VHCC Governor's School Mathematical Modeling Summer 2010


Your first set of tasks:

 

Hands-on activity 1:  Submit Data Form and Pendulum Count.

This activity will be explained when the time comes.  It will be explained in class.

Some First-day Results

 

Java Applets

Second-day notes from students

Third-morning questions

three graphs

Day 3 Quiz

Fourth-morning questions

day_4_afterlunch_quiz.htm

 

Problem Assignment for First Weekend

list of questions days 4-6.htm

2d_weekend_assignment.htm

 

Fifth-morning questions

DERIVE:

day_5_afterlunch_quiz.htm

 

Day 6

Do the game with the grids (take turns sketching segments)

Run the Timer Experiment and submit your results using the current version of the Submit Data Form

Testing Hypothesis regarding Time Intervals.  Hang on to your document until the Submit Data Form has been modified to accept your work.

 

Here's a set of calculations I got last night from a very good student, who set the problem up beautifully, and who should have recognized that there was an obvious error in the arithmetic:

26.5g * (1 mol/(196.9 g)) * ((6.02 x 10^23) / 1 mol) = 8.10 x 10^22 atoms
26.5g * (1 mol/(107.9 g)) * ((6.02 x 10^23) / 1 mol) = 1.48 x 10^22 atoms

Why is it so obvious that there is an error in his results?  How many obvious signs are there that he had an error?

Sixth-morning questions

Day 7

Seventh-morning questions

Last day

Click on the link below to obtain your username, password, related instructions and other necessary information. 

Accessing Login Information; Obtaining Help; VIVA; Accessing your Student Email

 

1.  On a 5 x 5 grid you can get distance 5 in two different ways, corresponding to the vectors <5, 0> and <4, 3>. 

Obviously this is also the case on a 10 x 10 grid.

On a 10 x 10 grid you can get distance sqrt(50) in two different ways, corresponding to the vectors <7, 1> and <5, 5>.

If you don't notice the repetitions, this affects your answer to the question of 'how many different distances are possible on the grid'.

On the final, many students listed the possible distances correctly, but failed to notice one or both of these repetitions (for example listing sqrt(50) twice).  Some student did notice one repetition or the other, but only one student noticed both. 

2.  For vectors A, B and C with the property that A + B = C, it is always true that || A || + || B || is at least a large as || C ||.

Can you give an argument proving that this is so?

3.  The merry-go-round problem will be described on the board.