Algebra 2 Syllabus

Algebra 2 Syllabus
ALGEBRA 2 COURSE SYLLABUS
2015–2016
Terrance M. Reece/Sierra Edwards
TMReece@fcps.edu/Ksedwards@fcps.edu
703–810–2450
I. Course Curriculum:
http://www.fcps.edu/is/pos/documents/coursecatalogs/HSStandardCourseCatalog.pdf
II. Program of Studies: http://www.fcps.edu/is/pos/hs.shtml
III. Standards of Learning (SOL): http://www.doe.virginia.gov/testing/index.shtml
IV. Textbook: Algebra 2. Charles, Hall, Kennedy, Bellman, Brag, Handlin, Murphy; Prentice Hall;
Pearson Education, Inc., New Jersey. 2012. The replacement cost of the Algebra 2 textbook is $81.
V. Assessment and Grading: http://www.fcps.edu/HerndonHS/academics/grading.html
 Grade Calculation: Each quarter and the final exam will count as 20% of the final year grade.
Students ... Show more content on Helpwriting.net ...
Please take this responsibility seriously.
VIII. Additional Information:
 Extra Help: Students are urged to seek help right away if they are having difficulties. Mr. Reece is
available during Stinger Time and after school on Thursdays. Math Honor Society tutoring will be
available Thursday after school in room 129 beginning in October. It is the student's responsibility to
stay after school for help when needed or to make up work that was missed due to absence.
 Communication: Parents are welcome to contact Mr. Reece with any concerns via email or via
phone. Mr. Reece can be reached at TMReece@fcps.edu, or 703 – 810 – 2450.
 Blackboard: Please check Blackboard regularly. Blackboard is a useful tool and will be kept up to
date with assignments and announcements. It can be accessed from the school website or directly at
http://fcps.blackboard.com.
All Hornets are capable of success, NO Exceptions!
With P.R.I.D.E. (Participation, Respect, Integrity, Diligence, and Empathy), Herndon High School
seeks to be an institution that empowers students to become lifelong learners and productive citizens
of the global
... Get more on HelpWriting.net ...

Algebra II Trigonometry: Using Logarithms In The Real World
In Algebra II Trigonometry, there are many equations and functions used to guide us for solving
problems, whether it be in real–world or hypothetical situations. Logarithms and exponential
functions are just some examples of those equations. Exponential functions and Logarithms work
well together because they "undo" each other, making them very useful and unique. Logarithms are
used more commonly in everyday life than you think. Using logarithms is an easier way to describe
numbers in powers of ten, such as if we are using terms like interest rate or double digits. The author
thinks it is important that they are the cause for an effect and the shared "effect" is seeing something
develop and become larger. From the article about Using Logarithms in the Real World, "logarithms
find a plausible cause for that effect and puts numbers on a human–friendly scale" (2). They
describe changes in terms of multiplication and when dealing with a series of multiplications,
logarithms help count them. An easier way to think of them is that it says how many of one number
you need to multiply to get another number. Logarithms show up in everyday life in six–figure
salaries or two–digit expenses where we describe numbers in terms of their digits. Logarithms are
none the less extremely important ... Show more content on Helpwriting.net ...
From the article about Applications of Exponential and Logarithmic Functions, it discusses how,
"the applications are drawn from many different disciplines, [but] the mathematics remains
essentially the same" (1). The author thinks it is important that although exponential functions are
used most commonly in the financial world, that does not mean we do not use it in other aspects of
life as well. Just remember when exponential functions are involved, functions are increasing or
decreasing very quickly. An exponential function is a mathematical function of the following

Analysis Of Letter By Gordon Adams
This analysis is set to discuss a letter written by Gordon Adams. He is a student at Arizona State
University and wants to become a lawyer. However, he finds he must take mathematics courses,
specifically college algebra, to graduate and move on into law school. He claims that he does not
need to take college algebra because he does not need it in his profession and because if he takes the
course, it will delay him into law school. We follow him through his endeavor with ASU's
mathematics committee to try to waive his requirement for college algebra. However, he fails at this
task and, with every argument, you can't always get what you want in return. Rhetorically, I think
his argument to the committee is a good way to write an argument, at least in my opinion. He asks
the question "Why do I need college algebra?"(Adams 19). I can relate to this as many of us in
today's society are in college and we look at our degree requirements and think "Why do I have to
take this class" to ourselves. In Adams case he only has "the benefit of a ninth grade education."
(Adams 18). It is clear that he needs algebra, but he tries to exempt himself from this requirement.
He contacts friends that are attorneys and they say that there are no courses in his profession that
even require algebra or more specifically, college algebra (20). Adams writes "I consulted Mr. Jim of
the Justice College and presented this question to him. He referred to the current ASU catalog and
delineated the

Paper Questions
2.4.2 Conceptions and Past Paper Questions
Norton & Irvin (2007) found that a considerable number of students who have difficulties
understanding fractions, negative numbers and ratios also struggle with solving algebraic problems.
Conception 1,2 and 3 are predominant in the GCSE foundation syllabus and in post primary
mathematics in general. It is evident upon research into examiner reports that students have
difficulties relating to these conceptions.
Below is an example of a question found in the 2014 Maths GCSE foundation exam.
Figure 1 (GCSE Math Jun 14 Foundation Tier Unit 2 Q.18)
The Chief examiner reported, 'Many candidates did not understand the meaning of 'Write an
equation in terms of w' and as a result lost all ... Show more content on Helpwriting.net ...
2.6 Creating an App
2.6.1 The Chosen Software
The first consideration for the app was the software needed to create it. As the developer does not
have advanced knowledge or expertise on coding, the software programme needed to match their
skills appropriately. Luterbach and The second point to consider was the desired outcome. The
overall aim of this project was to create an engaging user– centred app, which highlighted two of the
misconceptions in GCSE algebra.
The software programme chosen enabled interactive elements and testing features to enhance
students learning and knowledge.
2.6.2 Using an app to teach algebra
"Technology is essential in teaching and learning mathematics; it influences the mathematics that is
taught and enhances students' learning."(McGehee & Griffith, 2000). Similar to McGehee and
Griffith, Ghosh (2012, cited Drijvers, 2016) believes that the integration of technology and ICT has
suggested a positive impact on the achievement of students in the general algebraic education but in
particular solving word problems.
The most recent phenomenon has been the

My Self Contained Algebra 1 Class
In my self–contained Algebra 1 class we have begun a new unit that involves unpacking polynomial
expressions. The common core standards that apply are; Expressions A–SSE.1 Interpret parts of an
expression, such as terms, factors and coefficients. Arithmetic with polynomials and Rational
Expression A–APR.1 Understand that polynomials form a system analogous to the integers, namely
that they are closed under the operations of addition, subtraction and multiplication; add, subtract,
and multiply polynomials. This particular unit is important because the skills learned helps lay the
foundation to all of the mathematical concepts learned in Algebra 1. Target student Yanni is a 9th
grade student who has difficulty keeping up with classmates of the same age in a developmentally
appropriate learning environment. Yanni has extreme difficulty with comprehending what he reads.
Since he doesn 't monitor his comprehension when he reads, he doesn 't recognize when he is
"getting it" and when he is not. He works at a much slower pace than other students and requires
extra time to complete certain tasks; he never forgets to do his homework and has no difficulty with
planning. Yanni has a hard time remembering information – memorizing is very difficult for him.
This leads to poor recall of facts, as well. Yanni prefers math to ELA. However, he continues to need
encouragement in math. He often gets confused in math and cannot communicate his thinking. His
basic math facts are not yet in

