198 results for “Algebra”.

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There are many other variables that would affect real-world riding speed, and the effort variable would also be far more complicated than represented here, but this should suffice for now. Several equations can be written using the variables defined here. For instance, to calculate the effort needed to go one kilometer (it's easier to go kilometers than miles, at least mathematically), or a thousand meters, in a given gear, the equation would look like this:

T) / G = E, where M. is the distance (in meters) of the journey, T is the circumference of the tire -- and therefore also the linear distance, G is the number of revolutions the tire goes per push of the pedal, which changes from gear to gear, and E. is the number of times the pedals have to go around, which is representative of the effort needed to push the bike forward for…

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Algebra

Like many other languages and sciences, Algebra can be useful in the explanation of real-world experiences. Linear algebra, in particular, holds a high level of relevancy in the solution of real world problems like physics equations. Since the key point of physics is to explain the world in proven observations, linear algebra is an ideal mode for discussion. Many real-world situations can be explained by algebra; for example, how does GPS work? The satellite-based Global Positioning System works by locking onto the system of three satellites and calculating a two-dimensional position from latitude and longitude, thus tracking movement. The location of objects can be determined by using linear equations to morph the data into identifiable locations, and with four or more satellites in view, altitude combines with latitude and longitude to determine the 3-D position.

A far more generic (but equally important) use of linear algebra in real world…

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By observing x on the graph, then we make the connection that the slope of x on the graph represents rate of change of the linear function.

Once we have done this, it is then possible to move to the development of a quadratic equation and see what the impact of the increase (or perhaps decrease) means to the data. Have we proven that the rate of change is linear? The graphical representation of the data may be misleading, so it would be good to be able to calculate the rate of change to see if it is significant.

We could assign to value of L1 to the year in which the students are enrolled collect this data in columnar form, still graphing it on our graph. We would then call L2 the number of students enrolled every year which corresponds to the year we have listed in L1. In…

Reference:

No Authors Listed. (1996) Achieving Mathematical Power. Mathematics Curriculum Framework. Accessed via the World Wide Web on July 17, 2005 at http://www.doe.mass.edu/frameworks/math/1996/patterns.html

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Those studying physics and astronomy, and perhaps other scientific disciplines as well, are accustomed to the use of scientific shorthand and in some fields it is essential -- the example above of distance between energy waves from supernovae is a good example. There is a high level of variation in these distances, so a shorthand like the one on financial statements would be apply, but the numbers are very small so the use of shorthand is necessary. It is interesting to note, however, that even those in fields accustomed to scientific notation sometimes avoid it, as is the case with distances between objects in space.

Another group that does something similar to astronomers is the archaeologists. They have found ways to talk about years without using scientific notation, even though events often date back millions or billions of years. Yet, when discussing the science behind dating their samples, they will…

Works Cited:

Hoflich, P.; Wheeler, J. & Khokhlov, A. (1997). Hard x-rays and gamma rays from type Ia supernovae. The Astrophysical Journal. Vol. 492 (1998) 228-245.

Lalho, J. (2010). Light quark physics from lattice QCD. The XXVIII International Symposium on Lattice Field Theory. Retrieved November 19, 2011 from http://docs.google.com/viewer?a=v&q=cache:gDvRm6TY1VMJ:arxiv.org/pdf/1106.0457+physics+1.5e+%2B+09&hl=en&gl=us&pid=bl&srcid=ADGEESj0lgK5NDCG9_6ieDz24CvN4cltyb2a6Rkcxewes9FXnLbXorx8egE4f6_a7wSR-YQXM9fvOSZ3D05z4ASakSK1f48HrDiYS0JnlOLNbF3-1-upjAM4N-DhnF8rUoEmdWRK-qQC&sig=AHIEtbQ5aUobZS_c9iSSgDQqnLuG1-Kw2Q

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Algebra

All exponential functions have as domain the set of real numbers because the domain is the set of numbers that can enter the function and enable to produce a number as output. In exponential functions whatever real number can be operated. (-infinity, infinity)

You have ln (x+4) so everything is shifted by 4. The domain of ln (x+4) is now -4 < x < infinity (Shifting infinity by a finite number gives you infinity again.) So,-4 < x < infinity is the domain of ln (x+4).

(2 [less than] t [less than] infinity)

For your function f (t) = 5.5exp (t) the function is continuous for all values of t as exp (t) is continuous for all values t, i.e. The domain of the function is -oo < t < oo

2a. subtracting 3 on the inside the function moves it 3 units to the right, that's the only…

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Algebra -- Trig --

Writer's Note: The symbol "n" should really be referred to as "pi" or "?" To prevent confusion within the problem. Also, there is a difference between "squared" and "square root." The case in these problems is to use the square root, so "sqrt (number)." I've only managed the calculations because I have presumed the indicated changes.

Using the periodic properties of trigonometric functions, find the exact value of the expression

cos-

cos (8?/5) = cos (2? + (2?/5)) = cos (2?/5) = cos (72) = 0.31

cos (8?/5) = 0.31.

The point P. On the unit circle that corresponds to a real number t is:

{ 5-2 6 squared}

} Find csc (t)

P is on the unit circle, therefore the coordinates are (cos (t), sin (t)). This leads to the following calculations:

sin (t) = -2sqrt (6)/7, and csc (t) = 1/sin (t) = 1/(-2sqrt…

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Algebra -- Trig

Evaluate the determinant: | 3-9 |

Determinant of a square matrix can be solved by the following equation: A = ad -- bc, where a = 3, b = 9, c = 6, and d = 4. Therefore, A = (3)(4) -- (9)(6) = 12 -- 54 = -42

Solve the following system of equations using matrices:

y + 4z = 6, 2x + z = 1, x + 5y + z = -9

[ 1-5-1 | -9 ]

Row 2: R2 -- 2R1 = [ 2-0-1 | 1 ] -- 2[ 1 -1-4 | 6 ] = [ 0-2 -7 | -11 ]

Row 3: R3 -- R1 = [ 1-5-1 | -9 ] -- [ 1 -1-4 | 6 ] = [ 0-6 -3 | -15 ]

New matrix:

[ 0-2 -7 | -11 ]

[ 0-6 -3 | -15 ]

Row 2: R2/2 =…

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Algebra, Trig

Solve the system: 7x + 3y = -2, -7x -- 7y =

(7x + 3y) + (-7x -- 7y) = (-2 + 14) 7x + 3y -- 7x -- 7y = 12 -4y = 12 y = -3

Substituting y for the first equation: 7x + 3(-3) = -2 7x -- 9 = -2 7x = 7 x = 1

x = 1, y = -3.

Solve the system: x + y = -5, x -- y = 12

(x + y) + (x -- y) = (-5 + 12) x + y + x -- y = 7 2x = 7 x = 7/2

Substituting x for the first equation: 7/2 + y = -5 y = -5 -- (7/2) y = -17/2

x = 7/2, y = -17/2.

Solve the system: y -- 3z = -12, -2x + y + 2z = 5, 2x + 3z…

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Algebra Lesson Plans and Curriculum for the 7th Grade Classroom

The National Council of Teachers of Mathematics (NCTM) provides a comprehensive set of principles and standards for developing curriculum for grades K. through 12th. Chapter two of their text Principles and Standards for School Mathematics specifies the six principles considered vital for the development of a coherent math plan. The principles are general enough to apply across a wide variety of disciplines as they are "not unique to school mathematics." (p. 16). However, chapter three dealing with the ten standards, themselves, makes quite clear (and rightly so) that math, unlike other disciplines, can benefit from a truly integrated approach: "Because mathematics as a discipline is highly interconnected the areas described by the Standards overlap and are integrated." (p. 30). In other words, the standards cannot be easily divided into particular grade levels (i.e. numbers/operations in K-2, geometry in 3-5, algebra…

References

Algebra for All - Not with Today's Textbooks, Says AAAS. (2000). Retrived April 1, 2003, at http://www.prject2061.org/newsinfo/press/r1000426.htm.

