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How to Solve It: A New Aspect of Mathematical MethodHow to Solve It: A New Aspect of Mathematical Method Book Description
George Polya was a Hungarian mathematician. He wrote this, perhaps the most famous book of mathematics ever written, second only to Euclid's "Elements." "Solving problems," The method of solving problems he provides and explains in his books was developed as a way to teach mathematics to students.
About the Author :
George Polya has contributed to How to Solve It: A New Aspect of Mathematical Method as an author.
Biography of George Polya Born in Budapest, December 13, 1887, George Polya initially studied law, then languages and literature in Budapest. He came to mathematics in order to understand philosophy, but the subject of his doctorate in 1912 was in probability theory and he promptly abandoned philosophy. After a year in Gottingen and a short stay in Paris, he received an appointment at the ETH in Zurich. His research was multi-faceted, ranging from series, probability, number theory and combinatorics to astronomy and voting systems. Some of his deepest work was on entire functions. He al
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The book How to Solve It: A New Aspect of Mathematical Method by George Polya, Sam Sloan
(author) is published or distributed by Ishi Press [4871878309, 9784871878302].
This particular edition was published on or around 2009-6-1 date.
How to Solve It: A New Aspect of Mathematical Method has Paperback binding and this format has 280 number of pages of content for use.
This book by George Polya, Sam Sloan |
Tappan Trigonometry bio part involves biology, the study of living things. The statistics part involves the accumulation, tracking, analysis, and application of data. Biostatistics is the use of statistics procedures and analysis in the study and practice of biology have utilized all levels of Algebra within classwork but more importantly in my engineering background and can show how it all applies. Algebra 2 has several different topics within it but still has some basics that you must master before performing well in it. Many skills acquired in Algebra I are often the holdup from someone mastering Algebra 2 |
Solutions Help Calculators
Algebrahelp Calculators
A collection of lessons, calculators, and worksheets. Many of the interactive worksheets and instant solution calculators include step by solutions.
webmath.com Webmath generates answers to specific math questions, as entered by a user of the site, many different types are supported. Webmath also attempts to show to the student how to arrive at the answer as well.
Quick Math
Contains many calculators that will help you solve equations and also show step by step solutions.
Scientific Calculator
This is an online javascript scientific calculator. You can click the buttons and calculate just like a real calculator. |
LabView for Engineers, CourseSmart eTextbook
Description
Based on the most current release of LabVIEW, LabVIEW for Engineers is designed for readers with little to no experience using LabVIEW.
Part of Prentice Hall's ESource Program: ESource enables instructors to choose individual chapters from published books in the Prentice Hall ESource Series. The content available in this online book-building system covers topics in engineering problem-solving and design, graphics, and computer applications. Using this program, instructors can create a unique text for the introduction to engineering course that exactly matches their content requirements and teaching approach.
Table of Contents
CHAPTER 1 INTRODUCTION
Sections
1.1 What is LabVIEW
1.2 Assumptions
1.3 Conventions in the Text
1.4 LabVIEW VIs
1.5 Starting LabVIEW
1.6 Creating a VI
1.7 LabVIEW Menus
1.8 Key Terms
1.9 Summary
1.10 Self-Assessment
CHAPTER 2 LABVIEW BASICS
Sections
1.1 Opening a VI
1.2 Basic Math in LabVIEW–Using Functions
1.3 Programming Preview: While Loops
1.4 Dataflow Programming
1.5 Data Types and Conversions
1.6 Documenting VIs
1.7 Printing a VI
1.8 Saving Your Work
1.9 Closing a VI
1.10 Key Terms
1.11 Summary
1.12 Self-Assessment
1.13 Problems
CHAPTER 3 LABVIEW MATH FUNCTIONS
Sections
1.1 Introduction
1.2 Basic Math Functions
1.3 Trigonometric and Hyperbolic Trig. Functions
1.4 Exponential and Logarithm Functions
1.5 Boolean and Comparison Functions
1.6 Programming Preview: Debugging
1.7 Key Terms
1.8 Summary
1.9 Self-Assessment
1.10 Problems
CHAPTER 4 MATRIX MATH USING LABVIEW
Sections
1.1 Working with Matrices and Arrays in LabVIEW
1.2 Extracting a Subarray from a Larger Array or Matrix
1.3 Adding Arrays
1.4 Transpose Array
1.5 Multiplying an Array by a Scalar
1.6 Matrix Multiplication
1.7 Element by Element Multiplication
1.8 Condition Number
1.9 Matrix Determinant
1.10 Inverse Matrix
1.11 Solving Simultaneous Linear Equations
1.12 Programming Preview: For Loops
1.13 Key Terms
1.14 Summary
1.15 Self-Assessment
1.16 Problems
CHAPTER 5 DATA ACQUISITION WITH LABVIEW
Sections
1.1 Overview of Data Acquisition
1.2 Sensors, Signals and Signal Conditioning
1.3 Data Acquisition Hardware
1.4 Using LabVIEW to Collect Data
1.5 Key Terms
1.6 Summary
1.7 Self-Assessment
1.8 Problems
CHAPTER 6 GETTING DATA INTO AND OUT OF LABVIEW WITHOUT DATA ACQUISITION
Sections
1.1 Introduction
1.2 Writing LabVIEW Data to a Spreadsheet File
1.3 Writing LabVIEW Data to a Measurement File
1.4 Reading a LabVIEW Measurement File
1.5 Reading a Spreadsheet File in LabVIEW
1.6 Using Spreadsheet Data to Initialize a Matrix Control
1.7 Key Terms
1.8 Summary
1.9 Self-Assessment
1.10 Problems
CHAPTER 7 GRAPHING WITH LABVIEW
Sections
1.1 Introduction
1.2 Using Waveform Charts
1.3 Using Waveform Graphs
1.4 Modifying Graph Features
1.5 Generating 1D Arrays for Graphing
1.6 Putting LabVIEW Graphs to Work
1.7 Using XY Graphs–2D Plotting
1.8 3D Graphing
1.9 Getting Graphs onto Paper and into Reports
1.10 Key Terms
1.11 Summary
1.12 Self-Assessment
1.13 Problems
CHAPTER 8 DATA ANALYSIS USING LABVIEW VIS
Sections
1.1 Introduction
1.2 Basic Statistics
1.3 Interpolation
1.4 Curve Fitting
1.5 Regression
1.6 Key Terms
1.7 Summary
1.8 Self-Assessment
1.9 Problems
CHAPTER 9 PROGRAMMING IN LABVIEW
Sections
1.1 Introduction
1.2 LabVIEW Programming Basics, Expanded
1.3 Structures
1.4 Key Terms
1.5 Summary
1.6 Self-Assessment
1.7 Problems
CHAPTER 10 LOOKING FORWARD: ADVANCED MATH USING LABVIEW VIS
Sections
1.1 Introduction
1.2 Working with Polynomials
1.3 Statistics: Hypothesis Testing
1.4 Differentiation
1.5 Integration
1.6 Runge—Kutta Integration
1.7 Exponential Filter
1.8 Spectral Analysis
1.9 Monte Carlo Simulation
1.10 PID Controller |
Math - Home
University Transfer
Learn more!
Sign up now for PierceConnect and keep up on the latest information about our courses, events and opportunities on campus.
In many disciplines, mathematics is used to help make sense of phenomenaobserved in the world. Math also can help us develop critical thinking and reasoning skills that can be used to solve problems in a variety of applications. Pierce College offers two sequences of math courses, pre-college and college-level, to meet the needs of the individual student and his or her goals.
