How To Have A Dream House, A Car, And A Vacation, Author(s): Jennifer French , Grade Level: 10-12, Subject Area: Mathematics, - Bring in sales advertisements for stereos, televisions, and other items (keep the cost under $500) that teens want. Let each students select an item they want to purchase. Ask the students how much they are willing to spend on the chosen item? Ask do you have the money right now to buy it? Suppose I offered to give you the item for $15,000 and how much it will ultimately cost. Use this as the start of a discussion about the expense of credit.

Planning Guide

Creating Learner-Focused
Schools

* Madison-Oneida BOCES- This document may not be reproduced in any form without the expressed written consent of the District Superintendent or his designee.

LU Title: How to Have a Dream House, a Car, and a Vacation	Author(s): Jennifer French (adapted from lessons created by Richard Morris of Watertown High School)
Grade Level: 10-12	School Address: Indian River High School, Rte. 11, Philadelphia, NY 13673
Subject Area: Mathematics	School Phone/Fax: (315)642-0125

CONTENT KNOWLEDGE

Declarative	Procedural
The different types of loans available	How to change percents to decimals
The I=PRT formula	How to solve for the missing variable in the I=PRT formula by constructing a table
Students discover the rule of 70	How to use an amortization table
Students establish the best situation for using each type of payment plan	How to create a spreadsheet
	Students investigate how long it takes money to double at a given Internet rate
	Students investigate the effects of compounding investments in intervals less than a year
	Students analyze the effect of making intervals smaller and smaller and begin to see and informal example of the concept of "limit" Students construct a payment schedule and determine how long it will take to pay off a loan and what the total cost will be Students will compare the effects of various monthly payments on total cost and payoff time Students compare how various time schedules affect monthly payment and total cost Students will compare the various scenarios between saving money and borrowing money (sometimes concurrently) to establish the best balance in a given budget

ESSENTIAL QUESTIONS

How much money can you save by putting away $20 a week for fifty years at an interest rate of 5%?
How can making minimum payments on a credit card affect the overall cost of the items purchased?
What are the advantages and disadvantages of mortgages that last 10, 20 or 30 years?
What is the difference between taking a loan from a bank or using "rent to own" credit?
Can you invest the money that you have for a down payment some other way to help your regular budget?

INITIATING ACTIVITY

Bring in sales advertisements for stereos, televisions, and other items (keep the cost under $500) that teens want. Let each students select an item they want to purchase. Ask the students how much they are willing to spend on the chosen item? Ask do you have the money right now to buy it? Suppose I offered to give you the item for $15,000 and how much it will ultimately cost. Use this as the start of a discussion about the expense of credit.

Connection to State Learning Standards

Content Area: Mathematics

Level: Commencement

Benchmarks: Students use technology to acquire, organize and communicate information by entering, modifying, retrieving and storing data.

Benchmarks: Students apply a problem-solving model to identify economic problems or issues, generate hypothesis, test hypothesis, investigate and analyze selected data, consider alternative solutions or positions, and make decisions about the best solution or position.

Students present economic information and conclusions in different formats, including graphic representations, computer models, research reports, and oral presentations.

Standard: Occupational Studies #3A: Information management focuses on the ability to access and use information obtained from other people, community resources, and computer networks.

Standard: Social Studies (economics): Economics requires the development and application of the skills needed to make informed and well-reasoned economic decisions in daily and national life.

Unit Theme: Personal Finance

Standard: MST #1: Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

Standard: MST #2: Students will access, generate, process, and transfer information using appropriate technologies.

Benchmarks: Students explore and solve problems generated from school, home, and community situations, using concrete objects or manipulative materials when possible. Students develop and present proposals including formal hypotheses to test their explanations, i.e., they predict what should be observed under specified conditions if the explanation is true. Students use various means of representing and organizing observations (e.g., diagrams, tables, charts, graphs, equations, matrices) and insightfully interpret the organized data.

Benchmarks: Students access, select, collate, and analyze information obtained from a wide range of sources such as research databases, foundations, organizations, national libraries, and electronic communication networks, including the Internet. Students understand and use the more advanced features of word processing, spreadsheets, and data-base software. Students discuss how applications of information technology can address some major global problems and issues.

Learning Experiences

Declarative Knowledge

What declarative knowledge should e in the process of acquiring & integrating? As a result of the unit, the student will know or understand…

What experiences or activities will be used to help students acquire & integrate this knowledge?

What strategies will be used to help students construct meaning, organize and/or store the knowledge?

Describe what will be done.

