to the class, yet have not been able to pass the course. Most students are freshman and sophomores, and there are some juniors and seniors. Their major obstacle seems to be motivating them to want to learn the material.
This unit tries to reverse this typical method of learning, by letting the theme (purchasing, owning, and selling a car) be the be the structure for the unit. The concepts learned and reinforced through drill and practice are to be seen as needed tools to be acquired in order to accomplish the goals of this theme. The idea of the unit is therefore to make the process of purchasing, owning, and selling a car a vehicle that carries the students through the process of learning mathematics (no pun intended).
Unit Summary
The unit is structured around 1) finding their own car, 2) purchasing and financing the automobile, 3) maintaining the automobile, and 4) selling the car. The students will be given a certain amount of money to begin with, and then be required to buy the car, insure it, and finance it for two years. They will then be given various exercises while owning their vehicle. They will then be required to sell the car after owning it foor only one year. The ultimate evaluation will then be having the students critically evaluate how much the vehicle cost to own, operate, and finance, They will be required to make evaluations of the selling value of the car (when factoring in depreciation values of one versus two years) as well as the financing costs (comparing what they intended to spend over two years to what they did spend over one).
Over the course of the unit, students will be doing drill and practice exercises from the text in one form of drill group (their drill groups). They will also be applying that math to their vehicle in another type of drill group (their cargroup). They will be required to keep a portfolio of information about each of their cars, as well as a writing journal for daily quick-write entries The unit is designed for a block schedule in high school pre-algebra. !The references for using a text are taken from Merrills Pre-algebra: A Transition to Algebra (1997). Final evaluation will be based on the students journal, classwork, and portfolio. The final exam will be a take-home where the students use the information in their journal to make a final evaluation of owning, and selling their own car.
Mathematics Topics Covered
The unit will address the various topics outlined in the California Standards for teaching mathematics. The topics covered are ratios, proportions, percent proportion, percentages, discount and interest (simple),gathering and recording statistical data, mean, median, and mode (measures of variation), scatter plots, frequency graphs (histograms), rates of change, and converting to and from units of measure. Implicit in th$e unit is that students will engage in real-world problem solving, making logical decisions based on their mathematical interpretations, which is prevalent throughout the framework/ standards. Because the unit is for a pre-algebra class, the standards are mostly drawn from those of 7-8 grade. However, the standards include some of those that are outlined for the 9th and 10th grade level.
The Idea Grounded in Theory
The overall theme of the unit is to get the students motivated to want to be involved in the learning process. It tries to harness the desire that adolescents have for responsibility and control of their lives, and is meant to make them feel fully competent by giving them activities that are more adult like, (Csikzentimihalyi and Schmidt, p.6-10). The intent is to address the motivation dimension of cognitive learning by giving students activities that make them more engaged through linking relevant day-to-day life experiences to their learning (McGilly, p.10) (Quartz, lecture notes). Since this age group usually lacks the motivation and interest in pre-algebra, and the topic itself and materials for it are designed for younger age groups, the concept of owning a car helps make the material more appropriate (since students are usually freshman and sophomores who will be learning to drive within the next two years).
Another key idea to the unit is the use of declarative and procedural knowledge (McGilly, p. 4). The unit tries to link together procedural and descriptive knowledge, so that neither type is isolated. By using both exercises, and hands on activities linked to their automobiles, the intent is to have students use and process what they learn in situations that are not isolated to a classroom context. This unit tries to have students learn mathematics not strictly as declarative knowledge (memorizing formulas, or memorizing rigid algorithms to solve problems of drill and practice), The intent is to integrate the learning of procedural and declarative knowledge. This can be pictured as in the diagram to the right. This unit tries to make the learning occur where th two different circles overlap, so that the students are able to two acquire and use both types of knowledge. Students will be required to do both drill and practice, and application of that to the real world exercise of owning a car.
Two different group structures
There will be two types of small groups, or familiar, repetitive participant structures (Brown & Campione, p. 235) the students will be involved in over the course of the unit. The first will be drill groups, and the second automobile groups. During the first week of the unit, students will be as-sembled into drill groups while trying to discover the issues of buying and owning a car. They will meet with these groups throughout the unit while working on regular exercises involving material from the book, and other drill and practice. The second type of group will be their own automobile groups. Once the students have chosen their own automobiles, allow them to group themselves how they wish. This will allow them to establish their own type of group identity, establishing a self-categorization (Rich Harris, p.141) where they can associate themselves with some sort of common experience (same types of automobiles, common interests etc.). This will be the group they work with when doing exercises that directly involve their own automobile. This will also become the group that gives a presentation of the material they put together over the course of the unit.