The Mathematics Of Algebra And Algorithms
Anna Safavi
Algebra and algorithm are two of the most used branches of mathematics. They are used in everyday
life, algebra is used in financial planning, physical health and cooking, and algorithms are used in
driving and finding the shortest path, scheduling and in computer programming.
The history of algebra dates back to 1800 BC, in countries such as India, China, Greece, Persia and
England. With the understanding that algebra and algorithms have a huge impact on our lives today,
we will take a look at the history of algebra and algorithms, notable people that helped in their
creation and the things that influenced what we know today about algebra and algorithms. This
paper will go into depth in the influences of Islam on the creation and growth of algebra and
algorithms as separate branches of mathematics. We will look at the Golden age of Islam and how it
influenced many scientists, astronomers, geographers and physicians as well as mathematicians.
Also we will take a look at one notable mathematician of that time, Al–Khwarizmi who created
algebra and algorithms, who is known as the father of algebra.
The work of mathematicians and scientists like Al–Khwarizmi in 820 CE is the result of the
influences of Islam on the culture and knowledge of a specific time in our world, which is also
known as the Golden Age of Islam. It was during that time that Al–Khwarizmi wrote the
"Compendious book of balancing and calculations" from which the word Algebra is derived from.
Later

Algebra Research Paper
Algebra is the bridge between basic and complex math; it ties together basic arithmetic with
complex formulas and proofs. The first time I encountered algebra was in 7th grade after learning
about graphing equations. Our curriculum is set up so that our minds learn what they have to first so
that when special maths such as Algebra. A person must first master the basic tools of mathematics
before they go into learning algebra. Perhaps what makes algebra so special is the fact that it can be
used along side any other math. It is never impossible to incomplete Algebra when problem solving.
Algebra first began in ancient Egypt and Babylon people first began solving linear equations.
Babylonians solved arbitrary quadratic equations by

Ashford Mth 222 (Intermediate Algebra) Entire Class
ASHFORD MTH 222 (Intermediate Algebra) Entire Class IF You Want To Purchase A+ Work Then
Click The Link Below , Instant Download http://acehomework.com/ASHFORD–MAT–222–
Intermediate–Algebra–Complete–Class–A–Work–65466.htm If You Face Any Problem E– Mail Us
At JohnMate1122@gmail.com Week 1 Assignment Solving Proportions Read the following
instructions in order to complete this assignment: a. Solve problem 56 on page 437 of Elementary
and Intermediate Algebra. Set up the two ratios and write your equation choosing an appropriate
variable for the bear population. b. Complete problem 10 on page 444 of Elementary and
Intermediate Algebra. Show all steps in solving the problem and explain what you are doing as you
go along. c. ... Show more content on Helpwriting.net ...
Solve problem 68 on page 539 of Elementary and Intermediate Algebra, and make sure to study the
given graph. For the purposes of the assignment, it would be helpful to copy the graph onto your
own scratch paper. b. Write a two to three page paper that is formatted in APA style and according to
the Math Writing Guide. Format your math work as shown in the example and be concise in your
reasoning. In the body of your essay, please make sure to include: § An answer to the three questions
asked about given real–world situation. § An application of the given situation to the following two
scenarios: o The Burbank Buy More store is going to make an order which will include at most 60
refrigerators. What is the maximum number of TVs which could also be delivered on the same 18–
wheeler? Describe the restrictions this would add to the existing graph. o The next day, the Burbank
Buy More decides they will have a television sale so they change their order to include at least 200
TVs. What is the maximum number of refrigerators which could also be delivered in the same
truck? Describe the restrictions this would add to the original graph. c. An incorporation of the
following math vocabulary words into your discussion. Use bold font to emphasize the words in
your writing (Do not write definitions for the words; use them appropriately in sentences describing
your math work.): § Solid line § Dashed line § Parallel § Linear inequality § Test point Week 2 DQ
One–Variable

The History Of Algebra, How It Started, The Most Study...
This paper will show the history of algebra, how it started, and how it grew to be what it is today. It
will show that it started it developments from the basic arithmetic operations that first were used to
solve simple addition, subtraction, multiplication, and division and how it went incorporating more
operations that permitted it to solve problems that involve abstract concepts. It will show that the
recorded history begins mostly with the Egyptian papyrus, and how it went passing from one
civilization. Moreover; it will show how each civilization contributed with something that at the end
helped it to become what it is today, the most study mathematical subject around the world.
1. Introductions
However; the recorded history begins with the Rhind Papyrus from Egypt and clay tablets from
Babylon, which describe the basic mathematical operations that include an unknown variable, then
it passed to India where written records in Sanskrit show that the Indian were already describing
verbally what seems to be the description of unknown variables. Next the recorded history passed to
the Greeks, where Diophantus published the b books that describe the syncopated algebra which are
considered to be the basis of all algebra used and studied by European mathematician.
Moreover; it was in Europe where the recorded history of the algebra really was taken to the next
level. The lead was taken by Fibonacci with is book liber abaci, who added the application of
sequences and crated a

The History of Algebra
The History of Algebra The history of algebra has been around for several decades, this method of
mathematics has been used during the beginning of time. The development of algebraic notation
progressed through out three stages: the rhetorical stage, the syncopated stage, and the symbolic
stage with which we are use to using in our daily usage of algebra. In ancient civilization math was
used to help leaders to strategically form how their troops should be lined up for battle and help
decide how to attack their enemies. Algebra was used in the many of these civilizations: Egypt,
Babylon, Greece, India, Europe, and most parts of the Middle East. In Egypt, the Egyptians used
mathematics which included Algebra to solve equivalent to a ... Show more content on
Helpwriting.net ...
They also were able to prove that the quadratic equations have two roots, and included the negative
as irrational roots. The Hindus used the astrology and astronomy to help determine directions in
which they should live their lives as if it was an almanac. The Hindus used this method of algebraic
equations to determine directions, farming, and behavior among their peers.
The Arabs in the Middle East helped improve the Hindus number symbols and was able to adopted
the same method of algebraic reasoning as the Greeks they reject the negative solutions that the
Hindus were using and would solve the quadratic equations by recognizing two solutions, possibly
irrational. The algebra of the Arabs in the Middle East was entirely rhetorical and like the Hindus,
the Arabs worked freely with irrationals. The Arabs used and improved the Hindus number symbols
and the idea of positional notation. These numerals (the Hindu–Arabic system of numeration) which
are used throughout the world today, however the Arabs contribution to the methods that are used in
algebra is the solution of cubic equations by geometric methods involving the intersection of conics.
In the 16th century of the European nations there were great theories about algebra, they rejected the
method that negative numbers could be used in an algebraic equation and many of the
mathematicians would quickly accepted zero as a number but

