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A tsunami is a series of waves most commonly caused by violent movement of the sea floor. In some ways, it resembles the ripples radiating outward from the spot where stone has been thrown into the water, but a tsunami can occur on an enormous scale. Tsunamis are generated by any large, impulsive displacement of the sea bed level. The movement at the sea floor leading to tsunami can be produced by earthquakes, landslides and volcanic eruptions.
Most tsunamis, including almost all of those traveling across entire ocean basins with destructive force, are caused by submarine faulting associated with large earthquakes. These are produced when a block of the ocean floor is thrust upward, or suddenly drops, or when an inclined area of the seafloor is thrust upward or suddenly thrust sideways. In any event, a huge mass of water is displaced, producing tsunami. Such fault movements are accompanied by earthquakes, which are sometimes referred to as “tsunamigenic earthquakes”. Most tsunamigenic earthquakes take place at the great ocean trenches, where the tectonic plates that make up the earth’s surface collide and are forced under each other. When the plates move gradually or in small thrust, only small earthquakes are produced; however, periodically in certain areas, the plates catch. The overall motion of the plates does not stop; only the motion beneath the trench becomes hung up. Such areas where the plates are hung up are known as “seismic gaps” for their lack of earthquakes. The forces in these gaps continue to build until finally they overcome the strength of the rocks holding back the plate motion. The built-up tension (or comprehension) is released in one large earthquake, instead of many smaller quakes, and these often generate large deadly tsunamis. If the sea floor movement is horizontal, a tsunami is not generated. Earthquakes of magnitude larger than M 6.5 are critical for tsunami generation.
Tsunamis produced by landslides:
Probably the second most common cause of tsunami is landslide. A tsunami may be generated by a landslide starting out above the sea level and then plunging into the sea, or by a landslide entirely occurring underwater. Landslides occur when slopes or deposits of sediment become too steep and the material falls under the pull of gravity. Once unstable conditions are present, slope failure can be caused by storms, earthquakes, rain, or merely continued deposit of material on the slope. Certain environments are particularly susceptible to the production of landslide-generated earthquakes. River deltas and steep underwater slopes above sub-marine canyons, for instance, are likely sites for landslide-generated earthquakes.
Tsunami produced by Volcanoes:
The violent geologic activity associated with volcanic eruptions can also generate devastating tsunamis. Although volcanic tsunamis are much less frequent, they are often highly destructive. These may be due to submarine explosions, pyroclastic flows and collapse of volcanic caldera.
(1) Submarine volcanic explosions occur when cool seawater encounters hot volcanic magma. It often reacts violently, producing stream explosions. Underwater eruptions at depths of less than 1500 feet are capable of disturbing the water all the way to the surface and producing tsunamis.
(2) Pyroclastic flows are incandescent, ground-hugging clouds, driven by gravity and fluidized by hot gases. These flows can move rapidly off an island and into the ocean, their impact displacing sea water and producing a tsunami.
(3) The collapse of a volcanic caldera can generate tsunami. This may happen when the magma beneath a volcano is withdrawn back deeper into the earth, and the sudden subsidence of the volcanic edifice displaces water and produces tsunami waves. The large masses of rock that accumulate on the sides of the volcanoes may suddenly slide down slope into the sea, causing tsunamis. Such landslides may be triggered by earthquakes or simple gravitational collapse. A catastrophic volcanic eruption and its ensuing tsunami waves may actually be behind the legend of the lost island civilization of Atlantis. The largest volcanic tsunami in historical times and the most famous historically documented volcanic eruption took lace in the East Indies-the eruption of Krakatau in 1883.
Tsunami waves :
A tsunami has a much smaller amplitude (wave height) offshore, and a very long wavelength (often hundreds of kilometers long), which is why they generally pass unnoticed at sea, forming only a passing "hump" in the ocean. Tsunamis have been historically referred to tidal waves because as they approach land, they take on the characteristics of a violent onrushing tide rather than the sort of cresting waves that are formed by wind action upon the ocean (with which people are more familiar). Since they are not actually related to tides the term is considered misleading and its usage is discouraged by oceanographers.
These waves are different from other wind-generated ocean waves, which rarely extend below a dept of 500 feet even in large storms. Tsunami waves, on the contrary, involvement of water all the way to the sea floor, and as a result their speed is controlled by the depth of the sea. Tsunami waves may travel as fast as 500 miles per hour or more in deep waters of an ocean basin. Yet these fast waves may be only a foot of two high in deep water. These waves have greater wavelengths having long 100 miles between crests. With a height of 2 to 3 feet spread over 100 miles, the slope of even the most powerful tsunamis would be impossible to see from a ship or airplane. A tsunami may consist of 10 or more waves forming a ‘tsunami wave train’. The individual waves follow one behind the other anywhere from 5 to 90 minutes apart.
As the waves near shore, they travel progressively more slowly, but the energy lost from decreasing velocity is transformed into increased wavelength. A tsunami wave that was 2 feet high at sea may become a 30-feet giant at the shoreline. Tsunami velocity is dependent on the depth of water through which it travels (velocity equals the square root of water depth h times the gravitational acceleration g, that is (V=√gh). The tsunami will travel approximately at a velocity of 700 kmph in 4000 m depth of sea water. In 10 m, of water depth the velocity drops to about 35 kmph. Even on shore tsunami speed is 35 to 40 km/h, hence much faster than a person can run.It is commonly believed that the water recedes before the first wave of a tsunami crashes ashore. In fact, the first sign of a tsunami is just as likely to be a rise in the water level. Whether the water rises or falls depends on what part of the tsunami wave train first reaches the coast. A wave crest will cause a rise in the water level and a wave trough causes a water recession.
Seiche (pronounced as ‘saysh’) is another wave phenomenon that may be produced when a tsunami strikes. The water in any basin will tend to slosh back and forth in a certain period of time determined by the physical size and shape of the basin. This sloshing is known as the seiche. The greater the length of the body, the longer the period of oscillation. The depth of the body also controls the period of oscillations, with greater water depths producing shorter periods. A tsunami wave may set off seiche and if the following tsunami wave arrives with the next natural oscillation of the seiche, water may even reach greater heights than it would have from the tsunami waves alone. Much of the great height of tsunami waves in bays may be explained by this constructive combination of a seiche wave and a tsunami wave arriving simultaneously. Once the water in the bay is set in motion, the resonance may further increase the size of the waves. The dying of the oscillations, or damping, occurs slowly as gravity gradually flattens the surface of the water and as friction turns the back and forth sloshing motion into turbulence. Bodies of water with steep, rocky sides are often the most seiche-prone, but any bay or harbour that is connected to offshore waters can be perturbed to form seiche, as can shelf waters that are directly exposed to the open sea.
The presence of a well developed fringing or barrier of coral reef off a shoreline also appears to have a strong effect on tsunami waves. A reef may serve to absorb a significant amount of the wave energy, reducing the height and intensity of the wave impact on the shoreline itself.
The popular image of a tsunami wave approaching shore is that of a nearly vertical wall of water, similar to the front of a breaking wave in the surf. Actually, most tsunamis probably don’t form such wave fronts; the water surface instead is very close to the horizontal, and the surface itself moves up and down. However, under certain circumstances an arriving tsunami wave can develop an abrupt steep front that will move inland at high speeds. This phenomenon is known as a bore. In general, the way a bore is created is related to the velocity of the shallow water waves. As waves move into progressively shallower water, the wave in front will be traveling more slowly than the wave behind it .This phenomenon causes the waves to begin “catching up” with each other, decreasing their distance apart i.e. shrinking the wavelength. If the wavelength decreases, but the height does not, then waves must become steeper. Furthermore, because the crest of each wave is in deeper water than the adjacent trough, the crest begins to overtake the trough in front and the wave gets steeper yet. Ultimately the crest may begin to break into the trough and a bore formed. A tsunami can cause a bore to move up a river that does not normally have one. Bores are particularly common late in the tsunami sequence, when return flow from one wave slows the next incoming wave. Though some tsunami waves do, in deed, form bores, and the impact of a moving wall of water is certainly impressive, more often the waves arrive like a very rapidly rising tide that just keeps coming and coming. The normal wind waves and swells may actually ride on top of the tsunami, causing yet more turbulence and bringing the water level to even greater heights. | 4.876635 |
Simple Equations Introduction to basic algebraic equations of the form Ax=B
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- Let's say we have the equation seven times x is equal to fourteen.
- Now before even trying to solve this equation,
- what I want to do is think a little bit about what this actually means.
- Seven x equals fourteen,
- this is the exact same thing as saying seven times x, let me write it this way, seven times x, x in orange again. Seven times x is equal to fourteen.
- Now you might be able to do this in your head.
- You could literally go through the 7 times table.
- You say well 7 times 1 is equal to 7, so that won't work.
- 7 times 2 is equal to 14, so 2 works here.
- So you would immediately be able to solve it.
- You would immediately, just by trying different numbers
- out, say hey, that's going to be a 2.
- But what we're going to do in this video is to think about
- how to solve this systematically.
- Because what we're going to find is as these equations get
- more and more complicated, you're not going to be able to
- just think about it and do it in your head.
- So it's really important that one, you understand how to
- manipulate these equations, but even more important to
- understand what they actually represent.
- This literally just says 7 times x is equal to 14.
- In algebra we don't write the times there.
- When you write two numbers next to each other or a number next
- to a variable like this, it just means that you
- are multiplying.
- It's just a shorthand, a shorthand notation.
- And in general we don't use the multiplication sign because
- it's confusing, because x is the most common variable
- used in algebra.
- And if I were to write 7 times x is equal to 14, if I write my
- times sign or my x a little bit strange, it might look
- like xx or times times.
- So in general when you're dealing with equations,
- especially when one of the variables is an x, you
- wouldn't use the traditional multiplication sign.
- You might use something like this -- you might use dot to
- represent multiplication.
- So you might have 7 times x is equal to 14.
- But this is still a little unusual.
- If you have something multiplying by a variable
- you'll just write 7x.
- That literally means 7 times x.
- Now, to understand how you can manipulate this equation to
- solve it, let's visualize this.
- So 7 times x, what is that?
- That's the same thing -- so I'm just going to re-write this
- equation, but I'm going to re-write it in visual form.
- So 7 times x.
- So that literally means x added to itself 7 times.
- That's the definition of multiplication.
- So it's literally x plus x plus x plus x plus x -- let's see,
- that's 5 x's -- plus x plus x.
- So that right there is literally 7 x's.
- This is 7x right there.
- Let me re-write it down.
- This right here is 7x.
- Now this equation tells us that 7x is equal to 14.
- So just saying that this is equal to 14.
- Let me draw 14 objects here.
- So let's say I have 1, 2, 3, 4, 5, 6, 7, 8,
- 9, 10, 11, 12, 13, 14.
- So literally we're saying 7x is equal to 14 things.
- These are equivalent statements.
- Now the reason why I drew it out this way is so that
- you really understand what we're going to do when we
- divide both sides by 7.
- So let me erase this right here.
- So the standard step whenever -- I didn't want to do that,
- let me do this, let me draw that last circle.
- So in general, whenever you simplify an equation down to a
- -- a coefficient is just the number multiplying
- the variable.
- So some number multiplying the variable or we could call that
- the coefficient times a variable equal to
- something else.
- What you want to do is just divide both sides by 7 in
- this case, or divide both sides by the coefficient.
- So if you divide both sides by 7, what do you get?
- 7 times something divided by 7 is just going to be
- that original something.
- 7's cancel out and 14 divided by 7 is 2.
- So your solution is going to be x is equal to 2.
- But just to make it very tangible in your head, what's
- going on here is when we're dividing both sides of the
- equation by 7, we're literally dividing both sides by 7.
- This is an equation.
- It's saying that this is equal to that.
- Anything I do to the left hand side I have to do to the right.
- If they start off being equal, I can't just do an operation
- to one side and have it still be equal.
- They were the same thing.
- So if I divide the left hand side by 7, so let me divide
- it into seven groups.
- So there are seven x's here, so that's one, two, three,
- four, five, six, seven.
- So it's one, two, three, four, five, six, seven groups.
- Now if I divide that into seven groups, I'll also want
- to divide the right hand side into seven groups.
- One, two, three, four, five, six, seven.
- So if this whole thing is equal to this whole thing, then each
- of these little chunks that we broke into, these seven chunks,
- are going to be equivalent.
- So this chunk you could say is equal to that chunk.