The distinction between is that the drill groups are intended for doing actual calculations or exercises of the math introduced from the book, or doing research. These groups should be heterogeneously mixed of students of varying levels of ability. These groups are intended to replace individual guided instruction during classroom teaching. Lectures about material from the book will be done while they are grouped together in these groups. The automobile groups are meant to be where the students apply what they have learned to their own automobiles. These groups can be based on how the students themselves want to be with. The idea is for the students to be able to apply and transfer the skills they use in one group to the other. They should be encouraged to carry the learning from one group to another.
Portfolio
Over the course of the units, students will keep a portfolio of the information for their car. This will be the main way of evaluating what the students have done. It will include pictures and statistics about their automobile as well as any information (graphs, charts, data) that they ultimately compute about their car. This will not be where they will be storing homework or exercises they have completed in order to learn the mathematics. Students will be encouraged to keep a separate notebook for their homework and class exercises, as well any notes they feel they need.
One of the reasons for the portfolio is that students will have at their use daily, and for ultimate evaluation, a reference to allow them to see what they have been learning in their own way. Their final evaluation for the unit will be an analysis of what they have learned through some sort of presentation. The students should be encouraged to use this information to make a presentation based on their own style of learning. While they will all be required to do the mathematical exercises, their ultimate evaluation should be flexible to allow for them to express their learning in a way that best fits their ability.
Journal
Students will be required to keep a writing journal in which they will do a quick write at the end of each day. The quick writes will consist of reflections about what they feel they learned during the instruction, how it applies to their life, and how they feel they are doing learning the material. This is intended to be a means of metacognition for assessing their selves so that they become more aware if their own pace of learning( McGilly, p.4). It is also intended as a method for teachers to be able to assess how the students are learning or how they perceive the material, in order to focus guided learning lectures to the students interests and abilities.
Evaluation
Evaluation of the work that the students do over the course of the unit is meant to not involve typical grading and points. The portfolio, and the final presentation should be used as the main methods of evaluation. Because students have differing types of ability, it is imperative that they be able to express themselves in different ways. All of the students should be required to perform the homework and exercises so that they are able to use this material in the setting of a standardized test. The exercises in the book are meant for this. The final evaluation, however, will be a critical evaluation in the form of a take-home exam. They will have to use the exam as a guideline for making their presentation, and for assessing the data they have accumulated. All the information will be included in the portfolio. The notebooks with problems from the book, as well as the journals will also be handed in, but are intended mostly for a means of assessing the students learning and understanding throughout the unit, not as a final means of evaluation,
Other Issues, Comments, Concerns
The teachers role: Ability and Gender
Over the course of this unit it will be important that the teacher be aware of a number of various issues that might arise. First, the nature of the unit is grounded in a real world experience that is made for students of all genders. Throughout the unit it should be emphasized that what the are learning is not a guy thing. Automobiles have the potential for gender biased because males typically have more interest in automobiles than women, and many professions involving automobiles (mechanics, auto dealers). It should be emphasized throughout the unit that women and men equally need skills in mathematics in order to do many things on a day to day basis, and this unit is one real-world snituation exhibiting that. The portion of the unit involving role playing, or scenarios is invented to address this, but one lesson cannot address the differences that exist between girls and boys with regard to self-esteem and their place in the mathematics classroom. Differences in self-esteem, achievement and views about mathematics differ significantly between boys and girls (Kimmel and Rudolph, p.51-53) Teachers treat girls and boys differently depending on their gender, and will show boys how to do things while doing those things for the girls (Kimmel & Rudolph, p.53). It is important then that the teacher try to encourage the open dialogue that the role playing lesson is intended to produce throughout the entire unit.
Second, the drill groups should be made and overseen to account for the issue of ability. Students will come to the classroom with diffe
ring skills and differing ways they exhibit their knowledge of mathematics. Students will participate in the groups differently. Since a good portion of the unit is done working in these small groups, the teacher needs to constantly be aware of status hierarchies that may develop within the small groups. The activities of this unit allow for students to have the flexibility of expressing their abilities in different ways, so the teacher has many opportunities to assign competence to the lower-status students of a group (Cohen, Kepner, Swanson, p.24) throughout the unit, so that no student is left feeling less competent or less able than their peers.. The teacher can do this by encouraging the students to share their work in a medium that is appropriate to their abilities, and by communicating the differing strengths of each students work to the other members of the class..
(The concerns about ability and gender will be referred to later in the specific lesson plans during the unit.)
Sources Cited
Brown, Ann L. and Campione, Joseph C. Guided Discovery in a Community of Learners. In Kate McGilly (ed.) Classroom Lessons: Integrating Cognitive Theory and Classroom Practice. Cambridge, MA: MIT Press, 1994. pp. 229-270.
Cohen, Elizabeth, Diane Kepner, and Patricia Swanson, Dismantling Status Hierarchies in Heterogeneous Classrooms. In Jeannie Oakes and Karen hunter Quartz (eds.) Creating New Educational Communities. (Chicago: Chicago University Press, 1995): pp. 16-31.