Initial placement in a sequence of courses depends on COMPASS placement test scores. The choices and the number of courses a student takes depend on their chosen field of study and other factors. See a faculty advisor for help.
Pre-College Math
The Mathematics department offers a sequence of introductory courses that build the basic quantitative and symbolic reasoning skills needed in almost all fields of study and professional/technical training.
These pre-college mathematics classes accommodate students entering the college with a variety of math backgrounds. These courses are offered in the Math lab, online, and in traditional classrooms.
Offered only at Pierce College Fort Steilacoom, the Math Lab provides students individualized instruction in pre-college level mathematics courses. Using one-on-one instruction, digital lectures, and computer tutors, the Math Lab tries to meet different learning styles.
Though most students will attend the lab on a fixed schedule, the lab offers flexible schedules when arranged with the Math Lab coordinator. The labs are open during the day and evening, Monday through Friday, and also on Saturday (if enrollment allows) during the fall, winter, and spring quarters. Summer quarter hours are limited. Additionally, mini-lectures are offered daily for MATH 051, 060, and 098. For enrollment, call (253) 964-6734).
Courses offered through the Math Lab:
MATH 042: Fractions, percents and decimals
MATH 051: Fundamentals of arithmetic
MATH 054: Pre-Algebra
MATH 058-059: Introduction to algebra I-II
MATH 060: Intro to algebra
MATH 098: Intermediate algebra
College-Level Math
Pierce College also provides a sequence of college-level math courses for students transferring to four-year colleges or pursuing technical vocational programs. These courses satisfy the math requirements for majors in mathematics, as well as business, accounting, economics, statistics, actuarial science, math education, engineering, and the sciences. These college-level courses include the math needed for the Associate in Science degree from Pierce College.
Each course includes examples of applications taken from many fields of study. Most of these courses require the use of graphing calculators, which may be rented for a nominal fee through the libraries.
College-level courses
The courses listed below satisfy the Quantitative Reasoning Skill (QS) requirement. The prerequisite for all these QS courses can be satisfied by MATH 098 with a grade of 2.0 or higher or placement above MATH 098 on the COMPASS placement test. MATH 095 with a grade of 2.0 or higher will serve as a prerequisite to MATH 107& and MATH& 146. Students unsure of their intended major are urged to take MATH 098 to allow for more options.
MATH& 107: Contemporary mathematics
MATH 114: Applied algebra, geometry, trig
MATH& 141: Pre-calculus I
MATH 156: Finite mathematics
MATH& 171: Structure of elementary mathematics I
MATH& 146: Intro to statistics
Mathematics major
The following courses should be taken,in addition to courses required for the AA degree:
MATH& 151-153: Calculus I-III
MATH 205: Linear algebra
MATH 224: Multivariate calculus
MATH 238: Differential equations
Courses in statistics and computer science are highly recommended for math majors. Math majors should also take one of the sequences of science courses such as physics or chemistry. See your advisor for specific recommendations. |
Purpose of Mu Alpha Theta
Mu Alpha Theta is the National High School and Two-Year College Mathematics Honor Society with
93,300 student members in June 2012 in more than 1950 schools. We are dedicated to inspiring
keen interest in mathematics, developing strong scholarship in the subject, and promoting the enjoyment
of mathematics in high school and two-year college students.
Mu Alpha Theta achieves these goals by:
Providing a method for schools to recognize
and encourage those students who enjoy and
excel in mathematics.
Organizing a
national convention for students and teachers to participate in math-related events and interact with
others from across the country.
Rewarding outstanding extracurricular achievement by offering
special
awards to both students and their faculty advisors. |
Call us today
Learn more
Call us today
Learn more
As a gateway to high school math, Algebra I plays a central role in every student's life
Revolution's Algebra I program offers the tools you need to be successful. This course is the perfect complement to core algebra instruction, supporting differentiated instruction for every student; providing teachers' access to detailed, real-time reports that track student progress. Students receive targeted lessons through Mentor Sessions that deliver extra practice in fundamental skills they need to stay on track and build confidence in algebra.
Algebra I Benefits
Revolution K12's adaptive, web-based instructional software has been proven to increase algebra pass rates, by scaffolding content to the foundations students need, providing comprehensive professional development to teachers, and customer support to schools and districts. The Revolution K12 model:
Fits your needs and schedule through flexible implementation models.
Increases students' understanding of Algebra, which leads to higher AYP and closes the achievement gap.
Offers prescriptive and diagnostic information in real time.
Allows for the individualized support students need on challenging mathematical topics.
What I see Revolution Prep doing is providing sort of a curriculum support for teachers, a way for teachers to fill in those gaps—to figure out what this student is having a particular problem with and how I can support them toward meeting this standard. With a scripted textbook curriculum, it's just not possible.
Algebra I Features
Provides extra practice in all key Algebra I concepts, with a scaffolded diagnostic process to build needed skills
Dynamically adaptive web-based program with a personalized skill-gap analysis
Aligned to state standards and Common Core standards
Provides text and audio in English and Spanish
Features ongoing progress monitoring and other Response to Intervention elements
We are able to pinpoint our instruction around certain concepts based on the Revolution data.
Meghan McGovern Math Teacher, Granada Hills
Algebra I Implementation
The Revolution K12 program supplements the traditional algebra class, or can be an integral part of a comprehensive independent study, homework, or credit recovery program. Our flexible implementation makes it easy for you to find the right solution. Possible implementation structures include:
Companion courses
Double periods
After school
Homework
Summer school
Intervention classes
Pull-out programs
When students get a question wrong, then it doesn't just go to the next question, it breaks it down.
Roger Fasting Principal, Pomona HS
Algebra I Course Concepts
Revolution K12's Algebra I course includes:
Using variables
Solving for variables
Representing data
Systems of equations
Factoring
Functions
Quadratic functions
Algebra I is viewed as the gatekeeper to a sequence of higher mathematics courses as well as the key to future academic success beyond high school. |
How To Study Mathematics . How to Study Mathematics . Written by Paul Dawkins . Before I get into the tips for how to study math let me first say that everyone studies ... may seem easy when watching the instructor, but it often is not so easy when it
Anyone can learn math whether they're in higher math at school or just looking to brush up on the basics. After discussing ways to be a good math student, ... Make sure that your notes are clear and easy to read. Don't just write down the problems.
How to Study for a Math Exam. ... Something that you have difficulty understanding may come easily to a study partner. Having his/her perspective on a concept may help you to comprehend it. 6. Have someone make up your problems for you to work them out.
The only way to study math is rigorously. You should understand the theoretical aspect of the material. ... Is there an easy way to study math properties? How to study maths easily? Tell me all the easy steps possible?
How to Study Mathematics Lawrence Neff Stout, Department of Mathematics, Illinois Wesleyan University, Bloomington, Il 61702-2900 ... For the mathematics major this question is easy to answer---a large portion of mathematics consists of proofs.
There are several ways to study math. Some students need to use as many practice questions as possible, while other students can benefit by listening to the math lecture over and over. Find out which math tips help you most.
Easy Ways To Learn Math For Kids. Learning math can be tricky and frustrating for many children. If your child is struggling to understand math concepts, you can work with her to boost her mastery of numbers and help her comprehend what they mean. Incorporating some entertaining ...
There are several ways to study math. Some students need to use as many practice questions as possible, while other students can benefit by listening to the math lecture over and over. Find out which math tips help you most.