- This chunk is equal to this chunk -- they're
- all equivalent chunks.
- There are seven chunks here, seven chunks here.
- So each x must be equal to two of these objects.
- So we get x is equal to, in this case -- in this case
- we had the objects drawn out where there's two of
- them. x is equal to 2.
- Now, let's just do a couple more examples here just so it
- really gets in your mind that we're dealing with an equation,
- and any operation that you do on one side of the equation
- you should do to the other.
- So let me scroll down a little bit.
- So let's say I have I say I have 3x is equal to 15.
- Now once again, you might be able to do is in your head.
- You're saying this is saying 3 times some
- number is equal to 15.
- You could go through your 3 times tables and figure it out.
- But if you just wanted to do this systematically, and it
- is good to understand it systematically, say OK, this
- thing on the left is equal to this thing on the right.
- What do I have to do to this thing on the left
- to have just an x there?
- Well to have just an x there, I want to divide it by 3.
- And my whole motivation for doing that is that 3 times
- something divided by 3, the 3's will cancel out and I'm just
- going to be left with an x.
- Now, 3x was equal to 15.
- If I'm dividing the left side by 3, in order for the equality
- to still hold, I also have to divide the right side by 3.
- Now what does that give us?
- Well the left hand side, we're just going to be left with
- an x, so it's just going to be an x.
- And then the right hand side, what is 15 divided by 3?
- Well it is just 5.
- Now you could also done this equation in a slightly
- different way, although they are really equivalent.
- If I start with 3x is equal to 15, you might say hey, Sal,
- instead of dividing by 3, I could also get rid of this 3, I
- could just be left with an x if I multiply both sides of
- this equation by 1/3.
- So if I multiply both sides of this equation by 1/3
- that should also work.
- You say look, 1/3 of 3 is 1.
- When you just multiply this part right here, 1/3 times
- 3, that is just 1, 1x.
- 1x is equal to 15 times 1/3 third is equal to 5.
- And 1 times x is the same thing as just x, so this is the same
- thing as x is equal to 5.
- And these are actually equivalent ways of doing it.
- If you divide both sides by 3, that is equivalent to
- multiplying both sides of the equation by 1/3.
- Now let's do one more and I'm going to make it a little
- bit more complicated.
- And I'm going to change the variable a little bit.
- So let's say I have 2y plus 4y is equal to 18.
- Now all of a sudden it's a little harder to
- do it in your head.
- We're saying 2 times something plus 4 times that same
- something is going to be equal to 18.
- So it's harder to think about what number that is.
- You could try them.
- Say if y was 1, it'd be 2 times 1 plus 4 times 1,
- well that doesn't work.
- But let's think about how to do it systematically.
- You could keep guessing and you might eventually get
- the answer, but how do you do this systematically.
- Let's visualize it.
- So if I have two y's, what does that mean?
- It literally means I have two y's added to each other.
- So it's literally y plus y.
- And then to that I'm adding four y's.
- To that I'm adding four y's, which are literally four
- y's added to each other.
- So it's y plus y plus y plus y.
- And that has got to be equal to 18.
- So that is equal to 18.
- Now, how many y's do I have here on the left hand side?
- How many y's do I have?
- I have one, two, three, four, five, six y's.
- So you could simplify this as 6y is equal to 18.
- And if you think about it it makes complete sense.
- So this thing right here, the 2y plus the 4y is 6y.
- So 2y plus 4y is 6y, which makes sense.
- If I have 2 apples plus 4 apples, I'm going
- to have 6 apples.
- If I have 2 y's plus 4 y's I'm going to have 6 y's.
- Now that's going to be equal to 18.
- And now, hopefully, we understand how to do this.
- If I have 6 times something is equal to 18, if I divide both
- sides of this equation by 6, I'll solve for the something.
- So divide the left hand side by 6, and divide the
- right hand side by 6.
- And we are left with y is equal to 3.
- And you could try it out.
- That's what's cool about an equation.
- You can always check to see if you got the right answer.
- Let's see if that works.
- 2 times 3 plus 4 times 3 is equal to what?
- 2 times 3, this right here is 6.
- And then 4 times 3 is 12.
- 6 plus 12 is, indeed, equal to 18.
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3rd Grade Oral Language Resources
Students will:• Learn about the concept of making journeys.
• Access prior knowledge and build background about different ways to make journeys.
• Explore and apply understanding of the concept of making journeys.
Students will:• Demonstrate an understanding of making journeys.
• Orally use words that identify different ways to travel.
• Extend oral vocabulary by discussing journeys and transportation.
• Use key concept words [journey, airplane, train, luggage, horse• drawn carriages].
Explain• Use the slideshow to review the key concept words.
• Explain that students are going to learn about making journeys:
• When people travel a great distance from one place to another, they make a journey.
• The various types of transportation that make journeys possible.
• Progress made in transportation over the years.
• The importance of being prepared for a journey.
Model• After the host introduces the slideshow, point to the photo on screen. Ask students: What are the people in these photographs doing? (traveling, flying on a plane, riding on a train, getting ready to drive somewhere, making journeys, and so forth).
• Ask students: What are some different ways to make journeys? (train, airplane, car, truck, boat, and so forth).
• Say: There are many ways to make exciting journeys. We take journeys to learn about other places and to learn about ourselves. What would you like to learn about? (answers will vary).
Guided Practice• Guide students through the next four slides, showing them different ways to travel. Always have the students discuss their favorite way to travel.
Apply• Play the games that follow. Have them discuss with their partner the different topics that appear during the Talk About It feature.
• After the first game, ask students to discuss their travel experiences. After the second game, have them discuss different things they would need to take with them on long journeys.
Close• Ask students: Where would you like to make a journey? How would you get there?
• Summarize for students that there are many different ways you can make a journey. Journeys can be fun but we need to be careful and we must remember to pack things that we will need in case of an emergency. Encourage them to think about how they can be careful when going on a journey. | 4.721492 |
Cross Contamination of Food
- It is important for students to know how to be safe when they
are cooking. In this lesson students will review what they know
about cross contamination and ways they can help prevent it.
Healthy or Not Healthy - Students
have to make choices every day about what they eat. Helping them
think critically about foods is important to encouraging them to
have a healthy lifestyle.
Matching Game - In this lesson, students have to match the correct
food to its place on the pyramid.
the Label - In this lesson, students will learn how to read a food
label. They will have to find information about ingredients, calories,
Food Shopping- Have students discover that nutritious food can be
bought and prepared more cheaply than "fast food".
a Few of my Favorite Things - In this activity, students learn about
the nutritional value of foods, calculate the measurements, and prepare
a healthy recipe for the class. Then students publish a class cookbook
with their recipes.
Junkie - Students analyze the nutritional value of their favorite
fast food meals and describe alternative choices for these unhealthy foods.
Counting Unit- Learn about the food pyramid. Learn about how much
fat is in our regular diets.
Food Groups - Students will differentiate between different types
of foods to determine which of the five food groups they belong in.
and Nutrition - Students will identify healthy, nutritious foods as
opposed to foods with little benefit to their health and be able to create
Pyramid - All students will be able to identify and then sort different
fruits and vegetables into their correct location.
Picnic - Teacher and students discuss the food pyramid and appropriate
choices for each food group. Students then plan a nutritional meal for
a picnic lunch and make a class book. As a culminating event, the class
plans and enjoys a picnic.
Snack - After completing a unit of study on nutrition, students work
as company managers to design and advertise healthy snacks to sell. A
list of ingredients will be listed for each snack and an advertisement
will be designed to promote their product.
the Food Pyramid - Students learn that the food pyramid is an important
nutritional tool. They classify foods and compare the number of servings
per group that are necessary for maintaining good health by placing empty
food containers in grocery bags.
Unit - February is Nutrition Month. Several activities for learning
about foods and nutrition.
with a Smile - This lesson is for Day 4 of the Beacon unit, Wellness
Wonders. Students will listen to a literature selection and then play
a game about personal health behaviors related to nutrition.
Your Plate - This activity is a fun way to teach students to analyze
what they eat for one day. The student analyzes the nutrients, calories,
and food groups using the USDA CNPP website Interactive Healthy Eating
Factory - Salad Factory allows students the ability to make their
own salad and have the salad computer analyze it for the nutritional content.
This is a great activity to help students realize how important plants
are in our diets and in our world.
'R Us - Students identify foods that make nutritious snacks. They
will analyze snack foods to determine their fat content by completing
of Healthy Foods - Students make an alphabet book of nutritional foods
using the information they learned about nutrition and the value of different
foods. Students also taste the foods represented by the letters they wrote
about in their alphabet books.
Guide Pyramid - This lesson introduces the Food Guide Pyramid and
Daily Guidelines for Americans and allows students to evaluate their current
nutritional habits and to create a plan for developing healthy habits
to last a lifetime.
What You Eat (Middle School) - Students research and prepare 20 cards
regarding nutritional needs, obesity, and health issues. Students determine
their ideal weights and how many calories should be consumed daily to
obtain the ideal weight and/or maintain it. | 4.708643 |
Recall 1. In the past we put quadratic equations in the form
y = ax2 + bx + c.
This makes the equation look nice and become more readable. For the purposes of graphing, we would rather alter this form slightly. Recall that we represented lines in standard form as
y = mx + b.
Then we were able to read the critical information about slope and y-intercept directly from the form of the equation. The slope is m and the y-intercept is b. We wish to do the same with the graphs of quadratic functions. We will use several ideas that were touched on in past hours to provide a scheme for knowing how to graph a quadratic function.
Recall 2 (The standard parabola centered at the origin.)
If you sketch the graph of the quadratic equation y = x*x, you find a curve that looks like the curve below This curve is called a parabola. The first thing to notice about a parabola is its symmetry. If you flip this parabola about the y-axis, you get the exact same parabola. Every parabola has such a line of symmetry. In the case of the parabola y = x2, the y-axis is the line of symmetry. The point at which the parabola meets its line of symmetry is called the vertex of the parabola.
Now, the basic shape and orientation will be determined
by the coefficients of the quadratic y = ax2 + bx + c.
We take one possibility at a time. Suppose that the coefficients b and c are both 0. In this case our parabola is given by the equation
y = ax*x.
The question should now be: What role does
a play in orienting or shaping the graph? To
out, let a be a
few different values and compare the values of a with the
shapes of the sketches that we get. The sketches below
role of a.
If the coefficient is negative, the parabola faces
If the coefficient is positive, then the parabola faces upward.
The absolute value of the coefficient determines the sharpness of the curve at the vertex--the higher the absolute value, the steeper and sharper the parabola.
Recall 3 . (The general case y = ax2 + bx + c.)
If we can put the equation into the form
y = a(x - h)2 + k,
h and k
are specific real numbers then we
would know the orientation
and position of
the parabola that is the graph of the
quadratic equation. It turns
out that this parabola has a
vertex at the point (h,k).
Again, the steepness of the
parabola, or the sharpness at the vertex is
determined by the
coefficient a--the larger its absolute
value, the steeper the
For example, the curve
y = 2(x - 5)2 + 7
is a parabola opening upward with vertex at (5,7). The line of symmetry in this case is the vertical line x = 5.
Recall 4. (Changing y = ax2 + bx + c to the form y = a(x - h)2 + k)
the form y = ax2 + bx
+ c can be changed to the form y = a(x -
h)2 + k,
if the proper values
of h and k can be found. The
process of finding such h and
k is called completing the
Here's how it works. Start with y = ax2 + bx + c and take a factor of a out from the first two terms of the right-hand side. (Remember a is different from 0, otherwise we would have the linear equation y = bx + c. ) We get
Notice that this is in the form y = a(x - h)2 + k, with h =-(b/2a) and k=(c-a(b/2a)2)
This means that our parabola has vertex at (-(b/2a), (c-a(b/2a)2))
Example 1. Find the axis of symmetry and the vertex of the graph of the function
f(x) = x2 - 6x + 11.
Solution: List the coefficients a = 1, b = -6, and c = 11. By completing the square for the equation y = x2 - 6x + 11, we find
y = (x2 - 6x ) + 11
=(x2-6x+9) + 11 -9
=(x-3)2 + 11 - 9
= (x - 3)2 + 2.
Therefore, the parabola faces upward (a is positive) and it has a vertex at (3,2) with a vertical line of symmetry x = 3.
Example 2. Find the axis of symmetry and the vertex of the graph of the function
f(x) = -2x2 + 16x - 35.