Csikszentmihalyi, Mihaly and Scmidt, Jennifer A., Stress and Resilience in Adolescence: An Evolutionary Perspective. In Katheryn Morman and Barbara Schneider (eds.) The Adolescent Years: Social Influences and Educational Challenges. Chicago: University of Chicago press, 1998: 1-17.
Kimmel, Ellen B., Tricia Rudolph. Growing Up Female. In Katheryn Borman and Barbara Schneider (eds.) The Adolescent Years: Social Influences and Educational Challenges. (Chicago: University of Chicago Press, 1998): pp.42-64.
McGilly, Kate. Cognitive Science and Educational Practice: An Introduction. In Kate McGilly (ed.), Classroom Lessons: Integrating Cognitive Theory and Classroom Practice. Cambridge, MA: MIT Press, 1994. pp. 3-21.
Rich Harris, Judith, The Nurture Assumption, chapter 7, Us and Them. New York: The Free Press, 1998. pp. 123-145.
9Materials needed
Newspapers
Harmons free guide to automobiles
Internet access
three ring binders for portfolio and notebook
blue books or black memo journals for writing journal
Goals
establish the unit overview with the students
determine what kind of car they want to buy
make a portfolio
establish automobile groups
Warmup
Do a warmup involving fractions and decimals to get students used to using those operations again
Instruction/Class Activity
Overview of the Unit
For the first day of class, inform the students that over the course of the following weeks they will each be purchasing and automobile. Let them know that they will be paying for it and maintaining it for what will be a period of two hypothetical years. Make an outline for them to record showing what they will be required to do during the unit. Each person will be required to:
buy a car for $20,000 or less
put $10,000 down payment and finance the remainder
learn about mathematwics through owning the car for a period of two years
keep a a notebook that will have 2 sections:
a portfolio section where they record all the information about their car, and where they keep the mathematical exercises for the car
a notebook section for the unit where they keep all their exercises from the book, or from other resources drills etc.
participate regularly in two-types of groups
make a small group presentation in the first week with their drill group
make a presentation with their automobile group
turn in the final portfolio with all the data about their car, and the homework, as well as a final analysis of their own automobile (to be described later)
Have the students work in arbitrary small groups to decide what car they would like to have. They will be required to decide during todays class to decide what kind of car they would like to have for less{ than $20,000. Have the students use newspapers, and Harmon's free guide for automobiles to find their car. Also if teachers have internet access in the classroom, they could visit http://www.uniontribune.com/marketplace/autobuying/index.html
which is a very useful site because it locates available models that you are looking for and lists links to the dealerships in the San Diego area that have many different cars that you are looking for. Students will be encouraged to choose the kind of car they want, or would desire to have if they could afford any car.
Once they have each decided on what kind of car they want they will the have locate an exact car and document the cost. It could be an advertisement they cut out or printout from the net. Have them record in their portfolio the name make and model, options listed, and any other descriptions they want. Try to encourage cutting out a picture, our download one from available web sites (the above web site has actual pictures of the cars the dealers are selling, so do individual companies like www.gm.com, www.ford.com etc.). Make sure they record the price they will be required to pay for the automobile. By the end of the class, they should have at least decided on what car they want.
Establishing Automobile Groups
Have the students group themselves into smaller groups that will be their automobile group. This can be any group of students they want. The goal for establishing the automobile groups is to have the students identify themselves as part of a group they themselves identify with. In contrast to the drill groups, this is meant to be a means for the students to distinguish their own group identity as different from the others so they have a feeling that they themselves had input into it. Possible themes could be the sports car group, or the mustang club, or the girls club etc. Encourage them to give themselves a name (the motor heads, the pony car club etc.).
Have the students realize this group will be one they are going to be working in regularly when doing problems relating to their cars.
Possible Quick Write in Journal
Talk about the numbers and figures you saw while looking for your car. Can you come up with any mathematical formulas that in volve some of the numbers you used?
Homework
By the next class have documentation of what car you want that includes the selling price, the options of the vehicle, and preferably a picture of the car you want. All this information should be recorded in the journal section of your portfolio.
Include with hat information the amount they will have to finance for their car (ie subtract $10,0000) from the list price
find sources for a fact sheet for car
Goal
have the students get organized into drill groups
use the jigsaw method of learning to discover the issues of buying a car
Warmup
Do problems involving multiplying and dividing fractions and decimals
Instruction/Class Activity
Establish Drill Groups
Before beginning the unit, divide the students into small drill groups. The grouping of students should be based on the instructors views of their abilities, grouping them heterogeneously. Assemble the students into groups of one fifth of the class. Have the students know that this will be their drill group that they meet with to do problem sets. It will also be the one where students perform exercise and drills from the book. Have the students realize this will be the group they will be involved with when learning new instructional material, and that they will meet regularly with each other.