Algebra: Some Common Misconceptions. (n.d.). Retrieved April 1, 2003 at http://www.quesnrecit.qc.ca/mst/mapco/pdf/algemisc.pdf.

Aziz, N., Pain, H.G., Brna, P. (1995). Modelling and Mending Students' Misconceptions in Translating Algebra Word PRoblems Using a Belief Revision System in Taps (Abstract).

Presented In the proceedings of the 7th World Conference on Artificial Intelligence in Education, AI-ED 95, Virginia, AACE. Retrieved April 1, 2003 from DAI Database.

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algebra or geometry have no use in "real" life, many people think that statistical analyses have no possible real-world applications. However, as the following scenario should make clear, statistical analysis can be extremely helpful in assessing quality control issues in the workplace. Using a specific type of statistical analysis, the supervisor at a former workplace was able to reduce costs while increasing customer satisfaction.

Analysis of variance (more generally referred to as an ANOVA test) is one of the most basic statistical tests that can be applied to a data set. It is used to provide an accurate way to compare the results from different groups (defined in ways that are relevant to the issue at hand). Such comparisons are useful because they provide information that allows processes to become more efficient or to meet other goals, such as increasing customer satisfaction.

For a number of years I have worked…

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3b. One method that can be utilized to help Martha with applying algebra to real world application is through interactions within her environment that will allow her to utilize these skills. Another method proven useful in building applicable skills and communication is online conferencing. This tool utilized in the class room can give Martha access to knowledge from other professors and learners that could not normally be possible in a standard classroom. A professor that may specialize in a specific method on how to understand certain terms or expressions would be able to share these applications with students globally through virtual conferences. Technological Horizons (1993), recant the significance of videoconferencing by reporting that the characteristics of videoconferencing may actually enhance the learning process. Teachers and administrators say that students who take distance education classes are scoring higher on basic skills tests than those who are in the same classroom with…

References

Fox, Christine. "Going virtual: online courses can get to people and places beyond the reach of the traditional school setting, serving the needs of students and teachers nationwide. (Using Technology to Expand Opportunity)." THE Journal (Technological Horizons In Education). 1105 Media, Inc. 2006. Retrieved September 10, 2010 from HighBeam Research: http://www.highbeam.com/doc/1G1-148856686.html

Olliges, Ralph; Sebastian Mahfood. "10. Resources.(Teaching and learning in the new millennium: transformative technologies in a transformable world)(Missouri Department of Education Commission)." Communication Research Trends. Centre for the Study of Communication and Culture. 2003. Retrieved September 10, 2010 from HighBeam Research: http://www.highbeam.com/doc/1G1-130975621.html

"CRITICAL THINKING SKILLS, MATH, SCIENCE DEMAND OF BusinessES, GLOBAL COMPETITION." U.S. Fed News Service, Including U.S. State News. HT Media Ltd. 2007. Retrieved September 10, 2010 from HighBeam Research: http://www.highbeam.com/doc/1P3-1248145301.html

"Videoconferencing bridges gaps in distance and curriculum for Alaskan students. (how the North Slope Borough School District uses VideoTelecom's MediaConferencing systems) (Multimedia)." THE Journal (Technological Horizons In Education). 1105 Media, Inc. 1993. Retrieved September 10, 2010 from HighBeam Research: http://www.highbeam.com/doc/1G1-14354264.html

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2007, p. 115). Likewise, a study by Wyndhamm and Saljo found that young algebra learners were more successful in their problem-solving efforts when collaborating in a group environment. According to these researchers, "An experiment involving 14 small groups of Swedish students (usually 3 per group) aged 10, 11, and 12 years shows that these students acting in groups and creating shared contextualizations were able to solve mathematics word problems calling for real-world knowledge. esearch has shown students acting alone to have difficulty with the same types of problems" (Wyndhamm & Saljo 1997, p. 361). Other teachers report that algebra story problems can help make learning more relevant to young people's lives. For instance, according to Homann and Lulay, "Algebra story problems are an important practical application of mathematics since real-world problems usually do not arise in terms of equations but as verbal or pictorial representations. The problems are solved by…

References

Barry, D. (1989) Dave Barry Slept Here: A Sort of History of the United States. New York:

Random House.

Dillon, R.F. & Sternberg, R.J. (1986) Cognition and Instruction. Orlando, FL: Academic

Press.

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Coding relational algebra operations varies from school to school. I wrote it according to my training, but there are variations. Review and rewrite in own words so as to preclude plagiarism.

What is a relation schema? What is the difference between a relation, a relation schema, and a relational schema?

A relation schema is the basic information that describes a table or a relation. This includes the set of column names, the data within the columns, or the name associated with the entire table.

For example 'Students' would be the relation (I..e category) name.

The relation schema for students may be expressed as following:

Students (sid: string, name: string, login: string, age: integer, gpa: real)

It has five fields or columns each having names or types.

The relation, in other words, is the topic / category (e..g 'student'), the relations schema is the property categories of the relation, or of…

Blaha, M. Referential Integrity Is Important For Databases http://www.odbms.org/download/007.02%20Blaha%20Referential%20Integrity%20Is%20Important%20For%20Databases%20November%202005.PDF)

What is a relation schema | Answerbag http://www.answerbag.com/q_view/730085#ixzz1ncwaYsPz

SQL Authority. SQL SERVER -- Difference Between Candidate Keys and Primary Key. http://blog.sqlauthority.com/2009/05/30/sql-server-difference-between-candidate-keys-and-primary-key/

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Intermediate Algebra

The formula is C=4d^-1/3b

D= 23,245 because it is the pounds

B= 13.5 because that is the height of the mast

C=4(23,245)^-1/3(13.5)

Because the exponent was negative it needed to be dropped down to the numerator. The fact that it was a fraction meant that 92980 needed to be cubed, since it was a 1/3 exponent. Then it could be multiplied with the B. value, which was 13.5 / This left the final answer to be 283.693745115.

C=4d^-1/3b

d=64b3/c3

In order to solve for D. you needed to move 4 and the variable D. To the other side. Then you have to log both sides, which leaves an exponent of 3 instead of -1/3.

This formula could definitely be very important in the real world. For one, it is needed to be able to properly sail a boat in various conditions. It is extremely important to understand the…

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College Algebra

Individual Project

Solve the following algebraically. Trial and error is not an appropriate method of solution. You must show all your work.

Solve algebraically and check your potential solutions:

x = -4 does not satisfy the equality. So the answer is only x = 5

Show the steps that you would take to solve the following algebraically:

Show your work here:

c) What potential solution did you obtain? Explain why this is not a solution.

This is not a solution because it makes the original equation indefinite. It makes the denominator zero.

The following function computes the cost, C (in millions of dollars), of implementing a city recycling project when x percent of the citizens participate.

a)

Using this model, find the cost if 60% of the citizens participate?

Answer:

million dollars

b)

Using this model, determine the percentage of participation that can be expected if $4 million…

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College Algebra

Graphing Transformations

a) Given the function f (x) = x^2 complete the following table. Must show all work for full credit.

f (x)

Show Work:

When x = 0, f (x) = f (0) = (0)^2 = 0.

When x = 1, f (x) = f (1) = (1)^2 = 1.

When x = 4, f (x) = f (4) = (4)^2 = 16.

When x = 9, f (x) = f (9) = (9)^2 = 81.