Solution: List the coefficients a = -2, b = 16, and c = -35. By completing the square for the equation y = -2x2 + 16x - 35, we find
y = -2(x2 - 8x) - 35
= -2(x2-8x+16)- 35 + 2*16
= -2(x-4)2 - 35 + 32
= -2(x-4)2- 3.
Therefore, the parabola faces downward (a is negative) and it has a vertex at (4,-3) with a vertical line of symmetry x = 4. Notice that the parabola has a sharper steepness than the one in the previous example, because a = 2.
A quadratic function is in the form f(x) = ax2 + bx + c. A quadratic function graphs into a parabola, a curve shape like one of the McDonald's arches. Every quadratic function has a vertex and a vertical axis of symmetry. This means it is the same graph on either side of a vertical line. The axis of symmetry goes through the vertex point. The vertex point is either the maximum or minimum point for the parabola.
|graph opens up and the
vertex is a minimum
graph opems down and the vertex is a maximum
|b2 - 4ac > 0
b2 - 4ac = 0
b2 - 4ac < 0
Graph has 1 x-intercept
Graph has no x-intercepts
|Vertex Point||at x = -b/2a
to find y substitute above value for x in the expression of the function
none if b2-4ac<0
|y-intercept||c value in ax2 + bx + c|
1. Plot the points (x,f(x)) at x = -4, -3, -2, -1, 0, 1, 2, 3, and 4 for the function f(x) = x2 -6x + 2. | 4.895547 |
Key Fact 3: There are a number of basic food skills which enable us to cook a variety of dishes.
a) To understand that there is a range of basic cooking skills.
Explain to the children that we need certain skills to be able to make snacks and meals. Ask them to recall some of the skills they used last session when making their playtime snacks.
- Cutting (with scissors).
You could make a list of these or display the appropriate Actions Cards 205.
Ask the children to think of other food skills which might be needed for cooking. What have they seen others do when cooking?
Show some or all of the following videos:
- Cous Cous Salad;
- Fruit Salad;
As you show each video, ask the children to identify 2-3 key skills needed for each recipe and keep a list, which can be seen by the whole class, of these skills under the heading of each recipe. You could use the Skills SMARTBoard activity 201 to help record this.
The children should decide on 2 of the recipe videos they have seen and, using the, Cooking skills Worksheet 206, illustrate 2-3 key skills needed in those recipes.
b) To be able to use basic cooking skills to make a dish.
In advance of the lesson, decide on 1 or 2 non heat cooking activities that will require children to use a knife, e.g. sandwiches, fruit salad, dip.
Organise the classroom, equipment and ingredients to allow a cooking session to take place. Plan how you will work with the children, e.g. half a class at a time. See Cooking Guide 205.
Explain to the children what they will be making. Talk through the hygiene rules for cooking. Use the Hygiene and safety checklist Guide 204 for reference and display the Let’s get ready to cook Poster 201 for the children to see.
Talk through the recipe and demonstrate what the children will have to do.
Be clear and precise when demonstrating how to use the knife in a safe and appropriate way. See Skills Guide 203. Demonstrate:
- Bridge Hold;
- Claw Grip;
- Fork Secure.
Use the Bridge Hold and Claw Grip Videos to reinforce good practice.
Ensure children understand that when they finish cutting they must put the knife down. They should not hold it while they do other things or move around the room. This rule also applies to other sharp or pointed equipment.
Allow the children to carry out their cooking activity.
Gather the children to look at what they have made. Question them:
- Did you enjoy making this?
- Would you make it again?
- Would you do anything differently?
- What equipment did you use?
- How did you use it safely?
- What can you do now that you had not done before?
Allow the children to taste what they have made. Remember to instruct the children on how to do this hygienically. See Tasting checklist Guide 200.
Ask different children to come to the front of the class and mime a food skill, e.g. grating cheese, washing grapes. See if other children can guess what they are doing. For each skill guessed, ask if anyone can name another food this skill could be used with.
Get the children to talk about the rules for tasting, being hygienic while cooking and using a knife safely.
Use other non heat recipes which allow children to explore different food skills. To help create time for more food work, link it into other curriculum subjects. | 4.74712 |
| The Civil Rights Act
July 2, 1964
The three Civil War Amendments to the Constitution - the 13th, 14th and 15th - were designed not only to end slavery, but also to secure blacks all the rights and privileges exercised by whites. However, these supposed guarantees were far more notorious in the breach than in the observance. Crusades by black leaders like Frederick Douglass and Booker T. Washington and their white supporters made no dent on the wall of prejudice. In the 1950s, blacks found a new leader: Rev. Martin Luther King, Jr., whose policy of non-violent resistance won the support not only of black, but of white opinion everywhere in the North. The violence with which Southern white authorities treated King and his followers inspired not only nationwide outrage, but more importantly, judicial and political intervention. By the time President Johnson succeeded to the Presidency, pressure for black equality was irresistible, and the Congress passed an all-embracing Civil Rights Act which, if enforced, should have ended discrimination in America forever. The Act outlawed racial discrimination in all public accommodations, in jobs and in public housing. It provided effective protection of blacks at the ballot box and authorized the Attorney General to intervene wherever necessary to enforce these laws. As long as the Warren Court lasted, the potentialities of the Civil Rights Act were fully realized; with the shift to a more conservative administration and judiciary that progress slowed down, and was, in part, reversed. This painting marks the anniversary of the signing of the Civil Rights Act on July 2, 1964. | 4.7129 |
After the Civil War, Congress championed the cause of newly freed African Americans by enacting the Thirteenth, Fourteenth, and Fifteenth Amendments to the Constitution. The Thirteenth Amendment abolished slavery. The Fourteenth Amendment provided citizenship and equal protection under the law. The Fifteenth Amendment guaranteed black men the right to vote. Other legislation to enforce these amendments followed.
However, between 1873 and 1883 the U.S. Supreme Court issued a series of decisions that set back federal efforts to protect the civil rights of African Americans until 1957, when the first civil rights law since Reconstruction was passed. In the South, where ninety percent of African Americans lived, state constitutions were amended to legalize disenfranchisement. The Ku Klux Klan resorted to beating, lynching, and burning homes to reinforce white supremacy. Black labor was bound to the land as peonage and sharecropping replaced the antebellum plantation system of slavery. In both the North and the South, African Americans were segregated by law and by custom in schools, public accommodations, housing, transportation, armed forces, recreational facilities, hospitals, prisons, and cemeteries.
In 1896 the Supreme Court sanctioned legal separation of the races in its ruling in the case of Plessy v. Ferguson, which stated that separate but equal facilities did not violate the Fourteenth Amendment. Science, history, and popular culture bolstered racial policy by promoting the myth of Negro inferiority. By the turn of the twentieth century, African Americans found themselves reduced to a color-caste system almost as oppressive and destructive as the chattel slavery they had endured. A new wave of racial violence swept the U.S., erupting in a torrent of lynchings and race riots. The worst of these riots occurred in Springfield, Illinois, in 1908. Read more about Prelude »
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Founding and Early Years
In response to the Springfield riot, a group of black and white activists, Jews and gentiles, met in New York City to address the deteriorating status of African Americans. Among them were veterans of the Niagara Movement (a civil rights group), suffragists, social workers, labor reformers, philanthropists, socialists, anti-imperialists, educators, clergymen, and journalists—some with roots in abolitionism. In the abolitionist tradition, they proposed to fight the new color-caste system with a “new abolition movement”—the National Association for the Advancement of Colored People. The NAACP pledged “to promote equality of rights and eradicate caste or race prejudice among citizens of the United States; to advance the interest of colored citizens; to secure for them impartial suffrage; and to increase their opportunities for securing justice in the courts, education for their children, employment according to their ability, and complete equality before the law.” The NAACP pursued this mission through a variety of tactics including legal action, lobbying, peaceful protest, and publicity. Read more about Founding and Early Years »
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The New Negro Movement
World War I created a transformation for African Americans from the “old” to the “new.” Thousands moved from the rural South to the industrial urban North, pursuing a new vision of social and economic opportunity. During the war black troops fought abroad “to keep the world safe for democracy.” They returned home determined to achieve a fuller participation in American society. The philosophy of the civil rights movement shifted from the “accommodationist” approach of Booker T. Washington to the militant advocacy of W.E.B. Du Bois. These forces converged to help create the “New Negro Movement” of the 1920s, which promoted a renewed sense of racial pride, cultural self-expression, economic independence, and progressive politics.
Evoking the “New Negro,” the NAACP lobbied aggressively for the passage of a federal law that would prohibit lynching. The NAACP played a crucial role in the flowering of the Negro Renaissance centered in New York’s Harlem, the cultural component of the New Negro Movement. NAACP officials W.E.B. Du Bois, James Weldon Johnson, Walter White, and Jessie Fauset provided aesthetic guidance, financial support, and literature to this cultural awakening. The NAACP’s efforts on the international front included sending James Weldon Johnson to Haiti to investigate the occupation of U.S. Armed Forces there. In the courts the NAACP prosecuted cases involving disenfranchisement, segregation ordinances, restrictive covenants, and lack of due process and equal protection in criminal cases. Read more about The New Negro Movement »
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The Great Depression
With the onset of the Great Depression of the 1930s, the NAACP confronted an internal dispute and external criticism over the merits of pursuing an agenda of civil and political equality versus an agenda of economic development and independence. The merits were debated at the Amenia Conference in 1933. In the political arena, the NAACP won the first successful campaign against a Supreme Court nominee, Judge John J. Parker, demonstrating the association’s growing influence. By 1931, the NAACP undertook the defense of the Scottsboro Boys, nine black youths wrongfully accused of raping two white women, before losing control of the case to the Communist-led International Labor Defense. Later, based on the findings of attorneys Nathan Margold and Charles H. Houston, the NAACP launched a legal campaign against de jure segregation that focused on inequalities in public schools. Towards the end of 1932, in response to employment discrimination, the NAACP sent Roy Wilkins, then the assistant NAACP secretary, and George Schuyler, a journalist and author, undercover to investigate conditions for the 30,000 black workers in the War Department’s Mississippi River Flood Control Project.
In 1939 the NAACP created its Legal Defense and Educational Fund, Inc., to litigate cases and raise money exclusively for the legal program. On the cultural front, the NAACP deliberated about the prospect of Jesse Owens’s and other black athletes’ participation in the 1936 Olympics in light of Nazi propaganda and urged them not to participate. After the Daughters of the American Revolution barred Marian Anderson from singing at Constitution Hall in 1939, the NAACP worked with the Franklin D. Roosevelt administration to stage a concert for her at the Lincoln Memorial. Read more about The Great Depression »
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World War II and the Post War Years
As the United States entered World War II, the NAACP joined union organizer A. Philip Randolph in support of a massive March on Washington to protest discrimination in the armed forces and defense industries. The march never took place. In the midst of the war, NAACP Executive Secretary Walter White toured the European, Mediterranean, and Pacific Theaters of Operation to observe and report on the experience of black soldiers. In 1945 the NAACP sent Walter White and W. E. B. Du Bois to the United Nations Conference on International Organization to propose the abolition of the colonial system. Du Bois reinforced the NAACP’s position in 1947 by submitting to the United Nations “An Appeal to the World,” a petition linking the history of racism in America to the treatment of people of color under colonial imperialism. The following year, in response to NAACP pressure, President Harry Truman issued two executive orders banning discrimination in federal employment and armed forces. On the legal front, the Supreme Court handed the NAACP important victories against all-white voting primaries, segregation in interstate travel, and restrictive covenants in Smith v. Allwright, Morgan v. Virginia, and Shelley v. Kraemer. Read more about World War II and the Post War Years »
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The Civil Rights Era
The NAACP’s long battle against de jure segregation culminated in the Supreme Court’s landmark Brown v. Board of Education decision, which overturned the “separate but equal” doctrine. Former NAACP Branch Secretary Rosa Parks’ refusal to yield her seat to a white man sparked the Montgomery Bus Boycott and the modern civil rights movement. In response to the Brown decision, Southern states launched a variety of tactics to evade school desegregation, while the NAACP countered aggressively in the courts for enforcement. The resistance to Brown peaked in 1957–58 during the crisis at Little Rock Arkansas’s Central High School. The Ku Klux Klan and other white supremacist groups targeted NAACP officials for assassination and tried to ban the NAACP from operating in the South. However, NAACP membership grew, particularly in the South. NAACP Youth Council chapters staged sit-in demonstrations at lunch counters to protest segregation. The NAACP was instrumental in organizing the 1963 March on Washington, the largest mass protest for civil rights. The following year, the NAACP joined the Council of Federated Organizations to launch Mississippi Freedom Summer, a massive project that assembled hundreds of volunteers to participate in voter registration and education. The NAACP-led Leadership Conference on Civil Rights, a coalition of civil rights organizations, spearheaded the drive to win passage of the major civil rights legislation of the era: the Civil Rights Act of 1957; the Civil Rights Act of 1964; the Voting Rights Act of 1965; and the Fair Housing Act of 1968. Read more about The Civil Rights Era »
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A Renewal of the Struggle
The NAACP struggled through the 1970s and 1980s, a period marked by change and many challenges. NAACP Executive Director Roy Wilkins ended his long tenure with the association (1931–1977) and Margaret Bush Wilson became the first black woman to chair the NAACP Board of Directors. The NAACP built on the legal and legislative victories of the civil rights era by supporting race-conscious initiatives to redress the legacy of racial discrimination. The NAACP backed busing to achieve school desegregation and affirmative action programs with the government and private sector. But by the mid-1970s, the NAACP faced the threat of bankruptcy as the result of two lawsuits and criticism about its relevancy from proponents of the Black Power Movement. In the 1980s, the Reagan administration reduced the budget of the Equal Opportunity Commission, tried to disband the U.S. Commission on Civil Rights, reduced the number of civil rights attorneys in the Justice Department, and urged the Supreme Court to end affirmative action. The confluence of challenges in the 1970s and 1980s spurred the NAACP to find new ways of defining its mission to address the issues of African Americans. Read more about A Renewal of the Struggle »
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Towards A New Century
During the 1990s the NAACP pursued economic empowerment, youth programs, and voter registration as top priorities. To "stem the tide of black land loss," the NAACP supported black farmers in a class action lawsuit against the U.S. Department of Agriculture alleging racial discrimination. The NAACP began a campaign to protest the flying of the Confederate flag in South Carolina. The NAACP also addressed the rise in hate crimes, evinced by a series of black church fires that swept the Southeast.