A book on how to learn Math and then how to use the principles in learning Math, ... It helped me a lot that I went on learning it the easy way. That method help me learn so well I managed to won Math competitions after Math competitions, ...
then you should read no further and return to the study of mathematics. I'd also like to meet you, please drop me an e-mail! Otherwise I'm hoping that ... Easily make logical connections between different facts and concepts. ...
... so that you can update it easily and can refer to it when needed. Write out the symbol in words, for example: ∑ ... plz .send me how do How to learn math formulas article . Murray says: 30 Nov 2011 at 4:49 pm [Comment permalink] @milad: ??
Mathsstudy:Site teaches easy math includes methods to study addition, subtraction, multiplication, square of a number, answer checker, Vedic maths useful for all students and for entrance exams like CAT, GATE
Learn How To Do Math Easily & Quickly! ... Can Division Games Really Help Kids Learn Math? Helping children become confident and skillful in mathematics is what you as their parent or teacher should think about.
Have you ever wanted to teach your child some simple math tricks that you learned many years ago but can't seem to remember them? Well you are not alone! With the amount of math tricks that are out there, it can be hard to remember all of them. Here are...
Easy Math (Speed Mathematics) ... they are easy to learn. I walk into a class of elementary school children and teach them the basic multiplication tables in half an hour -- up to the twenty times tables.
Teach Kids Math: The Fun and Easy Way. For quite sometime in the past, ... Studies have been made that children learn faster and retain more of the lessons taught them when it is done in a fun and easy way.
The only way to learn mathematics is by understanding it. Try to make it a pleasant experience. Reward yourself with, say, a candy every time you make even a small success. Practice it as often as you can. ... Math is easy if you let it be so.
You can't learn math by guessing, but by learning and applying the rules in mathematics. Rules have to be precise and not confusing. ... Three Easy Ways to Help With Elementary Math: 6 Word Problem Solving Strategies to Help Reduce Math Anxiety:
"How to learn math and physics" - the title is deliberately provocative. Everyone has to learn their own way. ... Next, here are some good books to learn "the real stuff". These aren't "easy" books, but they're my favorites |
Specification
Aims
The programme unit aims to provide a firm foundation in the concepts and techniques of the calculus, including real and complex numbers, standard functions, curve sketching, Taylor series, limits, continuity, differentiation, integration, vectors in two and three dimensions and the calculus of functions of more than one variable.
Brief Description of the unit
The unit introduces the basic ideas of complex numbers relating them to the standard rational and transcendental functions of calculus. The core concepts of limits, differentiation and integration are revised. Techniques for applying the calculus are developed and strongly reinforced. Vectors in two and three dimensions are introduced and this leads on to the calculus of functions of more than one variable, vector calculus, integration in the plane, Green's theorem and Stokes' theorem.
Learning Outcomes
On successful completion of this module students will have acquired an active knowledge and understanding of the main concepts and techniques of single and multivariable calculus.
Future topics requiring this course unit
Almost all Mathematics course units will rely on material covered in this course unit.
Syllabus
Foundations: algebra of real and complex numbers; simple functions based on power-laws, their graphs and basic properties (including limits at zero and plus or minus infinity); derivative (slope) of a power-law function and its integral (area under a curve and indefinite integral); differentials as describing tangent lines; definitions, graphs, derivatives and limits of sine, cosine, exponential and hyperbolic sine and cosine; basic trigonometric and hyperbolic identities.
Power series: notion of a power series as a limit of polynomials, its derivative and integral; Taylor series; series for exponential, sine, cosine and other functions; radius of convergence; truncation of power series, error terms and big-O notation.
More on complex numbers: Euler's formula and de Moivre's theorem; polar form of complex numbers; roots of unity; polynomials with real coefficients; complex forms of sine and cosine, relationship to trigonometric and hyperbolic identities.
Functions of more than one variable: partial derivative, chain-rule, Taylor expansion; turning points (maxima, minima, saddle-points); Lagrange multipliers; grad, div, curl and some useful identities in vector calculus; integration in the plane, change of order of integration; Jacobians and change of variable; line integrals in the plane, path-dependence, path independence; Green's and Stokes' theorem in the plane. |
The real numbers -- those comprising the integers, fractions, and non-repeating, non-terminating decimals -- are the key players in algebra. True, the complex numbers -- those of the form a + bi, such that a and b are real numbers and i^2 = -1 -- are studied in algebra and do indeed have important applications in various real world sciences, yet the real numbers are the ones that have the predominant role. Reals behave in predictable ways. By mastering the basic properties of this set, you will be in a much stronger position to master algebra.
The Google Docs Viewer allows you to quickly view many file types online, including PDFs, Microsoft Office files, and many image file types. It also allows you to create a link that allows other people to view your document quickly and easily in any browser.
Google Docs is a suite of products that lets you create different kinds of online documents, work on them in real time with other people, and store your documents and your other files -- all online, and all for free. With an Internet connection, you can access your documents and files from any computer, anywhere in the world. (There's even some work you can do without an Internet connection!) This guide will give you a quick overview of the many things that you can do in Google Docs |
Algebra City is a mathematics intervention program created especially to help students build an understanding of key concepts, procedures, and representations needed to master and pass Algebra I. When traditional texts frequently can be "a mile wide and an inch deep," Algebra City encourages students to delve deeply into the most critical content: the 28 common misconceptions where students have the most difficulties in algebra. Each of the four Student Editions covers seven of these misconceptions.
Strategies for Differentiation focused on struggling students and English language learners
Connections to technology and the real world to help prepare students for the 21st century
Flexibility in Program Delivery -- Targeted instruction enables Algebra City to be used in inclusion settings, individualized or small-group instruction, tutoring, double-period or shadow classes, and summer school.
Student Edition -- Single Pack includes four Student Editions (Books 1–4) covering all 28 misconceptions. 5-Pack includes 20 books total (5 each of Books 1–4).
Teacher's Kit -- Includes four Teacher's Editions that correspond to the Student Editions, ExamView Assessment Suite CD, Keys to the City Teacher's Resource CD, and Algebra City Interactive Activities (web-based practice problems).
Classroom Starter Pack -- Includes all the items in the Teacher's Kit plus a 10-pack of Student Editions.
Practice is an Adventure with
Algebra City Interactive Activities!
Web-based activities provide additional concept practice in a fun and motivating way. The Algebra City Interactive Activities consist of an introduction reviewing the story and 28 adventures that correspond directly to the 28 most common misconceptions in the Student Edition.
Students choose their own web-based practice activities on the interactive Algebra City map from among adventures corresponding to the 28 misconceptions.
Still Have Questions? Call Us at 1-800-594-4263
PCI Education Breaks New Ground in Algebra Intervention
Date: Monday, January 30, 2012
Algebra City Focuses on the 28 Most Common Misconceptions about Algebra as Part of Assessment-Driven Intervention
SAN ANTONIO (Jan. 30, 2012) – With many states requiring Algebra I to graduate from high school, algebra has become one of the gateway courses to school and career success. Yet upwards of 60 to 70 percent of students struggle with algebra or fail to pass state-mandated proficiency exams.PCI Education, the premier provider of resources for students with specialized instructional needs, introduces Algebra City™, a blended intervention program focusing on the 28 most common algebraic misconceptions.
