Will meteorites hit : CATHY JONES Secondary Math Instruction Specialist Center for Mathematics and...

Will meteorites hit

CATHY JONESSecondary Math Instruction SpecialistCenter for Mathematics and Science EducationArkansas NASA Education Resource Center346 N. West Avenue, Room 202Fayetteville, Arkansas 72701(479) 575-3875(479) 575-5680 (FAX)e-mail: cej001@uark.eduhttp://www.uark.edu/~k12 info/

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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 Showers…..

Meteorite Hunter finds alien roc...

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.

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

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

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

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

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

“The forecast was 30% chance of rain.”

Red hot meteorites Simulation!

Will meteorites hit

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.

1. Identify key components and assumptions of

the problem.

2. Select a random device for the key components.

3. Define a trial.

4. Conduct a large number of trials, and record the information.

5. Use the data to draw conclusions.

Van de Walle p 412

Simulations A series of steps

Directions:

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

Red Hot Meteorites Simulation

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.

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

Download the REDHOT program

Predict and Drop

Turn the calculator on. Clear.

Clear all PLOTs at the top of the screen

Clear any equations, insert the following equation:

(Why this equation?)

21 1 xy

Predict and Drop

This is a circle with radius of 1 unit.

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

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.

What quadrant do we need? quadrant 1

We must set the WINDOW!

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

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

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.

TechnologyWhere does it fit in the Data Analysis

and Probability Standards?

Van De Walle p. 412 “Technology Note”

1.Using hands-on devices to explore probability takes a lot of time to produce a large number of trials.

2.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.

AGREE OR DISAGREE -

Write the mathematical expression. Solve. Put the answers in numerical order from greatest to least and you’ll be ready for LIFT OFF!

Be careful and use the proper Order of Operation when solving.

Use the following blanks to record the answers from the problem cards. Then order them from greatest to least.

Read the problem cards and solve for the variables. Put the answers in numerical order from greatest to least and you’ll be ready for LIFT OFF!

Solve for the variables. Put the answers in numerical order from greatest to least and you’ll be ready for LIFT OFF!

See if you can unscramble the variables to spell a SPACE WORD.

If: I = 3 F = 1 T = 10 O = 12 then L = __________

Ratios

&Proportions

The scale of the sun to Jupiter is approximately 10 to 1. That means the sun is about 10 times larger than Jupiter. Measure the sun and the circle you chose for Jupiter and see if you are correct, or find the correct one.

The scale of the sun to Earth is about 109 to 1. That means the sun is 109 times larger than Earth. Also, the scale of Jupiter to Earth is approximately 11.2 to 1. That means Jupiter is about 11.2 times larger than Earth. Measure the circles you selected for these planets and see if you are correct, or find the correct ones.

The diameter of Earth is only about 400 miles larger than the diameter of Venus. So at this small scale they are almost the same size. Look at the circles you chose for these planets and see if you are correct, or find the correct ones.

The scale of Venus to Mercury is approximately to 2.5 to 1. Measure the circles you selected for these planets and see if you are correct, or find the correct ones.

The scale of Mars to Mercury is approximately to 1.4 to 1. Measure the circles you selected for these planets and see if you are correct, or find the correct ones.

The scale of Neptune to Mars is approximately to 6.7 to 1. Measure the circles you selected for these planets and see if you are correct, or find the correct ones.

The diameter of Uranus is only about 1,000 miles larger than the diameter of Neptune. So at this small scale they are almost the same size. Look at the circles you chose for these planets and see if you are correct, or find the correct ones.

Saturn is approximately 1.9 times larger than Uranus. Measure the circles you selected for these planets and see if you are correct, or find the correct ones.

The scale of Saturn to Pluto is approximately to 53 to 1. Measure the circles you selected for these planets and see if you are correct, or find the correct ones.

Sizing Up the Solar System Student Sheet Name:______________________________________

1. What tool did you use for measuring the model SUN? _____________________

Record the measurement you got, label the units, and the part of the model this measurement represents.

_________________________________________________________________________________________________________

Write the proportion or mathematical process used for each card:

4. ______________________________________ Approximate measurement of diameter of Jupiter: ___________ ______

5. ______________________________________ Approximate measurement of diameter of Earth: _____________ ______

6. ______________________________________ Approximate measurement of diameter of Venus: ____________ ______

4. ______________________________________ Approximate measurement of diameter of Mercury: ___________ ______

5. ______________________________________ Approximate measurement of diameter of Mars: ______________ ______

6. ______________________________________ Approximate measurement of diameter of Neptune: ___________ ______

7. ______________________________________ Approximate measurement of diameter of Uranus: ____________ ______

8. ______________________________________ Approximate measurement of diameter of Saturn: ____________ ______

9. ______________________________________ Approximate measurement of diameter of Pluto: _____________ ______

Will meteorites hit : CATHY JONES Secondary Math Instruction Specialist Center for Mathematics and...

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