The various parts of mortgages including principal, rate and time

Interest Formulas I=PRT formula

The different types of loans available

Students discover the rule of 70

Students establish the best situation for using each type of payment plan

Direct Teaching

Direct Teaching with Hands On Practice

Internet Research along with comparing advertisements

Students will complete a large number of examples involving the investment of money at various rates and times

Students will use the scientific method to hypothesize and test their hypothesis to draw conclusions

KWL

Practical examples will be used to help students see how their money will increase pending various interest rate and lengths of times

KWL

The teacher will help students to discover new information for themselves

Students will draw conclusions and organize their thoughts using charts and graphs

Instructor will discuss the parts of a mortgage

Students will practice their algebra skills while solving interest problems, some problems will be done singularly, while others will involve a team approach

Students will complete a chart based on the results of their calculations, they will be asked to work in small groups

Students will complete a chart based on the results of their calculations

Students will investigate a large variety of payment plans (One's that allow low monthly payment, credit cards that do not preplan the time (length) of the loan and bank loans that require higher payments over a predetermined length)

Students will prepare a detailed writing assignment incorporating graphs and charts to support the arguments established for using each payment plan

Learning Experiences

Procedural Knowledge

What procedural knowledge will students be in the process of acquiring & integrating? As a result of this unit, students will be able to:

What will be done to help students construct models, shape & internalize the knowledge?

Describe what will be done.

Change percents to decimals

Solve for the missing variable in the I=PRT formula by constructing a table

How to create a spreadsheet

How to use an amortization table

Students investigate how long it takes money to double at a given interest rate

Students investigate the effects of compounding investments in intervals less that a year

Students analyze the effects of making intervals smaller and smaller and begin to see an informal example of the concept of "limit"

Students will compare the effects of various monthly payments on total cost and payoff time

Students compare how various time schedules affect monthly payment and total cost

Activation of Prior Knowledge, Mnemonics will be used to assist them in retaining the information

Practice and error analysis

Students will have the opportunity to practice the steps of entering the correct formulas

Over the course of the unit they will create a number of spreadsheets, varying the compounding interval

Students will use charts, pairs will share what they discover about the types of mistakes they made and point them out to the class

A class discussion will occur with reciprocal teaching to discuss the used of the rule of 70

Students will practice changing the intervals and record results in an organized chart to allow them to make conjectures

Students will fill in charts and use deductive reasoning to answer teacher directed questions

This exercise always results in students thinking their spreadsheet is broken because when the payments become to low, the loan is never paid off

The shock of seeing how long making minimum payments takes and the cost always causes a major discussion with the students explaining to one another why this can happen

Group discussion will occur as students will offer suggestions on how to convert percents to decimals and decimals to percents, they will then test their hypothesis and try to come up with a method to help other students remember the rules

Students will work out a variety of examples, they will be encouraged to look for patterns and make estimations

Students will work in pairs following a set of directions, they will test their spreadsheet with given examples to verify the formulas are entered correctly

The students will complete worksheets in dyads to check their answers

Students will enter various information in the table and determine the total cost of the loan, they will see how different interest rates or number of years to pay off the loan will effect the total cost

**Students will use an amortization table to change the compounding interval, they will then compare the investments after twenty years and see how the interval effects the final result

Students will use a spreadsheet to change the interval, they will investigate how compounding in small intervals will reap higher returns

Students will use a spreadsheet to change the number of compounding intervals from yearly, to quarterly, to monthly to daily, they will then compare the final cost of the loan

The students will systematically change the monthly payment on a "credit card" loan, each time making it smaller, they will record the length of time it takes to pay off the loan as well as the total cost of the loan

Learning Experiences

Extending and Refining

What knowledge will students be extending and refining? Specifically, they will be extending and refining their understanding of…

What reasoning process will they be using?

Describe what will be done.

Understanding of loans and investments. They will try to establish a balance between the two in a given budget.

Comparing

Classifying
Inductive Reasoning

Deductive Reasoning

Error Analysis

Analyzing Perspectives

Constructing Support

Abstracting
Other:

Students will be asked to decide how they will live within a given (bare bones) budget over a five year period. They will have options to borrow and save money while being required to have a car and various other "toys". They will have to decide the best balance between borrowing and saving money. They will be asked to write the rationale for their choices.

Planning Guide

Unit:

Step 1	Step 2	Step 3
*What knowledge* will students be using meaningfully? Specifically, they will be demonstrating their understanding of and ability to...........**	What reasoning process will they be using?	Describe student's products and performances and the criteria for evaluation.
Students will be able to calculate interest on loans and savings compounded over a variety of intervals. They will be able to read on amortization table to determine payments and costs on a mortgage. They will be able to look at payment plans and determine which ones are "rip offs".	[X] Problem Solving (seeking to achieve a goal by overcoming constraints or limiting conditions) [X] Experimental Inquiry (generating an explanation for a phenomenon and testing the explanation) [X] Systems Analysis (analyzing the parts of a system and how they interact) [ ] Other:	Products/Performances Students will research the best price on an item using the Internet with bookmarked sites. Once the best price is found, they will research to find three different loan options. They will write up an explanation for the plan they choose. Specific graphs and explanations must be given to substantiate their decisions.
		Criteria for evaluation Accuracy of the research. Creating accurate graphs that illustrate the benefits of their plan of choice. Providing an accurate explanation of their plan of choice.

Rubric:

Key Questions: This rubric will be used to evaluate the students' final projects.