Research shows that many students misunderstand the concepts, procedures and representations needed to master and pass Algebra I. Algebra City aims to keep students on track by using pinpoint assessment to identify where a student is struggling conceptually, and providing thorough and multiple approaches to correcting the misconception. Algebra City may be used for intervention with any core Algebra I curriculum.
According to Algebra City author Dr. Donna Craighead, the program's four Student Editions differ from traditional algebra textbooks. Whereas textbooks use a linear model, as an intervention program Algebra City uses assessment data to target instruction only where needed. The graphic novel-style Student Editions use avatar-like characters to encourage students to re-engage with algebra in new and exciting ways, including an online adventure island where students can solve practice problems.
Aligned to the Common Core State Standards, Algebra City is a four-part series, with each book covering seven misconceptions. The series is divided into Algebra Essentials, Equations & Inequalities, Graphing, and Polynomials & Factoring. The ExamView Assessment Suite for Algebra City includes readymade pre- and post-tests at the program, book and unit levels, an item bank and test generator, and robust reporting.
"Too often, students struggle to learn critical algebra skills they need both inside and outside the classroom," said Lee Wilson, president and CEO of PCI Education. "Algebra City is targeted intervention that encourages students to reconnect to algebra in one or more areas of misunderstanding, while allowing teachers to leverage the investment in their core algebra curriculum."
Algebra Cityis one of five new offerings from PCI Education that provide intensive intervention and remediation in reading, writing, and math for students in grades 6-12. |
Sponsors
App Activity
About AppShopper
Algebra I Review
iOS iPhone
YayMath.org and Study By App, LLC have partnered to create a comprehensive Algebra 1 app. The Yay Math movement and this project are built on an understanding of Algebra's importance, not just for this class, but also for advancing to next levels. The consciousness of this app is in decreasing student anxiety over math, clarifying topics that regularly confuse students in the classroom, and meeting the unique needs of the busy, time-deprived, always on-the-go student.
With this app, students receive 12 audio lessons each of which contains complete step-by-step guides and examples and 25 robust flashcards, constructed in easy to understand, succinct terms. Each lesson also has a 50-question multiple choice test with carefully crafted hints for approaching the problems and complete explanations for incorrect answers. In addition, the app allows students to track performance and time. Those lessons are:
What stands out about this app is exactly at the heart of what makes Yay Math special: energy. Informal language, disarming tone, positive approach, thorough step-by-step instructions, and a constant mindfulness of student achievement are the platform from which the content is delivered. Your success is valuable, and it is with that sentiment that this app was made. Best wishes in all your endeavors.
Algebra App development, biography: This app was developed by Robert Ahdoot, a full-time high school math teacher since 2005, and founder of YayMath.org. The Yay Math video project is a free service dedicated to meeting the growing need for math success in a positive, lively, and confidence-boosting way. Yay Math stands as the only online video lesson series filmed in a live classroom, with real student interaction. It has grown into a global movement, boldly redefining how people perform better in their math coursework. |
Product Description
Algebra 1/2 Home Study Kit includes the hardcover student text, softcover answer key and softcover test booklet. Containing 123 lessons, this text is the culmination of prealgebra mathematics, a full pre-algebra course and an introduction to geometry and discrete mathematics. Some topics covered include Prime and Composite numbers; fractions & decimals; order of operations, coordinates, exponents, square roots, ratios, algebraic phrases, probability, the Pythagorean Theorem and more. Utilizing an incremental approach to math, your students will learn in small doses at their own pace, increasing retention of knowledge and satisfaction!
Product Reviews
Algebra 1/2 Home School Kit, 3rd Edition
5
5
22
22
working well for my 8th grader.
We were looking for a program that my 8th grader could basically on his own. He picks up things slow, and when we just had the book he tended to skip the instructions. He also loves to do anything on the computer. This is working very well for him. The instruction portion of each lesson takes usually 30 minutes, an goes through everything from the book, for him he needs that. It may be too drawn out for some kids (get bored), but works well for us. He is able to do math completely on his own (so far after 6 weeks of school).
September 21, 2012
Very good product.
Very good product. I recommend buying Saxon teacher.
September 7, 2012
Perfect for homeschooling.
We are totally happy with our purchase. It is exactly what we hoped and expected. Thank you.
February 21, 2012
This is a great product! I was able to purchase it at a reasonable price.
November 16, 2011 |
The Role and Use of Sketchpad as a Modeling Tool in Secondary Schools. Edition No. 1
VDM Publishing House, March 2010, Pages: 268
Over the last decade or two, there has been a discernible move to include modeling in the mathematics curricula in schools. This has come as the result of the demand that society is making on educational institutions to provide workers that are capable of relating theoretical knowledge to that of the real world. Successful industries are those that are able to effectively overcome the complexities of real world problems they encounter on a daily basis. This book focuses, to some extent, on research conducted at a secondary school. The book, initially, looks at the various definitions of modeling with examples to illustrate where necessary. More importantly though, this work attempted to build on existing research and tested some of these ideas in a teaching environment. This was done in order to investigate the feasibility of introducing mathematical concepts within the context of dynamic geometry. Learners, who had not been introduced to specific concepts, such as concurrency, equidistant, and so on, were interviewed using Sketchpad and their responses were analyzed.
Vimolan, Mudaly. I taught Mathematics at secondary schools and at the University of KwaZulu-Natal for the past 24 years. Mathematics teaching methodologies has become a passion for me and I'm currently engaged in research in Modeling, Visualisation and in particular, the use of diagrams in mathematics problem solving and proving. |
Abstract
Many engineering undergraduates have problems with mathematics. Even areas of school mathematics – invariably including algebra - sometimes have to be reinforced at
undergraduate level. A bar to learning is often a lack of an understanding and this is where visualisations sometimes help - either by setting problems in an engineering context, or by using graphical visualisations. In the latter case, the maxim, "A picture is worth a thousand
words" is most appropriate. Even if students have problems rearranging mathematical equations, they can, almost always,
"read", understand and draw graphs. Now a graph is basically a visualisation of a mathematical equation, be it as simple as the straight-line equation or as complicated as the solution of a second-order partial differential equation. Consequently, displaying the graph of
(i.e. visualising) an equation can help deepen student understanding of the mathematics behind that equation. During the early 1990s, the author wrote and presented for student use some graphical mathematics software using Visual Basic. Through its use, students began to
realise what was happening with the equations they were investigating - and realised that engineering mathematics could be enjoyable (evidenced, in part, by students talking and enthusing about mathematics, and using the software in their own time). With the bursary accompanying a UK National Teaching Fellowship, the author is currently
developing the above-mentioned work into the MathinSite web site using interactive Java applets with a strong graphical content. This paper will discuss the rationale and philosophy behind the use of MathinSite in deepening engineering students' mathematical understanding - a rationale and philosophy that could be adopted in other areas of engineering education. |
Workshop 2: Math. Analysis - Why do we do proofs? The fourth class in Dr Joel Feinstein's G12MAN Mathematical Analysis module aimsSimpson's paradox); the ansAnimation of GC solvent focusing This site has very good animations related to separations. It deals specifically with solvent focusingM.E. Muller Institute for Microscopy This website is a nice primer for those who are interested in atomic-level surface imaging of biological samples with atomic force microscopy (AFM). The accompanying graphics are illustrative of what can be done and at what resolution. Note the material is a little dated (1996), but is still very useful.