When x = 16, f (x) = f (16) = (16)^2 = 256.

b) Using the table from part a, graph the function f (x) = x^2 . For a tutorial on creating graphs in Excel and inserting graphs of functions please see the Assignment List.

c) Given the function f (x) = (x +1)^2 complete the following table. Must show all work for full credit.

f (x)

Show Work or…

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Managerial Math

Solve each of the following equations for the unknown variable.

a) 15x + 40 = 8x -

15x +49 = 8x

49= -7x

b) 7y - 1 = 23-5y

Y=

c) 9(2x + 8) = 20 - (x + 5)

= 15-x

d) 4(3y - 1) - 6 = 5(y + 2)

Y = (20/7)

Bob Brown bought two plots of land for a total of $110,000. On the first plot, he made a profit of 16%. On the second, he lost 4%. His total profit was $9,600. How much did he pay for each piece of land?

X= price of the first plot

Y= price of the second plot

X+Y= 110,000

.16x-.04y=9600

x=110,000-y

.16(110,000-y)-.04y=9600

17600-.16y-.04y=9600

y=40,000

x=110,000-40,000=70,000

A major car rental firm charges $57 a day with unlimited mileage. A discount firm offers a similar car for $24 a day plus 22 cents per mile. How far…

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Solve the following quadratic equation by factoring:

A) X2 + 6x -16 = 0

(x-2) (x+8)= 0

(x+2) (x-8) = 0

x=-2, x-8

b) solve the quadratic equation 6x2 +3x-18 = 0 using the quadratic formula x= - b +/- ?(b2- 4ac)

+/- ?[32- (4*6*-18c)]

x = 3/2; x= 2

c) Compute the discriminant of the quadratic equation 2x2-3x - 5 = 0 and then write a brief sentence describing the number and type of solutions for the equation.

If x= - b +/- ?(b2- 4ac), then (b2- 4ac) is the discriminant b2- 4ac= -32- (4*2*-5) = 49

There are two solutions for the equation, 1 and 2 1/2, which one gets by plugging the discriminant into the quadratic formula and solving for x.

Use the graph of y=x2+4x-5 to answer the following:

a) Without solving the equation or factoring, determine the solution(s) to the equation, x^2 + 4x -…

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Financial Polynomials

Solution for the problem: (-9x3 + 3x2 -- 15x)

The division process for the polynomial above can be approached in the same way as dividing whole numbers. The polynomial (-9x3 + 3x2 -- 15x) is the dividend, while (-3x) is the divisor. To easily facilitate the division process, the whole equation will be multiplied by "-1." The new equation is: (9x3 -- 3x2 + 15x) / (3x). Writing the question in long division form, begin dividing (9x3) first by (3x), which is equal to (3x2). To cancel the first part of the equation, the first part of the quotient must be negative. Thus, 3x2 becomes (-3x2). Place (-3x2) above the division bracket as shown below.

) 9x3-3x2 + 15x

Multiply (3x) by (-3x2), which is equal to 9x3. Placing 9x3 below (-9x3) then subtract them, resulting to zero. The remaining parts of the equation must be divided in…

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Algebra, Trig

Algebra-Trig

Find the slope of the line that goes through the following points: (-4, 6), (-8, 6)

Slope: m = (y2 -- y1) / (x2 -- x1) = (6 -- 6) / (-8 -- (-4)) = 0 / (-4) = 0

m = 0.

Determine whether the given function is even, odd or neither: f (x) = 5x^2 + x^

To test a function for even, odd, or neither property, plug in -- x for x, and simplify.

f (-x) = 5(-x)^2 + (-x)^4 = 5x^2 + x^4.

Because the final expression remains the same for -- x, it stands that the function is even.

f (x) is even.

Find the slope of the line that goes through the following points: (-1, 1), (-2, -5)

Slope: m = (y2 -- y1) / (x2 -- x1) = ((-5) -- 1) / ((-2) -- (-1)) = (-6) / (-1) =…

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f (x) = 3 if x>2 otherwise f (x) = -2 Function: every x value corresponds to only one f (x) value

c. f (x) = 7 if x>0 or f (x) = -7 if x

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Algebra, Trig

Find the radian measure of the central angle of a circle of radius r = 4 inches that intercepts an arc length s = 20 inches.

The formula for an arc length is a = r?, where'd is the arc length, ? is the central angle in radians, and r is the radius. That said, s = 20, r = 4, and ? is unknown.

= 5 radians

The central angle is 5 radians.

In which quadrant will the angle 100 degrees lie in the standard position?

The angle of 100 degrees will lie in Quadrant II.

In which quadrant will the angle -305 degrees lie in the standard position?

The angle of -305 degrees will lie in Quadrant I.

Find the length of the arc on a circle of radius r = 5 yards intercepted by a central angle 0 = 70 degrees.

The formula for an…

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Algebra, Trig

Given f (x) = -3x + 2 and g (x) = 2x + 9: find (g 0 f)(x)

(g 0 f)(x) = 2(-3x + 2) + 9 = -6x + 4 + 9 = -6x + 13

(g 0 f)(x) = -6x + 13.

Given f (x) = 5x + 7 and g (x) = 5x -- 1: find (f 0 g)(x)

(f 0 g)(x) = 5(5x -- 1) + 7 = 25x -- 5 + 7 = 25x +

(f 0 g)(x) = 25x + 2.

Given f (x) = 5x + 4 and g (x) = 3x -- 8, find fg = f (x) * g (x) = (5x + 4)(3x -- 8) = 15x^2 -- 40x + 12x -- 32 = 15x^2 -- 28x --

fg = 15x^2 -- 28x -- 32.

Given f (x) = 2 -- 2x and g (x) = -6x +…

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Algebra, Trig

Perform the indicated operation and simplify completely: (x + 10)(x^2 + 9x - 8)

(x + 10)(x^2 + 9x - 8) = x^3 + 9x^2 -- 8x + 10x^2 + 90x -- 80 = x^3 + 19x^2 +82x --

Perform the indicated operation and simplify completely:

(5x + 5) / (5x + 9) + (5x + 13) / (5x+9)

(5x + 5) / (5x + 9) + (5x + 13) / (5x+9) = (5x + 5 + 5x + 13) / (5x + 9)

= (10x + 18) / (5x + 9) = 2(5x + 9) / (5x + 9) = 2

Perform the indicated operation and simplify completely:

(8x^6 + 7x^3 + 3x) + (3x^6+5x^3 -5x)

(8x^6 + 7x^3 + 3x) + (3x^6+5x^3 -5x) = 8x^6 + 7x^3 + 3x + 3x^6 + 5x^3 -- 5x

= 11x^6 + 12x^3 -- 2x

Perform the indicated operation and…

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05x)

Option for Plan B:

$20 + (0.10x)

Determine the best option given two plans

Step 1: $30 + (0.05x) = $20 + (0.10x)

Step 2: Subtract (0.05x) from both sides-

$30 + (0.05x) -- (0.05x) = $20 +(0.10x) -- (0.05x) ? $30 = $20 + (0.05x)

Step 3: Subtract $20 from each side-

$30 - $20 = $20 -$20 + (0.05x) ? $10 = (0.05x)

Step 4: Divide both sides by (0.05) to isolate x:

$10 / (0.05) = (0.05x)/(0.05)

200 = x

After making 200 phone calls, both plans will break even so it doesn't matter which plan you are choosing if you are making 200 phone calls.

If you plan on making less than 200 phone calls, then one should assign a random value to x less than 200:

$30 + (0.05 x 100)= $35

$20 + (0.05 x 100) = $25

If making less than 200…

One such body is the American National Standards Institute or ANSI which is a non-profit private organization that surprisingly institutes standards the industry accepts voluntarily. Other influential standards organizations include the Institute of Electrical and Electronic Engineers or IEEE and the Organization for Standardization or ISO. The IEEE was the organization that defined LAN standards in the Project 802 or the 802 series. These projects could be the blueprints that could be used to make XML more effective by using PAT Algebra Operators for query needs.