As it celebrates its centennial, the NAACP is reflecting on the progress made and the work still to be done. At the dawn of the twenty-first century, the NAACP continues to seek new ways of defining its mission. The organization is endeavoring to expand membership and build coalitions by reaffirming its origins as a racially and ethnically diverse human rights organization. While supporting enforcement of existing civil rights laws, the NAACP is devising new strategies to redress racial disparities in education, employment, housing, health care, the criminal justice system, civic engagement, and voting rights. As long as racial hatred and discrimination exist, the NAACP will wage a relentless campaign “to ensure the political, educational, social, and economic equality of rights of all persons.” Read more about Towards A New Century »
View all items from Towards A New Century » | 4.790338 |
Since we often see exponents throughout all math courses, it is important to understand the rules of exponents. We need to understand how to distribute, add, multiply and divide exponents in order to simplify expressions or manipulate equations that have exponents. The rules of exponents, like those involving multiplication of terms, are important to learn and will be used throughout Algebra I and II and Calculus.
So as you know an exponent is the little number above a base, so if you have like 3 squared, the 2, 3 the second is your exponent. And basically all it's telling you is to multiply the base times itself that many times. So 3 to the fourth is just 3 times 3, times 3, times 3. Or 3 times 3 is 9 times 3 is 27, times 3 is 81. Okay and with exponents come a long a bunch of rules that we're going to go through one at time. Okay so let's start over here, our first rule is that, if our bases are the same we're multiplying 2 terms of exponents and our bases are the same we can just add our exponents together. So let's say I have 3 squared times 3 to the third. Basically I have 2 times 2 here, 2 times 2 times 2 here in that sense where I really have is 5 2's and this I just going to equal 2 to the fifth.
The other way of doing that is just adding 2 and 3. Similarly if we are dividing okay, if have the same base and have our exponents we then just subtract. And this one actually depends on which number is bigger, so if we have 3 to the fourth over just say 3 there's really a imaginary one right here. So only have 3 to the 4 minus 1, this is just going to be 3 to the third okay. If our power in the denominator is larger we're just going to be left with a power in the bottom okay. So another example of this we'd say like 5 squared over 5 to the fourth. We still go 5 to the numerator exponent minus denominator exponent but what we end up with is 5 to the negative second. We'll talk about it in a minute but basically what that negative exponent means is it's left in the denominator.
Okay so really the easiest way to look at this is first just look at your exponent see which one is bigger your numerator or denominator and that's going to be where your term ends up being. Okay another rule is anything to the zero power is equal to 1, easy enough 4 to the zero 1, 822 to the zero 1, okay anything to the zero of power is just going to be 1. This one is already touches back to what I talked about over with the division one. Anything to a negative exponent is basically going to put that in the denominator of a fraction so if we have 4 to the negative third this is just equal to 1 over 4 to the third okay. Basically it takes the same term, the same number just moves it down to the denominator. Common mistake is people like to think that okay this 3 can come out in front and makes the entire thing negative. No it just moves a term that's normally in the top down to the bottom.
Likewise if we have a negative exponent in the denominator, it's just going to move it up to the top okay. So anytime you see negative exponent really all that does is it takes something in the numerator moves it to the denominator, something in the denominator moves it up to the numerator okay. Moving on if we have a fraction to a power that power gets distributed into everything okay. So what we really end up doing is taking the m and putting it to both the a and the b ending up with a over m, b over m okay. So alright a to the m, b to the m, so example if we have 2 third squared what we really end up with is 2 squared over 3 squared which is the same thing as 4 over 9. That pen is about dead.
Alright same idea for multiplication, if we are multiplying inside of parenthesis and we have to a power this power can be distributed in. So say we have 3x to the fifth that 5 can get distributed in to both the 3 and the x giving us 3 to the fifth x to the fifth okay. Couple more to go, anytime we have an exponent, a term to an exponent to an exponent we just multiply these out okay. So what we end up with is a to the m to the n just turns up to a to the m times n. Example of this say we have 2 cubes to the fourth okay, all we have to do is say 2 to the 3 times 4 which turns into 2 to the twelfth okay. You could just write this out if you wanted to this is really 2 cubed, times 2 cubed, times 2 cubed, times 2 cubed each one has 3 so in essence we have 12 twos but this is a good shortcut to keep in mind.
And our last rule that we're going to talk about is anything, a fraction to a negative power okay, this is basically just going to be the denominator to this power over the numerator to the power. Reason being is we can go back to this statement up here and basically distribute this negative and n, and what would end up with then is a to the negative n over b to the negative n. Remembering our rules and negatives from over there a to the negative n is just going to be a to the n in the denominator b to the negative n is just going to be a b to the n in the numerator. So really all we did is distribute this term n and then the negative flips our fraction okay. So a lot of different rules they do take sometime to get used to and remembering how they work but the main thing is remember if you are multiplying your bases you add your exponent if you are taking a power to a power you multiply and anytime you see a negative exponent that is just going to flip where your term is. If it was in the numerator it goes to the denominator, denominator it goes to the numerator and if you have a fraction the negative exponent is just going to flip your fraction altogether.
Okay so a lot to remember but take sometime play around with them a little bit and I'm sure you'll be fine. | 4.820379 |
Students engage in several online simulations and in-class investigations related to the density of liquids, solids, and gases. They apply new understanding about density to the design and construction of hot air balloons. They make informed predictions about the variables that may affect the launch of their homemade hot air balloons and test them. The finale is the “Got Gas?” rally where students display their balloons and use multimedia presentations to demonstrate the principles of density used in the construction of their hot air balloons.
View how a variety of student-centered assessments are used in the Density: Got Gas? Unit Plan. These assessments help students and teachers set goals; monitor student progress; provide feedback; assess thinking, processes, performances, and products; and reflect on learning throughout the learning cycle.
Present the Essential Question, How is science applied in the real world? Hold a general discussion on this question. Discuss properties of matter, such as color, shape, flexibility, strength, and as many other properties that students can brainstorm and why the properties might be important. Tell students that for the next few weeks, they will be investigating the property of density. Have them write everything they know about density and why density might be important.
Have students investigate specific properties of matter with the layered liquids lab. In this lab, students layer mystery liquids and compare their relative densities. Give each team one set of equipment (see materials on the lab worksheet). The liquids are as follows:
Each group should have 5 ml of each unknown liquid. Directions for the students are given in the "Procedure" section on the lab sheet. (Note that this procedure can also be done as a teacher-only demonstration.)
Explain that students will move from comparing the density of liquids to investigating the density of solids. Have students navigate to Density*, an online simulation that encourages students to experiment with different variables and determine the effects of mass and volume on density. A teacher’s guide and related materials are included on the site.
For extended learning, students can complete the Buoyancy Lab*, an online simulation that helps students further explore density properties by adjusting the density of a liquid to determine the effects on buoyancy of a solid object. Related handouts and materials are included on the site.
Through these online simulations, students should make a connection between the Layered Liquids Lab and the online density labs. After the labs, discuss the Content Question, What are the relationships among mass, volume, and density?
Expand on the investigations from the online density labs by discussing operational definitions and how to calculate density using the How Dense? lab. Explain to students that they will measure the absolute densities of liquids from the Layered Liquids Lab. Note that the liquids are the same as those compared in the Layering Liquids Lab. Each group's lab setup requires 25 ml of each sample liquid. Discuss procedures and data collection in advance of the activity. Explain to students that a bar graph would be appropriate for this type of data. Also, this would be a good opportunity to use a spreadsheet program to input the data and make various types of graphs. This would allow students to quickly see which types of graphs are most revealing and useful.
For further investigation, students can navigate to Determination of Density of a Solid*, an Online Labs simulation that allows students to determine the density of various solids by using a virtual spring balance and a measuring cylinder. Before beginning, ask students what they learned about comparing the density of fluids that might help them think about measuring the density of a solid. (Mass is determined by comparing an object of unknown mass to an object of known mass, using a balance scale.) You may wish to review the lab animation* and answer any questions before students enter the simulator. After completing the simulation, have students complete the online quiz* to check for understanding.
If you have limited Internet access or computing equipment, you can use the optional Solids Lab procedure instead. Following the procedures outlined in the document, students should be able to find the density of a variety of objects using the appropriate method by the end of this session. Note that students will need two cubes made from different materials (for example, steel and aluminum) and an irregular sample of either steel or aluminum to complete this lab.
Ask students, If you put hot and cold water together, what will happen? Discuss predictions and then do the following hot/cold density demonstration:
Ask students what the explanation might be for what was observed. Have students write or discuss what ways temperature affects density. Use online simulations to demonstrate what happens to gas molecules under different temperatures. Some recommended simulations include:
Discuss scientific modeling and explain how molecules have been modeled in different ways over time. Discuss the density of gases as compared to solids and liquids.
Applying Density Concepts to Hot Air Balloons
Students are now ready to apply their knowledge about density in the construction of a hot air balloon. Present the Unit Questions: How does the density of specific matter affect the construction process? and What principles of density are applied in hot air balloons?
Divide students into small groups. Announce that the class will be hosting the “Got Gas”? Hot Air Balloon Rally. The students’ task is to construct hot air balloons that will give riders the smoothest and longest flight. The students will work in groups and research how hot air balloons work and which variables to consider when constructing balloons. Guide this activity with the balloon research worksheet. Have groups create a balloon name and list as many variables that affect flight time as they can. Discuss these variables as a class, and have students expand and modify notes accordingly.
Give each student an experiment data sheet, and present the problem, What causes some hot air balloons to have longer flight times than others? Instruct students to discuss this within their groups, and write hypothesis and prediction statements. (Help narrow the choices of independent variables to those relating to balloon weight, temperature difference inside and outside the balloon, wind speed, and direction.) Have each group make a chart showing independent, dependent, and constant variables.
Instruct students to research the materials needed to build their balloons using the Internet sources listed. Students should consider the density of each of their chosen materials (such as straws, plastic sheeting, string, paper cups, and so forth) and provide a rationale for their choices. Have groups turn in a list of supplies needed to build their balloon and have those supplies ready by the next class or have students bring in their own supplies. A pattern of a hot air balloon is included as an example, or each group can find or make their own pattern.
Students are now ready for construction day. Explain that groups should document the density of each type of material used in their hot air balloon and the rationale for choosing the material. They should also describe how they used principles of density to ensure a long flight time and smooth ride.
