### Walking, Marching, and Tossing; An Introduction

FIRST TRANSPARENCY • Marching Onto Stage

Ladies and Gentleman - students of all ages:

Welcome to “Out Juggling In My Class.”

A celebration of my thirty four years of teaching mathematics.

That you are here for this
/___M_O_M_A_T_Y_C__And __A_r_k_M_A_T_Y_C___/
/___DeKalb__College__Mathematics___/

Conference means you are outstanding.

Right?

SECOND TRANSPARENCY • Physics of WMT

When you march and toss a ball, the toss looks like a two dimensional parabola.

Maybe y = -(1/4) x² + 16.

The crowd along the street sees a three dimensional pattern of a ball

moving down the street going from side to side.

If marching about "pi" mph, then y = -(1/20) x² + 16 is the corresponding

parabola that a person in the crowd may see.

Let's see ... how fast do you walk?

Some people know from their treadmill experience.

But others may need to experiment.

However, suppose you walk one hundred feet in twenty five seconds.

100 feet in 25 seconds is four feet per second or forty eight inches per second.

At four feet per second, how many miles would you walk in one hour?

I will give you some time to calculate that answer now.

PAUSE costume transition time while they calculate

2.7 plus miles so your rate, r, would be about "e" mph

AHA! You may see a distance formula hidding here.

My students sometimes simulate a Gregorian chant to memorize a formula, like this:

CHANT distance equals rate times time!

Right?

THIRD TRANSPARENCY • Chanting the distance formula

CHANT That is Galileo's constant speed linear model for uniform motion.

Ok, all together now slowly:

CHANT distance equals rate times time.

Ok - so you are not enchanted but -

I know you can be loud, give it another try.

CHANT distance equals rate times time.

Great!

Now we will consider another type of motion.

PROP - Get a bounce ball out.

Please raise your hand if YOU ever used s = (1/2) a t² in your math or science classes.

Remember the constant 980 cm per second squared?

Inches may be a better unit to use for the distances we will talk about today.

Please convert 980 cm per second squared into inches per second squared units.

Use 2.54 cm = 1 inch.

Take some time to calculate that answer now.

PAUSE and encurage them to calculate

Ok, you got it!?!

Then you know, s = (1/2) a t² is the free fall motion equation.

Thank You!

ACTION Drop the bounce ball as you say:

Some students do not realize the gravity of this situation, but on planet EARTH,

acceleration constant "a" is near three hundred eighty six inches per second squared.

FOURTH TRANSPARENCY • Chanting the free fall formula

CHANT So Galileo's constant acceleration parabolic model for free fall motion is:

all together again

CHANT S equals one hundred ninety three T squared inches.

Once more? OK - - -

Wonderful and you sound good!

From your response, I can tell that you are outstanding in the field of mathematics.

However, farmers are often found out standing in their fields.

FIFTH TRANSPARENCY • Lake Shelbyville Daily Union Newspaper

In fact, this newspaper's front page may show you where I am out standing.

Sometimes, In Hot Water! YEP,

Lake Shelbyville Illinois Reservoir on a hot summer day,

flippin and jugglin, and to continue this metaphor:

People ask me what I plan to investigate and teach in the future.

Well, I pooled juggling and mathematics material together to

form a reservoir of studies that I call the MAJOR.

So please consider this lake - AH - field of short courses?

Ok, let's get started on some MAJOR research.