XML PAT Algebra Operators

The internet is based on a foundation of distributed hypertext. There is also plenty of proof that the internet could be regarded as a large distributed database where there are million to billions of queries processed daily. "XML is too slow an exchange format for any large volume of data transfer. It is fine for exchange of small amounts of…

References

Avolio, Frederick M. (2000, March 20). Best Practices In Network Security -- As The Networking Landscape Changes, So Must The Policies That Govern Its Use. Don't Be Afraid Of Imperfection When It Comes To Developing Those For Your Group. Network Computing.

Dekker, Marcel. (n.d.). Security of the Internet. Retrieved on January 17, 2005, at http://www.cert.org/encyc_article/tocencyc.html#Overview

Gast, Matthew. (2002, April 19). Wireless LAN Security: A Short History. Retrieved on January 17, 2005, at http://www.oreillynet.com/pub/a/wireless/2002/04/19/security.html

Oasis. (n.d.). XML: Overview. Retrieved on January 17, 2005, at http://xml.coverpages.org/xml.html#overview

..an approximation for ?, which is surprisingly accurate. The value given is: = 3.1416. With little doubt this is the most accurate approximation that had been given up to this point in the history of mathematics. Aryabhata found it from the circle with circumference 62832 and diameter 20000. Critics have tried to suggest that this approximation is of Greek origin. However with confidence it can be argued that the Greeks only used ? = 10 and ? = 22/7 and that no other values can be found in Greek texts." (Indian Mathematics, 2009)

There is stated by Selin (2001) in the work entitled: "Mathematics Across Cultures: The History of Non-Western Mathematics" to be "...no evidence of the method for extracting cube roots having been known earlier than Aryabhata I." (Selin, 2001)

Conclusion

Aryabhata made great contributions to mathematics and algebra and his greatest contribution to Algebra was that of his…

Bibliography

Selin, Helaine (2001) Mathematics Across Cultures: The History of Non-Western Mathematics. Vol. 3 Science Across Cultures. Ubiratan D'Ambrosio 2001.

Dutta, Amartya Kumar (2002) Mathematics in Ancient India. Resonance Journal Vol.7, NO. 5 April 2002.

Hooda, D.S. And Kapur, J.N. (2001) Aryabhata: Life and Contributions. New Age International 2001.

Indian Mathematics (2009) Aryabhata and His Commentators. History online available at: http://www-history.mcs.st-and.ac.uk/Projects/Pearce/Chapters/Ch8_2.html

The method the teacher uses encourages students to discover the answers for themselves rather than accept the right answer as a matter of rote learning. finally, the class is frequently divided into groups, both small and large. The groups vary to encourage maximum student interactions. Through cooperative learning the students share their suggestions and brainstorm. Finally, the teacher employs some self-directed learning strategies that allow students to ponder the equations on their own for brief periods of time. This helps the teacher make assessments during class while it also helps the students work independently.

D. The lesson addresses a variety of learning styles and intelligences.

Another major strength of this lesson is the way it addresses a variety of learning styles and intelligences. Algebra is traditionally taught using the abstract method; students must visualize the concept of alphabetical variables. The notation used in traditional algebraic equations might work for students…

References

Pan-Algebra: Pan Balance Equations." WGU Teacher's Resource Library. Retrieved July 10, 2007 at http://www.teachscape.com/ts2/lb

6. The rabbits will never die.

The question was how many male/female rabbit pairs will be there after a year or 12 months?

When the experiment begun, there is a single pair of rabbits.

After duration of one month, the two rabbits have mated though they have not given birth. As a result; there is still only a single pair of rabbits.

After duration of two months, the initial pair of rabbits will give birth to another pair. There will be two pairs.

After duration of three months, the initial pair will give birth again, the second pair mate, but do not give birth. This makes three pair.

When four months will elapse, the original pair gives birth, and the pair born in the second month gives birth. The pair that is born in month in the third month will mate, but will not give birth. This will make two…

References

Buchanan, R. (2010). Addition and subtraction with polynomials, http://banach.millersville.edu/~bob/math101/AddSubPoly/main.pdf, assessed on February, 24, 2010

Anderson, M; Frazier, J and Popendorf, K. (1999). The Rabbit Problem,

http://library.thinkquest.org/27890/theSeries2.htm. Assessed on February 24, 2011

Beckmann, P. (1976). A History of Pi, St. Martin's Griffin.

Read the following instructions in order to complete this assignment, and review the example of how to complete the math required for this assignment:

Use the properties of real numbers to simplify the following expressions:

2a (a -- 5) + 4(a -- 5)

3(w -- 4) -- 5(w -- 6)

(0.3m + 35n) -- 0.8(-0.09n -- 22m)

Problem #1

2a (a-5) +4(a-5) I multiply 2a by each term…

My interests in other areas have also been diversified; I have pursued many adventures, participated as president of many clubs, and won many competitions in music, sports, dance and more. My strength has always been academics however. During high school I was presented the unique opportunity to come to the United States and continue my education. It was here that I decided to study history initially. Though my parents pressured me to study finance or business, I found such work tedious at least initially. I did however entertain my parents and begin taking more classes in finance. This was probably the best decision I have ever made and helped create the professional I am today.

The more I learned the more I came to understand that finance was more than…

movie Stand and Deliver (Menendez & Musca, 1988), which is based on the true story of Jamie Escalante, an individual who overcame ethnic, cultural, and socioeconomic issues to become a highly successful mathematics teacher. Discuss the beliefs he held and the strategies he employed in his classroom that contributed to high achievement levels in his students.

The final report of the National Mathematics Advisory Panel (2008) presents a three-pronged argument for an effective math curricula: 1) It must foster the successful mathematical performance of students in algebra and beyond; 2) it must be taught by experienced teachers of mathematics who instructional strategies that are research-based; and, 3) the instruction of the math curriculum must accomplish the "mutually reinforcing benefits of conceptual understanding, procedural fluency, and automatic recall of facts" (National Mathematics Advisory Panel, 2008, p. xiv). Jamie Escalante began teaching before this report was released, but he knew from experience…

References

____. (2004, April 13). "Hero'" Teacher Escalante Addresses Students At Wittenberg Commencement May 9. Wittenberg University. Retrieved http://www4.wittenberg.edu/news/1998/commspeaker.shtml

____. (2008). National Mathematics Advisory Panel, Foundations for Success. The Final Report of the National Mathematics Advisory Panel, U.S. Department of Education. Washington, D.C. Retrieved http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

Barley, Z., Lauer, P.A., Arens, S.A., Apthorp, H.S., Englert, K.S., Snow, D., & Akiba, M. (2002). Helping at-risk students meet standards: A synthesis of evidence-based classroom practices. Retrieved March 20, 2008, from the Midcontinent Research for Education and Learning [Web]. Retrieved http://www.mcrel.org/PDF/Synthesis/5022RR_RSHelpingAtRisk.pdf

Berkas, N., & Pattison, C. (2007, November). Manipulatives: More than a special education intervention. NCTM News Bulletin. Retrieved March 20, 2008, from the National Council of Teachers of Mathematics [Web] Retreived http://www.nctm.org/news/release_list.aspx?id=12698

e. all loans. The same basic formulas using logarithms can be used to calculate the needed number of investments and/or the time period of investments at a given growth rate that will be needed in order to reach a target level of investments savings (Brown 2010). Both of these applications have very real implications for many individuals, whether they are trying to buy a home or planning for their retirement, as well as a n abundance of other issues related to personal banking. Logarithms are not only useful in highly technical scientific pursuits and investigations, then, but are directly applicable and necessary to situations that directly relate to and have an effect on people's daily lives.

What I found most interesting and surprising about the development of logarithms is that they are something that needed development in the first place. I suppose it is similar to having taken any invention…

References

Brown, S. (2010). "Loan or investment calculations." Oak road systems. Accessed 4 April 2010. http://oakroadsystems.com/math/loan.htm

Campbell-Kelly, M. (2003). The history of mathematical tables. New York: Oxford university press.