Drill group activity
Have the groups brainstorm about what they think are the issues of going out and buying a car. Encouraged each group to develop their own ideas. The main emphasis should be on making/finding what they think the tasks of purchasing a car entail, not the math.
Once they have developed lists, put all of the ideas on the board for the entire class to discuss. Have the students write in their portfolios all of the issues they have discussed. Then as a class have them come up with what areas of math they may need to know in order to buy a car. Then make an outline on the board of the mathematical concepts they think are necessary in order for them to purchase an automobile. Have them record this information in their portfolio as well. They will want to have their ideas in their portfolio in order to compare them later on in the unit with what they actually did.
Using the Jigsaw Method of learning, give each of the groups one of the following topics and assign the accompanying assignments. They should work on these assignments as groups and will have to report back to the entire class and present their findings.
insurance costs-liability, comprehensive
what are the typical insurance costs for this age group, and what are the factors involves that determine that cost (age, type of car, grade point average, having had drivers education in high school)
the minimum amount required-liability, comprehensive
liability is required by law-you cant drive it off the it without it. It is independent of the cost of the vehicle. Why is it higher for people without drivers education, or higher if the car is a sport car or high performance vehicle?
comprehensive and collision (and theft) is tied directly to the cost of the vehicle/value of the car.Their is collision and theft requirement for those who have a loan (or lease) on a vehicle.
titles fees, registration fees, sales taxes
where do you have to go, and what do you have to pay in order to get titles, registration, and what do dealer take care of?
sales tax is a straight percentage of the final purchase price
California registration and title fees are based on the value of the vehicle
financing
what is financing a vehicle
what is the difference financing from a bank or from the company you are buying the car from
new vehicle pricing
what is included in the list price of a new car
what is the difference between the dealer invoice and the list price
what added costs do options on the vehicle add to the cost
how do dealers try to hide costs, or make deals by trying to include options (or add things like undercoating where they charge you extra
The intent is to have the students find the numbers involved with each of these issues, and have them return to the class some sort of numbers. Encourage them to try to discover how those numbers become equations and the topics that the unit is going to address (percent, ratio, interest). In addition, try to identify if students~ take an interest to finding out about any specific area.
Each group is going to have the responsibility to bring back resources about their topic for the other group members to use. Each member should be responsible for returning to the class one resource where they can go to get information about their topic. Possible resources could include web sites, magazines, phone numbers, yellow page advertisements. Each person should be required to bring back numbers, facts, and figures they obtained form that resource and express it somehow as a mathematical equation.
The timeframe for this could be approximately a week for the students to gather the information in class. Visiting the should be scheduled for the next class, so have the groups be aware they will be able to use the library, to finalize their assignment. The students may need time to screen it with the teacher to amake sure the information is accurate before they present it to the class. Accurate in the sense that the students bring information relevant to the units emphasis of mathematics, and that they do not have any erroneous equations. The presentation of each groups material would be variable time. Allow for the students as much time as needed in order to present their information, explore any ideas other students have, but keep the emphasis on the units outline.
Possible Quick Write in Journal
Was I aware of all the issues involved in buying a car?
Do I know, or are familiar with these areas of math involved with purchasing a vehicle?
Homework
Begin working on finding answers to the questions for your drill group
be prepared to work in the library the next class period
Materials Needed
Scheduled day in the library
Goals for lesson
drill groups will have found information for their presentation on their assigned topics
each student will have found a stat sheet or detailed description of their own car
Warmup
none
Instruction/Class Activity
This period is intended for the students to have enough information for their own automobile and for their drill groups presentation. Thy should be encouraged to find such resources as consumer reports, road and track, and especially the internet
Possible Quick Write in Journal
Write down any possible math equations or formulas that you found while doing your research today in class. Talk about how you might need to know how to use that math if you were going to go the the library to find out about other things you might have to eventually but (ie a washing machine, radio, TV, house, job).
Homework
Have your drill group information prepared for the next class.
Have a statistics sheet read for the next class. drill groups will be given some time the next period to finalize their presentation
Goals for the class
Each group will report back their findings
each person in the group is responsible for providing one resource
member of the other groups will take notes about what each group has found
every student will record to resources that are provided
Warm Up
Continue with operations involving fractions and decimals-simplifying and identifying which fractions are the same. Use a few problems involving percent to see if any class members already understand it.
Instruction/Class Activity
Each drill group will present their information to the entire class. They should write down the resources they found, the actual statistics, and the mathematical equations. What they present should be documented by each of the other people in their portfolios so they can use it as reference. The students will need some f the material for later in the unit.