Higher Order Essay
Higher Order Thinking and Diverse Learners
Grand Canyon University: Secondary Methods and Data–Driven Pedagogy
April Smith
GCU: SED–444
August 25, 2013
Grand Canyon University: Secondary Methods and Data–Driven Pedagogy
April Smith
GCU: SED–444
August 25, 2013
This unit is designed for students in beginning Algebra classes. It is an introduction to the basic
functions of algebra including the definition of an equation, using basic mathematical skills to solve
equations, and applying equations to problem solving.
South Carolina Standard 8–3: Through the process standards students will demonstrate an
understanding of equations, ... Show more content on Helpwriting.net ...
Algebraic Equation Unit Plan | Knowledge | Comprehension | Application | Analysis | Synthesis |
Evaluation | Algebraic Equations | State the definition of an Algebraic Equation? Explain how to
identify an Algebraic Equation? | Describe the parts of an Algebraic Equation including variables,
like terms, and coefficients. | Apply labels to the parts of equations and illustrate knowledge of like
terms. | Classify problems as Algebraic Expressions or Algebraic Equations. | As a group create
sample problems and then share with the class the results. | Students will complete a group quiz and
label each part of an equation. They will also explain the difference between an expression and
equation. | Algebraic Equations using Addition and Subtraction | Students will tell how addition and
subtraction can be applied to solving an equation? | Students will restate the steps involved to solve
an equation using addition and subtraction. | Students will practice solving equations using addition
and subtraction. | As a group students will compare their results in their practice problems and create
questions for discussion. | With a partner, students will compose equations and exchange with
another group. | Students will evaluate another group's equations and share with the class their
results. |

Algebra And Algebraic Thinking Sets Essay
Algebra is a major mathematical strand that has been incorporated across all year levels within the
Victorian Curriculum. The many components within and interrelated with algebra and algebraic
thinking sets children up, not only for formal algebra in high school, but for life (Reys, et al., 2012).
This paper will be addressing some of the main ideas and understandings associated with Algebra.
Key skills, strategies and ways of thinking will also be explored along with strategies for teaching
the content effectively.
Literature review (up to 800 words)
Algebra is a critical aspect of mathematics which provides the means to calculate unknown values.
According to Bednarz, Kieran and Lee (as cited in Chick & Harris, 2007), there are three basic
concepts of simple algebra: the generalisation of patterns, the understanding of numerical laws and
functional situations. The understanding of these concepts by children will have an enormous
bearing on their future mathematical capacity. However, conveying these algebraic concepts to
children can be difficult due to the abstract symbolic nature of the math that will initially be foreign
to the children. Furthermore, each child's ability to recall learned numerical laws is vital to their
proficiency in problem solving and mathematical confidence. It is obvious that teaching algebra is
not a simple task. Therefore, the importance of quality early exposure to fundamental algebraic
concepts is of significant importance to allow all

Doing Well In Algebra Class
I am doing well in Algebra 1 and I think Im doing well in that class because I understand what im
getting tought and I really understand the subject well and can do the work very easily. I think to
keep doing well in that class I have to keep paying attention and asking for help when I dont
understand something. I think the habit of heart and mind im using to do good in this class is effort
because im putting a lot of effort to do good. Another class that im doing well in is biology because
I have an A+ in that class and I will contuine doing well in that class by trying to do all my
homework and finishing projects that are a signed by my techer. The habit of heart and mind im
doing for that class is responsibility because I have done all

Lee Stiff To Math
History Lee Stiff is an African American Math education professor in the Department of
Mathematics at North Carolina State University. Lee Vernon Stiff was born in 1949. His father
provided for the family by working in a factory with a third– grade education level. While
researching Stiff, no information was found about his mother or siblings (if he had any). This essay
will provide information about the life of Lee Stiff and how he contributes to mathematics.
Education
In the year of 1971, Stiff received his Bachelor's degree in Mathematics from The University of
North Carolina at Chapel Hill additionally, He received his Master's Degree from Duke University
(1974) and his PH. D from North Carolina University (1978). (Lee V. Stiff (852), ... Show more
content on Helpwriting.net ...
He has many publications, including the authorship, co–authorship, or editorship of textbooks in
middle grades and high school mathematics, six professional books and eight book chapters. Dr.
Stiff is a textbook author for the Houghton Mifflin Harcourt Publishing Company and McDougal
Littell. ''Houghton Mifflin Math'' is an elementary textbook series, K–6; and McDougal Littell's
titles, such as Math Course 1Algebra 1, Geometry, and Algebra 2 which is usually middle and high
school math textbooks. (Lee V. Stiff (8301), 1999) This is a list of some current textbooks that was
credited by Lee Stiff: Developing Mathematical Reasoning in Grades K–12, Geometry: Reasoning,
Applying and Measuring and Heath Algebra1: An Integrated

Assignment 2: Linear Algebra
Task #2: Linear Algebra
Competency 209.8.4: Vector Spaces
Jennifer Moore
Western Governor's University
Part A: To show that is a vector space, Laws 3 – 10 in the definition of vector space must be proven.
If Laws 3–10 are proven to be true, then is a vector space. This paper will show the proof of Laws 3
– 10.
Proof of Law 3 – The Commutative Law :
Let vectors X and Y in be represented by: where x1, x2, y1, and y2 are real numbers. by substituting
coordinate form of vectors by the definition of vector addition by commutativity of addition of real
numbers by the definition of vector addition by substituting vector form of coordinates
Since by a string of equalities above, then vector addition ... Show more content on Helpwriting.net
...
Proof of Law 5 – Additive Inverse Law "For every X ∈ V there is a vector –X such that X+(–X)=0,
where –X is called the additive inverse of X":
Let vector X in be represented by where x1 and x2 are real numbers. Let 0 be the zero vector in be
represented by . Let vector –X in be represented by where –x1 and –x2 are real numbers (Vector
Spaces). by substituting coordinate form of vectors by the definition of vector addition
Since x1 and –x1 are real numbers, their sum is a real number because of the closure of addition of
real numbers, so the first coordinate of that vector is real.
Since x2 and –x2 are real numbers, their sum is a real number because of the closure of addition of
real numbers, so the second coordinate of that vector is real. Thus, are real and exist in (Lay, 2015).
by the inverse property of real number addition by substituting vector form for

Academic Performance : Grade Algebra 1
1. My (restated) research problem is:
__Students in my school's population frequently do not graduate on time. One of the factors appears
to be academic performance in ninth grade Algebra 1. My school is enrolling students into Algebra 1
as 8th graders in an attempt to provide students in a lower Socio–Economic Status with an extra
year of Algebra to bolster their mathematical success in high school. Students that are successful in
Algebra 1 for 8th Grade will be advanced just as their counterparts in Accelerated Math and Gifted
Math. However, students that are not as successful will have the opportunity to retake the course as
9th graders.
Many teachers are skeptical because rising 8th graders will have some gaps. They are concerned
about the lack of parental support and the apparent lack of intrinsic motivation. Some teachers are
not willing because of the intensive work that might be necessary to insure students' success.
Since the above problem spans a longer period of time than is feasible for my project, I realize that
one aspect that I can focus on is the concept of functions. Using functions is vital to understanding
other studies including the higher mathematics, physics, and physics–based studies. The majority of
my students are visual learners as denoted by a simple learning styles assessment. If I am to assist
my students' success in Algebra 1, then I might need to research a visual method of helping them to
learn.
2. My research question(s) is/are:
What is the