Spiritus Temporis. (2005). "Logarithm." Accessed 4 April 2010. http://www.spiritus-temporis.com/logarithm/history.html

Tom, D. (2002). "Use of logarithms." The math forum. Accessed 4 April 2010. http://mathforum.org/library/drmath/view/60970.html

Syntax and Semantic Analysis

-- The Syntax errors involved misuse of keywords.

The Semantic errors involved misuse of columns and tables - there were incompatible data types.

To elaborate, the syntax refers to the structure of the program and syntactic analysis checks for errors in aspects like spelling or whether ibraces are missing in which case the program would fail syntactically.

Semantic errors, on the other hand refer to the essential meaning of the content -- whether it all makes sense and whether it is accurate (for instance writing "the sun rises in the west") is a semantic error for this is incorrect. I would have to ascertain that all data placed in tables and columns was accurate in both context and form.

b. Query Transformation

I transformed the query into simplified and standardized format based on relational algebra. Some query transformations…

For my entire life, acting as a caregiver has been an integral part of my identity. I come from Cuba, and caring for the old and sick is considered to be a very important obligation. I was the child who took care of the needs of my grandmother and grandfather as they aged, as well as my father who died all too young of cancer. As emotionally difficult as these experiences were, I felt privileged to be able to do something for the people who had given so much to me. I also learned how gratifying it was to nurse someone and to provide them with a sense of self-worth and empowerment, even when they were facing their own mortality. To make this my career would be my dream come true.

I wanted to become a nurse while still living in Cuba but unfortunately Cuban nursing schools…

National and State Subject Matter Content Standards for Math

According to the California standards for high school students, the geometry curriculum contains six critical components: "to establish criteria for congruence of triangles based on rigid motions; establish criteria for similarity of triangles based on dilations and proportional reasoning; informally develop explanations of circumference, area, and volume formulas; apply the Pythagorean Theorem to the coordinate plan; prove basic geometric theorems; and extend work with probability" (Common Core Standards, California Department of Education: 69). The elucidated standards are often quite specific in terms of how students are asked to apply basic concepts such as measuring angles; understanding the different properties of parallel lines; and manipulating various polygons. Not only must the students prove theorems but they must also be able to construct such shapes using a variety of methods in a hands-on fashion (Common Core Standards, 2013, California Department of Education: 70).…

Works Cited

Common Core Standards. California Department of Education. ca.gov. [21 Oct 2013] http://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf

Common Core Standards. Official Website. [21 Oct 2013]

Teaching as a Career

Teaching Special Education requires a gentle temperament and devotion to the children. Maturity, regardless of age, and patience is very important. Special Education teacher must be loving, kind, and nurturing in order to make the children feel safe and secure. He or she must also be focused and creative in teaching methods. nd most importantly, present a positive role model for the children. I feel that I have the qualities and experience to become an effective Special Education teacher.

My background is vast and varied. I worked as a secretary at the University of California - Los ngeles for two years. The department in which I worked dealt with the clubs and fraternities on campus, therefore, I was constantly involved with the students and problems that arose from their activities. I spent a little over two years working as an office manager for a doctor's office.…

A then studied and received my real estate license. I worked as an agent for approximately seven years. This position required much the same skills as my other positions, flexibility, patience, and an aptitude for detail. It also required social skills, self-motivation and the ability to enjoy working with people from varying backgrounds. Between 1999 and 2000, I worked 900 hours as a substitute Educational Assistant for all grade levels in Special Education. In this position I worked with mildly to severely mentally challenged students. In 2000, I was hired full time as an Educational Assistant in the Resource Center, and am currently still employed in this position. I tutor multiple subjects, science, consumer math, algebra, social studies, and English, to special educational students. These students are mainstreamed into regular educational classes, however, still need tutoring. I have approximately 700 hours in this position.

As a wife and mother, I have devoted my life to my family and was always involved with my children and their activities. I have raised two sons, both graduated college. I have an Associate of Arts degree and will be returning to college to work towards a degree in education, with a teaching certificate and an endorsement in Special Education.

The years that I spent working as a substitute, and now full time as an Educational Assistant has given me the opportunity to understand and fully appreciate this field of study. I feel my diverse working background and life experience gives me the foundation for dedication in this area. I enjoy teaching and working with the students is very rewarding for me. I am confident that I have chosen the right career to move into at this time in my life and feel comfortable that I possess the qualities to become an effective teacher.

On the other hand, because the college authorities' argumentation is based on all kind of fallacies, clearly dismantled one by one in Gordon's argumentation, it is my opinion that Gordon should be…

Organizational Health

Educational institutions generally approach organizational improvement by addressing the performance standards to which students, educators, and administrators are held. The standards movement has been a dominant theme in educational policy arenas and in the public eye. With roots in the 1950s Cold War mentality, the thrust of educational improvement has been prodded by perceptions of international industrial and scientific competition. If the rigor of educational standards in the nation -- according to the logic of this argument -- falls below that of other countries, our economy will falter and the balance of trade will be compromised, perhaps beyond the point of recovery.

Fears for the future of the country and our citizens run deep; these fears propel a course of action that is not particularly based on rational thinking and lacks a base of evidence. The course of action adopted by educational policy makers and educational leaders in…

References

Barth, P. (1997, November 26). Want to keep American jobs and avert class division? Try high school trig. Education Week, 30,33.

Bosch, G. (2000). The Dual System of Vocational Training in Germany. In Tremblay, D.-G. And Doray, P. (2000). Vers de nouveaux modes de formation professionnelle? Le role des acteurs et des collaborations. Quebec: Presses de l'Universite du Quebec.

____. (1998). Business Coalition for Education Reform. The Formula for Success: A Business Leader's Guide to Supporting Math and Science Achievement. Washington, DC: U.S. Department of Education.

Hacker, A. (2012, July 20). Is algebra necessary? The New York Times [national ed.], SR1, SR6.

Unemployment in America

Policy makers in the United States continuously seek the silver bullet(s) -- plural solutions because there is clear recognition that the issue is multifaceted -- that will achieve healthy levels of employment in the nation. Certainly there some paths to increasing employment in the country are less expensive than others, and proposed solutions range across a wide array of complexity and practicality. Invariably, today, education becomes a focal point for discussions and debates about how to increase employment in any nation. This is due largely to the potential promise that solutions based in education can act as levers that are sufficiently effective to induce change.

Thesis Statement

Solutions to unemployment must be developed through the perfection of the alignment between the education young American receive -- in both secondary (high school) and post-secondary (college / university) educational systems -- and the actual labor market.

In his article…

References

Friedman, T.L. (2010, November 23). U.S.G. And P.T.A. The Opinion Pages. The New York Times. Retrieved http://www.nytimes.com/2010/11/24/opinion/24friedman.html?_r=1& ;

Hacker, A. (2012, February 28). Is Algebra Necessary? The Sunday Review. The New York Times. Retrieved http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html

These include: question/answer, lecture, demonstration, discussion, individual student projects, laboratory, technological activities, and supervised practice. Previous research has demonstrated that the use of informal knowledge, real world settings and opportunities to apply mathematical thinking are effective instruction methods for introductory algebra. For this reason, instructional factors are related to achievement in algebra (p. 102).

When comparing the test scores from Japan and the United States, House and Telese (2008) found a correlations between positive beliefs in the student's mathematical ability and their test scores. Those who believed they could do well in math performed better than those who expressed a negative opinion about their skills, when compared to their peers. In addition, students who worked problems on their own had higher test scores. This supports Silver's (1998) analysis that much of the reason why American students have poorer test scores than their international peers is due to the classroom instructional…

References

Falco, L., Crethar, H. & Bauman, S. (Apr 2008). "Skill-builders: Improving middle school students' self-beliefs for learning mathematics." Professional School Counseling, 11(4). p. 229-235.