Hold the “Got Gas?” Hot Air Balloon Rally! Assign each group a designated flight time. Flight is judged by time, integrity of materials, and smoothness of ride. Tell students to set up a data table and graph while waiting for flight times, and work on their presentations by drawing illustrations of their project to scan into later publications and/or taking pictures. Students can also use photo editing software or online drawing programs to create high-quality visual representations of their project.
Share the student example slideshow and discuss the criteria for the presentations. Introduce the presentation rubric and keeping track brochure checklist. Explain that students are to complete two presentation projects:
Have groups present their multimedia presentations and display their brochures. Have students self- and peer-assess their collaboration skills using the peer rubric and their presentations using the presentation rubric.
Note: In addition to the student brochure and slideshow presentations, students may develop a class wiki* on the topic of density.
Students use the density test practice to review the concepts of the density lessons and prepare for the short-answer and practical exam.
Present the Essential Question again, How is science applied in the real world? Use density as the focus this time. Encourage students to further investigate this question by researching other examples when knowing the density of matter is applied to other situations (such as density of gold to identify fool’s gold, packaging material, body density, all construction projects, and so forth).
English Language Learner
Gina Aldridge participated in the Intel® Teach Program, which resulted in this idea for a classroom project. A team of teachers expanded the plan into the example you see here.
Grade Level: 6-9
Subject(s): Physical Science
Topics: Properties of Matter
Higher-Order Thinking Skills: Analysis, Experimental Inquiry
Key Learnings: Density, Scientific Method
Time Needed: 4 weeks, 50-minute lessons, daily
Background: From the Classroom in Mesa, Arizona, United States | 4.852394 |
Comprehension Skills, Strategies & Best Practices
This module explores comprehension strategies and their benefits. Examine descriptions of each type of comprehension strategy, instructional implications for teaching comprehension, and sample lessons.
Although word recognition, decoding, and fluency are building blocks of effective reading, the ability to comprehend text is the ultimate goal of reading instruction. Comprehension is a prerequisite for acquiring content knowledge and expressing ideas and opinions through discussion and writing.
Comprehension is evident when readers can:
Comprehension strategies work together like a finely tuned machine. The reader begins to construct meaning by selecting and previewing the text. During reading, comprehension builds through predicting, inferring, synthesizing, and seeking answers to questions that arise. After reading, deeper meaning is constructed through reviewing, rereading portions of the text, discussion, and thoughtful reflection. During each of these phases, the reader relates the text to his own life experiences.
Comprehension is powerful because the ability to construct meaning comes from the mind of the reader. Therefore, specific comprehension instructionmodeling during read-alouds and shared reading, targeted mini-lessons, and varied opportunities for practice during small-group and independent readingis crucial to the development of strategic, effective readers.
There are six main types of comprehension strategies (Harvey and Goudvis; 2000):
Students quickly grasp how to make connections, ask questions, and visualize. However, they often struggle with the way to identify what is most important in the text, identify clues and evidence to make inferences, and combine information into new thoughts. All these strategies should be modeled in isolation many times so that students get a firm grasp of what the strategy is and how it helps them comprehend text.
However, students must understand that good readers use a variety of these strategies every time they read. Simply knowing the individual strategies is not enough, nor is it enough to know them in isolation. Students must know when and how to collectively use these strategies.
Modeling through think-alouds is the best way to teach all comprehension strategies. By thinking aloud, teachers show students what good readers do. Think-alouds can be used during read-alouds and shared reading. They can also be used during small-group reading to review or reteach a previously modeled strategy.
Wilhelm (2001) describes a think-aloud as a way to:
There are many ways to conduct think-alouds:
When you introduce a new comprehension strategy, model during read-aloud and shared reading:
Use the following language prompts to model the chosen strategy :
Determine Text Importance
Revisit the same text to model more than one strategy. For example, on Monday, use a text to model what's important versus what's interesting. On Tuesday, use the text to model how to identify big ideas. On Wednesday, use the big ideas to summarize and synthesize.
Extend the text as a reader-response activity. For example, on Monday, use a text as a shared reading lesson to model how cause-and-effect relationships help determine text importance. On Tuesday, extend thinking: map the cause-and-effect relationships onto graphic organizers, synthesize big ideas, and draw conclusions.
Strategy: Determine Text Importance (Main Idea/Supporting Details)
Text: greeting card, Benchmark Education Company's Comprehension Strategy Poster Safety Signs
Main Idea: Read the title and the first sentence. Ask: Is the author telling us the main idea here? Model thinking about the strategy: The title of the selection is Signs. This is the topic, which gives us a clue about the main idea. In the first sentence, the author states that it is easy to read road signs if you look at their colors. That sounds as though it is an important concept the author wants us to know about signs. Now I'll keep reading to see what types of signs the author mentions to support this idea.
Supporting Details: Read the second, third, and fourth sentences. Ask: Does the author tell us supporting details here? How do you know? Model your thinking: The author describes three different colors of signsred stop sign, a yellow be careful sign, and an orange work sign. These examples support the main idea that colors help us read road signs.
Strategy: Determine Text Importance (Implied Main Idea/Supporting Details)
Text: Benchmark Education Company's text PlantsLevel 12 (G)
Use a real-life example to model how to infer.
Say: Listen carefully to the following sentence: Even though the children wore heavy coats, they were shivering as they waited for the bus. I'm giving you a hint as to what season it might be. I don't tell you, but you can use the clues in the sentence to infer that it is winter. Many times, authors do not directly state information in the text. To be good readers, we have to infer as we read. We use clues and evidence to figure out what the author hints or implies.
We're going to find an implied main idea for two different parts of a book. We know that the main idea is the most important information that the writer wants us to understand. In this case, the topic is plants. We'll need to think carefully about what the authors tell us about plants so that we can understand the implied main idea. Remember, the main idea will not be directly stated.
Create a graphic organizer.
To activate students' prior knowledge about plants, creating a KWL chart. Record what they already know about plants in the K column and what they would like to know in the W column. Tell them that they will complete the L column after they read.
Preview the book.
Hold up the book. Ask: What do you see in the photograph on the cover? What do you think the girl is doing? What kind of plant is shown on the cover?
Look at the title page. Ask: What do you think these children are doing? How are plants involved? What things are the children using as they work with the plants?
Preview the photographs in the book, reinforcing the language used in the text. For example, say: On page 2, I see three kinds of plants. What are some ways that plants are alike?
Set a purpose for reading.
Say: I want you to see if you can find answers to the questions on our KWL chart. Monitor students' reading and provide support as necessary.
Discuss the reading and complete the graphic organizer.
Ask students to share answers to any questions from the KWL chart that they found during the reading. Complete the L column of the chart.
Sample Small-Group Reading Lesson
Model how to determine the implied main idea utilizing a graphic organizer.
Remind students that to infer means to understand clues and evidence that the author has provided for us in the text. Implications are not directly stated.
Say: The first part of the book (pages 211) gives me many details about the parts of a plant. One detail is that roots help a plant stay in the ground. The book also tells me that roots help a plant get water. I'll write these facts in the first Supporting Details box. Now I'll look for other details to add to my chart. Leaves make food for the plant. Stems take water to the leaves and flowers. Flowers make seeds. New plants grow from seeds. All these details tell me how the parts of a plant help it grow and stay alive. Even though the author didn't directly state this as the main idea, the clues and evidence imply it. I'll write this on the chart where it reads Main Idea #1.
Main Idea/Supporting Details
Guide students to identify the second implied main idea.
Briefly review pages 1216. Then ask students to select the most important details and use those as clues and evidence to find the implied main idea. If students need additional modeling and think-alouds, complete the remainder of the graphic organizer together. If they seem to understand the concept, allow them to complete the graphic organizer in small groups, pairs, or individually. Monitor their work and provide guidance as necessary. Allow time for students to share their recorded information.
Main Idea/Supporting Details | 4.70965 |
Lesson 1: Probability Basics
In this lesson, students use the flipping of a coin to understand the relationship between probability and real-word outcomes. They also practice using diagrams, tables, and the fundamental counting principle to calculate probability.
- Students will understand that probability can be expressed as a fraction, a decimal, or a percentage; and
- Students will use tree diagrams, tables, and the fundamental counting principle to calculate probability.
- one coin (for demonstration)
- Worksheet 1 Printable (PDF): "Smartphone Test Prep"
- Resource: Worksheet Answer Key (PDF)
- Resource: Mini-Poster (PDF)
- Resource: Standards Alignment Chart (PDF)
- Bonus Activity: Online Probability Challenge
Click for whiteboard-ready printables.
1. Show the class a coin. Ask the class whether it will land on heads or tails if flipped. Students should answer that it could land on either heads or tails. Ask if there is a way to quantify the chance that it will land on heads. If the class doesn't mention the word probability, introduce it and note that it means "a fraction, decimal, or percentage describing the likelihood of an event occurring." Explain how no event can have less than a 0% chance or more than a 100% chance of occurring.
2. Ask for examples of how probability is used in the real world. The topic of weather forecasts may be mentioned. Make sure the class understands that a 40% probability of precipitation means that there is a 40% likelihood that precipitation will fall within a given area. Gaming/odds may also be mentioned. You can also introduce to students the fact that companies (insurance and financial companies in particular), statistical experts such as actuaries, and individuals in daily life use probability to make reasonable predictions about the future and to assess risk.
3. Ask what the probability is of a flipped coin landing on heads (1/2). Ensure that the class understands that the numerator (1) represents the number of favorable outcomes (heads) while the denominator (2) represents all possible outcomes (heads and tails). If students haven't mentioned it, ensure that they are also able to express the probability as .5 or 50%.
4. Ask what outcomes (i.e., heads/tails combinations) are possible if the coin is flipped two times, e.g., heads/heads or tails/heads. If students begin to offer outcomes in a haphazard order, ask them how they could make sure they recorded all possible outcomes without double counting. Suggest, for example, a tree diagram and model how it can be used to identify the four different outcomes. Ask what the probability is for any one outcome (1/4, .25, or 25%).
5. Model for students how a table or an organized list could be used to determine the number of possible outcomes. See poster for example if necessary.
6. Ask what the probability is of flipping one head and one tail. There are four possible outcomes and two favorable ones (heads/tails and tails/heads). Point out that even though this would initially be depicted as 2/4, we would want to reduce to lowest terms, so our final answer would be 1/2, .5, or 50%.
7. Now ask how many outcomes are possible if the coin were flipped three times (eight outcomes). Ask students to explain how a tree diagram, a table, or an organized list could be used to solve the problem in an organized way. Demonstrate if necessary.
8. Ask students if there is a way to determine the number of outcomes without using a table or a tree diagram. Demonstrate how the fundamental counting principle could be used, i.e., two possible outcomes for the first, second, and third flips or 2 x 2 x 2 = 8 or 23.
Have students use the Online Probability Challenge to practice using probability skills for real-life purposes. This interactive online activity challenges students to use probability to help Rick and Athena plan a summer concert tour. This activity can be used as an in-class lesson activity or an out-of-the-classroom extension. | 4.868611 |
MATHEMATICS OF FAIR GAMES
Grades 4 - 5
The students will learn about mathematicians' notion of fairness
in games of chance. They will work in pairs to perform three different experiments
using macaroni and paper bags. They will record their results on charts
to compare data and make conjectures regarding the role that fairness over
Square One TV: Challenge Round - Focus on Probability (Children's
Students will be able to:
- Describe what makes a game of chance fair or unfair.
- Explain why repeated trials are necessary in an investigation.
- Make predictions about whether a given game is fair or unfair.
- Carry out several investigations.
- Display data in a chart.
- Compute class totals using a calculator.
- Draw conclusions based on the data obtained in the investigations.
- List the mathematical possibilities for all possible outcomes.
- Compare the results of the investigations to the true mathematical
Each pair of students:
- small paper bag
- three shell shaped macaroni
- two elbow shaped macaroni (or any other small contrasting shapes or
- six sheets of three inch by three inch Post-It notes
- magic marker
- tally sheet and a calculator
- one large piece of newsprint paper should be prepared ahead of time
to receive the Post-It tallies for each pair
- fair game
Ask the students,"Have you ever heard someone flip a coin
to decide something and say 'Heads I win, tails you loose.?' What are the
elements that make a game fair?" Discuss what fairness means in games.
Students should understand that although they may have heard "That's
not fair" during a game, any good game must be fair so that each player
has an equal chance at winning.
The focus for viewing is a specific responsibility or task(s)
that focuses and engages student's viewing attention. Tell the students
to think about what it means to be a fair coin.