8th Grade Algebra
Eighth–Grade Algebra 1 Advice Hi, and welcome to Algebra! I know that right now this class seems
difficult and confusing, but it does eventually make sense. It is my job to prepare you for the coming
year and to make sure that everything goes smoothly. So let's get to that. The first things you should
know about algebra are, of course, the basics. First: Don't be afraid to ask your tablemates for help.
They are a valuable recourse when you just don't understand something, however even though just
getting the answers from them sounds like a good idea, it really doesn't give you the information
that you need to help you in the long run. Second: Professor Burger is going to be your best friend.
Seriously, all you have to do is go to the Holt ... Show more content on Helpwriting.net ...
This is my personal favorite chapter. You can factor polynomials in a few different ways: by GCF,
through the form X2+BX+C, through the form AX2+ BX+C, and by graphing. There is a way that
Mrs. Ladner teaches to factor called "Big X Bottoms Up" that uses either the X2+BX+C or
AX2+BX+C. To do this method of factoring you first need to draw an X. Then, after that, you
multiply A and C (if there is no A it means that A=1), and put it in the top of the X. Put B in the
underside of the X. Factor AC until you find the pair that equals B when either added or subtracted
to or from each other. Divide these by A and put them in the proper

Jacqueline Gandara
The Math Autobiography of Jacqueline Gandara Mathematics is the study of the sciences of
numbers, quantities, geometry and forms. ("Mathematics dictionary definition | mathematics
defined", 2016) It is a subject that is simple as well as complex. Over the years I have learned that
math is not my cup of tea. I think I liked it more when I was younger, when it was simple, and
easier. I guess you could say that I liked basic math, like adding, subtracting, and multiplying.
Growing up, I actually had no problem with basic math. It was easier when I was in elementary
school. It was until I arrived to middle school and high school that I realized that math wasn't as
simple as I thought it was. Math did not really influence my life until I reached ... Show more
I use math to shop for things at the store, to cook, bake, and to keep track of my expenses. Math will
also be used in the career I have chosen. According to CFNC.org, math is a necessary skill for a
career in Customs and Border Protection, but it is not as important as reading comprehension,
writing and speaking skills. Level 2 math is used in this career and it is most likely not used on a
daily basis. (Corporation, 2016) However, basic math is necessary to get through some of the rules
and regulations. For example, let's say someone attempts to cross the border with 39, 12 oz. cans of
beer and 6, 12 oz. cans of ale. This is legal by law if the person meets the legal drinking age of 21.
However, there is a limit of 40 oz. of liquor, wine or 24, 12 oz. cans or bottles of beer or ale. This
person has passed the limit so, he has to pay a fine of 94 cents for every can that he has gone over.
You have to use your basic math skill to figure out how much money this man owes for bringing
extra liquor. 45 cans (what this guy is bringing) minus 24 (the limit) equals 21 cans. 21 multiplied
by $0.94 cents is $19.74. This man owes a total of $19.74 for his extra liquor. (Corporation, 2016)
The math class I plan to take for my major is college Algebra. Even though I probably will not use it
in my career, I have chosen to take it because I am pretty good at it and it is also essential for a
bachelor's

The Pros And Cons Of Supportive Reasoning
supportive reasoning. Consider a unique scenario where 'fa', 'ga', 'hb, and 'Ib' subjects are the stock
of belief and thereby the belief of 'a=b' aspect is assumed, as soon as one accepts the identity he/she
automatically owes a justification to his/her supportive reasoning in relation to the contextual basis,
the three variables are basically related and mutually interlinked. Frege does assume that, depending
on the preposition expressed, the 'a=a' expression is considered a priori while the second clause
expression 'a=b' is a posteriori. The aspect behind this is that the formulation of the expression is
often considered by many as a petition principal to favor the perception that the sentences
respectively express different propositions. It is possible to formulate and state Frege's puzzle in a
better way without necessarily committing on either positive or negative side of the question or
context, besides the formulation, the understanding of the puzzle doesn't necessarily involve two
singular terms 'a' and 'b,' (Eros & Jerome 2). In addition, the identity "a=b" can be contrasted into
two uses to derive both informative and uninformative sentences, and the number of singular terms
used doesn't matter. Lastly, being distinctive in the relevant notations of the original Frege's puzzle
is likewise important: cognitive value, from the typical puzzle, 'a=b is informatively expressed
contrary to 'a=a', cognitive content which is the part of information associated with the sentence
subject, information content which is what an individual learns and perceive the case by simply
understanding and thereafter accepting, in other words, it is the state which approves a sentence to
be true and lastly semantic content which implies the entire meaning decoded from the sentence and
the individual strictly respond to what the sentences basically expresses.
Solution to Frege's puzzle Incorporation of a metalinguistic approach which is related to Milian
view. This method is based on identity statements for instance "Hesperus is Phosphorus" are
utterances that are related to language rather than the identity per the see. Although the expressed
statement might lack knowledge aspect, the acquired knowledge could be

Birth Of Algebra Research Paper
How Much Do You Know about the Birth of Algebra?
Jiawei Xue
Azusa Pacific University Abstract
Typically, Arabic civilization had significant contribution to algebra we use today. On the other
hand, the famous Arab mathematician Al–Khwarizmi own the title the father of algebra. However,
there is evidence that the ancient Babylon had stone tablet where looks like people exploring
fundamental idea of algebra around 2000BC. Additionally, there are other civilizations and
mathematicians such as Egyptian, ancient Greek, and Chinese also made significant contributions to
algebra we use today. The concept of algebra was used is widely used by different civilizations.
Overall, the evidences shows that the birth of algebra was not created by ... Show more content on
Helpwriting.net ...
(n.d.). Elementary number Tnheory and its applications. The
Mathematical Gazette, 162–162.
Boyer, C., & Merzbach, U. (1991). A history of mathematics (2nd ed.). New York: Wiley.
Connor, J. & Robertson, E. Abu Ja'far Muhammad ibn Musa Al–Khwarizmi. Retrieved from
http://www–history.mcs.st–and.ac.uk/Biographies/Al–Khwarizmi.html Greenberg, M. (2008).
Euclidean and non–Euclidean geometries: development and history
(4th ed.). New York: W.H. Freeman.
Helm, C. (1977). The Muslim contribution to mathematics. Atlantic Highlands, N.J.: Humanities
Friberg, j. & Marzahn, j. A chain of trapezoids with fixed diagonals. Retrieved from
http://www.worldscientific.com/doi/pdf/10.1142/9789812708847_bmatter Kvasz, l. (2004). The
invisible link between mathematics and theology. Perspectives on Science and Christian Faith,
Vol.56, pp.111–116
Merzbach, U.C. & Boyer, C.B. (2011). A history of mathematics (3rd ed). Hoboken, NJ: John
Wiley & Sons, Inc.
Sesiano, J. (2009). An introduction to the history of algebra: Solving equations from
Mesopotamian times to the Renaissance. Providence, R.I.: American Mathematical Society.
Shid, R. (2009). Al–Khwārizmī: The beginnings of algebra. London:

Why Do Americans Stink At Math?
Americans teach math totally different then Asia, in United States math divide to 4 different class ' '
algebra1&2 , geometry ,trigonometry and calculus ' ',students will choice the one they think is fits
,there is different way in Asia, in Asia Ministry of Education will map out the system ,and every
year they will change different book ,inside the book not just algebra1&2,geometry and
trigonometry and calculus is everything mix together ,students can not choice, every year is more
difficult and precise.
For some reason Americans always thinks Asia math is better then they, is because Asia teach
different way not just one things teach one year they have a lot of different math ,is good so you will
try to think different in every time not just sit inside the class use same equation again and again for
one year, change or no the answer is already come out.
Why do Americans stink at math? Takahashi, who is 58, became one of his country's leading math
teachers, once attracting 1,000 observers to a public lesson. But in 1991, when he got the
opportunity to take a new job in America, teaching at a school run by the Japanese Education
Ministry for expats in Chicago, he did not hesitate. With his wife, a graphic designer, he left his
friends, family, colleagues – everything he knew – and moved to the United States, eager to be at the
center of the new math.As soon as he arrived, he started spending his days off visiting American
schools. One of the first math classes

Algebra Research Paper
Algebra is used everyday in everyone's life. People use algebra to find out how much of a product
can be bought while staying under a certain price. Algebra is used in daily life, including a large
number of careers and jobs. Three careers that require algebra are chemical engineering, mechanical
engineering, and civil engineering.
To start with, a career that uses algebra is chemical engineering. Algebra is used in chemical
engineering to identify how the speed a fluid can move through a pipe into a tank and how much of
that fluid can be stored in said tank. To do this, chemical engineers use algebraic equations to detect
the rate of which the fluid is moving. Algebraic equations are also used to see how much fluid goes
through the pipe

What Role Does Diophantus Play In The Evolution Of Algebra
Algebra is the basis of all math and its advancement took place in three major steps. The first stage
of algebra is rhetorical algebra dating back to before 275 BCE. Rhetorical algebra was a form of
algebra that contained no symbols so to them +,–, and*, did not exist. It was usually explained orally
or written on scribes. They were able to do things such as find squad and cubed roots, solve linear
equations, and explain fractions. As well as recognizing irrational numbers and identifying that
quadratics had two answers. The next phase in algebra's evolution was Syncopated math. This was
most popularly used between 275 BCE – 1600. Diophantus played a crucial role in this stage by
being the first to develop algebraic notations and abbreviations.

Computer Algebra Systems ( Cas )
Introduction About CAS Calculator Computer Algebra Systems (CAS) were first introduced in the
early 1970s on large frame computers and are now accessible on a hand held CAS calculator that is
increasing in popularity and affordability for high school students (Kendal, 2006). The CAS
calculator is a multi–representational too with symbolic, graphical and numeric capabilities and a
large variety of procedural skills that include calculus, drawing graphs, and the execution of
numerical, vector, matrix, and statistical calculations (Zbiek, Heid & Hirsch, 2009). The CAS
calculator is a powerful dynamic tool that offers opportunities of learning new concepts and
experiences and allows teachers to use the CAS to help students focus on either a more targeted or a
global view of their work with symbolic representations, depending on the instructional goal (Zbiek,
Heid & Hirsch, 2009). Bert Waits, co‐founder of T3 (Teachers Teaching with Technology)
mentioned that graphing calculator is a great pedagogical tool as it offers multi‐representational
approaches in teaching and learning of mathematics (Parrot & Eu, 2014). Paragraph 1 How is it used
in the VCE Maths Methods study design & Textbooks Its been incorporated into year 12 In 2001 the
Victorian Curriculum and Assessment Authority (VCAA) allowed the year 11 cohort to use the CAS
calculator (Ball, 2014). Mathematical Methods 1&2 was taken by 3 Year 11 classes in 2001 with the
students taking Mathematical Methods 3&4 the final

Mathematics : High School Algebra
PART A
Region: WA– Washington Essential Academic Learning Requirements Framework–Grade Level
Standards (2012)
Subject: Mathematics, 2008
Grade level: High School Algebra I (Ninth Grade)
Standard: A1.4. Linear functions, equations, and inequalities (Algebra) Students understand that
linear functions can be used to model situations involving a constant rate of change. They build on
the work done in middle school to solve sets of linear equations and inequalities in two variables,
learning to interpret the intersection of the lines as the solution. While the focus is on solving
equations, students also learn graphical and numerical methods for approximating solutions to
equations. They use linear functions to analyze relationships, represent and model problems, and
answer questions. These algebraic skills are applied in other Core Content areas across high school
courses.
PART B
Ninth Grade Algebra
1 A1.4. A Write and solve linear equations and inequalities in one variable
2 A1.4. B Write and graph an equation for a line given the slope and the y–intercept, the slope and a
point on the line, or two points on the line, and translate between forms of linear equations
3 A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for
parallel and perpendicular lines. (Perma–Bound, 2016)
PART C
Write and solve linear equations and inequalities in one variable.
C1. On a multiple–choice quiz, students will be given ten–word to convert to

Competency 209 Week 1 Assignment 1: Linear Algebra
Task #1: Linear Algebra
Competency 209.8.5: Linear Transformations 209.8.6: Matrices
Jennifer Moore
Western Governor's University
Part A: The rotation matrix is "a matrix, which moves a body as a rigid unit without altering its
internal geometry" (Turkenburg). The work below shows a rotation matrix that is different from the
Identity Matrix, I.
Work Justification The rotation matrix Substitute a theta that will not result in the identity matrix .
Calculate sin and cos for this theta and the final matrix to the left is the 2x2 matrix A. Matrix A is
not the identity matrix.
To determine the location of point (3,2) when rotated using matrix A, matrix multiplication must be
applied. The work below shows ... Show more content on Helpwriting.net ...
Once the values of the determinant are assigned, then solve for x. This will give you the fourth entry.
The fourth entry of this matrix is 1, which since matrix B was used it should have been 1.
Part C: According to Theorem 4, a 2x2 matrix A, , is considered invertible the determinant, which is
, does not equal zero (Lay, 2015). The work below shows that matrix M is invertible by having a
nonzero determinant.
Work Justification This is the given matrix M.
Since matrix M has a nonzero determinant, this matrix is invertible.
Theorem 4 also states that if the determinant does not equal zero is true, then (Lay, 2015). The work
below shows that matrix M is invertible by computing the inverse using the inverse formula for 2x2
matrices above.
Work Justification The given matrix Using the inverse formula for 2x2 matrices, the inverse of the
matrix M is .
Two matrices are row equivalent if one matrix can be changed to the other matrix by a sequence of
elementary row operations. Theorem 8, The Invertible Matrix Theorem, part b says, "A row is
equivalent to the nxn identity matrix" (Lay, 2015). The work below shows the matrix M is row
equivalent to the identity matrix.
Work