House, D. & Telese, J. (Feb 2008). "Relationships between student and instructional factors and algebra achievement of students in the United States and Japan: An analysis of TIMSS 2003 data." Educational Research & Evaluation, 14(1). p. 101-112.

Silver, E. (Mar 1998). Improving mathematics in middle school. Lessons from TIMSS and related research. Retrieved December 14, 2010, from http://www2.ed.gov/inits/Math/silver.html .

Once the concept of factoring is understood, technology can be used to assist the students with solving quadratic equations and equalities. The website (http://www.coolmath.com/algebra/) will be references, but the students will have to write explanations showing that they understand how at least two homework problems were solved.

4. By the time we are ready to learn inverse functions, students will have a review of everything learned during the school year building up to inverse functions. Again, technology will be used via (http://www.coolmath.com/algebra/). tudents will again be asked to write an explanation for various homework problems demonstrating that they understand the concepts behind solving it.

Evaluation Procedures:

A quiz once per week

Midterm exam covering current quarter

Final exam covering current and previous quarters

Written homework explanations demonstrating how certain problems were solved

Review near the end of the school year for all concepts learned

End of year final exam

Resources:…

Sample of Text Resources:

Cummings, J., McClain, K., & Malloy, C. (2007). Algebra: Concepts and Applications

(First Edition ed.). New York: GLENCOE/MCGRAW-HILL.

These exams would also tap teaching performance and other capabilities unlikely to be adequately assessed using conventional paper along with pencil instruments." (Shulman, 1986, pp. 4 -- 14)

These different elements are important, because they are providing a foundation for helping the schools to become more competitive in mathematics. As, they are working together to create a basic standard for: improving learning comprehension and provide the ability to solve more complex issues. Over the course of time, this will help to increase the student's ability to understand a wide variety of concepts. This is the point that they will be more prepared to deal with the various challenges that they are facing in the 21 century. Once this occurs, it will help them to establish a foundation for adapting to the changes that they will have to deal with from: shifts in technology and through these transformations because of globalization.…

Bibliography

Content Knowledge for Teaching. (2010). Bill and Melinda Gates Foundation.

Diagnostic Mathematics Assessment. (2011). University of Louisville. Retrieved from: http://louisville.edu/education/research/centers/crmstd/diag_math_assess_middle_teachers.html

Elementary and Secondary Education. (2004). NSF. Retrieved from: http://www.nsf.gov/statistics/seind04/c1/c1s1.htm#c1s1l3a

Frequently Asked Questions. (2011). Core Standards. Retrieved from: http://www.corestandards.org/frequently-asked-questions

He looks at thee methods: histoy (melding infomation about the divese geogaphical oigins of algeba with the poblems themselves), multiple epesentations (using notation, naative, geometic, gaphical, and othe epesentations togethe to build undestanding), and the object concept of function (teaching functions without genealizing about how taits of an individual elate to taits of a goup). The aticle seves to offe some inventive solutions to a common poblem in math education: How to make mateial elevant and compelling to a beadth of students.

Matinez, a.A. (2010). Tiangle sacifice to the gods. 1-11.

The aticle looks at Pythagoas, paticulaly the mythology suounding his life and his most famous discovey, the Pythagoean theoem. It calls into question the histoical evidence on which mathematics teaches base thei teaching of this theoy. The autho points out how vey little is known about Pythagoas and how he has been canonized by the math discipline because his…

references the impact that Newton's work had on mechanical applications. Lastly, the piece points out how Newton used the thought patterns associated with calculus in what appears to the modern reader as a work of geometry (with respect to his book "The Principia"). In this way, the article functions as a reminder of how scientific discoveries are created, which is by building upon the theories of others and by giving weight to the importance to mathematical principles.

Education: Teaching Math to Students ith Disabilities

orking with students with disabilities (SD) can be quite challenging, especially for teachers working on a full-time basis. Almost every classroom today has one or more students dealing with either an emotional, educational, or physical disability; and teachers are likely to find themselves looking for resources or information that would enable them teach all their students in the most effective way. There are numerous special-education websites from which teachers and instructors can obtain information or lessons on teaching their respective subjects. Five websites available to the math special education teacher have been discussed in the subsequent sections of this text.

Teacher Resources

Teachers Helping Teachers: http://www.pacificnet.net/~mandel/

This online resource provides teaching information for all teachers, with a 'Special Education' segment that provides a number of activities meant specifically for instilling basic conceptual skills in learners with special needs. The activities are submitted by…

Works Cited

Oldham County Schools. "Instructional Resources for Math." Oldham County Schools, n.d. Web. 17 August 2014 http://www.oldham.k12.ky.us/files/intervention_resources/Math/Instructional_Resources_for_Math.pdf

Starr, Linda. "Teaching Special Kids: Online Resources for Teachers." Education World, 2010. Web. 17 August 2014 from http://www.educationworld.com/a_curr/curr139.shtml

conveyed in an effective manner to meet the needs of students. It is an important aspect of differentiating instruction. Students with diagnosed learning disabilities will receive an IEP designed to address their specific learning issues and deficits. Presentation, response, timing (scheduling) and setting can all be addressed in differentiation. Memory; auditory, visual, and even motor processing; attention deficits; abstract reasoning issues; and organizational problems can all cause issues for students that can be improved with differentiated instruction (Ginsberg & Dolan, 2003, p. 87).

In-class assessment can take place in both in traditional formative and performance-based ways. Formative assessment is used during the learning process so the teacher can check in to see what the student has retained. This can be observational or in the form of quizzes or other graded formats. But while performance-based assessment can take the form of conventional tests there are other methods besides exams, including flexible…

Chapter 6: Algebra

Algebra is often taught relatively early in a student's middle school or high school career but many students, particularly students with learning disabilities, struggle to grasp its basic concepts (Lannin & Van Garderen, 2013, p.141). Weak abstract reasoning skills, combined with computational and memory deficits as well as low self-esteem all conspire to make learning algebra especially difficult for LD students. The most basic concepts of algebra can be fostered as early as grade school, when children learn the intrinsic properties of numbers such as even and odd and zero. Even elementary school children should understand that adding and subtracting the same thing does not change the property's intrinsic value (Lannin & Van Garderen, 2013, p.146). By grade 6 or so they should be able to write their own equations to understand simple word problems; by grade 8 they should understand linear functions (Lannin & Van Garderen, 2013, p.148). But always, the emphasis must be on real understanding. Tables, graphs, and other methods can be useful although it is important for the instructor to be focused on conveying the meaning of the equation to the student, above all else. Linking the equation to a physical representation is key, not simply using a graphic without an expressed pedagogical purpose (Lannin & Van Garderen, 2013, p.152).

For LD students in particular, developing a step-by-step method to approach algebraic equations is critical. Pictorial representations can also be useful. Finally, self-monitoring is important, given that LD often have a weak skill set in this area. All of these approaches can be useful for all students but a teacher must be especially mindful of using this approach with LD students. Both authentic tasks and cognitive understanding is essential for true mastery (Lannin & Van Garderen, 2013, p.157). Peer-based learning can be helpful to enhance motivation.