START the video at the beginning and PAUSE it
after the game show host says, "The focus is probability." Ask
the students what experiences they have had with probability and what it
means to them. RESUME the video. PAUSE it after the game show
host says, "I have a fair coin." Discuss with the students what
it means to have a fair coin and how this connects to the concept of probability.
RESUME the video. PAUSE it after the game show host says,
"Which is more likely on my next flip, heads or tails?" Ask the
students how they think the celebrities will respond. RESUME the
video. After the celebrities have given their responses, PAUSE the
video when the game show host says, "Think about it and write down
your answers." Give the students a few minutes to do the same. RESUME
and PLAY video to the end.
Remind the students that the reason the coin used in the video
was a fair coin was because each side had an equal chance of turning up
when the coin was flipped. The probability of getting a head was one-half
and the probability of getting a tail was also one-half each time the coin
was flipped. Discuss how this concept might apply to fair games and then
pass out the prepared materials necessary to play the games. Call the students'
attention to the newsprint chart at the front of the room. Tell them that
they are going to test the fairness of the three games described on the
newsprint. Ask for a volunteer to be your partner to help demonstrate the
Place two shells and one elbow in the paper bag. Ask them to think about
game # three. (See newsprint.) If partner # one was to score a point each
time the two noodles selected from the bag were the same and partner # two
scored a point each time the noodles selected were not the same, would this
be a fair game or does one of the players have a better chance? Demonstrate
this scenario twenty times for the students keeping a tally on the board
for when the noodles were the same and when they were different.
Call their attention to the three games for investigation (on the newsprint).
Game #1 - three shells, one elbow
Game #2 - two shells, two elbows
Games #3 - two shells, one elbow
Tell them that their job is to investigate which, if any, of these games
is fair. Discuss their predictions. Have them experiment twenty times with
each game, keeping a tally for each trial. As they finish each game they
record the totals of "same" and "different" on their
post-its and place the post-its on the newsprint chart.
Ask students who finish early to calculate the class totals. (There will
be opportunities for six pairs of students to do this.) Have each partner
double-check the total found with a calculator and record it on the newsprint
chart. When all of the statistics have been recorded and calculated, have
the class draw conclusions about fairness based on the data obtained in
Only one version of the game is mathematically fair - version # one. This
seems counter intuitive to many students and the data may or may not support
it. List the possibilities for drawing two noodles from the bag to explain
this concept. (See attached worksheet.)
- Students may take a field trip to a toy store that has a variety of
different types of games and discuss some of the games with a knowledgeable
representative. For instance, which games are games of chance and which
are games of strategy? They could compile a list of questions to ask the
- A speaker from a toy company may be invited to the classroom to explain
the process involved in determining rules for fair games.
- Students may wish to write to companies who create board games. Addresses
can be found in a library or Web site. Students can inquire about how companies
think up new games, the guidelines they use to design them, and the marketing
concerns they need to consider.
Students can bring to class games of their own and explain how
they demonstrate this concept. Tell them to consider whether it is a game
of chance or of strategy. You may wish to tell them to analyze the rules
for fairness and probability.
Students can create their own games describing the rules for play and explaining
why the game is fair and then present the game to the class.
Students can investigate games from different cultures such as Dreidel which
is traditionally played at Chanukah.
Science: Students can investigate how this concept applies to dominant and
Students can discuss how they think chance affects population growth in
Master Teacher: Mary Ellen Baron
Springfield School Department, Springfield, MA
Lesson Plan Database
Thirteen Ed Online | 4.71441 |
In this chapter rotational motion will be discussed. Angular displacement, angular velocity, and angular acceleration will be defined. The first two were discussed in Chapter 5.
Angular Displacement: The symbol generally used for angular displacement is θ pronounced "teta" or "theta." θ is the angle swept by the radius of a circle that points to a rotating mass, M, under study. Below, the symbol ω is pronounced "omega" is used to denote angular velocity.
Example 1: An object travels around a circle10.0 full turns in 2.5 seconds. Calculate (a) the angular displacement, θ in radians, and (b) its average angular speed, ω in (rd/s).
Solution: (a) θ = 10.0 turns ( 6.28 rd / turn ) = 62.8 radians.
(b) ω = Δθ / Δt = 62.8 rd / 2.5s = 25 rd/s.
Angular Velocity (ω): Angular velocity is defined as the change in angular displacement, θ, per unit of time, t.
ω = Δθ/Δt ; [rd/s]
Angular Acceleration (α): Angular acceleration is the change in the angular velocity, ω, per unit of time, t.
α = Δω/Δt ; [rd/s2]
The symbol α is pronounced " Alpha."
Example 2: A car tire is turning at a rate of 5.0 rd / sec as the car travels along a road. The driver increases the car's speed, and as a result, each tire's angular speed increases to 8.0 rd /sec in 6.0 sec. Find the angular acceleration of the tire.
Solution: α = Δω / Δt ; α = (ωf - ωf) /Δt ; α = ( 8.0 rd/s - 5.0 rd/s ) / 6.0s = 0.50 rd/s2.
As can be seen, there is an excellent correspondence between the linear formulas we learned in Chapter 2 and the angular formulas defined here. The following chart, shows the one-to-one correspondence between the linear and angular variables and formulas:
Variables: x, t, v, and a
v = Δx / Δt.
a = Δv / Δt ; a = ( vf - vi ) / Δt.
x = (1/2) a t2 + vi t.
vf2 - vi2 = 2 a x.
θ, t, ω,
ω = Δθ / Δt.
α = Δω / Δt ; α = ( ωf - ωi ) / Δt.
θ = (1/2) α t2 + ωi t.
ωf2 - ωi2 = 2 α θ.
The Relations between Linear and Angular Variables:
Each of the angular variables θ, ω, and α is related to its corresponding linear variable x, v, and at by factor R, the radius of rotation.
x = Rθ ; v = Rω ; at = Rα . (at means tangential acceleration).
This can be easily verified by the following simple mathematics:
Starting with s = Rθ, or x = Rθ and writing as Δx = RΔθ, and then dividing both sides by Δt, yields:
Δx/Δt = RΔθ/Δt ; the left side is v and the right side is ω ; therefore, v = Rω.
If v = Rω is divided through by Δt , yields:
Δv/Δt = R Δω/Δt ; the left side is at and the right side is α ; therefore, at = Rα.
s = Rθ
v = Rω
at = Rα (tangential acceleration)
Note in the 3rd figure that there are two types of acceleration in rotational motion. One type is at , the tangential acceleration that is responsible for the change in the magnitude of the linear velocity, v. Pushing a merry-go-round, gives it tangential acceleration because the push is tangent to a circular path.
The other type is ac, the centripetal acceleration that is responsible for the change in the direction of v. This acceleration is always directed toward the center of rotation (not shown here to keep the diagram more clear). It was discussed in Chapter 5.
Example 3: As a car starts accelerating ( from rest ) along a straight road at a rate of 2.4 m/s2, each of its tires gains an angular acceleration of 6.86 rd/s2. Calculate (a) the radius of its tires, (b) the angular speed of every particle of the tires after 3.0s, and (c) the angle every particle of its tires travels during the 3.0-second period.
Solution: (a) Since a linear variable and its corresponding angular variable are given, the radius of rotation can be
calculated. at = Rα ; R = at /α ; R = [2.4 m/s2] / [6.86 rd/s2] ; R = 0.35m = 14 in.
(b) α = (ωf - ωi)/Δt ; α Δt = ωf - ωi ; ωf = ωi + α Δt ; ωf = 0 +(6.86rd/s2)(3.0s) = 21 rd/s.
(c) θ = (1/2)α t2 + ωi t ; θ = (1/2)( 6.86 rd/s2)(3.0s)2 + (0) (3.0s) = 31 rd.
Example 4: The canister of a juicer has 333 grams of pulp distributed over its inside wall at an average radius of 8.00cm. It starts from rest and reaches its maximum angular speed of 3600.0 rpm in 4.00 seconds. For the pulp, determine (a) the angular acceleration, (b) the angle (radians) it travels during this period, (c) the tangential acceleration, (d) the linear velocity at t =2.00s and t = 4.00s, (e) the centripetal acceleration at t = 2.00s and t = 4.00s, and ( f ) the tangential and centripetal force on it at t = 2.00s and t = 4.00s.
Solution: (a) First calculate ω in (rd/s) ; ω = 3600 [rev/min] [6.28 rd/rev] [1 min / 60s] = 377 rd /s.
α = (ωf - ωi) /Δt ; α = ( 377- 0 ) / (4.00s) = 94.3 rd/s2.
(b) θ = (1/2) α t2 + ωi t ; θ = (1/2)(94.3 rd/s2)(4.00s)2 + 0 = 754 rd.
(c) at = Rα ; at = (0.0800m)(94.3 rd/s2) = 7.54 m/s2. (Refer to at in the above figure).
For Part (d), the values for final angular speed, ωf , must be calculated both at t = 2.00s and t = 4.00s.
α = (ωf - ωi) /Δt ; α Δt = ωf - ωi ; ωf = ωi + α Δt ; (ωf)1 = 0 +(94.3rd/s2)(2.0s) = 189 rd/s.
From the problem, at t = 4.00s, ω = 3600 rpm = 377 rd/s or, (ωf)2 = 0 +(94.3rd/s2)(4.0s) = 377 rd/s.
(d) v1 = R(ωf)1 ; v1 = (0.0800m) (189 rd/s) = 15.1 m/s.
v2 = R(ωf)2 ; v2 = (0.0800m) (377 rd/s) = 30.2 m/s.
(e) (ac)1 = v12 / R ; (ac)1 = (15.1 m/s)2 / 0.0800m = 2850 m/s2.
(ac)2 = v22 / R ; (ac)2 = (30.2 m/s)2 / 0.0800m = 11400 m/s2.
(f) Ft = Mat ; ( Ft )1 = ( 0.333 kg )( 7.54 m/s2 ) = 2.51 N ; ( Ft )2 = 2.51 N (Constant tangential force)
Fc = Mac ; ( Fc )1 = ( 0.333 kg )( 2850 m/s2) = 949 N
( Fc )2 = ( 0.333 kg )( 11400 m/s2) = 3800 N (3 sig. figures) ( Variable centripetal force)
Chapter 8 Test Yourself 1:
1) In Fig. 1, the angular displacement of mass M is (a) arc AB = S (b) ω (c) angle θ. click here
2) In Fig. 1, the linear displacement of mass M is (a) arc AB = S (b) ω (c) angle θ.
3) The relation between angle θ and arc S, the arc opposite to it, is (a) S = 2Rθ (b) S = Rθ (a) S = πRθ.
4) The symbol for angular speed is (a) θ (b) ω (c) S. click here
5) The relation between angular speed and linear speed is (a) S = Rθ (b) V = Rω (c) S = 2πR.
Problem: The angular speed of a wheel is such that it makes 80.0 turns in 20.0 seconds. The radius of the wheel is 35.0cm.
Answer the following questions:
6) The angular speed of the wheel is (a) 240 rpm (b) 4.00 turns/s (c) 25.1 rd/s (d) a, b, & c. click here
7) The linear speed of any point on the outer edge of the wheel is (a) 879 cm/s (b) 8.79 m/s (c) a & b.
8) The angular acceleration of the wheel is (a) half of its centripetal acceleration (b) a nonzero constant (c) zero, because the angular speed is constant. click here
9) The tangential acceleration of the wheel is (a) half of its centripetal acceleration (b) a nonzero constant (c) zero, because the linear speed is constant.
10) The centripetal acceleration of any point on the outer edge of the wheel that is at a radius of R = 35.0cm is (a) 25.1 m/s2 (b) 221 m/s2 (c) 221 rd/s2.
11) The variables in uniformly accelerated motion (motion along a straight line at const. velocity) are: x, t, v, and a. Write down the counterpart variables for rotational motion. Ans.: .................................... click here to check your answer.
12) Without referring to Table 1 above, try to write down the formulas you know for linear motion from Chapter 2. Then write down the corresponding angular formulas. Pay attention to the one-to-one correspondence between the variables and formulas.
Problem: Make sure you perform all calculations even if they seem obvious to you. We all know that our planet completes one revolution about its own axis every 24 hours. Answer the following questions:
13) The angular speed of the Earth in revolving about its own axis is (a) 1 rev./24h (b) 2πR/ 86400s (c) 6.28 rd/86400s (d) 7.27x10-5 rd/s (e) a, c, & d. click here
14) Any person who lives on the equator is at a radius of rotation of R1 = 3900 miles. He/she has a linear speed of (a) 0.283mi/s (b)456m/s (c) both a & b.
