: 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: firstname.lastname@example.org http://www.uark.edu/~k12 info/.
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) 575-5680 (FAX)
Will meteorites hit
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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.
Meteorite Hunter finds alien roc...
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.”
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.
A series of steps
Van de Walle p 412
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.
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
Turn the calculator on. Clear.
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
What quadrant do we need?
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.
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
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.
Where does it fit in the Data Analysis and Probability Standards?
Van De Walle p. 412 “Technology Note”