If one is interested in learning about biological imaging with other methods as well, it is recommended to open the home page site ( Author(s): Daniel J. Muller, Ueli Aebi and Andreas Engel
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Simplex Optimization Methods This site, from the developers of the software program Multisimplex, provides a basic introduction to simplex optimization. Topics include the basic simplex method, the modified simplex method and evolutionary optimization. Although the mathematical details are not included, the site provides flow charts showing the logic behind the optimization. The site assumes that the user understands the need for optimization and, therefore, is less suitable for beginners. Author(s): Grabitech
Steps in conducting a systematic review This RLO outlines the five fundamental steps to conducting a systematic review of health care research so as identify, select and critically appraise relevant research. Author(s): Creator not set
Building a Business: Negotiation Skills Owen Darbishire, University Lecturer at the Said Business School, presents the seventh lecture of the 2010/11 Building a Business lecture series. Author(s): Owen Darbishire
In
This Key Skill Assessment Unit offers an opportunity for you to select and prepare work that demonstrates your key skills in the area of information literacy2.1 Some basic concepts |
LIFEPAC Pre-algebra & Pre-geometry I provides an exciting, fun-filled study on geometry. Students can work independently because lessons explain challenging concepts one at a time. Worktexts discuss: Geometry, Rational Numbers, Sets and Numbers, Formulas and Ratios, and Mathematics in Sports. Additional topics covered are data, stats, graphs, and a review of whole numbers, multiplication, and division. Adding, subtracting, multiplying, and dividing fractions is included in an easy-to-follow, comprehensive format. The LIFEPAC Pre-algebra & Pre-geometry I Set contains ten worktexts and a teacher's guide that may be purchased individually. |
Using Matrices to Solve Linear Systems by Christopher Monahan
It is not uncommon for a car dealership to have multiple stores across a geographic region. Consider the case of the US Auto Import chain with stores in Yonkers, Croton-on-Harmon, Saratoga Springs, Syracuse, and Ithaca. The May inventory is taken of four of its best sellers: the Toyota Avalon, the Dodge Durango, the Jaguar S-type, and the BMW 530i sedan. Table 6.1 shows how many of each model are in stock at each location.
TABLE 6.1
The wholesale price of each model (that is, the price that US Auto Import paid for each model) is given in Table 6.2.
TABLE 6.2
Example 1: Compute the value of the inventory for the month of May at each of the five US Auto Import stores.
For each store, multiply the number of each model by the wholesale cost of the model.
We will now use this example to illustrate the mathematical construct called a matrix. A matrix is a rectangular array of numbers. Ignoring the labels that are included to help read the tables, Table 6.1 has five rows and four columns. Rows are read horizontally and columns vertically. Table 6.2 has four rows and one column. The dimensions of a matrix are determined by the number of rows and the number of columns.
To enter a new matrix in TI 83 + /84, the keystrokes are 2nd x-1, left arrow, ENTER, and type the dimensions of the matrix. The dimensions of the matrix, 5 rows and 4 columns, are displayed on the top line of the screen as 5×4. The notation A5,4 indicates that the matrix has dimensions 5×4.
Notice the number in the lower left-hand corner of the screen. The entry in column 1 row 1 is 0. For this problem, row 1 corresponds to the inventory in Yonkers. Enter 25 and press e.
As 25 is entered into the calculator, Screen D shows the display. After the ENTER key is struck, the calculator moves to the second column of row 1 and indicates that the current entry is 0. Finish entering the inventory values for matrix A. The limitations of the screen size and the size of the data prevent you from seeing all the data at once, but you can use the left and right arrows to scroll across the screen to be sure you have entered the data correctly (Screen F).
Edit matrix B to be 4×1 (4 rows, 1 column), and enter the values for the wholesale costs in a similar manner. Quit, and return to the home screen. Multiply matrices [A] and [B] by typing 2nd x-1 ENTER x 2nd x-1 2 to get
These are the same values calculated in the solution to Example 1; they reflect the total value of the inventory for each store. This tells you the process in which multiplication of matrices occurs. Starting with row 1 of the left-hand factor, each number in row 1 is multiplied by a number from column 1 in the right-hand factor, and these products are added to give the result.
Matrix multiplication and the inverse of a matrix can be used to solve systems of linear equations. For instance, consider the following system:
This is the equivalent of the matrix equation
Observe that the first matrix contains the same numbers as the coefficients from the system. The second matrix contains the variables of the system. The third system contains the constants of the linear equations. When you perform the matrix multiplication on the left, you see the same terms as appear on the left side of the system of equations.
This matrix equation can be written as [A][X]= [B]. In Algebra 1, you would solve the equation ax = b by dividing both sides of the equation by a to get x = b/a. However, you can't divide matrices. You could also solve the equation by multiplying both sides of the equation by the multiplicative inverse of
, which gives the same result, x = b/a. Multiplication of matrices is not a commutative operation, so the order of operations must be adhered to carefully. For the purposes of solving the system of equations, you need to multiply with the inverse as the left factor. (If you try to multiply with the inverse as a right factor, the calculator will give you an error message.) |
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Algebra Through Visual Patterns: A Beginning Course in Algebra
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This two volume set of teachers guides provides a semester's worth of student activities designed to help teachers address algebra instruction. Students learn about and connect algebra and geometry through the use of manipulatives, sketches, and diagrams. The course also links the resulting visual developments to symbolic rules and procedures.
The ideas and lessons presented are appropriate for all students learning first-year algebra whether their instruction is taking place in middle school, high school, or community college.
The Algebra Manipulative Kit is optional and sold separately. Although blackline masters of required manipulatives are included in the teachers guide, the manufactured items in the manipulative kit are more colorful and durable. |
MATH 712: Problem Solving for Teachers
Course ID
Mathematics 712
Course Title
MATH 712: Problem Solving for Teachers
Credits
3
Course Description
This course is for middle and high school mathematics teachers who are interested in improving their own problem-solving skills and are looking for ideas about how to implement more problem solving into their classrooms. The first part of the course will engage the student in problem solving and mathematical modeling. The specific problems will depend on the interest and background of the class. The remainder of the course will focus on curricular issues and ways teachers can teach via problem solving. |
Maths
Mathematics
Why study Maths?
Mathematics is imperative because it is the most widely used subject in the world. Every career uses some sort of mathematics. More importantly, doing math helps the mind to reason and organized complicated situations or problems into clear, simple, and logical steps. However, within the mathematics department we strive to make mathematics enjoyable and differentiated so that everyone can access it.
A few examples of careers for people with a mathematics degree include Engineering, Civil Servant, Software development and working in the Finance industry.
Course Overview
We are currently teaching from the Collins Framework. This covers Algebra, Handling Data, Number and Shape, Space and Measure. It also entails functional skills topics which will assist students when then start Key Stage 4. Students also have the opportunity to complete projects such as Money Sense, Financial Capability and Statistics.
Students start their two year Edexcel Linear GCSE mathematics course in Senior 1. This course covers Algebra, Handling Data, Number and Shape, Space and Measure. Due to changes in the syllabus from 2010 onwards this GCSE includes functional skills and written quality communication. Students sit their GCSE at the end of Senior 2 and a number of Senior 3 students are offered the chance to resit their GCSE to improve their grade and to complete other courses such as GCSE Profiency in Number Level 1 and 2. Other students who have reached grade A/A* start to prepare for A-Levels and International Baccalaureate.
Further Study
Students have two paths within mathematics; either A-level mathematics or mathematics within the International Baccalaureate.
