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: CATHY JONES Secondary Math Instruction Specialist Center for Mathematics and Science Education Arkansas NASA Education Resource Center 346 N. West Avenue, Room 202 Fayetteville, Arkansas 72701 (479) 575-3875 (479) 575-5680 (FAX) e-mail: cej001@uark.edu http://www.uark.edu/~k12 info/.

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slide1

:

CATHY JONES

Secondary Math Instruction Specialist

Center for Mathematics and Science Education

Arkansas NASA Education Resource Center

346 N. West Avenue, Room 202

Fayetteville, Arkansas 72701

(479) 575-3875

(479) 575-5680 (FAX)

e-mail: cej001@uark.edu

http://www.uark.edu/~k12 info/

Will meteorites hit

Your City?

Presented by:

Download all materials from this session at

www.cmasemath.pbwiki.com

slide2

Meteorite Showers…..

Meteoroids that experience disruption in the atmosphere may fall as meteorite showers, which can range from only a few up to thousands of separate individuals. The area over which a meteorite shower falls is known as its strewn field.

slide3

Meteorite showers may contain large numbers of individual meteorites.

  • more than 100,000 fell at Pułtusk, Pol. in 1868
  • possibly 14,000 fell at Holbrook, Ariz., U.S. in 1912
  • thousands fell at Chihuahua, Mex., in 1969
  • 2,000–3,000 fell at L’Aigle, France, in 1803
  • 200–300 fell at Stannern, Moravia (now Stonařov, Cz.Rep.), in 1808.

Meteorite Hunter finds alien roc...

slide4

What do the following Questions and

the meteorite question all have in common?

“The forecast was 30% chance of rain.”

YOUR city lies on the edge of the predictedstrewn field for the meteorite shower.

What is the probability that meteorites will fall on YOUR city?

“Certain diets may result in higher likelihood of heart disease.”

“Win the lottery? It’s one in a million.”

“You’re more likely to get struck by lightning, than die in a plane crash.”

simulation
Simulation

A technique used for answering real-world questions or making decisions in complex situations where an element of chance is involved.

Van deWalle, Elementary and Middle School Mathematics Teaching Developmentally, Pearson, 5th ed., p. 411.

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Simulations

A series of steps

  • Identify key components and assumptions of the problem.
  • Select a random device for the key components.
  • Define a trial.
  • Conduct a large number of trials, and record the information.
  • Use the data to draw conclusions.

Van de Walle p 412

slide8

Red Hot Meteorites Simulation

Directions:

Each group should have a small cup of red hots and a pizza box with a quarter circle drawn in it.

You will drop the red hots from above the box. Count and record how many fall inside the curve, outside the curve, and the total in the trial. Continue until time is called.

Record the results on chart paper and then find the total of all your trials and report what fractional part of the red hots landed inside the curved area.

slide9

Predict and Drop

Download the REDHOT program

Turn calculators on. Clear. Connect linking cords.

Press 2nd X which is LINK enter

RECEIVER: Arrow to RECEIVE, enter

SENDER: 3(Prgm)…Select REDHOTS…arrow to TRANSMIT…enter

slide10

Predict and Drop

Turn the calculator on. Clear.

Press

Clear all PLOTs at the top of the screen

Clear any equations, insert the following equation:

(Why this equation?)

This is a circle with radius of 1 unit.

Note: Equation of a circle (x-h)2 + (y-k)2 = r2

slide11

Predict & Drop

What quadrant do we need?

quadrant 1

We must set the WINDOW!

X min = 0

X max = 1

X scl = 1

Y min = 0

Y max = 1

Y scl = 1

Press GRAPH…Is this picture correct?

Press ZOOM, 5(Z Square)

Is this picture correct?

Press PRGM, select REDHOT, enter

Type in Number of redhots, enter.

slide12

Predict & Drop

How do you determine probability?

Probability(event)=successful trials divided by total possible

In this case the Theoretical probability of the predicted strewn field = area under the curve divided by the total possible area

P(meteorites in strewn field) = area of ¼ of a circle ÷ total area of box

1/4 r² ÷ r2 or approximately 0.785

Probability for hitting YOUR city = 1- 0.785

slide13

What Did We Learn?

Sampling is an estimated procedure, and it must be repeated several times in order to find the best estimate.

The larger the sampling size or number of trials, the closer it will approach the Theoretical Probabilities.

technology

AGREE OR DISAGREE -

Technology

  • Using hands-on devices to explore probability takes a lot of time to produce a large number of trials.
  • Students are more likely to believe the random outcomes of electronic devices such as calculators and computer software over those they get from hands-on random devices such as spinners, dice, or cubes drawn from a bag.

Where does it fit in the Data Analysis and Probability Standards?

Van De Walle p. 412 “Technology Note”