Summarizing and Note-TakingAbstractNote-taking is the primary method students use to record what they capture during a learning session with a teacher. According to cognitive psychologists, summarizing is done to; fill the missing parts and as a method of synthesizing information to a better understandable and simple form. The amount of notes taken is in direct proportion with achievement. To make notes worth-while, researchers suggest that students should consider them as a work in progress thus revised accordingly as new information is available. However, note-taking doesnt work for all students, especially those with learning disabilities, hence the concept of guided notes. Guided notes are prepared by the teacher and given to the students as handouts. Guided notes are a vital tool in improving learning, and their effective can be increased depending on how they are used. Using guided notes has a beneficial effect, especially on students test performance. In my class,…

ReferencesBrooks, B., Brown, J., Faust, T. & Ward, C. (n.d.). Summarizing & Note Taking. Dean, C. B. (2012). Classroom instruction that works: Research-based strategies for increasing student achievement. ASCD.Konrad, M., Joseph, L. M., & Itoi, M. (2011). Using guided notes to enhance instruction for all students. Intervention in school and clinic, 46(3), 131-140.Loucks-Horsley, S., Stiles, K. E., Mundry, S., & Hewson, P. W. (Eds.). (2009). Designing professional development for teachers of science and mathematics. Corwin Press.Marzano, R. J., Gaddy, B. B., & Dean, C. (2000). What Works in Classroom Instruction.Ottmar, E. R., Decker, L. E., Cameron, C. E., Curby, T. W., & Rimm-Kaufman, S. E. (2014). Classroom instructional quality, exposure to mathematics instruction and mathematics achievement in fifth grade. Learning Environments Research, 17(2), 243-262.

Students will work together in groups of at least four to answer the questions on the exercise. Then, they will be required to present their findings to the class in a short, five-minute group presentation.

3. In order to familiarize students with the concepts and properties of triangles, quadrilaterals and other polygons, students will access the website, (http://www.explorelearning.com). Under the Mathematics Gizmos section of this website, students will select the following: Grade 9-12 > Go > Geometry. Students will be required to perform all of the interactive activities in the Triangles and Quadrilateral and Polygons sections. Students will be required to write a brief explanation of understanding for each exercise.

4. Students will pick up where they left off in the first semester by continuing to use the website (http://www.explorelearning.com) for the entire second semester. The will follow the similar path that they did during the third unit: Grade 9-12…

Resources:

Monroe, Kara, Wilson, Margaret Mary, Bergman, Kathleen and Marisa Nadolny.

(2009). High School Math Made Simple (2009/2010 ed.). New Jersey: TutaPoint,

LLC.

Environmental classes could chronicle their observations of the weather, for example, and post the results of their class observations online. Creating attractive, scientifically literate material online is an important skill that students should learn. New equipment is also needed in the laboratories to conduct more accurate measures of experiments. This is necessary to improve student performances at local science fairs.

Funding for field trips to science museums and other on-site locations to supplement education:

Interacting with science and technology in a hands-on fashion; visiting science laboratories that use technology; and meeting with individuals who use science and technology in their vocations are all ways to get students excited about technology and its applications.

Hiring a part-time or full time teacher of technology

This professional would be officially in charge of acting as a facilitator between the math and science departments; teach elective courses in technology; and conduct laboratories and educational…

References

McQuinland, Larry & Louise Kennelly. (2005, November 22). New study finds. American Institute for Research. Retrieved March 19, 2010 at http://www.air.org/news/documents/Release200511math.htm

, 2007).

The use of the Cognitive Tutor not only enriches students' experience at the academic task-level but also impacts the teachers' instructional practices and relationship with her students (Level 3) A district-wide survey of high school teachers using the program reveals that the Cognitive Tutor allows them more time to provide individual assistance to students; gives them the opportunity to adjust their instructional practices as a result of students progressing in problem solving; and makes Algebra more interesting and relevant to students (Schneyderman, 2001). These views imply that the use of the program makes teaching less burdensome in the sense that the teacher acts as facilitator of learning rather than instructor, which is one of the arguments for educational technology in general.

Due perhaps to the wide acceptance of the use of Cognitive Tutor and other instructional software in American classrooms, the "No Child Left Behind" Act called for…

Research evidence on implementation factors may suggest some explanations for the above findings. First, there are teacher-related issues. Technology products places demands on teachers' time and skills as they have to prepare the product, transfer the students to computer labs, maintain the technology, and monitor and help students as they use the software (Dynarski et al., 2007). Many teachers also feel that they have a significant need for professional development on how to manage classroom activities that integrate computer technology (Adelman et al. 2002 in Dynarski et al., 2007). In the ED study, although teachers underwent training and were confident at the end to use the products in their classes, their confidence dropped to some degree after they began using the products in the classroom (Dynarski et al., 2007). This may have been due in part to technical difficulties, which is another implementation factor issue. For instance, computer access may be limited, hardware can be unreliable, computer networks unstable, and technical support inadequate (Cuban, 2000 and Culp et al., 2003, in Dynarski et al., 2007). In the ED study, however, technical difficulties were considered "minor" as they were easily corrected or worked around (Dynarski et al., 2007).

These observations show how the other levels of school organization may affect the success of novel learning tasks and instructional design. Specifically, the teacher's belief about her efficacy and classroom management practices (Level 3) can send implicit and explicit messages to her students, that in turn may influence their academic performance (Eccles and Roeser, 1998). Hence, one of the recommendations of the ED study is to evaluate a second batch of students with the same teachers' implementing the products in their classroom. They hope to see the effect of teachers having prior experience and improved skills in using the products on students' performance (Dynarski et al., 2007). School resources (Level 5) in terms of adequate materials and technical capacity are also thought to be important for children's learning (Eccles and Roeser, 1998). Hence, it would be worthwhile to include recommending the upgrade of school computer networks and labs for Phase 2 of the ED study.

In summary, computer software such as the Cognitive Tutor can be beneficial for middle school and older students to improve their academic outcomes in challenging subjects like Math. For younger students such as those in grade school, the effectiveness of some computer software seems to be influenced by teacher and school factors. Although there is conclusive evidence from an ED study that reading and mathematics software don't significantly impact the performance of grade school and some middle school students, it could be worth addressing these contextual factors in a sequel study to re-evaluate the findings.

Thus, in 1 Kings 7:23, the word "line" is written Kuf Vov Heh, but the Heh does not need to be there, and is not pronounced. With the extra letter, the word has a value of 111, but without it, the value is 106. (Kuf=100, Vov=6, Heh=5). The ratio of pi to 3 is very close to the ratio of 111 to 106. In other words, pi/3 = 111/106 approximately; solving for pi, is pi = 3.1415094... (Tsaban, 78). This figure is much more accurate than any other value that had been calculated up to that point, and would hold the record for the greatest number of correct digits for several hundred years afterwards. Unfortunately, very few people know this fact.

Archimedes of Greece was the first person to make serious use of the pi calculation. In 287 to 212 BC, he focused on the polygons' perimeters as opposed to…

References

Archimedes. "Measurement of a Circle" in Pi: A Source Book. Heidelberg: Springer

Verlag, 1997.

Baumgart, J.K.J.K.)." The history of algebra: An overview." In Historical topics for the mathematics classroom. 31st National Council of Teachers of Mathematics Yearbook. Washington, DC: NCTM, 1969

Blatner, David. The Joy of Pi. Walker Publishing Company, Inc. New York, 1997.

First, math courses are required as part of college work in the pursuit of most degrees in the health care field. The level of required achievement is different, depending on the degree sought. For example, a student pursuing an LPN may take a semester or two of college algebra. A pre-med student is often required to take one or two semesters of calculus. A student pursuing a master's degree in health care administration will take courses in statistics, finance and accounting. The master's candidate can perhaps more easily see the relevance of the required math courses toward the future career. For the nursing student studying algebra or the pre-med student struggling through calculus, the correlation between academic study and actual practice may be unclear. They may wonder why they must undertake these courses, which seem to have little to do with the work in which they will eventually be engaged.…

References

Marketplace Money. (2011). The cost of the common cold. American Public Media.

Retrieved from http://marketplace.publicradio.org/display/web/2011/01/21/mm-why-its -

so-expensive-to-get-a-cold/

Paris, N. (2007). Hawking to experience zero gravity. London Telegraph 26 Apr 2007.

