Math: Find the area of a circle.
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Transcript of Math: Find the area of a circle.
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Math: Find the area of a circle.
Science: Describe the impact of catastrophic events on the Earth (Earthquake)
By Alfonso Salinas, Oralia Fernandez and Diana De Alba.
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Pre-requisites: Math and Science
• Circumference (radius, chord, diameter, arch)
• Concept of Area • Coordinate Plane
• Rates
• Tectonic Plates
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Activity to discover “Area of a circle”Organize class into groups.
Distribute:
a) Template of a Circleb) Rulerc) Scissors
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E x p l o r e ! Step 1. Students are to sketch 6 more diameters on the given template of a circle.
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Step 2. Students are to cut out the circle through one of the diameters.
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Step 3. Cut out the circle through all the radii towards the circumference
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Step 4. Try to fit the pieces you have into a known polygon
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How does it looks like?
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How does it looks like?
Rectangle, parallelogram
What parts could you label in this figure?
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What parts could you label in this figure?
Base or Length
Height or
Width
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Develop the formula for the area of a circle based on the formula for the area of a rectangle or
parallelogram
Area of a Rectangle = Length x Width
A = L . W A = (½ C ) (radius)
A = (½ )2πr.r
A = 2πr.r
2
A = π r.r
A = πr2
This is the formula for the Area of a circle.
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How does an Earthquake wave travel?
Observe the following animation
How fast red, yellow and blue lines travel ?
USGS Science for a changing world
http://neic.usgs.gov/neis/eq_depot/2002/eq_021103/ak_seismic_waves.html
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Types of Earthquake Waves
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Types of Earthquake Waves
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AREA = 1,385.44 Km2
Source http://nemo.sciencecourseware.org/VirtualEarthquake/VQuakeExecute.html
r=21Km
If the average velocity of a P-Waves is
7 Km/Sec.
Find the area of seismic activity within
three seconds.
Types of Earthquake Waves
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AREA = 706.86 Km2
Source http://nemo.sciencecourseware.org/VirtualEarthquake/VQuakeExecute.html
r=15Km
If the average velocity of a S-Waves is
5 Km/Sec. Find the area of seismic
activity within three seconds.
Types of Earthquake Waves
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Earthquakes Effects
Let’s Analyze in the following Earthquake simulator The Earthquake effects.
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Earthquakes Effects
What is the relationship for destruction compared to Increasing the magnitude of the movement in the Earthquake simulator ?
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How does Mathematicians find some “centers”
The Centroid of a triangle is the point where the three medians of the triangle intersect.
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How does Mathematicians find some “centers”
The Circumcenter The point where the three perpendicular bisectors of a triangle meet.
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How does Mathematicians find some “centers”
The orthocenter of a triangle is the point where its altitudes intersect.
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How does Mathematicians find some “centers”
The Incenter of the triangle is the point where the three angle bisectors of a triangle meet.
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If dermis is the skin and epidermis is the outer layer of the skin. What do you think would be the meaning for “epi”?
EP/EPI comes from Greek and means variously “upon,” “besides,” “attached to,” “over,” “outer,” or “after.”
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An epicenter is the portion of the earth’s surface directly over the focus of an earthquake.
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How does scientists find and epicenter of an earthquake?
1. Calculate the S-P time for at least 3 seismograph recordings. The P-wave is the first wave spike, the S-wave is the much bigger wave spike just after the P wave.
2. Using these measurements to find the distance from the epicenter using a standardized P and S wave chart.
3. Use these the distance at each station to draw a circle of that radius around the station
4 After drawing at least 3 circles, the intersection of the circles is the epicentre.
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How does scientists find and epicenter of an earthquake?
Find the area of seismic activity
for each seismograph.
A = πr2
Scale 1cm = 100 km
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How does scientists find and epicenter of an earthquake?
Scale 1cm = 100 km