Home            Forums            Grades Pre K-2            Grades 3-5            Grades 6-8            Grades 9-12

 

 

Instructional Plan Template

Mathematics Governor’s Institute 2004

(Download as Microsoft Work document or .jpg: Too Fast and Furious.doc, vocabulary.doc, Modeling example 1.jpg, Modeling examole 2.jpg, Modeling example 3.jpg, PROBLEM.doc, Frayer model.jpg, Project Fast and Furious.doc)

 

Names of group members: Anne Caggiano, Martin Carr, Lucille Pritchard, and Denise Byars

 

Topic/Theme: Depreciation /Exponential Decay

 

Level: Algebra I and Algebra II

 

Time Element: 2 class periods or 1 block

 

NCTM Standards Addressed: Algebra and Data Analysis

 

PA Math Standards Addressed: 2.6 and 2.8

 

Math Assessment Anchors Addressed: M11.D.1, M11.D.3, M11.D.4, M11.E.1, and M11.E.4

 

Reading Assessment Anchors Addressed: R.11.A.2

 

Objectives: Students will analyze collected data.  Students will explore depreciation by analyzing data and finding the exponential equation.

 

Instructional Strategies and Plan (include strategies used to help different types of learners, i.e. auditory, visual, etc):

1.      Pre-teach vocabulary, review content

2.      Model worksheet

3.      Complete worksheet

4.      Analyze data

5.      Generalize results both algebraically and graphically

6.      Predict future car values

 

Materials/Resources:

1.      Internet (Kellybluebook.com and newcar.com)

2.      Newspapers

3.      Car dealerships

4.      Calculator

5.      Charts/tables/spreadsheets

6.      Graph paper

7.      Rulers

8.      Worksheets

9.      Overhead projector

10. Overhead calculator

 

Interdisciplinary Connections:

·         Reading: Vocabulary

·         Technology: TI-83 PLUS calculator, computer

·         Other: Science, Business, Consumer Math, Life Skills

 

Assessment Strategies:

·         Formative Evaluation (checking student understanding during the lesson):

1.      Teacher will check student’s work.

2.      Teacher will question students.

 

·         Summative Evaluation (How will it be determined that the objectives were achieved?):

1.      Teacher will conduct a post research discussion

2.      Students will complete the Frayer Model for concept reinforcement

3.      Teacher grading of worksheets

 

Correctives/Remediation:

Students will conduct a second exponential decay problem:  NCAA  Tournament, electronic equipment, endangered species, etc.

 

Extensions/Enrichment:

1.      Students will predict which car depreciates the least and why.

2.      Students will be able to find both time and value.

3.      Students will be able to complete the project “Fast and Furious”—Follow up discussion

4.      Students will be able to investigate other examples of depreciation

 

Special Accommodations (special needs students)

·          Description of the Special Needs student selected:

1.      Severe hearing loss in both ears

2.      Language comprehension, expressive skills, and reading skills are 4 years below grade level

3.      Basic math computation is above grade level

4.      Difficulty with word problems and abstract concepts

5.      Uses an assistive listening device

6.      Has difficulty comprehending lengthy verbal explanations

7.      Does not use sign language

8.      Learns best when using visual representation of information or a process

 

·          Accommodations to use with this student:

1.      Special seating

2.      Provide a buddy

3.      Teacher microphone system

4.      Overhead projector

5.      Create a quiet classroom atmosphere

6.      Abbreviate verbal instructions.  Speak clearly and avoid long-winded verbalizations when possible.

7.      Written directions

 

 

DEPRECIATION AND EXPONENTIAL DECAY

 

 

VOCABULARY

 

 

 

 

Depreciation

 

 

Initial value

 

 

Base

 

 

Exponential Equation

 

 

Decay graph

 

 

Resale Value

 

 

Net Change

 

 

Data

 

 

Scatter Plot Graph

 

 

Prediction

 

 

Regression Equation

 

 

 

 

 

 

 

 

 

 

 

 

Depreciation                                                                                                                   Name______________________

 

 

CLASS WORKSHEET 1  (Use Chart 1)

 

 

 

Pat wants to buy a used car, which has the best resale value.

 

Pat plans to sell the car after three years.

 

The following chart gives the current values and the rate of depreciation of some cars.

 

Find the value of each car model after three years, by completing the given charts.

 

Which car is best for Pat?