15) Any person who lives exactly at the North Pole or the South Pole where the Earth axis passes through, is at a radius of rotation of R4 = (a) 3900mi (b) almost 0 (c) neither a, nor b.
16) Whoever lives exactly at the North Pole or the South Pole, has an angular speed of (a) 7.27x10-5 rd/s (b) almost 0 (c) neither a, nor b. click here
17) A person who lives exactly at the North Pole, has a linear speed of (a) 456 m/s (b) almost 0 (c) neither a, nor b.
18) The radius of rotation of a person who lives in between the equator and the North Pole is (a) less than 0 (b) more than 3900mi (c) less than 3900 miles.
19) The radius of rotation for the people who live 45º above the equator is R2 = (a) [3900/2] miles (b) [3900/45º] miles (c) 3900cos45º miles. click here
20) The linear speed of the people who live 45º above the equator is (a) 323 m/s (b) 0.200 mi/s (c) both a & b.
21) The tangential acceleration of any person on this planet because of Earth motion about its own axis is (a) 9.8 m/s2 (b) 0 (c) 456 m/s2.
22) The centripetal acceleration of a person living on the equator because of the Earth's rotation about its own axis is (a) 9.8 m/s2 (b) 0 (c) 0.0331 m/s2. click here
23) Because of the Earth motion about its own axis, the direction of the centripetal acceleration vector for those who live on the equator is (a) parallel to the direction of g (b) perpendicular to the direction of g (c) neither a, nor b.
24) The direction of the centripetal acceleration vector for those who live 45º above the equator is (a) parallel to the direction of g (b) perpendicular to the direction of g (c) neither a, nor b.
25) The direction of the centripetal acceleration vector for those who live close to the North Pole (a) parallel to the direction of g (b) almost perpendicular to the direction of g (c) neither a, nor b. click here
Problem: Again, make sure you perform all calculations even if they look obvious to you. We all know that our planet completes one revolution about the Sun every year. Assume circular orbit for simplicity. Answer the following questions:
26) The angular speed of the Earth in its rotation around the Sun is (a) 2πR/yr (b) 6.28 rd/yr (c)1.99x10-7 rd/s (d) b&c.
27) Knowing that the average Earth-Sun distance is 150,000,000km, the linear speed of the Earth in its motion around the Sun is (a) 30mi/h (b) 30 km/s (c) 19 mi/s (d) b & c. click here
Problem: In the TV game "Price is right", suppose a person gives an initial angular speed of 2.0 rd/s to the wheel and the wheel comes to stop after 1.5 turns. Answer the following questions:
28) The final angular speed is (a) 2.0 rd/s (b) 0 (c) 1.5 rd/s. click here
29) The angular displacement, θ, before the wheel comes to stop is (a) 9.42 rd (b) 0.80rd (c) 6.28 rd.
30) Since time is not given, one good way to solve for the angular acceleration, α , is to use the equation.............................. . Write the equation first, and then check your answer. For answer, click here.
31) The value of α is (a) 0.21 rd/s2 (b) -0.21 rd/s2 (c) -0.21 rd/s.
32) The elapsed time is (a) 2.8s (b) 1.4s (c) 9.5s.
Problem: A car is traveling at a constant speed of 18.0m/s. The radius of its tires is 30.0cm. Answer the following:
33) The linear speed of every point on the outer edge of its tires that perform circular motion is (a) 18.0 rd/s (b) 18.0 m/s (c) neither a, nor b.
34) The angular speed ω of each tire is (a) 60.rd/s (b) 30. rd/s (c) 30. cm/s.
35) The angular acceleration of each tire is (a) 540 rd/s2 (b) 18 rd/s2 (c) 0.
36) The equation of its angular motion is (a) θ = αt2 + (60.0 rd/s)t (b) θ = (60.0rd/s)t (c) θ = ωt.
37) The angle each tire rotates in 45 seconds is (a) 2700 turns (b) 2700º (c) 2700 rd.
1) Calculate (a) the average angular speed of the Moon about the Earth that completes each turn in about 29 days, and (b) its average linear speed in its motion about the Earth. The average distance from here to the Moon is 384,000km.
2) A juicer reaches its maximum angular speed of 3600rpm, 2.00s after start. Find (a) its angular acceleration, (b) maximum linear speed of its porous cylinder wall if its radius is 12.0cm, (c), the centripetal acceleration of points on its inner cylinder wall when at maximum speed, and (d) the angular displacement of any point on its cylinder during the acceleration period.
3) A car tire is spinning at 377 rd/s in a tire balancing equipment. If it is slowed down to 251 rd/s in 3.00s, calculate (a) its angular acceleration, (b) the angle traveled during slowing down, (c) the number of turns made during slowing down, (d) the equation of its rotation, and (e) the angle traveled during the 3rd second.
4) Starting from rest, a mother pushes her daughter in a merry-go-round uniformly for 1/4 of a turn where she reaches a running speed of 6.0m/s. If the daughter's seat is at an average radius of 5.0m, calculate (a) her initial and final angular speeds, (b) her angular acceleration within the 1/4 turn, (c) the elapsed time, and (d) her tangential and centripetal acceleration when at 1/4 turn position.
5) For rotation about the axis of the Earth, find (a) the angular speed, (b) the linear speed, (c) the angular acceleration, (d) the tangential acceleration, and (e) the centripetal acceleration of the people who live at the 60.0º latitude above the Equator. Draw a sphere, select a point at the 60º latitude, and show both of centripetal acceleration and the gravity acceleration vectors at that point. Note that people at the Equator are at 0º latitude and the people at the North pole are at +90º latitude. The radius of rotation at the Equator is 6280km( the radius of the Earth), and the radius of rotation at each of the poles is zero. The radius of rotation about the Earth's axis at 60º latitude is (6280km)cos60 =3140km.
Answers: 1) 2.5x10-6 rd/s, 960m/s 2) 188 rd/s2, 45.2m/s, 1.70x104m/s2, 377 rd
3) -42.0 rd/s2, 942 rd, 150 turns, θ = ½ α t2 + ωi t, 272 rd
4) 0 and 1.2rd/s, 0.46 rd/s2, 2.6s, 2.3m/s2 and 7.2m/s2
5) 7.27x10-5 rd/s, 228m/s, 0, 0, 0.0166m/s2 | 4.814847 |
Reading to Learn: Comprehension Strategies
Rationale: In order to gain insight while reading one must be able to comprehend. However, students often fail to comprehend (and remember) what they have read. Because of this, teachers have been given comprehension strategies that can be taught to children in order to give them a helping hand. One such strategy is called story-grammar. The following activity will show children how to use the story-grammar strategy to help them comprehend what they are reading.
Materials: You will need two copies of ten different conventional stories (The Orphan Kittens by Margaret Wise Brown, Oliver Finds a Home by Justin Korman, Bambi by Felix Salten, Paul Revere by Irwin Shapiro, etc.) that the children will find interesting, Charlotte's Web by E.B. White (with highlighted passages for modeling), a question-answer sheet, and a pencil.
Procedure: 1. Explain to the boy's and girl's that today
they will be learning a strategy that will show them how to go about comprehending
what they read.
2. Have each child come up and choose a book from your selection (There should be two children throughout the room with the same book). Next pass out two question-answer sheets to each child. Tell the children to put the book and one of the question-answer sheets under their desk to be used at a later date.
3. Explain to the children that you want them to listen to you read Charlotte's Web. Tell them that after you read for a few minutes, you will stop, think about the first question on the sheet, and then answer it. Explain that you want them to answer the same question at their desk. You will do this throughout the reading of the book.
4. Now begin reading. After reading a few paragraphs (Read only the highlighted passages for modeling) ask the children to answer the first question: Who are the main characters? Give them two or three minutes to answer, and then read on. After you have read a few more passages, ask them to answer the second question: Where and when did the story take place? Continue this until you have read the entire story and the children have answered the other three questions consisting of What did the main characters do?, How did the story end?, and How did the main character feel? Be sure to let the children know there is no right or wrong answer for the question How did the main character feel? because itís is an open-ended question (Depends on readers interpretation of the story). Now have a class discussion about their answers.
5. The second part of the lesson requires the children to read silently (which is very good for a lot of reading skills such as fluency and comprehension) at their desk for ten minutes. (Model reading silent by telling the students to read by thinking the words in their head without saying them out loud). Ask the children to take out the book that they choose earlier along with the second question-answer sheet. Explain to them how you will set a timer for ten minutes, during which time they are to be reading the book they choose. When the ten minutes are up, ask the children to answer the first question on the sheet in front of them. Give them ample time to reflect on what they have read and then set the timer again. Do this throughout the entire book. (You may want to choose shorter stories or treat this as a daily but weekly, meaning they work on the same books all week, assignment).
7. When the children have finished the book and answered all the questions, have them pair up with the other person in the room who read the same book. Explain how you want them to discuss their answers with each other. If there is a disagreement among them, tell them to talk it over to see why. This will help them see how someone else came to their conclusions. Don't forget to read silently along with the children. (You may want to have one of your students read the same book that you are reading and then discuss it with them. If you do this, write your answers in their language). (This will keep them from feeling over-powered).
8. For a review you can ask the children what five questions they should ask themselves, while reading, to help them comprehend what they have read.
References: Pressley, M., Johnson, C. J., Symons, S., McGoldrick, J. A., & Kurity, J. A. (1989). "Strategies That Improve Childrenís Memory and Comprehension of Text. The Elementary School Journal, (1990, Pp. 3-32).
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In this lesson, students will learn about choices and opportunity costs that occur every day. While this lesson will go on throughout the day, the actual lesson is short.
- Keep a class list, noting the choices made as a class throughout the day as well as what was given up to make those choices.
- Complete a printable worksheet demonstrating an understanding of opportunity cost.
- Discuss the class chart that was kept until the end of the day.
- Complete the extension activity as homework with parents/guardians (If applicable).
In this lesson, you and your students will take a closer look at the choices that are made in the classroom everyday. At the end of the school day, you will discuss with them that every one of the things your class chose or did not choose has consequences that are either good or bad. Students will get a better idea about why it is important to think before they act and they will also gain a better understanding of why you do some things the way you do. You might even surprise yourself and find some things you could do better in your classroom!
"Choices Matter" Activity. Students can use this activity to aid their understanding of the impact of choices.
"My Choice" Worksheet. Students give an example of a choice that they have made and relate it to the opportunity cost of their decision.
"Choices, Choices!" Worksheet. Students write down there choices at home and bring them to class for discussion.
Begin a discussion about making choices. Ask the students to tell you some of the choices that they made before coming to school. As the students provide examples, make a list of these examples on the board. Then ask that student what they did not choose to do instead and write this example next to their '"choice". Before moving from one student to the next, ask that student if the thing they did not choose was the next best thing that they could have chosen to do. If not, have the student provide an example of what the next best choice would have been. Explain to the students that the next best thing that they didn't choose is their "Opportunity Cost" (Definition: The second-best alternative (or the value of that alternative) that must be given up when scarce resources are used for one purpose instead of another, e.g. If they chose to brush their teeth their opportunity cost might be eating candy.) Discuss with them whether or not the choice they made was good or bad and why. Once the concept of "opportunity cost" is understood, tell the students that you will be spending the day recording decisions that are made.
Using a large piece of poster paper divided into two columns with one column "choice" and the other "opportunity cost." List the choices made during the day. During the day, provide opportunities for the class to vote on things like whether to do math first or do puzzles first. Record the choices and at the end of the day discuss whether they made good decisions. Circle the ones students think should have been made differently and discuss what they should have considered when they were making those choices...
Remember, the list can include academics, activities, or behavior. Try to keep the list relevant to the class as a whole and not individuals.
Have the students complete the printable version of the activity called "Choices Matter".
Explain to students that there are choices that need to be made and they have to circle the best choice and put an X on the "opportunity costs."
Give each student a piece of paper (at least 8.5X11) or a copy of the printable worksheet "My Choice". Ask the students to explain and draw a picture of a choice that they made either before or during school on the top half. Tell them you would like to see examples of choices made outside of the classroom. Then have them explain and draw a picture of what the opportunity cost for that choice is on the bottom half. Remind students they may choose to draw a bad choice that they made, but if they do, the "opportunity cost" needs to be a picture of what would have been a better choice.