A-level mathematics course includes:
Core 1
Algebra and functions; co-ordinate geometry in the (x,y) plane; sequences and series; differentiation and integration
Topics studied within the Mathematical Studies course are as described in the IB syllabus overview, and are listed below with timings for Standard Level (SL)
Topic 1 – Introduction to the graphic display calculator 3 hours
Topic 2 – Number and algebra 14 hours
Topic 3 – Sets, logic and probability 20 hours
Topic 4 – Functions 24 hours
Topic 5 – Geometry and trigonometry 20 hours
Topic 6 – Statistics 24 hours
Topic 7 – Introductory differential calculus 15 hours
Topic 8 – Financial mathematics 10 hours
Project 20 hours
Internal (20 %)
The students will complete a project that is an individual piece of work involving the generation of measurements or the collection of information, and the analysis and evaluations of the measurements or information. The project is internally assessed by the teacher and externally moderated by the IBO using assessment criteria that relate to the objectives for group 5 mathematics. |
0131848682
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Introduction to Mathematical Thinking: Besides giving readers the techniques for solving polynomial equations and congruences, An Introduction to Mathematical Thinking provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus. This book introduces proofs and mathematical thinking while teaching basic algebraic skills involving number systems, including the integers and complex numbers. Ample questions at the end of each chapter provide opportunities for learning and practice; the Exercises are routine applications of the material in the chapter, while the Problems require more ingenuity, ranging from easy to nearly impossible. Topics covered in this comprehensive introduction range from logic and proofs, integers and diophantine equations, congruences, induction and binomial theorem, rational and real numbers, and functions and bijections to cryptography, complex numbers, and polynomial equations. With its comprehensive appendices, this book is an excellent desk reference for mathematicians and those involved in computer science. «Show less
Introduction to Mathematical Thinking: Besides giving readers the techniques for solving polynomial equations and congruences, An Introduction to Mathematical Thinking provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus.... Show more»
Rent Introduction to Mathematical Thinking 1st Edition today, or search our site for other Gilbert |
Mathematics, General Colleges
A general program that focuses on the analysis of quantities, magnitudes, forms, and their relationships, using symbolic logic and language. Includes instruction in algebra, calculus, functional analysis, geometry, number theory, logic, topology and other mathematical specializations |
Mathematics
This first year regents course studies many major topics in mathematics including solving equations, factoring polynomials, probability, statistics, graphing functions, number systems, and real world applications.
Integrated Algebra Extended 1 is the first year of a two year extended regents course. This course will study the same content as the Integrated Algebra Regents course, but will provide more time to develop specific algebra skills.
Integrated Algebra Extended 2 is the second year of a two year extended regents course. This course will study the same content as the Integrated Algebra Regents course, but will provide more time to develop specific algebra skills.
Pre-Calculus is designed to provide students with a solid foundation for calculus. This course provides an extensive treatment of the necessary topics from algebra, trigonometry, and analytic geometry.
The objective of Financial Topics 1 is to provide students with a solid foundation for the application of high school mathematics in the real world. The focus of the course will be to prepare students for the reality of finances in the real world.
The objective of Financial Topics 2 is to continue to provide students with a solid foundation of applications of mathematics in the real world. Topics will include mathematical appreciation, design and engineering mathematics, real estate, retirement planning and building a house.
Computer Programming 1 is an introduction to the problem solving tools needed to successfully design, write, and debug computer programs using Visual Basic. The goal of this course is to introduce Visual Basic and its wide variety of tools to students.
Computer Programming 2 is an introduction to the problem solving tools needed to successfully design, write, and debug computer programs using Visual Basic. The goal of this course is to introduce Visual Basic and its wide variety of tools to students. |
The object of this class is to introduce you to problem-solving techniques useful for tackling advanced problems in undergraduate mathematics. The sessions will be devoted to collective problem solving and to discussions of problem-solving strategies. Many of our examples will be drawn from past years of the William Lowell Putnam Competition.
Class attendance is required. Please contact me in advance if you have a conflict that will require you to miss a session.
Larson's book is an excellent resource for
anyone who wants to hone their problem solving skills, and especially
for those wishing to prepare for an exam like the Putnam. While the
book is not required, it is strongly recommended, and I
expect that many of the examples we discuss in class will be taken
from this text.
The grading for this class is S/U. To receive an S in the course, you must attend class faithfully and must write-up solutions to at least five problems over the course of the semester. There are no exams.
I would strongly encourage you to work with others
on the problems, and to share your ideas and strategies with your classmates (both in and out of class). As iron sharpens iron, so one man (or woman!) sharpens another.
However, please make sure that you understand everything you turn in; if requested, you should be able to verbally explain your solutions to me. While it is OK to write-up problems whose solutions we discuss in class, you are not allowed to turn in a solution based on something you looked up online.
Special accommodations
Students with disabilities who may require
special accommodations should talk to me as soon as possible.
Appropriate documentation concerning disabilities may be required.
For further information, please visit the Disabilities Resource
Center page at <URL: |
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Introduction
Many decisions we make in our everyday financial lives can be captured as systems of equations. We might do the computations outside of math class without seeing them as systems of equations, but if we capture those computations and consider them algebraically, we can gain some insight into how to make better financial decisions.
This packet considers two examples using real data: (1) Deciding how to print out your work as a college student, and (2) Buying a car based on gas consumption.
In both cases, we will have to make some simplifying assumptions-that is true whenever we want to do a mathematical analysis. The fewer simplifications we make, the better our mathematical model and the better decisions we can make. But these are introductory-level problems, so we will keep things simple.
Example 1: Printing costs
A student has three main options for printing out her work this semester:
Option 1: Buy a laser printer
Laser printers are expensive. The student has found a good, reliable one for $150. It prints 2000 pages on one toner cartridge and a new cartridge costs $30.
Option 2: Buy an inkjet printer
Inkjet printers are cheap. The student has found a good, reliable one for $30. It prints 500 pages on one ink cartridge and a new cartridge costs $30.
Option 3: Print at school
The college this student attends provides $5.00 in free printing each semester and charges $0.05 per page after that.
What should the student do?
Writing equations for the first two options
This packet describes the process of turning the first two options into equations by the use of the given information, tables and first differences.
Writing the third equation
Looking at the system graphically
This video demonstrates representing the three equations as a system and then considering whether there are solutions to the system of three equations, or to one or more subsystems of two equations at a time.
Example 2: Buying a fuel-efficient car
In our second example, a young man is about to buy a new car. He is interested primarily in fuel consumption and he is especially interested in the cost of gasoline. Presently, the cost of gas is $3.00 per gallon and he knows that he is going to drive long distances on the highway.
He wonders whether it would be more economical-from a fuel-consumption point of view-to buy a Toyota Corolla (cheaper, but not as efficient) or a Toyota Prius (more expensive to buy, but more efficient).
Using the system to make a decision
Summary
In conclusion, whenever we represent a real-world decision with a system of equations, we need to make some simplifying assumptions. Having done that, we can solve our system.
But the solution itself doesn't tell us what to do. The solution to a system of equations tells us when the two lines cross-when the inputs and outputs are the same for both functions. In the car problem in this packet, the solution tells us how many miles we have to drive each car in order for the gas cost together with the purchase price to be equal.
The system does not make the decision. Instead, it gives us information to use for the decision. The other information we use to make the decision is our set of constraints. Constraints in this case might include a government rebate for buying a fuel-efficient hybrid car, or the number of miles we intend to drive each year, or that we will drive total before giving the car away. Maybe a constraint is that our spouse insists on the most fuel-efficient car, regardless of the cost. Another constraint might be that we expect the cost of gas to increase sharply in the next few years.