 

Chart 1

 

 

Year/model of car

 

Used car price

Rate of depreciation (%)

Rate of depreciation (decimal)

 

1 - decimal (base)

 

Equation for depreciation

 

Value in 3 years

2001 Corolla

9,940

9.50%

 

 

 

 

2001 Jetta

10,000

6.50%

 

 

 

 

2001Malibu

9,940

14.30%

 

 

 

 

1996 Maxima

9,800

4.70%

 

 

 

 

1999 Miata

7,000

5.40%

 

 

 

 

1998 Sunfire

7,000

12%

 

 

 

 

 

 

 

 

Depreciation                                                                                                                                                  Name ________________________

 

 

CLASS WORKSHEET 2 (Use Chart 2)

 

Complete the Chart 2.

 

New car

Price

Rate of depreciation (%)

Rate of depreciation (decimal)

1- decimal

(base)

Equation for depreciation

over 8 years

Acura RSX

24,000

6%

 

 

 

Ford F150

21,000

8.7%

 

 

 

 

Saturn

11,800

11.2%

 

 

 

Sebring

22,000

9%

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Make a scatter plot graph for one of these cars for 8 years.              

 

Identify the graph.

 

Report similarities and differences.

 

Give other examples of depreciation

 

Number of years

Value of car

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Depreciation                                                                                               Name_____TEACHER_____

 

 

CLASS WORKSHEET 1  (Use Chart 1)

 

 

 

Pat wants to buy a used car, which has the best resale value.

 

Pat plans to sell the car after three years.

 

The following chart gives the current values and the rate of depreciation of some cars.

 

Find the value of each car model after three years, by completing the given charts.

 

Which car is best for Pat?

 

Chart 1

 

 

Year/model of car

 

Used car price

Rate of depreciation (%)

Rate of depreciation (decimal)

 

1 - decimal (base)

 

Equation for depreciation

 

Value in 3 years

2001 Corolla

9,940

9.50%

0.095

 

0.0905

Y = 9940(0.905)^3

7368

 

2001 Jetta

10,000

6.50%

0.065

0.935

Y = 10000(0.935)^3

8174

2001Malibu

9,940

14.30%

0.143

0.857

Y = 9940(0.857)^3

6256

1996 Maxima

9,800

4.70%

0.047

0.935

Y = 9800(0.953)^3

8482

1999 Miata

7,000

5.40%

0.054

0.946

Y = 7000(0.946)^3

5926

1998 Sunfire

7,000

12%

0.12

0.88

Y = 7000(0.88)^3

4770

 

 

 

 

Depreciation                                                                                                              Name _____________TEACHER_________

 

 

CLASS WORKSHEET 2 (Use Chart 2)

 

Complete the Chart 2.

New car

Price

Rate of depreciation (%)

Rate of depreciation (decimal)

1- decimal

(base)

Equation for depreciation

over 8 years

Acura RSX

24,000

6%

0.006

0.94

Value = 24000(0.94^number of yrs)

Ford F150

21,000

8.7%

0.087

0.913

Value = 21000(0.913^number of yrs)

 

Saturn

11,800

11.2%

0.112

0.888

Value = 11800(0.888^number of yrs)

Sebring

22,000

9%

0.09

0.91

Value = 22000(0.91^number of yrs)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Make a scatter plot graph for one of these cars for 8 years.              

 

Identify the graph.

 

Report similarities and differences.

 

Give other examples of depreciation

 

Number of years

Value of car

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                                                                                                                            

 

 

 

NAME_________________________

 

 

 

DEPRECIATION PROJECT

“FAST AND FURIOUS”

 

 

Choose a new car to depreciate over 8 years, which you believe has the best resale value.

 

You may use Kellybluebook.com, newcar.com, other websites, newspapers and car dealerships to get your information.

 

The car you choose may not be one we already discussed.

 

Cite your references.

 

 

1.      Give the make/model

 

2.      Provide a picture of car (if possible)

 

3.      Find rate of depreciation

 

4.      Give the value of the car each year in a table

 

5.      Graph the information

 

6.      Give the resale value

 

7.      Find the regression equation

 

8.      Present your findings by: (choose one)

           

·        Overhead presentation (using chart/graph)

 

·        Power Point presentation

 

·        Written report

 

       9.   Due Date ________________________

    

 

 

Home            Forums            Grades Pre K-2            Grades 3-5            Grades 6-8            Grades 9-12