For each group a general outline for what each of the students will need should be
Sales Tax and Registration fees
What is the California sales tax. What are the registration fees
Sales tax is a straight percentage of the final purchase price. California registration fees are based on the value of the vehicle.
The groups can develop or approximate a generalized equation in the form:
total registration fees = minimum registration fee + x% of current value.
Insurance Costs:
The groups need to provide information where the other students can go to find insurance to get a quote for their own car.
Liability insurance as required by law is generally independent of the value of the car (it will be higher for people without drivers Ed or with poor driving records and may be higher if the car is a high performance, sports or muscle car?).
Collision and Comprehensive (Theft, etc.) are tied directly to the value of the car. If there is loan or lease on the car, collision & theft insurance are required be the lender/lessor.
A possible generalized equation:
total insurance costs = cost of liability insurance + (Collision cost factor X value of car) + (Comprehensive cost factor X value of car)
New Vehicle Pricing:
Consumer Reports provides list prices of cars in their annual auto issue, together with a cost factor indicating the % of list price that a dealer pays to buy the car. Generally, more expensive cars have fatter profit margins. (Examples being: Acura Integra: $16,200-$21,600; cost factor 89%, BMW 318ti: $21,390; cost factor 90%, Chevy Cavalier: $11,610-$19,410; cost factor 93%, Chrysler Sebring, Convertible: $20,575-$25,840; cost factor 92%. Dodge Neon: $11,000-$11,455; cost factor 94%. Isuzu Trooper: $26,650; cost factor 85%. List prices are also available from the manufacturers web sites.)
Most dealers will not sell for less than 4% or $400 over their invoice. Cash back can be applied to the answer before or after deriving dealer cost (Im not sure how it works in real life, but you just pick one).
a possible general equation for purchase price would be:
(average list price X cost factor) + dealer profit - cash back
Financing
Financing costs and the maximum term of the loan will vary based on the age of the vehicle and the % amount to be financed. Loans on new cars may be allowed payoff terms as long as 60 months. Used cars seldom go beyond 3 years. Interest rates tend to be higher on used cars and may be higher with no money down, or if the term is beyond 36 months.
A possible general equation: total cost of the vehicle = principle +IPR
Possible Quick Write in Journal
Do I already know the mathematics behind each of these issues? Have I seen and used percentages regularly before?
Homework
Find out how much the cost of insurance for your vehicle will cMost. Bring that amount to not the next, but the class after that.Materials needed
Class book
notebook portfolio
Goals for the lesson
be able to identify proportions and ratios, the percent proportion, and percentage
be able to use ratios and proportions in relation to their car
establish automobile groups
each student will determine the final cost of each of their vehicles when factoring in sales tax, and registration fees
Warmup
do five problems multiplying and dividing fractions and decimals
Instruction/Class Activity
Drill Group Activity
Use the teachers edition and teach from chapter 9-1,9-2, 9-3, 9-4 on ratios and proportions, percent proportion, and percent. Make this lesson be laying the groundwork for using percentages later in the unit, especially for the next lesson involving percent. Since the students have mos`t likely seen these topics before, make the lesson from the book using selected problems from each chapter. Have the drill groups assemble before instruction, and teach the lesson as they are seated in those groups. Have each group then work through guided practice exercises from the book, as well as independent problems.
Automobile Group Activity
L While assembled into the automobile groups, have each student figure out the final cost of their vehicle when factoring sales tax, registration fees.
Possible Quick Write in Journal
Did I realize that percent and percentage were just ratios? How often during the past week, outside for school activities have I used the ratios, proportions?
How often outside of class on a daily basis do I use percent and the percent proportion?
How am I doing understanding the new material?
Homework
Selected problems from chapters 9-1, 9-2, 9-3, 9-4
have exact figures for how much i t will cost you to insure your carMaterials needed
information recorded in the portfolio regarding interest and financing
each student has to have the information for insurance for their own vehicle
Goals
each student will figure out their own insurance cost for their vehicle
each student will learn what the equation IPR means
each student will be able to calculate the cost of their own vehicle at different rates of financing over the course of two years using a simple IPR calculation
Warmup
review exercises from the previous chapters. Do one on proportion, one on ratio, and three on percent and percent proportion. Try to have the students do these problems without using the calculator.
zInstruction/Class Activity
Drill Group activity
Begin the lesson by addressing the topics of chapters 9-7, solving percent equations, and 9-8 Discount and interest while students are assembled in their drill groups. Through guided practice make sure students grasp the understanding of simple interest (i=prt) as well as compound interest. Do guided independent practice using selected problems from these chapters. Assign approximately 10 problems from the book and have the drill groups work together to come up with the answers for them.
Automobile Group Activity
At this point, the students know how much their car will cost them. They also know how much they will be required to finance. Reassemble them into their automobile groups and have them calculate the following:
Using the formula for IPR calculate, have them make a table of the different amounts of cost over the periods of one to 5 years using %9 %9.5, %10, %10.5 rates of financing.
