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Chapter 1: Modeling

Greetings--Welcome to the new school year!

Entry Task



Find your seat efficiently and honestly.
Meet your peers & teacher, orient to the class, and prepare for the years’ learning.

JR: What are your goals in this class for this year?
Complete Getting to Know You.

Return signature from the course Syllabus.

Bring two hardbound "theme books"--one for journal and one for homework.
Define "Pi."  Note: write this in your homework notebook, NOT your journal.  :-) Begin Olympic Games graph.

JR:  What is the difference between a table and a list (according to a TI-83+ or TI-84+ calculator)?  Note: explicate a difference rather than merely defining or describing each.
Graph the Olympics Games data on paper.  Include all relevant parts of the graph and use your graph to estimate the winning times for 2012 & 2032.  Be sure to show all relevant work.
How confident are you in your prediction of the winning times for 2012 & 2032? Locate the winning times for 2012 and compare to your estimate.  How did the actual time for 2012 compare to the estimate you computed?

Share graphs in your area.  After seeing all eight graphs, discuss similarities and differences.

Modeling data on the calculator.

Create an account on ClassMarker.  Save your password in a secure place!!!

JR:  Give several reasons why the estimates of the winning times for 2012 & 2032 varied so much across the class.
Enter the Olympic Games data into your calculator's lists and model as
  • Linear
  • Power
  • Exponential
then use the models to estimate the winning times for 2012 & 2032.  Comment on your confidence in these estimates. Show all your work and explain your process.
Open a browser page on your computer pointed to the class Website.  Open your copy of the class syllabus.
Take the syllabus quiz on ClassMarker.  You will have a maximum of 15 minutes.  Log off the Website and close the lid of your computer when finished.

More about modeling data on the calculator.

Graph Pressure vs. Altitude (by hand).  Find a part of the data that is approximately linear, draw the line on your graph, and determine the slope of the line.  Note that you are NOT being asked to model the data set!

JR:  What are some other models for data besides linear, power, and exponential? Explain their similarities and differences.
Finish the graph and question.
Of what benefit is the knowledge of air pressure versus altitude? Give several examples. Graph and model the Pressure vs. Altitude data on your calculator.  Try various models for fit and indicate which one you believe models the data best.

JR:  Use your graph to explain at what altitude air pressure will be zero.  Tell how this is reasonable.
Continue creating models for the pressure vs. altitude data.Which one(s) appear to fit the data the best?  Explain.
Block Period
Suggest a method to measure a person's forearm length using meter sticks wherein the least amount of measurement variability is introduced.  You may discuss this with your table partner. Collect personal measurement data (height, arm span, forearm length, foot length) for each person in class.  Measure carefully!!!  Distribute the data to all class members and Dr. Edge.

JR:  List several "practical applications" in the real world that would use the outcome of today's investigation.  List all "confounding conditions" (when the relationship will give the wrong answer) and explain why.
Graph (by hand) height vs. forearm length on graph paper & create a mathematical model.  Include all relevant parts of the graph and use your model to estimate the forearm length for persons 200 and 150 cm tall.  Comment on your confidence in this estimate.
Get ready for the quiz!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Quiz: data modeling.

JR:  Explain why one would create a model for data, under what circumstances the model would be appropriate for the data, and the circumstances for which a model would not be appropriate.
Graph (by hand) height vs. arm span on graph paper & create a mathematical model.  Include all relevant parts of the graph and use your model to estimate the arm span  for persons 200 and 150 cm tall.  Comment on your confidence in this estimate.
Compare your estimates from the last two homeworks with the students at your 4-top.  Look for
  • Which model was applied to the data.
  • The model written explicitly.
  • Substitution into the model and all steps to a solution.
  • Answer written in sentence form.
  • Statement on confidence is present and makes sense.
Are all of the above in agreement?  Why/why not?
Debrief of personal measurement investigation.

JR:  Explain how "confidence" could be improved in the personal measurement investigation and how confidence relates to data collection techniques, the choice of measurement tools, and which mathematical model is employed.  
Read the Trig Overview on  Copy the diagrams along with the second and third tables into your homework notebook.

Remember to bring your ruler, protractor, and compass!

Please complete the Student Consent form for Mr. G's TPA requirement, regardless whether you give permission or not.
Give an example  of a trig problem you know how to do.
Complete the online Trigonometry Online Test.  Calculator allowed.  Note: this is NOT for a grade--it is a pre-test of your understanding.  Work all problems in your homework notebook.

When finished with the test: create an account, view your score, WRITE your score in your homework notebook, and review each problem.  Mark each of your correct answers with a check-mark, each incorrect with an x-mark.  Report your score to Dr. Edge.

JR:  Explain how to compute where to place the foot of a 6 m ladder relative to the base of a wall so the angle the ladder makes with the ground is 60°.  Include a diagram.
Find a long, straight object, such as a ladder.  Measure its length, then lean it against a wall.  Perform the following measures
  1. The height of the top of the object from the base of the wall.
  2. The distance of the foot of the object from the base of the wall.
  3. The angle the ladder makes with the horizontal surface on which it rests (presumably a floor or the ground).
Compute each of the following
  • The length of the ladder using measures #1 and #2 above.
  • Measure #1 using measure #3 and the known length of the ladder.
  • Measure #1 using the known length of the ladder and a new measure for #2 that is 20% larger than the previous one.
Record all facts and calculations in your homework notebook.
*Unless otherwise noted, homework is due the next class day.