Hypatia of Alexandria, daughter of Theon. Specifically, it will examine the life of Hypatia, especially her mathematical accomplishments. Hypatia was the first female mathematician that left a record that historians can trace. She was a philosopher, mathematician, and teacher who lived in Alexandria, Egypt from about 350 to 415 A.D. She was the daughter of Theon, a renowned mathematician and head of the library in Alexandria.

Historians do not agree on the year Hypatia was born. Some estimate it at around 355, while others place it as late as 370. What is known of Hypatia is that she was extremely influential in mathematics and philosophical thought. Hypatia was born in Alexandria and most historians believe she spent her entire life there. Some historians believe Hypatia studied mathematics in Athens, and then traveled through Europe (Coffin, 1998, p. 94), while others believe her father taught her most of what she knew…

References

Coffin, L.K. (1998). Hypatia. In Notable women in mathematics: A biographical dictionary, Morrow, C. & Perl, T. (Eds.) (pp. 94-96). Westport, CT: Greenwood Press.

Osen, L.M. (1974). Women in mathematics. Cambridge, MA: MIT Press.

Russell, N. (2000). Cyril of Alexandria. London: Routledge.

Williams, Robyn. (1997). Ockham's razor. Retrieved from the ABCNet.au Web site: http://www.abc.net.au/rn/science/ockham/or030897.htm 8 Aug. 2005.

In 2002, Michael M. Crow became the University's sixteenth president. In his inaugural address, he outlined his vision for the transformation of the school into a prototype for a new American university. This future institution will be a comprehensive research university that continues its academic excellence as well as have a strong commitment to social, economic, cultural, and environmental issues to meet the needs of the growing Phoenix area. The city has…

Take for example a human resource manager who is interested in how three different departments in a business situation waste time on the internet on a given day when they should be doing company business. The human resource person would collect data through a time study process and determine the number of times each employee in each department logs on and off the internet for personal business. The times would be collected, added together and the times of each department converted to percentages. In the example presented, the human resource manager can report that, cumulatively, the employees in Department 1 spent a total of 5 hours a day on the Internet, Department 2 employees 2 hours a day and Department 3 spent 6 hours. The raw numeric count is then converted to percentages and the pie chart would look like the following (Ohlson, 2005):

The solution to the data presented…

References

Ohlson, E.L. (1998). Best Fit Statistical Practices. Chicago: ACTS Testing Labs. p.43

Weirs, Ronald M. (2005). Introduction to Business Statistics. Scranton, PA: Brooks/Cole

Publishing Company.

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ATHLETIC DIRECTOR -- COACH -- ADMINISTRATOR -- TEACHER

Professional, experiences, articulate and student-focused professional with proven expertise in motivating you to achieve appropriate goals. Prioritizing strategies for wining school athletic programs without losing sight of team-building, social, and sportsmanship training. Holds students, parents, staff in high-esteem while ensuring that students of all levels are accountable for their performance and attitude, on and off the field. Interacts with colleagues and administrators with a high degree of professionalism and personal integrity. Background includes pedagogical leadership and business. Extremely dedicated to student and staff development. Proficient with athletic scheduling software. Adept at training programs for all levels.

ATHLETIC EXPERIENCE

LONG BEACH HIGH SCHOOL, Long Beach, CA

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Athletic Director, Boys Football and Basketball Coach

Reorganized football and basketball programs and exceeded California Athletic Association Standards

Created new policies and…

Inverse Equations

Problem "a" is an example of substitution equations. In this case, it is asking the two equations to be subtracted and the number four substituted for "x." In order for this operation to be properly accomplished, order of operations requires that the two problems be simplified to their final state before being combined.

Proof a.

(f-h)(4)

Problems "b" are examples of inverse functions. Here, a secondary function is being placed in the original function's "x" position. Once this is accomplished, order of operations and rules of simplification allow for the simplifying of the final expression. These cannot be entirely solved as there is no value given for "x."

Proof b.

2(x^2 -- 3) +

2x^2 -- 6 +

2x^2 -- 1

(7 -- (x^2 -- 3)) /

(7 -- x^2 + 3) /

(10 -- x^2) /

Problems "c" are examples of finding the inverse of a single…

Works Cited

Chen, C.H. (1987). Applications of algebra of rotations in robot kinematics.Mechanism and machine theory, 22(1), 77-83.

McKeague, C.P. Elementary and Intermediate Algebra. Cengage Learning.

Disequilibrium in Learning

Piaget's concept of disequilibrium in learning makes a great deal of sense both in terms of child development and in terms of the general way in which humans tend to think and act. Piaget bases much of his theories on evolutionary biology, and so adaptation necessarily plays a certain role in his thinking. He theorizes that the student is always active and that learning is an action by which one constructs knowledge (hence consctructivism), but that at the same time humans tend towards stagnation, seeking to "continue in past patterns as long as possible" (Doll, 1993, p. 83) Piaget supposes that it is necessary for the teacher to create a sort of cognitive dissonance and discomfort which will shock the student out of their complacency and force them to evolve and learn. He calls this state of uneasiness which is necessary to learning "disequilibrium." The social aspect…

References

Doll, W.E. (1993). A Post-Modern Perspective on Curriculum. New York: Teachers College Press.

Forman, E. & McPhail, J. (1993). "Vygotskian perspectives on children's collaborative problem-solving activities." In E.A. Forman, N. Minick, & C. Addison Stone (Eds.). Contexts for learning. Sociocultural dynamics in children's development. Oxford: Oxford University Press

Woolfolk, A. (2003). Educational Psychology. New York: Pearson Allyn & Bacon.

Precalculus With Limits by on Larson

This book as well as the other two books are for college freshman level or college introductory level mathematics courses. The strengths of the book are mainly focused on its layout. For example, the book has a great way to demonstrate a varied and large amount of information easily and simply. This means that people reading the text just have to look for certain visual cues like colors or pictures that will point the information they seek. For example, the diagrams have a different background color than the text. All of this removes time spent looking for things. The use of bold also further differentiates the text, highlighting key words, phrases and things to memorize.

The weaknesses are in lack of context surrounding the topics and footnotes. Another book reviewed has footnotes and yet another provides adequate background for each topic. This book sacrifices…

References

Larson, R., Hostetler, R., & Edwards, B. (2011). Calculus I, with precalculus (3rd ed.). Boston: Houghton Mifflin.

Larson, R., Hostetler, R., Edwards, B., & Heyd, D. (2013). Precalculus with limits (3rd ed.). Boston: Houghton Mifflin.

Mirsky, L. (2012). Introduction to Linear Algebra. Dover Publications.

For this he can use the FOIL method. FOIL means FIST OUTSIDE INSIDE LAST. This order can help erase the confusion that arises with understanding of order in which equations are to be solved. This technique falls in the category of Mnemonics which was one of the strategies recommended for Jeffery's case. Mnemonics are any sentences or pictures that help students make connections and understand concepts.

Students often are befuddled with the use of complex terms in mathematics and hence it's recommended that they become familiar with some commonly used terms before they are used in the context of mathematics or algebra. For example students can be told what a variable is without actually referring to any mathematical equation. Variable is simply any letter in which a value can be stored. 4x for example would be the number 4 with a variable x that also contains a value though hidden…

References

Marcee M. Steele and John W. Steele (2003). Teaching Algebra to Students with Learning Disabilities. Mathematics Teacher, Volume 96, Number 9; December, 2003; pp.622-624.

Blessman, J., & Myszczak, B. (2001). Mathematics vocabulary and its effect on student comprehension. Saint Xavier University & Skylight Professional Development. (ERIC Document Reproducion Service No. ED455122).

Rubenstein, R. (2007). Focused strategies for middle-grades mathematics vocabulary development. Mathematics Teacher, 10(4), 200-207.

Schoenberger, K., & Liming, L. (2001). Improving students' mathematical thinking skills through improved use of mathematics vocabulary and numerical operations. Saint Xavier University and Skylight Professional Development. (ERIC Reproduction Service No. ED455120).

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