Also have them calculate the monthly costs of these.
Try to take information that was provided from the drill groups on interest rates from various agencies. Then have them construct a table that will have the amounts of payments they would have to make for the vehicle.
Possible Quick Write in Journal
Based on the number entered in the table so far, does it seem like it would make more sense to pay the car off over the course of one year as opposed to 5 years? What difference would the financing rate have on those figures?
Homework
complete the table started in class
use the information for insurance cost you found, and add an additional column to the table for insurance costs over the time frame of the car.Materials Needed
class books
graphing paper, rulers
Goals for lesson
students will be able to gather and record data in a frequency table, and be able to make percentage calculations based on that data
students will understand measures of central tendency (mean median and mode) and be able to make simple calculations using that material
Warmup
Do two or three basic problems on percent and percentage. Do three problems using the IPR formula, adding one that includes discount
Instruction/Class Activity
Drill Group Activity
In order to prepare for later portions of the unit, stu>dents will need to learn the topics covered in Chapter 10-statistics and graphs. The goal of this lesson is to get them acquainted with the principles found in 10-1, gathering data and recording data, as well as 10-2 measures of central tendency, 10-4 measures of variation, and chapter 10-6 on scatter plots. The emphasis should be placed on the understanding of average, or mean, median and mode.
Automobile Group Activity
As an activity have the students group themselves into their automobile groups with the information of the cost of their vehicle, cost or yearly insurance. Give each group enough graphing paper for 3 pages per student.
Have the groups each construct a table of the list price, price paid, total cost of their vehicle of paying for fees, and yearly cost of their insurance, what their monthly payments would be for financing the car over the course of 2 years based on a %10 yearly finance rate (taken from the figures they figured out during the previous class). The table each student makes should include each of the other students cars as well. Have the students add up each of the columns, and sum it at the bottom. Then have them divide this number by the number of people in the group (finding the average), and record the average of each column below. The students will probably be familiar with doing this, so introduce the topic of average, and mean for now.
Construct a table on the board that will allow for each group to make an entry in one of four columns. Have the students, group by group, come to the board and place the amount they paid for their car, the list price of the car, the yearly insurance in the appropriate places in the table. Also have them record the average cost for the vehicle they got for their group. Each group, and every student should use a second sheet of paper to make table of the entire classes data.
Have the students organize into heir drill groups and take the class data collected earlier and make a new frequency table on their third sheet of graph paper, organizing the class data by the following intervals based on list price ranges: under $7,999, $8,000-$10,000, $10,0001-$12,000, $12,001-$14,000, $14,001-$16,000, $16,001-$18,000, $18,001-$20,000. There should be enough space below the information to make a histogram of the frequencies of the class data. Have them answer the following questions:
what is the sample size?
How much did the greatest number students pay for their car?
What are the percentages of each categories frequency of the entire class?
As another assignment, to be continued as a homework assignment, have the students find the following information:
What the mean, median and mode of the list price, the final paying price, the cost of yearly insurance, the cost of monthly payments after financing of the entire classes vehicles.
How much above or below the average of the class your own vehicles data stands.
Possible Quick Write in Journal
What is the shape of the bar graph (histogram) that we made in class? What would happen if we connected the tops of the bars to one another? What shape might it have?
Where else have I used mean median and mode outside of math class? Do I use it on a daily basis? Write one example of n average, mean or median that I have used outside of class in the last day and week.
Homework
Complete the assignment started in class using mean median and mode, and record in your portfolio to be checked and used in the next class.rGoals:
Students will be able to work as groups to find create solutions to various sceneries
develop open dialogue surrounding some of these issues
work effectively in small groups
work effectively in large groups
solve some simple problems involved with maintaining an automobile
Warm Up
As warm up for this class, begin by discussing openly the idea that men are usually seen as being better in math. Pose the following questions:
Are cars guy things?
Is purchasing and owning a vehicle something both men and women have to do?
Why are most of the automobile dealers and car salesmen men?
Do you think this has an affect on how women go about purchasing a car?
Should women be required to do things like change the oil or make small repairs to their cars?
Why do you think there arent a lot of women mechanics?
How do you think that affects how women go about fixing their cars?
Are men better a doing math than women?
Do you think men or women are better at doing the math required for buying, and owning a car (as well as other other life situations)?
Instruction/Class Activity
Drill Group Activity-Small Group Skits
Have the students get into their drill groups. Each will be given one of the following sceneries, and then be required to devise their own performance that will be a short (5 minute) acting situation. Give each group one of the following sceneries, written on a sheet of paper, and have them discuss the situation and then make a skit resolving their scenario. Have two copies of the questions so that two different groups get the same question.