When the students are finished, you can call on volunteers to share and explain their pictures.
As a homework assignment, ask the students to solicit the aid of their parents and keep a journal for the remainder of the day about the choices made and what they gave up until bedtime (for younger students, the parents may need to do the recording).
You can have students decide as a class some things to put on a check list that could be used for the remainder of the day. It could include things such as: brushing their teeth or eating candy, staying up ten more minutes or having a bedtime story, etc.
You can use the printable sheet "Choices, Choices!"
Then use these activities for discussion the next morning.
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The 15th Amendment, granting African-American men the right to vote, was formally adopted into the U.S. Constitution on March 30, 1870. Passed by Congress the year before, the amendment reads: "the right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of race, color, or previous condition of servitude." Despite the amendment, by the late 1870s, various discriminatory practices were used to prevent African Americans from exercising their right to vote, especially in the South. After decades of discrimination, the Voting Rights Act of 1965 aimed to overcome legal barriers at the state and local levels that denied blacks their right to vote under the 15th Amendment.
More to Explore
Reconstruction refers to the period of upheaval in the American South after the Civil War and abolition of slavery.
The 14th Amendment granted citizenship and equal civil and legal rights to African-Americans and slaves who had been emancipated after the American Civil War.
The 1965 Voting Rights Act aimed to overcome legal barriers at the state and local levels that prevented African Americans from exercising their right to vote.
The American Civil War, fueled by the debate over slavery and states' rights, pitted North against South in the costliest conflict fought on U.S. soil.
Did You Know?
One day after it was ratified, Thomas Mundy Peterson (1824-1904) of Perth Amboy, New Jersey, became the first black person to vote under the authority of the 15th Amendment.
The 15th Amendment: Ratification
In 1867, following the American Civil War (1861-65), the Republican-dominated U.S. Congress passed the First Reconstruction Act, over President Andrew Johnson's veto, dividing the South into five military districts and outlining how new governments based on universal manhood suffrage were to be established. With the adoption of the 15th Amendment in 1870, a politically mobilized African-American community joined with white allies in the Southern states to elect the Republican Party to power, which brought about radical changes across the South. By late 1870, all the former Confederate states had been readmitted to the Union, and most were controlled by the Republican Party, thanks to the support of black voters.
In the same year, Hiram Rhoades Revels (1827-1901), a Republican from Natchez, Mississippi, became the first African American ever to sit in the U.S. Congress, when he was elected to the U.S. Senate. Although black Republicans never obtained political office in proportion to their overwhelming electoral majority, Revels and a dozen other black men served in Congress during Reconstruction, more than 600 served in state legislatures and many more held local offices.
The 15th Amendment: Post-Reconstruction Era
n the late 1870s, the Southern Republican Party vanished with the end of Reconstruction, and Southern state governments effectively nullified the 14th amendment (passed in 1868, it guaranteed citizenship and all its privileges to African Americans) and the 15th amendment, stripping blacks in the South of the right to vote. In the ensuing decades, various discriminatory practices including poll taxes and literacy tests, along with intimidation and violence, were used to prevent African Americans from exercising their right to vote.
IThe 15th Amendment and the Voting Rights Act of 1965
The Voting Rights Act, signed into law by President Lyndon Johnson (1908-73) on August 6, 1965, aimed to overcome legal barriers at the state and local levels that denied African Americans their right to vote under the 15th Amendment.
The act banned the use of literacy tests, provided for federal oversight of voter registration in areas where less than 50 percent of the nonwhite population had not registered to vote, and authorized the U.S. attorney general to investigate the use of poll taxes in state and local elections (in 1964, the 24th Amendment made poll taxes illegal in federal elections; poll taxes in state elections were banned in 1966 by the U.S. Supreme Court).
After the passage of the Voting Rights Act, state and local enforcement of the law was weak and it often was ignored outright, mainly in the South and in areas where the proportion of blacks in the population was high and their vote threatened the political status quo. Still, the Voting Rights Act gave African-American voters the legal means to challenge voting restrictions and vastly improved voter turnout.
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Elements of Language: 8th Grade - The Phrase (Ch. 14)
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[FROM THE TEXT]
A “phrase” is a group of related words that is used as a single part of speech and that does not contain both a verb and its subject. A “prepositional phrase” includes a preposition, the object of the preposition, and any modifiers of that object. An “adjective phrase” modifies a noun or a pronoun. An “adverb phrase” modifies a verb, an adjective, or an adverb. A “verbal” is a word that is formed from a verb but is used as a noun, an adjective, or an adverb. A “participle” is a verb form that can be used as an adjective. Present participles end in “–ing.” Past participles usually end in “–d” or “–ed.” Some past participles are formed irregularly. A “participial phrase” consists of a participle together with its modifiers and complements. The entire phrase is used as an adjective. An “infinitive” is a verb form that can be used as a noun, an adjective, or an adverb. Most infinitives begin with “to.” An “infinitive phrase” consists of an infinitive together with its modifiers and complements. The entire phrase may be used as a noun, an adjective, or an adverb.
[ABOUT THE COURSE]
This online version of “Elements of Language” features your textbook and a variety of interactive activities. The Second course is aimed at Eighth Graders. The Elements of Language Online Edition offers activities from these workbooks: * Communications * Sentences and Paragraphs * Grammar, Usage, and Mechanics Language Skills Practice * Chapter Tests in Standardized Test Formats. It provides practical teaching strategies, differentiated instruction, and engaging presentation tools that offer more ways to reach more students than ever before. | 4.724691 |
In this lesson our instructor talks about conditional statements. She talks about if then statement and other forms such as without then, using when, and hypothesis. She discusses identifying the hypothesis and conclusion. She then teaches writing in if then form. She also talks about converse statements , converses and counterexamples, inverse statement, and contrapositive statement. Four complete extra example videos round up this lesson.
If-then statements are called conditional statements or conditionals.
The conditional statement: If
p, then q.
Given statements can be written as condition statements in 3 other forms: converse statements, inverse statements, and contrapositive statements
The converse of a given conditional interchanges the hypothesis and the conclusion. This statement can be true or false. If q, then p.
The denial of a statement is called a negation. Inverse statements are formed by negating both the hypothesis and conclusion.
A contrapositive statement is formed by exchanging and negating the hypothesis and conclusion of the given conditional.
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. | 4.724667 |
Dataset Card for Fineweb Ultra Mini
Fineweb Ultra Mini is a dataset derived from the original Fineweb dataset made by huggingface (see here: https://huggingface.co/datasets/HuggingFaceFW/fineweb). The dataset focuses on extracting high quality data from the Fineweb dataset, from the 1-0.5% range. If you would like more data, though slightly sacrificing quality check out fineweb ultra mini, which focuses on the 2-3% of high quality data originally found in fineweb.
Dataset Details
Dataset Description
Below outlines the steps which were taken to curate this dataset:
- Data Source: The original FineWeb dataset from Hugging Face.
- Filtering: A text classification model was trained on H100s to identify the top 2-3% of documents.
- Data Preparation: The selected documents were processed to ensure consistency and quality.
- Dataset Creation: The filtered and processed data was organized into the Hugging Face dataset format.
- Curated by: ReflexAI Open Source Engineering Team
- Funded by: Modal Grant Program
- Language(s) (NLP): English (more coming soon)
- License: odc-by
Intended Uses
The fineweb-ultra-mini dataset is intended for a variety of natural language processing tasks, including:
- Language Modeling: Training large language models on high-quality text data.
- Text Summarization: Extracting key information from web documents.
- Question Answering: Answering questions based on the information in web documents.
- Text Classification: Categorizing web documents based on their content.
Out-of-Scope Use
Commercial Use
Commercial use is permitted under the ODC-By (Open Database License - Attribution) license, allowing individuals and organizations to use, modify, and distribute the dataset for commercial purposes, provided they comply with the attribution requirements. This includes using the dataset in commercial products, services, research, or any other profit-generating activity.
However, it is important to highlight the following limitations and conditions: 1. Attribution Requirement: Any use of the dataset, including commercial use, must provide proper attribution to the original creators of the dataset. This attribution must be clear and visible in any products or services that incorporate the dataset. 2. Redistribution and Derivative Works: While derivative works (e.g., modified versions of the dataset) are permitted, they must also adhere to the attribution requirement. Moreover, any redistribution of the dataset must include the same ODC-By license to ensure that others are also informed of these conditions.
Unethical Activities
Despite the commercial use allowance, certain activities involving the dataset remain strictly out of scope due to ethical concerns. These include, but are not limited to: 1. Data Manipulation for Malicious Purposes: Using the dataset to manipulate or fabricate data in a way that misleads or harms individuals, communities, or organizations, including but not limited to creating deep fakes, misinformation, or defamation. 2. Surveillance and Privacy Violations: Using the dataset for surveillance activities or any practices that infringe on the privacy rights of individuals, including profiling, tracking, or unauthorized data collection, is strictly prohibited. 3. Discriminatory or Harmful Practices: Employing the dataset in ways that may promote or perpetuate discrimination, hate speech, violence, or any other harmful practices, including using the data to reinforce or exacerbate biases. 4. Violation of Laws and Regulations: Any use of the dataset that violates local, national, or international laws, such as engaging in illegal surveillance or using the dataset in activities prohibited by data protection and privacy laws, is not allowed.
By adhering to these guidelines, users of the dataset can ensure its ethical and responsible use while contributing positively to commercial endeavors and research.
Bias, Risks, and Limitations
Bias
Datasets often reflect the biases inherent in the data collection process, sources, or the methodology used in their creation. It is crucial to be aware of the following potential biases in the dataset: 1. Selection Bias: The dataset may not be fully representative of the entire population or domain it is intended to represent. Certain groups or perspectives might be overrepresented or underrepresented, which can lead to skewed outcomes when the dataset is used in analysis, modeling, or training AI systems. 2. Cultural Bias: If the dataset is sourced from a particular cultural or geographical context, it may carry cultural biases that are not universally applicable. For example, language use, social norms, and values represented in the data may not align with those of different cultures or regions. 3. Algorithmic Bias: When the dataset is used in machine learning or algorithmic processes, any existing biases in the data can be amplified or perpetuated by algorithms, potentially leading to discriminatory or unfair outcomes in automated decisions or predictions.
Risks
The use of this dataset carries several risks that users should be aware of, especially when deploying the data in real-world applications or commercial products: 1. Model Performance Risks: If the dataset is incomplete, imbalanced, or biased, it may result in inaccurate or unreliable models. This can impact decision-making, predictions, or analysis, especially in critical sectors such as healthcare, finance, or legal systems. 2. Reinforcement of Existing Inequalities: When used to train models or systems, biased datasets can reinforce existing societal inequalities. For example, models trained on biased data can inadvertently perpetuate stereotypes or exacerbate disparities in areas such as hiring, lending, and law enforcement. 3. Reputation Risks: Misuse or unethical use of the dataset may lead to reputational damage for both individuals and organizations. Public backlash can arise if the dataset is used in ways that are perceived as discriminatory, harmful, or unethical. 4. Legal and Regulatory Risks: Depending on the dataset’s content and intended use, there may be legal risks associated with its use, especially when dealing with sensitive or personally identifiable information (PII). Users should be cautious of potential violations of data privacy laws, including GDPR or CCPA, and ensure compliance with relevant regulations.
Limitations
While the dataset provides valuable insights and utility, it is important to recognize its inherent limitations: 1. Scope and Completeness: The dataset may not cover all aspects of the domain it represents, leaving gaps that could affect its applicability in certain contexts. Users should assess whether the dataset aligns with their specific use case and complement it with additional data if necessary. 2. Quality and Accuracy: The accuracy of the dataset may vary, and errors, inconsistencies, or outdated information could impact its reliability. It is essential to validate the dataset before using it in high-stakes applications. 3. Generalization: Models trained on the dataset may struggle to generalize well to new or unseen data, especially if the dataset is narrow in scope or lacks diversity. Overfitting to the dataset’s specific patterns can lead to poor performance in real-world scenarios. 4. Maintenance and Updates: Datasets can become outdated over time as the world evolves. Users should be prepared to update the dataset regularly to ensure it remains relevant and reflects current trends, information, and developments in the field.
By understanding and addressing these biases, risks, and limitations, users can take a more informed and responsible approach to utilizing the dataset, ensuring its effectiveness and minimizing potential negative consequences.
Recommendations
Users should be made aware of the risks, biases and limitations of the dataset. More information needed for further recommendations.
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