Each of these constraints should affect how we interpret the solution to the system we wrote. The constraints help us decide what to do, as does the solution to the system.
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"Great real world application. I really enjoyed the Prius and Corolla example. I also appreciate that you reminded learners that there are other variables that they must simplify for these types of problems. " |
Math: Algebra
Learn about basic algebra principles. These sites have information on how to simplify using the distributive property, and how to transform using the commutative and associative properties, and solving systems of equations with two variables. Investigate quadratic equations. Includes links to eThemes resources on geometry and conic sections.
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Look at "Graphing Equations and Inequalities" and use the interactive graphing program. "Two Step Equations and Inequalities" has a four step lesson on how to solve two step equations. There are unit quizzes provided. NOTE: The site includes pop-up and banner ads.
Learn what variables and algebraic expressions are, how to get the value of a variable from an algebra expression, and how to write an English phrase in an algebraic expression. Examples and practice problems with explanations are included.
This site shows how to perform a trick or a puzzle dealing with calendars. The trick uses many of Algebra's basic skills, and application of math. Practice translating from words to math's numbers and symbols, as well as solving for variables.
This site uses a software simulation to help students understand ideas about functions and representing change over time. In this simulation, students control the speed and starting point of the runner, watch the race, examine a graph, and analyze the time-versus-distance relationship. NOTE: It is recommended that the teacher go to this site to read about and practice with this applet before using this lesson with students.
These sites have information on geometry for junior high and high school students. There are several interactive sites that allow the manipulation of geometric shapes. Also includes hands-on classroom activities and online quizzes. There are examples on how geometry is used in the real world such as geometric shapes in buildings and orienteering. |
APM4810 - An Introduction to The Finite Element Method
Duration:
NQF Level - 8
Credits - 12
Purpose: I want to introduce you to a module on Finite Elements. This module will develop the basic mathematical theory of the Finite Element Method (FEM).This method is the most widely used technique for engineering design and mathematical physics. In studying this module the student will obtain a clear knowledge of what the Finite Element Method is, how it works and how to use it to solve boundary-value problems. The Finite Element Method is a general technique for constructing approximate solutions to boundary-value problems. The method involves dividing the domain of the solution into a finite number of sub domains, the finite elements, and using variational concepts to construct an approximation of the solution over the collection of finite elements. |
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Mathematics
Course Description-Mathematics
HS Mathematics - (Algebra 1, Geometry and Algebra 2/Trignometry) - This is a three-year sequence consisting of the integration and unification of the traditional topics of Algebra, Geometry, Intermediate Algebra, and Trigonometry. Practical aspects of mathematics have been introduced through the study of logic, probability, and statistics.
Algebra 1 (ME21&ME22)- This course introduces variables, constants, expression of equations and with a strong emphasis in problem solving. Topics covered include: algebraic concepts of signed numbers, polynomials, equations and inequalities, introduction to geometry, real numbers, factoring, quadratic equations, systems of equations, graphs of both linear and non-linear, and data analysis. Students needed extra time to master the concepts and skills in the course will take Regents Prep, an enrichment lab course. In addition, students will have the opportunity to pratice math concept through the Math Application course, Geometer Sketchpad. click here. Prerequisite: None *Students take Algebra 1 Regents in June
Math Lab(ME1ER)- This course is a comprehensive review of algebraic concepts designed to meet the needs for Regents Examination. The course is designed to strengthen basic math skills and to establish Co-requisite: Algebra I Prerequisite: None
Algebra 1 /Bilingual Spanish *Students take Algebra 1 Regents in June
new Geometry (MG21&MG22)- In this math course, student will identify and justify geometric relationships, formally and informally. Students will be expected to develop a list of conjectured properties of the figure and to justify each conjecture informally or with formal proof. In addition, students will also be expected to list the assumptions that are needed in order to justify each conjectured property and present their findings in an organized manner. Prerequisite: Algebra I or Placement Test *Students take Geometry Regents in June
Geometry (MG21S) –Geometry/Bilingual Spanish *Students take Geometry Regents in June
Algebra 2/Trig (MR21&MR22) – This third-year course in mathematics includes number systems and their properties, rational expressions and quadratic equations, irrational numbers, complex numbers, relations and functions. In second semester, topics include: trigonometric functions, identities, trigonometric equations and their graphs, trigonometric applications, trigonometric formulas and inverse functions, and exponential and logarithmic functions, series, sequences and a continuation of probability and statistics. Success in this course is an indicator of college readiness. Students will take the Algebra II/Trigonometry Regents exam in June. Prerequisite: MG22 Precalculus (MPC1/MPC2) –This one-year course is designed to include various advanced mathematical Concepts. Topics covered are: theory of equations, relations & functions, sequences & series, conic sections, matrices & vectors, polar coordinates, and complex numbers. The course culminates with an introduction to calculus through basic theory of limits, derivatives, and integrals. To find out more about MPC1/2 click here. Prerequisite: MR22 Co-requisite: MR21 or MR22
Introduction to Calculus (MEC1/2) – This is a year course (one period /day) offered to students who do not want to take the rigorous Advanced Placement Calculus course which is a double period each day. Topics covered include: Limits, Differential Calculus. Graphing calculators are required for this course. Prerequisite: MPC2
Statistics (MES1/2) –a one year course for 4th year students that will need an understanding of statistics for their college academic programs such as the social sciences of psychology and sociology, education, business and economics, engineering, the humanities, the physical sciences and liberal arts. A strong background in algebra and geometry IS NOT NECESSARY. Topics will include interpreting data thru mathematical analysis with technology such as computers and/or graphing calculators. Prerequisite: Seniors who have completed at least 4 credits in mathematics.
Advanced Placement Calculus (MC1XPAB/2) and (MX1XPBC/2) – These are one year courses offered to students who are ready for a college-level learning experience. Courses are challenging and thought-provoking ones, that meet a double period each day. Topics covered include: Limits, Differential Calculus, and Integral Calculus. Students will be offered the opportunity to take the Advanced Placement Test in the Spring Semester and upon successful performance on the exam, receive up to two or one semesters of credit in College Calculus. Graphing calculators are required for this course and for the Advanced Placement Examination. Prerequisite: MR22 and MPC2
Advanced Placement Statistics (MS1X/2) –a one-year course introducing students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students who successfully complete the course and the Advanced Placement Examination may receive credit for a one-semester introductory college statistics course. At least one statistics course is typically required for majors such as engineering, psychology, sociology, health science, and business. A graphing calculator (TI-83 Plus) is required for this course. Prerequisite: MR22
SAT MATH (MSA1)– [MAY BE AN AFTER SCHOOL CLASS] Course to prepare Sophomores/Juniors for SAT Examinations
Research Math (MER1) – [MAY BE AN AFTER SCHOOL CLASS] This course is intended for students who demonstrate a particular aptitude for and interest in mathematics. The course will introduce the student to various topics not usually covered in the high school mathematics curriculum and lead towards original research on some problem in mathematics. |
Graphing
$9.95
This program generates graphs that students read and interpret data using specific vocabulary; least and most, fewest and greatest. Additionally, this program also provides the data and the student must place the corresponding information on the graph. |
Microsoft Mathematics 4.0 4.0 includes a full-featured graphing calculator that's designed to work just like a handheld calculator. Additional math tools help you evaluate triangles, convert from one system of units to another, and solve systems of equationsHave you listened to The Morning Jam aka "The Shareen and Joe Show"? If not, you should. And I'm very sure those who have listened, you would have all heard the jingle regarding Joe Augustin's Little Cupboard. I just happened to have the chance to actually see the cupboard and take a few photos of it. I couldn't believe he actually created a studio from a corner cupboard. This is where our favourite Joe Augustin does his voice overs and other recordings. Apparently, Shareen actually sits behind Joe whenever "The Shareen and Joe Show" gets recorded. |
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MATH 6104 - Multivariate & Vector Calculus
This course is designed as a continuation of MATH 2094. Topics will include: parametric equations, polar, cylindrical and spherical coordinate systems, vectors and vector valued functions, functions of several variables, partial derivatives and applications, multiple integrals, and vector analysis, including Green's theorem, Stokes' theorem, and Gauss' theorem. The course will include several major projects outside of class. |
Mathematics All Around Plus MyMathLab Student Access Kit
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Book Description st... More students understand the math, not just get the correct answers on the test. Useful features throughout the book enable students to become comfortable with thinking about numbers and interpreting the numerical world around them.