Mathematics : The Joy Of Mathematics In The World
Mathematics is defined as "the abstract science of number, quantity, and space", and to many
individuals, this definition is very black and white (Definition of mathematics in English by Oxford
Dictionaries). Copious people do not like mathematics, as they do not have an appreciation for it.
Before I took this class, I had a much narrower understanding and weaker background on
mathematics due to how I was taught these topics throughout my time in primary schooling. After
taking The Joy of Mathematics, this course has significantly affected my appreciation of
mathematics in general application and in terms of its history and importance in our world. To
begin, mathematics serves as a very universal language. Its origins are very diverse and many
nations and peoples have contributed to the beauty of math, making it even more exquisite.
Mathematical writings date back as far as 2000 B.C., with discoveries in different areas of the
world. The earliest mathematical writings available are Plimpton 322, from Babylon in 1900 BC, the
Rhind Mathematical Papyrus, from Egypt in 2000–1800 BC, and the Moscow Mathematical
Papyrus, also from Egypt in 1890 BC (History of Mathematics). Since then, many diverse areas in
the world have contributed to mathematics, including the Greeks, Egyptians, Babylonians, Chinese,
Indians, the Islamic Empire, and Europeans (History of Mathematics). Today, mathematics is still
evolving and individuals are constantly researching and striving to discover more

Algebra 1: Math Curriculum Paper Written by Middle School...
I am a mathematics teacher, with a middle school education degree (grades 5–9) with an emphasis in
mathematics and social studies, teaching at an area high school. I have decided to focus on Algebra I
for this curriculum paper, because it requires more abstract thought and problem solving. I will
address the following areas: curriculum standards (national, state, local (district)), textbook
adoption, community, and design of my classroom. This paper will relate the standards at these three
levels, discuss procedures for adopting textbooks, focus on the community background and describe
my classroom procedures. The first area that I would like to address is curriculum standards.
According to the National Council of Teachers of ... Show more content on Helpwriting.net ...
The Program of Studies lists five critical areas that must be met in the Algebra I class. The first of
the five is linear equations, inequalities, and functions and this area relates to 2.7, 2.8, 2.9 2.10, 2.11,
and 2.12 of the Academic Expectations. Nonlinear functions: quadratics, exponential and absolute
value are related to 2.7, 2.8, 2.9, 2.11, and 2.12. The third area, proportional reasoning connects to
2.7, 2.8, 2.9, 2.11, 2.12, while the fourth area sequences relates to 2.7, 2.8, 2.9, 2.11, and 2.12. The
last of the areas is probability and it relates to 2.7, 2.8, 2.11, 2.12 and 2.13. Now that we know
which Kentucky Academic Expectation numbers relate to the Program of Studies critical areas, we
need to know what each number covers. The Kentucky's Academic Expectations 1.5 to 1.9,
Mathematical Communication and Reasoning; 1.16, Technology; 2.7, Number Concepts; 2.8
Mathematical Procedures; 2.9, Space and Dimensionally; 2.10, Measurement; 2.11, Change; 2.12,
Mathematical Structure; 2.13, Probability and Statistics; Goal 5, Think and Solve Problems; and
Goal 6, Connect and Integrate Knowledge. Every high school course should incorporate problem
solving, mathematical communication, and connections and mathematical reasoning. The Core
Content for mathematics assessment specifics what content will be assessed from the Kentucky
Academic Expectations and Program of Studies. The four areas are the same

Annual Islamic Symposium On The Arts And Sciences
Siddarth Kumar H Block Mathematics News Article Annual Islamic Symposium on The Arts and
Sciences Inside Dover–Sherborn Regional High School In Room 214 the Annual Islamic
Symposium on The Arts and Sciences has just concluded. The symposium was one of the most
important events of our time, where notable scholars and key figures met in the "House of Wisdom"
in order to hold panel discussions and present displays on the advancements in the fields of Art and
Science through the 15th century. Mathematics took center stage at the symposium with Al–
Khwarizmi speaking about history of his field during the Arab empire and discussing major
contributors to the field. Arabic Mathematics derived from the simple system of finger reckoning,
using one 's fingers in order to do basic forms of arithmetic. After some time "Finger reckoning
started to disappear with the introduction of Hindu arithmetic, the base for the current scheme of
numeration and calculation" (Esposito 184). Hindu numerals were used for these basic forms of
arithmetic more efficiently than Finger reckoning. This numeric system was easier for calculations,
rather than using Roman numerals, which is why it is considered a great achievement–moved the
possibilities of mathematics ahead. It was a base ten counting system that originated in India and
Al–Khwarizmi was the first person outside of India to rework this system, giving us the Arabic
numerals, which the numbers we use today are derived from. The abacus was the

Math : My Math Test
Math has never been the easiest thing in the world for me. I have taken all of the core math classes,
and an extra math during my senior year. During this class, I took one Placement math pretest and
tried my best to show all of my work and give it my all. We were assigned to do
25 questions, and while some I did not understand, I felt confident with most of them. I did not
study before the test or even review any of the material that was present that I learned several years
ago. Yet, I felt like I did a good job on the practice quiz. Knowing this, I feel more prepared for this
test than I have ever been, and I feel like I can pass it. However, like every test that exists, three key
things are needed to prepare and pass it. I believe that ... Show more content on Helpwriting.net ...
I will have to practice long division and multiplication, how to deal with decimals and fractions
easier, etc. I believe I can do all of this; I just need to study.
The Second thing I believe I need to do to pass the Math Placement exam is to review everything.
While researching common information about these pretests, I found that although there is a large
amount of algebra, there is mostly a mixture of almost any kind of math. These include Arithmetic,
Algebra, Geometry, trigonometry, Reading comprehension, Elementary
Math, and many other possibilities. For this type of test, I do not feel prepared at the moment– at
least not nearly as prepared as I could be. I know that I can achieve being prepared by doing
everything listed above. Reviewing everything that I have learned would be a perfect way to
prepare, as everything from elementary math to trigonometry can appear on it.
The third and final way I believe I need to pass the Math Placement exam is to have confidence.
There could be a person who knew every single answer on the exam. Without confidence in his or
her best–educated decision, they might as well not know anything at all. My final goal with
preparing is to be able to get to a certain answer and have full assurance and confidence that it is the
right answer. I believe confidence will help boost my score, and eliminate second guessing myself
after every question. In conclusion, this is how I believe I can best prepare

