TITLE: Buying on the Installment Plan
LESSON DEVELOPER: Mr. Richard Glueck
CONTENT AREA AND GRADE: Consumer, Family, and Life Skills - Grade 9-12
TARGET TEACHING DATE: March 2, 2007
SCHOOL: John F. Kennedy High School

STANDARDS:

STANDARD 9.2 (CONSUMER, FAMILY, AND LIFE SKILLS): All students will demonstrate critical life skills in order to be functional members of society.

Strand E. Consumer and Personal Finance: Building upon the knowledge and skills gained in the previous grades, by the end of Grade 12 students will:

5. Use comparative shopping techniques for the acquisition of goods and services.

MATHEMATICAL PROCESSES - K-12

STANDARD 4.5 MATHEMATICAL PROCESSES: All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas.

Strand C. Connections: At each grade level, with respect to content appropriate for that grade level, students will:

3. Recognize that mathematics is used in a variety of contexts outside of mathematics.

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PERFORMANCES:

  • The students will calculate the finance charges and total cost of items they buy on the installment plan.
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SETTING:

Real World Setting: Money management

You are a consumer looking to buy a car. You are faced with buying a car that is listed for $10,000. You have no choice but to finance your purchase. You must determine the amount of your down payment, then calculate your finance charges to determine the final price you will be paying. Once you have completed your calculations, you will discuss with the sales manager who is selling you the car whether or not you want to go through with the deal.

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SMARTSKILLS:

Level I: Acquiring Data - Data students will acquire in this standards-based task:

  • Skills: Using basic math skills such as multiplication and addition to determine down payments, amount financed and final installment price.

Level II: Visualizing Information - Data from Level I that are visualized as information in this standards-based task:

  • Organizing: Students will be able to recognize the steps needed to figure out their final costs of buying an item on the installment plan. 1) Calculating the down payment. 2) Calculating the monthly payment x the number of months. 3) Adding the down payment and the amount resulting from step 2 and subtracting the list price.

Level III: Applying Knowledge - Visualized information from Level II that is applied knowledge in this standards-based task:

  • Making decisions: Student to determine whether they can afford to make a purchase of that magnitude.
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PREFERENCES:

  1. The students will complete the task individually.
  2. Students with special needs will require the following electronic devices:
    Calculator
  3. The school will provide classroom materials such as pencil, paper, notebooks, and classroom time to complete the task
  4. The student's teacher will be involved in assessing student work generated to complete the lesson:.
  5. Performance assessment will be used to determine progress and results:
  6. The assessment results will be reported as a score point on a rubric.
  7. The estimated time needed to plan, teach, and score this task is one to three class periods
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ACTIVITIES:

20-60-20 Teaching Model

Segment One: Mini-Lesson - Estimated Time: 20% of allocated time

During this segment of the lesson:

  1. Teacher will have on the board - as well as in a handout - the objectives which will state that the students will learn the process of buying on the installment plan and calculating the cost of borrowing money.

  2. Teacher will question the students on what they know regarding borrowing money from a lender. This will lead into a discussion of borrowing money. Also, students will be given an Applied Math exercise where they will practice calculating percentages - the foundation needed for calculating the cost of money when borrowing on the installment plan.

  3. I will use a real world example of myself when I purchased my Hyundai Sonata five years ago. I will talk about the things I thought about and discuss why it was important for me to know how to calculate the cost of money.

Technology for this segment: Overhead projector
Materials for this segment: Pencils, calculators, textbook
Student product or performance for this segment: NA
Scoring tool for this segment: Teacher will review the students answers to the applied math. Also, teacher will collect the papers for further analysis and then feedback to students. This will determine if calculating percentages needs to be taught before going into the guided practice portion of the lesson.

Segment Two: Practice - Estimated Time: 60% of allocated time

During this segment of the lesson:

  1. The opening discussion in Segment One will help me to determine their strength of knowledge or weakness of knowledge about the topic of borrowing money. Determining their strengths and weaknesses regarding the math skills needed for this topic was done via the applied math exercise. Also, teacher will introduce the key terms as described in the smart skills section of this lesson plan.

  2. Teacher will explain that by the end of the lesson the students will know how to calculate the cost of borrowing money. They will know: 1) How to calculate the amount of down payment to put down: 2) How to calculate the interest charges on the amount financed: How to calculate the total cost of an item bought on the installment plan. Also, students will be expected to memorize and apply the definitions of the key terms in a real world situation (The purchase of a car on the installment plan).

  3. Students will be follow along in a guided practice exercise - talking the teacher teacher through the steps where applicable. If students cannot talk the teacher through a step, the teacher will model AND explain the step and why the mathematical operations in that step are the way they are.

  4. Teacher will discuss that in the real world they will at some point have to buy a car. Most people do not have enough money to pay cash for the car and avoid the finance charges.

  5. Teacher will encourage dialog during the sample problem, relating each step to a real world scenario when buying a car.

  6. Teacher will model how to: 1) Calculate the purchase of a down payment; 2) Calculate the total finance charges: 3) Calculate the total cost of borrowing money.

  7. After the lesson is modeled - The teacher will field questions from the students to provide further clarification where needed. Students will then do an Independent Activity where they will go into a dealership and calculate the costs of a car costing $10,000, using a calculator. The students will then calculate the same activity on the computer. Teacher will have a pre-formatted document prepared in excel. Teacher will explain that computer spreadsheets make these calculations a lot easier. Teacher will model the activity, then students will complete on the computer. Since this is not a computer class students will not be graded on how well they use the computer. This activity is being used as further enrichment.