	Element #1	Element #2	Element #3	Element #4
Elements Scale	Accuracy of the research	Creating accurate graphs that illustrate the benefits of their plan of choice	A clear connection is made between student writing and graphs	Conclusion
Weights	1	2	4	1
4	Student is able to accurately obtain pricing on item and select loan information appropriate to their item	Appropriate type of graph chosen, information entered accurately, and graph is formatted neatly	Writing clearly defends the student's choice and includes accurate references to the attached charts	Students accurately applied appropriate payment plans
3	Student is able to accurately obtain pricing on item but incorrectly selects loan information that is inappropriate to their item	Appropriate type of graph chosen, information entered accurately, but graph is not properly formatted	Writing is evasive but accurate references to the charts are included	Students accurately applied inappropriate payment plans
2	Students obtains inaccurate pricing on item but correctly selects loan information that is appropriate to their item	Graph chose does not illustrate the student's purpose or information is entered inaccurately	Writing is clear but references to chart are missing or incorrect	Student inaccurately applied inappropriate payment plans
1	Student is unable to accurately obtain pricing on item and incorrectly selects loan information that is inappropriate to their item	Graph chosen does not illustrate the student's purpose and information is entered inaccurately	Writing is unclear and references to charts and graphs are inaccurate or missing	Student inaccurately applied inappropriate payment plans
0	Student does not obtain pricing or loan information	Graph is omitted	Writing assignment not submitted	Payment plans are not used

NOTE: Rubric or other performance assessment instruments may be used.

Finance Unit Writing Rubric

+5 Response Shows Maximum Effort	+4 Good Effort Shown	+3 Some Effort Shown	+2 Minimum Effort Shown	+1 No Effort Shown
Response is written in complete sentences	Response is written in complete sentences	Response is written in complete sentences	Attempted to respond but some parts were incomplete	Response is incomplete
Responds to all parts of the questions	Responds to all parts of the questions	Responds to most of the questions	Attempted to write sentences completely	Did not write in complete sentences
Uses specific detail to support their ideas about characters and their plan of choice	Used some specific detail to support ides about their plan of choice	Used a little specific detail to show support for ideas about their plan of choice	Little specific details were used for support	No specific details to support the response, too much general information
Opinion state-ments or general-izations have been supported fully or "proven" using specific detail from the graphs	Provided a fair amount of detail from the graphs to support opinion statements and generalizations	Attempted to support opinions and generalizations using specific detail from the graphs	Generalizations or opinions were not fully supported or explained	Only opinion statements were given (show me - don't tell me)
Real life examples are thoroughly explained and specific examples have been given	Real life examples had a fair amount of specific detail to provide a clear explanation	Attempted to explain opinions but did not fully support them	Some parts of the response are unclear	Response does not make sense and fails to respond to the question
Response is clearly written and logically responds to the question	Response is clearly written and logical	Real life examples lacked detail and were unclear	Real life examples were not explained or specific

Have You Considered These Yet?

Learn to Learn Skills: Students will learn skills about how to use a spreadsheet that will apply to many other situations. They will learn how to find an Amortization table using the Internet that can be used outside of school when a loan is needed. They will also use the Internet for research, thus practicing this real life skill.

Assessment Modifications: Cooperative learning groups and peer tutors will assist students who are struggling with concepts. Real life examples will be used whenever possible to invoke meaning.

Unit Schedule/Time Plan: Unit takes approximately eight weeks to complete. Some lessons can be shortened if time becomes an issue.

Written Overview: Americans are involved in a plastic society. When we buy merchandise on credit, it is important that we know what we are getting ourselves into. As we gain liquid assets, we need to know how to analyze investment programs to see how our money will grow. It is important that we all understand the concepts of simple and compound interest. We all need to develop an intuitive feel for the relationships between amount of principal, interest rate, time, intervals of compounding, down payment and payments to principal.

The methods used to investigate the relationships in this unit are exploitative and systematic. Formulas are not evaluated by algebraic methods, but rather by systematic approximations. At first, calculators suffice to make decisions. However, students are quickly working on solving problems where a spreadsheet is necessary to facilitate the analysis.

The main objective is that after completing the unit, they will be better able to make sensible decisions regarding credit. They will be able to determine when charging is a sensible thing to do and when it makes sense to save, lay away or go without. Students must realize that the "I want it now" attitude is a very expensive one and one that may lower their standard of living for life. Hopefully, they will gain the ability to compare credit plans between company A and company B. In addition, they should be able to determine if their monthly bills are correct, or at least reasonable correct. Students must realize that their ignorance and desires make them prey for many so called "business people".

Mastery is determined by the ability to answer worksheet questions correctly and an increasing ability to get a good first approximation when solving the problem solving activities. The latter implies an increase in the powers of estimation and that an intuitive feel for this area of study has been attained.

All work is to be completed under the supervision of the classroom teacher. Homework should be related projects. Students should always have a project to work on that counts at least 10% of their grade. Students who complete classroom work will either assist another students having difficulty or continue working on their project.

It is expected that at first, most students work in dyads. As most of them become adept at using the spreadsheet, they will begin working independently.