Linear Algebra Toolbox
ICSSP–2014
LINEAR ALGEBRA TOOLBOX FOR GNU RADIO
Kokila M, KaviNandhini M, Vishnu R, Gandhiraj R*, Soman K P
Center for Excllence in Computational Engineering and Networking,
*Department of Electronics and Communication Engineering, Amrita School of Engineering,
Amrita Vishwa Vidyapeetham ,Coimbatore,Tamil Nadu–641112
Email.id:kokilamani024@gmail.com,mkavinandhini@gmail.com
A B S T R A C T
The goal of this paper is to bring Linear Algebra and Digital Signal Processing together for
efficiently solving the applied signal processing problems. Linear Algebra tool box is created to
visualize the signal by just clicking and dragging the concerned module. In MATLAB and other
platforms, tapping of the signals cannot be done and conventional code has to be written for solving
the problem. GNU Radio is a freeware software for processing signals through which tapping of
signal can be done .The module is created in GNU Radio with predefined template and the platform
used here is C++.Further, the code is glued to Python using swig. The blocks are created in order to
estimate energy, check orthogonality, compute unit normalization, find Euclidean norm of a signal
and least square fitting. The end user can visualize the signal in various plots. KEYWORDS: Linear
Algebra, GNU Radio, MATLAB.
1. Introduction
GNU Radio is a free and open source software development toolkit that provides signal processing
blocks to implement software radios. This free software toolkit for

Medicine In The Islamic Empire
Other than providing much of the grounds of modern medicine, medicine in the Islamic Empire was
innovatory, pre–eminent and revolutionary. For instance, in 706 CE, the first hospital was built by
Muslims in Baghdad and the building of hospitals were continued until every major city in the
Islamic world had several hospitals, some specialised for certain areas of disease, including mental
and emotional. These hospitals were places of clinical training and learning for aspiring doctors as
well as treatment centres for patients. After performing physical examinations, working at ward
rounds and attending lectures, students were required to pass practical and oral exams for a doctor's
license. As well as having futuristic systems to supply a certified ... Show more content on
Helpwriting.net ...
Advanced technology supported the high standard of living of the general population, and is still
upholding much of our standard of living today. A large proportion of today's technology is derived
or constructed upon the work of Muslim Inventors. During the 10th and 11th century, a famous Arab
astronomer and mathematician of the age, Ibn Al–Haytham, became the first to have a correct
understanding of the human vision and was therefore able to create the first effective camera which
without, the modern camera would be impossible. The Da Vinci of the Islamic world, Ibn Firnas,
devised a flying costume during the 9th century. He launched himself off the side of a mountain
wearing his invention in order to test his device and became the first man to attempt controlled
flight. The experiment was partially successful as he remained aloft for a few seconds. The
somewhat successful glider later inspired Leonardo Da Vinci to design his own flying device which
provided the foundations of modern flight. The first automatic and mechanical clocks were also
introduced by Muslim inventors, most remarkable of which is the elephant clock – a sizeable,
automatic clock that used Greek water–raising technology, an Indian elephant, an Egyptian phoenix,
Arabian figures and Chinese

Integrated 1 And Macdougall Littel Algebra Summary
Review of Standards of Text
Amanda E.L. Kent
Chico State University, Chico
November 18, 2014
Professor Matthews
Author Note
Review of Sequences in CPM Common Core Integrated 1 and MacDougal Littel Algebra 2
The introduction and understanding of sequences, arithmetic and geometric in 8th grade was
reviewed for content and standards in CPM CC Integrated 1 and MacDougall Littel Algebra 2.
Sequences are defined as an ordered list of numbers that are in a specific pattern. Arithmetic
Sequences are an ordered list of numbers where the difference between successive numbers is a
constant value. Geometric sequences are an ordered list of numbers where the successive numbers
differ by a common ratio.
Sequences in California ... Show more content on Helpwriting.net ...
Make sense of problems and persevere in solving them. In each section 5.2.1–5.2.3 the students are
required to make sense as a group and persevere in solving the problems. Example of the practice is
seen in 5.2.1 5–42, 5.2.2 5–59, and 5.2.3 5–74. Each problem in this text is recommended that the
students work in groups and there are no formulas, or rules given until the students have reasoned
out the problem and solved as a group. By having the student reason and understand, then persevere,
the student gains an understanding of the concept in sequences rather that the rule. Given that many
of the lesson plans are built around the students making sense of conceptual problems this practice
seems to be the focus of the sections. Used beyond moderately, it is the stepping stone to the

history of algebra Essay
Unlike geometry, algebra was not developed in Europe. Algebra was actually discovered (or
developed) in the Arab countries along side geometry. Many mathematicians worked and developed
the system of math to be known as the algebra of today. European countries did not obtain
information on algebra until relatively later years of the 12th century. After algebra was discovered
in Europe, mathematicians put the information to use in very remarkable ways. Also, algebraic and
geometric ways of thinking were considered to be two separate parts of math and were not unified
until the mid 17th century.
The simplest forms of equations in algebra were actually discovered 2,200 years before Mohamed
was born. Ahmes wrote ... Show more content on Helpwriting.net ...
Omar was also a poet, philosopher, and astronomer. Omar's works were translated in 1851, which
was research on Euclid's axioms. In the medieval period, he expanded on Khwarizmi's and the
Greeks mathematic works. He only worked with cubic equations only and focused on geometric and
algebraic solutions of equations. In 1145AD, Al–Khwarizmi's book was translated by Robert
Chester, which made it possible for algebra to be introduced to Europe. After algebra was introduced
in Europe, European mathematicians developed and expanded on algebra concepts. Even though
algebra began in the Arabic countries, once European mathematicians obtained the information of
algebra, they became the leaders of mathematical discoveries in the world ("Mathematics").
From the period of 1145AD – the late 16th century, many mathematicians developed on algebraic
concepts. However, it was not until the 1680's that the most remarkable discoveries were made using
algebra. Sir Isaac Newton was a very famous mathematician, English physicist, astronomer,
philosopher, and alchemist. During his period of study, he used algebra to describe universal
gravitation, develop the laws of motion, found orbits of the planets to be elliptical, discovered that
light was made of particles, discovered the rate of cooling objects, and the binomial theorem. His
most important works were the development of calculus. However, Newton did not work alone on
creating the

The Purpose Of This Assessment Is To Demonstrate In A Clear,
The purpose of this assessment is to demonstrate in a clear, precise way, how to answer identified
NAPLAN (National Assessment Program – Literacy and Numeracy) questions. NAPLAN is a
standardised test developed by Australian Curriculum, Assessment and Reporting Authority
[ACARA] (n.d.). This assessment will provide answers to each question and will indicate the
confidence with the approach used, how each answer was formulated, the steps taken or knowledge
used and whether that knowledge was known or investigated. This assessment will also show what
other way could have been used to answer each question. Precise mathematical procedures will be
used to solve these equations, moreover as much detail as possible will be provided to produce ...
Show more content on Helpwriting.net ...
Observing problems in concrete form aids in my understanding and therefore the solution.
Conversely, the drawing of the diagram in a two–dimensional form helped to deliver the correct
answer. I approached this question with the required knowledge and confidence to solve it
immediately.
Question 5, NAPLAN (Year 9 non–calculator), ACARA (2012)
Approach: The approach used to solve this scale was ratio set up in the form of a fraction.
Workings: To calculate the ratio, the actual length measurement is divided by the drawing length
measurement. The measurements need to be represented in fraction form. The drawing length is
4cm and the actual length is 8mm.
Actual length over the drawing length: 8mm/4cm.
Simplify this fraction by determining the largest common denominator of both numbers. The largest
common denominator of both numbers is 4.
8mm/4cm : 2mm/1cm . Drawing length becomes 1cm and actual length becomes 2mm. The scale is
1cm represents 2mm.
Another way to solve this question would be by using data measurement with the mathematical
concept of division, using part/whole method. Both shapes were square and would be able to be
divided equally. Using the part/whole method and establishing the number four was one of the
common denominators for both lengths.
DL = 4cm. 4cm ÷ 4 = 1cm : AL = 8mm. 8mm ÷ 4 = 2mm
Scale of drawing = 1cm represents 2mm
I was confident