The boys are in a c7ar that has broken down on the side of the road, and none of them know how to fix it. A car full of women pull up to help, and they know how to fix your car. What do you do?
You have to have some work done on your car, you dont know anything about cars. You go to the mechanic and she wants to charge you a thousand dollars for a break job. What do you do?
Each of you in the group is a married couple looking for a car. None of the men know anything about automobiles, and the women know a lot. The women are also the better ones with using math and numbers. (To each couple): A male salesmen come to speak to you and begins by talking to the men. He has a great deal for your car. What do you do?
Have the students work with each other for about 15 to 20 minutes devising their scenario. Then have the two groups with the same questions give their skit. When the two are done discuss the scenario and what each group chose to do and why.
Possible Quick Write in Journal
When all groups are finished, have the students write a reflection about what they did in their journal.
Automobile Group Activity
Have the students assemble into their automobile groups. As an activity to be entered into their portfolio, have them perform the following exercises, for the remainder of the class period. If they do not complete the work, have them finish it for homework.
Given the following information, develop a table of annualized and monthly costs based on a two year ownership of a vehicle that is driven for 10,000, 15,000, 20,000, and 30,000 a year
brakes cost $250 and must be done every 40,000 miles
Tires cost $300 and must be replaced every 35,000 miles
Oil changes cost $25 and must be done every 3000 miles
Unscheduled repairs might average $300 for a year
Homework
Complete assignment started in class.Goals
determine when a ratio is a rate
simplify rates into unit rates
use the formula r=d/t
Warmup
give five sample problems of ratios
Instruction/Class Activity
Drill Group Activity
Begin teaching chapter 9-1 on rates of change, and revisit 9-3 on using proportions in order to give them a feel for how miles per hour, and miles per gallon are examples of proportion. Use the miles per hour, and the miles per gallon figures for examples of the car to give an example of how ratios are used in every day life.
Use the example from one of the students cars of taking the number of pounds the car weighs, and then divide it by the number of horse power that the car has. Show how this is a unit ratde, and discuss how it can also determine how the car performs affecting speed and miles per gallon.
Automobile Group Activity
Have the students arranged in their automobile groups and use their stats sheet, or detailed description of the automobile they own in order to figure out the costs of paying for fuel. Have them look through the specs sheet of their cars and highlight the miles per gallon their car is gets, and the miles per hour their automobile is capable of doing. Also have them highlight the number of gallons each one of their cars tanks of gas has. Use these as examples of unit rates.
Have each group determine how many miles a week they feel is a reasonable amount that they think they would be driving an automobile. Once the groups decide, share it as a class and write each amount on the board. Have the groups write out how much the& classs average weekly mileage is.
Show how to arrive at the unit rate for miles per gallon by dividing this number by various amounts of gallons. Begin with a very large number, and a very small number and show how as the numbers decrease/increase you arrive at a realistic number of miles per gallon their cars get.
With this figure have each student figure out the number of gallons of gas required for one week, one month, and one year based on the city and highway estimates given on each of their stats sheets. Then have them average the city and highway mpg and do the same with this averaged rate. Have them then take the average of the figures they got for the city and highway numbers separately to see if their calculations agree. Have them record this as a table in their portfolio.
Using the number of gallons each of their tanks of gas has, have the students then calculate how many tanks of gas they would be required to use over those time periods. Using the an arbitrary average for cost of a gallon of gas (maybe $1.15 a gallon) have them compute the cost of fueling each of their vehicles over those time frames.
As an exercise in r=d/t, have the students take the amount of weekly miles they are driving, and divide it by varying amounts of time arriving at a unit rate for miles per hour. Like the mpg above, begin with a small and a large number and show how you get closer to a reasonable number for miles per hour as those numbers increase/decrease. Have each student then figure out how much time they would spend in the car if they averaged 30,35,40,45,50 and 50 miles an hour while driving.
Possible Quick Write in Journal
Other than miles per hour and miles per gallon, where have I seem a rate, and ratio in the newspaper, on TV or in a magazine?
Homework
Find two examples each of a rate and ratios in the newspaper.
Make a simple equation for each of the ones, labeling the units of measurement for the rates, and the labels for the ratios. Write about the difference between the two. Goals
be able to identify and define the different measures within the metric system
be able to convert measures within the metric system
be able to convert measures the metric system to other measures
Warmup
have students do five exercises involving proportions and ratios
Instruction/Class Activity
Drill Group Activity
As an introduction to chapter 7-8 on using the metric system, pose the question of how to figure out how many mile you would get to a tank of gas if your tank was a 20 liter tank. Have students look through the specs sheets of their cars and see if their cars gas tanks are listed in gallons or liters. Then have them look through their sheets and see if the measurement are given in inches or centimeters or millimeter etc. Have the students do exercises involving defining the differences in metric measures prefixes (milli, deci, kilo etc.) and then converting between those different measures.
