**1-3 Mathematical Models**

By

The

Way,

Here in 20012 AD,

The World

IS ENDING

Katelyn Barnett

So the Council of Elders and Global Elder Harvi-San,

Decided to send out teams to the past,

to change the future

And thu

And thus was born our Mission!

h

phase five

grow old and die

heros

**Fall 2013**

Agenda:

Discuss/Turn in HW

Types of Models

Developing a Math Model

Introduction to Logger Pro or Graphical Analysis from Vernier (easy graphing software)

Turn in HW:

**Thursday, 8/29/2013**

Any questions?

Models instead of "Truth"

Create interpretations of natural phenomena to organize experience.

Examine experience for additional data to support or contradict the interpretations.

Use the interpretation, or alter it as necessary when data doesn't fit.

MODEL DEVELOPMENT:

MODEL TESTING:

MODEL DEPLOYMENT and RE-MODEL:

Key scientific ideas which will permeate Unit 1:

2. Measurement

4. Graphs & Variables

3. Evidence Based Conclusions

Unit 1: Scientific Thinking & Measurement

1. What is science?

Announcements:

Lab #1 is split into two parts.

Part A will be due 1 week from today, Tues 9/3/2013.

Part B will be due on Mon 9/9/2013.

When you turn in Part A, be sure to keep data from Part B; we will discuss how to analyze it next week so you know what to include in Part B's report.

Types of Models:

Mathematical Models:

can provide successful quantitative predictions

e.g. finding a linear equation to fit some data

NOT an exact reproduction of what is really happening

extremely useful, but always remember its LIMITATIONS

Working Models:

simplified mental images for physical systems

e.g. the sphere model for the earth

...the particle model for the solar system

=

structural complexities are neglected

always simplified or idealized

Does this mean these working models are not useful?

Limitations of Working Models:

Analogue Models:

make an

analogy

between something already known and something new

e.g. the human circulatory system may be

analogous

to your homes' hot water heating system

~

the analogous system is more familiar than the new system

Are systems and their analogue models

equivalent?

Advantage of Analogue Models:

Does this mean analogue models should not be used?

The graph pictured shows some data about the growth of Ms. Warble’s son Jaen. When Jaen’s weight and age were plotted, it made a fairly straight line. Ms. Warble drew a “best fit” line through the data. Use it to answer the questions:

Example2:

Example 1 (cont):

d. Calculate baby weight at an age of 20 weeks.

Model Deployment:

e. Calculate when the baby will weigh 60 lbs.

f. Calculate baby weight at an age of 20 YEARS.

Example 1 (cont):

a. How many pounds does the baby gain each week?

b. How much did the baby weigh at birth?

c. Write an equation that matches the baby’s graph.

Model Development/Test:

Re-modeling:

h. Is a LINEAR model good for the entire baby's life? What might be a better model? Explain.

g. How would this equation change if Jaen actually lost weight each week? What about if he was born at a different weight? Explain.

Example 1 (cont):

Independent vs. Dependent Variable

Use the description to identify the variables and discuss what needs to be controlled for a "fair test":

A science class puts wide wheels onto a small cart and lets it roll down an inclined ramp and then across the floor. They measure the distance the cart travels. The investigation is repeated using the same cart but this time fitted with narrow wheels. The angle of the incline of the ramp remains constant. The mass of the cart is kept constant.

Example 1:

Graphing Data to get a Mathematical Model

Traditionally, the independent variable goes on the horizontal axis.

wheel width

distance

Lab Report Format

This will be the format for Lab #1B Circle lab.

Purpose

Apparatus/Procedure

Raw Data

Evaluation of Data

Conclusion

See more details on blackboard under "Course Information" tab in Lab Information folder.

Find the mathematical model.

Interpret the graph and equation.

"Analysis of Data" section of Lab Report.

Make an appropriate graph.

Apps on "my asu"

Look for My Apps

Log in again

Look for Graphical Analysis

See if you can make it run and let me know!

Graphing Technology:

Vernier Software

Graphical Analysis

Logger Pro

Available anywhere from an APP on my asu

Free download link available on blackboard under Course Information tab

Now finish Classwork 1-3. For the back, you may want to access graphing technology.

Homework:

Lab 1A due Tuesday.

HW 1-3 will be posted on blackboard with due date-will consist of graphing practice