Visualizations

1
Visualizations

• In
• Middle School
• Math and Science

Revitalise Project Illinois and North Carolina
http//revitalise.ncsa.uiuc.edu/
2
Programs Resources

• GnuPlot
• Perl
• Internet

• EasyViz
• Excel
• Clyde/AVS

3
MathActivities
4
Three Dimensional Visualization of Home Mortgage
Interest Forfeiture

• Excel and EasyViz graphics illustrate how loan
  amount, interest rate and repayment time effect
  total amount of interest lost during loan
  repayment

5
Purpose

• Three dimensional visualization software is a
  valuable tool to give a comprehensive overview of
  data. Students benefit from this technology when
  it is available in their math classes, as it
  gives them an opportunity to see how the data
  pieces fit together.

6
Presented by

• Becky Ibele
• Teacher of regular 8th grade math and high
  school Algebra 1 and high school Geometry
• E. B. Aycock Middle School
• Pitt County School System
• Greenville, N. Carolina
• Participant in the Revitalise collaborative
  learning experience, locally at East Carolina
  University

7
Appropriate Course Level

• Algebra 1
• Algebra 2

Algebra 1 may be taught in 8th grade.
8
Prerequisites

• Knowledge of Microsoft Excel Spreadsheet
  application
• Access to EasyViz software, available over the
  web through Revitalise
• Students should have explored elementary
  exponential functions and their graphs prior to
  this experience, using graphing calculators with
  2 dimensional visualization

9
The Money Reality Show

• For an earlier class project, to set the
  stage for the topic of this presentation,
  students became homeowners, and were randomly
  assigned a home purchase price, down payment
  amount, interest rate and loan pay back period.
• They used a formula found in their
  textbook to calculate the total amount of
  interest lost, above and beyond the amount to pay
  back the original loan.

10
Why bother?

• Excellent object lesson for students who will one
  day own credit cards.
• Easy way for students to see how their mortgage
  compares to those of other students. Who loses
  the most interest?
• Useful introduction to future classroom activity
  involving students imaginary purchase of a car.

11
Module Description

• Students were introduced to the formula which is
  used to calculate total interest lost on a loan
  of amount A
• Total Int. Lost
  A(in/(1-(1i)-n)-1)
• Here the annual interest rate, divided by 12
  (monthly rate), is i, and n is
  the number of months over which the loan is
  repaid.
• Students next enter the formula into Excel
  spreadsheet, a portion of which is displayed on
  the next slide.
• Two possible 3D graphs from Excel will follow.

12
Portion of Excel Spreadsheet

• annual ir 0.05 0.055 0.06 0.065
• monthly ir 0.00416 0.00458 0.00500 0.00542
• no. of months total interest lost per 1000 of
  loan amount
• 12 27.29 30.04 32.80 35.56
• 24 52.91 58.30 63.69 69.11
• 36 78.95 87.05 95.19 103.36
• 48 105.41 116.31 127.28 138.32
• 60 132.27 146.07 159.97 173.97
• 72 159.56 176.33 193.25 210.31
• 84 187.25 207.08 227.12 247.35
• 96 215.35 238.33 261.58 285.08
• 108 243.87 270.08 296.62 323.49
• 120 272.79 302.32 332.25 362.58
• 132 302.11 335.04 368.45 402.34
• 144 331.84 368.25 405.22 442.77
• A 12 year (144 month) loan at 6 rate produces a
  loss of 405.22 per 1000 of loan, or a total of
  81,044 interest lost during repayment of a
  200,000 house loan.

13
The S values show annual interest rate, the time
in years for the mortgage loan ranges from 1 to
30 years, and the display shows total interest
paid per 100 of loan amount. Notice widths of
color bands.
14
Observation

• Examine band widths on the next slide. The
  graph helps to envision the rate of growth of
  total interest lost in mortgage payments

15
An alternate graph from Excel, showing total
amount of interest as about 95 interest per 100
loan for a 30 year mortgage at 5, or about
237,500 interest lost on a loan amount of
250,000. (An amortization table will give the
result that 233,300 is lost.)
Follow at this height (5) between red bands on
backdrop.
Height is at about 95
16
Noticing a trend?

• The next slide shows a result from EasyViz where
  color bands group outputs that appear in equal
  size ranges of output data.

17
The color bar at the far left shows amount of
interest lost per thousand dollars of loan
amount. For a 29 year repayment period this
would be about 1517 per thousand, for a 5 loan.
18
Assessment Techniques

• The second excel spreadsheet will be projected
  onto a screen at the front of the classroom.
  Students will go to the front and show
  approximately where their data fits into this
  graph, using an appropriate pointer. They will
  also display on a large sheet of paper their
  interest rate and time repayment period.
• Reflective writing should follow this activity.

19
Amazing Discoveries

• A 200,000 home loan for 30 years at 5 interest
  causes 186,640 interest lost, not much less than
  the original amount financed for the home.
• The same home loan amount, if financed for 15
  years, at the same 5 interest rate, loses a
  total of
• 84,760 amount interest, using greater
  monthly payments. This saves over 100,000
  dollars.
• At 10 interest rate, the same 200,000 home loan
  would involve 187,000 interest lost, if repaid
  in 15 years, and 432,160 interest lost, if
  repaid in 30 years, more than twice the home loan
  amount!!!

20
Relevant Links/ Related Resources

• An excellent link to an interactive web site is
  www.bankrate.com/gookeyword/amortization-calculato
  r.asp
• A related site is at http//www.interestratecalcul
  ator.com/mortgage/index.html

Surf the Web
21
National Standards Addressed

• Grades 912 Expectations all students should
• understand and perform transformations such as
  arithmetically combining, composing, and
  inverting commonly used functions. . . using
  technology to perform such operations on
  more-complicated symbolic expressions . .
• interpret representations of functions of two
  variables

22
ScienceActivities
23
Presented By

• Vivian Roebuck Smith
• 7th Grade Science
• EB Aycock Middle School
• Greenville, NC
• Pitt County Schools

24
Purpose

• To expose students to visualizations to enhance
  instruction.
• To allow students the opportunity to create
  visualizations in various content areas.

25
GnuPlot Activities

• Chernobyl The spread of radiation to the United
  States
• Glaciers Mass Changes
• Glaciers Air Temperatures

26
(No Transcript)
27
Alaskan Washington State Glaciers
USGS Website http//ak.water.usgs.gov/glaciology/

28
Glacier Pictures
Wolverine Gulkana
South Cascade
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
Excel Activities

• Cancer in the US
• Breast Cancer (used Perl)
• Bladder, Brain, Colon, Hodgkins, Leukemia, Liver,
  Lung, Melanoma

33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
Internet Resources

• Seasonal Migration of Snow Cover Animation
  http//www.classzone.com/books/earth_science/terc/
  content/visualizations/es1501/es1501page01.cfm?cha
  pter_novisualization
• Various Weather Related Visualizations
  http//earthsci.org/weather/weaimages/weaimages.ht
  ml
• Tornado Animation http//www.sci.utah.edu/
  sci_gallery/2003_lig_3Dvector-fields/splash.mpg
• Brain Tumor Visualization
  http//www.sci.utah.edu/sci_gallery/vol-rend_brain
  /2002_tumorvis.mpg

38
Summary

• Three dimensional visualization needs to be used
  in the math and science classrooms. It
  synthesizes a total picture from the clues
  delivered by data samples of real life. It gives
  us a more comprehensive view our world.