Automobile Group Activity
Have the students grouped into automobile groups and use their specs sheets or each of their cars to identify all of the metric measures they can find. As an exercise have them calculate:
how many kilometers per hour their car goes
how many liters of gas they get per hour
the dimensions of their vehicles in cm and meters
how many gallons of gas their tank holds if it is listed in liters on the specs sheet, (or) how many liters of gas their tank hold if it is listed as gallons on the specs sheet
how many quarts of oil they would require if the oil capacity is given in liters
Possible Quick Write in Journal
Where in our country do we use the metric system? Do I see it a lot or a little?
Homework
find five examples of metric units at home and perform the conversions done in classMaterials Needed
Edmunds/NADA blue book
newspaper classifies
graphing paper
Goals
students will be able to use percentages in figuring out the depreciation of their own automobiles
students will be able to understand how to make a scatter plot to look at the classes overall data
Warmup
five exercises involving the use of percent
Class Activity/Instruction
Drill Group Activity
Inform the students that it is time for them to sell their car, and they have to find out what is a good deal. Students will begin by assauming they have driven the car for approximately 1 year. Even though they were financing their automobile for two years, they have decided to sell their car after only one.
As a class introduce the topic of depreciation, describing how much value the car loses over the course of owning a car. Discuss how more mileage on the car brings the value down. Have them work through some examples of percentages of depreciation.
Automobile Group Activity
Have them get together in their automobile groups and investigate how much their car has depreciated in price. Make a random amount of miles the cars have all accumulated and throw them in a hat. Have the students individually pick out a mileage amount for their car. Make the mileage amounts between 12 and 25 thousand miles.
Bring in copies of the NADA blue book, or visit
http://www.edmunds.com/edweb/used/usedcars.html
to get the three book value prices for a vehicle of their age and mileage. Have each student record the three values in their portfolio. Have them figure out what the depreciation of trier own vehicle was. Have them record what the three book values of their car are, and comparing them to the beginning price, figure out the percent value their car has lost.
Make a large x -y coordinate system on the board, and have the students come up as groups and put the original value of the car (x-axis) versus the final value of the car (y-axis). Next to the graph, make a table of depreciation percentages of the entire class. After each student plots their values, they will enter the percent depreciation into the table. Each student should record all of this information into their portfolio.
Possible Quick Write in Journal
Where else have I seen depreciation? Do things like land value appreciate or depreciate?
How am I doing understanding the material we have discussed in the last week?
Homework
this homework assignment will be given as preparation for working out an analysis of their final exam
Students will have to determine how much they still have to pay off on the amount they financed for their automobile.
Students will have to determine what is a reasonable selling price for the vehicle while considering how much they still have to pay off in the amount they financed.
Have the students look through the newspapers at a variety of cars approximately the same age in order to make a god judgment about what they think they can sell their vehicle for.
Have them decide on a number they will sell the car for using the blue b'ook as well as the advertisements they see as a reasonable estimate of what they think they can get for the car.
As a final evaluation for the unit, a report for every students automobile will be given. Students will use the information they have put together in their portfolio to make a final presentation about purchasing, owning and selling their vehicle. A critical evaluation of their own car should be made comparing what the cost of owning the vehicle for one year was as opposed to the two years they had intended to finance the vehicle for. The report should be a concise description of the following information, using the concepts they learned during the course of the unit:
Detail the price you paid for the automobile and calculate the cost of financing the automobile over the course 4of two years at 10.5%, 10%, and 9.5% interest rates, putting $10,000 down and financing the remainder.
You sold the car after one year.
Show how much your car has depreciated in value, and assume that you sold it for that amount. Calculate the remaining portion of your loan that has to be paid off.
Determine the amount of total interest you paid.
Determine the interest you would have paid had you financed the car over the entire two years.
Determine what the value of the car would have been after depreciation after two years.
Calculate the cost of fueling the vehicle for the one year, assuming you drove the car for 12,350 miles.
From your statistics sheet for fuel economy, using the average of city and highway driving calculate the cost of paying for the fuel for the vehicle assuming you spent an a0verage of $1.15 per gallon of gas.
Represent your data describing how many tanks of gas you required monthly, and annually and calculate the monthly and annual cost of fuel.
Calculate how many miles and kilometers, cm and millimeters you drove, how many gallons and liters of gas you used.
Determine the cost of changing your oil every 3,000 miles at a cost of 25.00 a change.
Calculate how many liters, gallons of oil your car used.
Using these numbers and the amount of insurance you had to pay for your vehicle, do a cost assessment of the total cost of owning and operating your vehicle.
Do all of the above for your vehicle over the course of the two years you expected to own the vehicle. Make a critical comparison of all the facts and figures above that compares these figures of one versus two years.PN>@+
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