Technology for this segment: Overhead projector
Materials for this segment: Pencils, calculator, textbook, workbook and hand out.
Student product or performance for this segment: Students will correctly calculate the costs of borrowing money (car buying).
Scoring tool for this segment: Holistic Rubric

Segment Three: Feedback - Estimated Time 20% of allocated time

During this segment of the lesson:

  1. Teacher will circulate from desk to desk to ensure student understanding. Also, teacher will go over the solution with the students on the overhead.

  2. Teacher will collect the students work to analyze, then provide feedback on what the student needs to be re-taught.

Scoring tool for this segment: Upon completion of the lesson - a formal quiz will be administered to the students covering vocabulary and practical application.

Source of 20-60-20 Model: Mergenthaler Vocational-Technical Senior High School, Baltimore, MD
http://www.learningfront.com/mergenthaler/pages/teaching.html

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SCORING:

New Jersey High School Proficiency Test (HSPT)

Holistic Scoring Guide for Mathematics Open-Ended Items (Generic Rubric)
3-Point Response

The response shows complete understanding of the problem's essential mathematical concepts. The student executes procedures completely and gives relevant responses to all parts of the task. The response contains few minor errors, if any. The response contains a clear, effective explanation detailing how the problem was solved so that the reader does not need to infer how and why decisions were made.
2-Point Response

The response shows nearly complete understanding of the problem's essential mathematical concepts. The student executes nearly all procedures and gives relevant responses to most parts of the task. The response may have minor errors. The explanation detailing how the problem was solved may not be clear, causing the reader to make some inferences.
1-Point Response

The response shows limited understanding of the problem's essential mathematical concepts. The response and procedures may be incomplete and/or may contain major errors. An incomplete explanation of how the problem was solved may contribute to questions as to how and why decisions were made.
0-Point Response The response shows insufficient understanding of the problem's essential mathematical concepts. Their may be no explanation of the solution or the reader may not be able to understand the explanation. The reader may not be able to understand how and why decisions were made.
Source: New Jersey State Department of Education

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RESULTS:

Organize: The following chart displays student data that I assessed and scored for the content standards in this lesson:

Data-Driven Results Disaggregated by Gender and All Students
Content Standard: Calculating down payment, amount financed, installment price, and finance charge.
Students
Scoring Results
Last Name and First Name
Male
Female
All Students
1.   Student 1
1
1
2.   Student 2
1
1
3.   Student 3
3
3
4.   Student 4
1
1
5.   Student 5
2
2
6.   Student 6
3
3
7.   Student 7
3
3
8.   Student 8
3
3
9.   Student 9
0
0
10. Student 10
3
3
11. Student 11   3 3
12. Student 12 0   0
13. Student 13   3 3
14. Student 14 0   0
15. Student 15 2   2
16. Student 16 1   1
17. Student 17 3   3
18. Student 18 3   3
# Of students at the Advanced Performance Level
2
7
9
# Of students at the Proficient Performance Level
2
0
2
# Of students at the Basic Performance Level 6 1 7
% of Students equal to or greater than the Proficient Level (Total # of students at the proficient and advanced levels divided by the total number of students) 40% 88% 61%
% Distance above or below school Annual Measurable Objective (AMO)     11%


Reflect: Out of the eighteen students evaluated in this lesson -- there were ten boys and eight girls. When analyzed by gender, Only 40% of the boys were equal to or greater than the Proficient level. For the girls, 88 percent were were equal to or greater than the proficient level. This particular group of students as a whole was 11% higher than the AMO statistic for mathematics - 2004-2005.

As I look over the results, I am amazed at the disparity in the proficiency percentage between the boys and girls. There is no doubt that for the 60% of the boys that were below proficiency, a supplemental lesson is necessary. The same can be said for the 12% of the girls that were not at the proficient level. As a whole, 61% of the population were equal or greater than the proficient level. With only 61% showing proficient or higher, a supplementary lesson will need to be taught in order to bring the less proficient students up to speed. It must be noted the one female students that scored below the proficient level is a special education student. The rest of the female population was at 100% proficiency or higher. For the the male population, of the 6 students that were not proficient, three are special education students, making the proficient or above percentage 57.

I strongly believe that we can increase the overall proficiency percentage from 61% to over 80% or more. My personal goal is to get EVERY child up to the proficiency level. This can happen by providing different activities for those students that "didn't get it". Either more hands or more visual activities or a combination of the two can help improve the assessment scores.

As I critique myself, the one thing I would do differently is have each student work a different step of the process on the board. I issued the students a handout with the steps as I modeled the procedures for calculating the costs of buying on the installment plan. They used the handout in order to solve the sample problem presented. If the students can recite the steps as they perform the process, the repetition that is being provided to them will prove to be valuable. Constant repetition is the key. Instead of one or two problems, the students will have five problems to solve. I think the biggest problem was memory recall. Once the students were aware of the steps, the calculations were worked out fine. The problem was that students couldn't remember the four steps in the independent exercise if they tried the process without the handout.

Action Plan: My next data-driven lesson will focus on:

Title: Check Writing
Content Area: Consumer/Career Education
Content Standard(s): NJCCCS 9.2
Intent: Students will have to master the necessary skills needed to write checks and balance their checkbooks. The next standard-based lesson will introduce the students the basic concepts used in check writing and balancing the check book.

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