Algebraic Algebra Research Paper
In the next few centuries, many ideas and procedures for algebra were developed by the Islamic
mathematicians. (Katz, 2007, p.192). In the twelfth and thirteenth centuries, Islamic algebra spread
to Europe. It was still in the static equation–solving phase. In the sixteenth century, the work of
Italian mathematicians brought a major advancement in mathematics. They found new methods to
solve equations. (Katz, 2007, p.193). In the seventeenth century, the point of view in algebra was
greatly changed. Because the mathematicians have also begun questioning about the equation
problems not just finding solutions. (Katz, 2007, p.194). Later in the eighteenth century, the
development in mathematics changed the notion of algebra. (Katz, 2007, p.196). ... Show more
Identifying, relating, spreading, and explaining patterns motivate them to reflect on solving
algebraic problems. Working with patterns enables young children to recognize relations and form
simplifications. (Taylor–Cox, 2003, p.15). Representing and investigating mathematical situations
and structures is a chief element of algebraic thinking. Children need numerous experiences with
mathematical situations and structures in order to build the concepts of commutativity, associativity,
and equality. If children begin to understand those concepts in early grades, particularly the equality,
then they would be able to solve the unknown variables. (Taylor–Cox, 2003, p.17). Mathematical
models of quantitative relationships are required to recognize and identify the values. The
instructors should encourage children by asking questions about quantities, situations, and kind of
patterns. These questions help to develop the thinking of quantitative relationships models in
children. (Taylor–Cox, 2003, p.19). Change is a fundamental concept of algebraic thinking. There
are two types of change in algebra: qualitative and quantitative. Qualitative change mathematically
labels as smaller, taller, and fuller terms and the quantitative change labels as numeric language. It is
essential for children to notice and think about both types of change. (Taylor–Cox, 2003, p.20). The
algebraic thinking opportunities are limitless. It is

My Experience : My Personal Experience In High School
During my high school experience there has been a growth on everything from when I was in
middle school. I have grown personally because I have made numerous new friends that I never
knew that I was going to encounter. I have grown academically by taking geometry this year, which
genuinely expanded my knowledge in math, especially since I desire to have a career in a math
related subjects. Finally I grew at sports because I have been doing much superior in my running. As
a freshmen at Godinez high school, I have grown personally, academically, and at sports. First of all,
I have personally grown because I met countless new friends this year and most of them were in
sports because I love to run. This year I was running with a running buddy that was the same speed
as me and that helped me because I do not have to run by myself; therefore we were helping each
other by pushing ourselves into getting a better time. I have also grown personally because I did
about 20 community service hours this year and that was a fun experience for me. I wanted to give
back to my community because the community has also helped me through a lot and I wanted a
clean and safer environment for everybody to live in. I did community service hours outside of
school, especially at the beach because I do not wish for the animals in the sea to become
endangered for something we humans are throwing away in the sea. Personally, we humans treat the
ocean like if it was our trash can because we get too lazy to walk a couple of feet, therefore we leave
the trash on the sand and that gets blown into the ocean. I have matured much more than last year
from when I was in middle school and when I was an eighth grader. I matured by not doing anything
child related by being respectful and by being responsible to adults as well as my classmates. Also,
in the beginning of the school year I was always unconfident and timid about myself because I was
not ready to start high school yet, but as the months passed by I became more confident about
myself because my new friends have helped me overpower that. Additionally, I have grown
academically by taking geometry, biology, spanish, and english. All students always have a problem
with procrastinating and

The Influence Of Algebra
Abstract
Modern Times has brought a wide range of systems and methods of mathematics. The beginning of
mathematics had focused on geometry and forms of mathematics, but then during the 16th and 17th
century, algebra started to be known and practiced. Mathematics begin to get more diverse in early
modern times. Throughout the history of algebra, many mathematicians were very focused on
finding solutions to problems and different methods to carry out mathematics. In early 19th–century
practices makes mathematics was based on physical variables. People were concerned with abstract
algebra with situations involving applied mathematics or physics that had expanded to include
abstract algebra. These methods and techniques were able to influence what people do today in
different areas of life. Without algebra solving complicated equations would not be possible, or it
would be more complicated than what it is today. Algebra is a main part in what our world is today
and without its ... Show more content on Helpwriting.net ...
These methods and techniques were able to influence what people do today in different areas of life.
Different areas can include the art world, a lot of scientific research, and also the daily lives of the
people of the world and without algebra, many of these things would be either impossible or close to
impossible to finding the answers that we need today (IAC Publishing, LLC, 2017).
Daily Life. Algebra in daily life allows people to calculate things quickly and easily. Algebra allows
people to figure out different prices on common objects like food and clothing to what cellular
provider is cheapest per month. People can sometimes use algebra many times during the day and
not even realize. Algebra has made it easier for people today and allows for simple connections in
life to be made possible (IAC Publishing, LLC,

Why Is Learning Algebra Essay
Introduction:
We all ask this question "Why Algebra is important in real life and wonder if math will be used one
day? ". In this investigation, I will be talking about why algebra is essential and what it means. Well,
the meaning of Algebra is part of mathematics in which letters and symbols are used together to
represent numbers and quantities in method and equations.
Algebra is the first thing we learn when we are kids. At an early age we learn how to count, building
blocks draw objects and learn shapes. All this is a preparation to Algebra. Algebra is not only
mathematics it is also geometry and analysis. The basic part of algebra is elementary algebra,
abstract algebra and modern algebra. Algebra is the key a successful life. If you know algebra it will
help you to excel in the field that you want to specialize in. Algebra is the beginning of a journey ...
Show more content on Helpwriting.net ...
Speed: We can use algebra to solve problems easily and efficiently in most of the careers. We use
simple algebraic equation to help you reduce the usage of food items in a menu or reduce food costs
or when we are doing menu engineering.
2. A Building Block: Algebra can assist as a building block that we can use to learn more advanced
math like statistics and calculus. It will make shifting easier from career to career. Learning algebra
is a life skill beneficial for upward mobility.
3. Avoid being taken advantage of by people who can "twist" the numbers in their favor. Understand
and critically evaluate the math done by others like banks, insurance, suppliers, etc.
To have an opportunity to be successful, ten we need to master and understand algebra. Algebra is
an important life skill.
Some occupations that requires Algebra:
After I made my research on how algebra is connected to real life situations, I have discovered that
most of the occupations require Algebra and I will be discussing about 6 different jobs that use

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