Problem Solving: Strategies and Principles; Set Theory: Using Mathematics to Classify Objects; Logic: The Study of What's True or False or Somewhere in Between; Graph Theory (Networks): The Mathematics of Relationships; Numeration Systems: Does It Matter How We Name Numbers?; Number Theory and the Real Number System: Understanding the Numbers All Around Us; Algebraic Models: How Do We Approximate Reality?; Modeling with Systems of Linear Equations and Inequalities: What's the Best Way to Do It?; Consumer Mathematics: The Mathematics of Everyday Life; Geometry: Ancient and Modern Mathematics Embrace; Apportionment: How Do We Measure Fairness?; Voting: Using Mathematics to Make Choices; Counting: Just How Many Are There?; Probability: What Are the Chances?; Descriptive Statistics: What a Data Set Tells Us |
Matrix Helper Pro
We believe that sometimes You just need to make quick calculations with matrix for solving linear algebra, for example. After downloading our app you can: 1) add up 2) multiply 3) transpose matrix with size up to 6x6.
See, I didnt take maths after my second year in high school so I have no idea how to use this, but I think its a good app for people who need it. Hell, if they had this calculator i probably would have decided to takes maths at school for a while longer... |
Fortunately, I was able to find an article ( that focuses on the class I will be teaching this summer: linear algebra. I have come to realize that linear algebra is a very interesting and challenging class to teach for several reasons. One, it is a class "in between" two types of math classes: computational (like the calculus sequence) and proof-based, rigorous upper division math classes, which will likely only be experienced by math majors. Some schools teach linear algebra as a purely computational subject the first time around, while other use it as an introduction to formal math logic. Most, like at this university, treat it as an in-between class. In particular, it is hard to justify to students who do not intend to take more advanced classes why they need to understand definitions and proofs when the calculus sequence did not emphasize this (which some contend is a problem with the undergraduate curriculum in the United States). At the same time, with this approach, many math majors will not learn linear algebra at the level that they will need in later classes, and in many cases (such as my own), will need to teach themselves advanced linear algebra later on.
But everyone agrees that linear algebra is one of the most important math classes for those who intend to pursue theoretical or applied mathematics, and it is one of the most important classes for students who major in any kind of technical field. Therefore, it is a necessity that we try to help the students not only perform computations but understand the concepts so that they will be able to utilize the techniques from linear algebra later in their career. So while this type of class may fall short in many ways, it is the least we must do.
There are several key concepts from linear algebra that students experience trouble with: linear transformation, basis, linearly independent, etc. This article focuses on the notion of a subspace and how students take what they visualize or already know about subspaces (such as the examples in 2 and 3 dimensions, a line or a plane) and how they reconcile this with the formal definition. The article calls the latter the students' "concept image." An advanced mathematics student will have a concept image of subspace that agrees with the formal mathematical definition and be able to explain why what they visualize, or their own stock examples, satisfy and also demonstrate the definition. This is the goal of such an "in-between" mathematics course: to produce students who can take their mathematical intuition, which is honed in calculus, and reconcile it with abstract, formal mathematics.
The paper explains results from a set of interviews with students who have just taken such a linear algebra course. The researchers picked 8 students, 4 male and 4 female, which had gotten grades from A-C, as representatives. The students described their concept image of subspace. Then they were given the formal definition and asked how it related to their concept image. Finally, the students were given a problem to solve ("Do these vectors form a subspace?") to see how students utilized both the concept image and the formal definition. Some of the students had a geometric/visual concept image of subspace (that is, they relied on visualization to understand its properties), and the paper argues that such students who do not also have an algebraic concept image will be led astray when solving linear algebra problems. This is consistent with my own experience teaching linear algebra and multivariable calculus—the students who rely on visualization find that they cannot solve problems consistently. Then there are students who never use visualization and who only rely on the rules given in the definition (this is how I was as a linear algebra student). The advanced students have both understandings, and they complement each other and are both utilized when solving problems.
One issue I did have is that, while they changed the names of the students, the pseudonyms were gendered, and all of the students who demonstrated "advanced" thinking were male, while there was one female student who clearly had the most trouble with the questions. I think that 8 is a very small sample size and it's hard to draw any conclusions, but I would be interested to know if they thought that there was a gender difference in terms of advanced understanding and if so, how would they explain that. It would be interesting to repeat such a project with a larger sample of students.
The paper was helpful to me in that it verified what I already thought about students' misconceptions in linear algebra. Students come in thinking of vector as a visual object, a line with an arrow, which is consistent with what they have been taught in calculus and physics, and teachers must build on this concept in order to introduce the notion of an abstract vector space. I hope that the actual material presented in the paper will help me construct effective peer instruction questions.
I found an article by David Concepcion called "Reading Philosophy with Background Knowledge and Metacognition" in Teaching Philosophy 27:4 (2004).
It gave a nice discussion of how one might teach students how to read articles in current analytic philosophy. He pointed out that this sort of task is necessary in order to get students to actually engage in philosophy rather than assuming they are reading the text to pillage a bunch of facts out of it. He incorporates this sort of instruction into the class by adopting the following methodology: (i) students read, summarize, and evaluate a short passage in class. (ii) they then describe the process they engaged in while doing this. (iii) they then read a "how to read philosophy" handout. (iv) they then re-read the passage using the skills outlined in the handout. (v) they compare this latest result with their previous one and note what they have learned. (vi) students look at each others self-assesments. (vii) students turn in a written summary of the text. (viii) questions from the "how to read handout" is included on the final exam to make sure that the students remember the skills they have learned.
Overall, Concepion brought out some interesting pedagogical points but I worry that his methodology won't work for all kinds of philosophical texts. In order to work, he needs (i) to distinguish what he calls problem-based philosophy from historical philosophy and (ii) assume that both could adopt a similar method. I'm not sure whether either of these assumptions are justified. Can we really get clarity on contemporary philosophical problems without attending to the way they have been historically and socially mediated? Can we really find a methodology that can apply to reading all different kinds of historical philosophers e.g. Hume, Leibniz, Kant, Hegel, Schelling, Hoelderlin, Nietzsche, Heidegger, Deleuze, etc.?
Tonight I read an article "Teaching Scholarship" from the December 2009 issue of Perspectives on History magazine, which is published by the American Historical Association. In the "Art of History" column, historian Caroline Walker Bynum discusses how to teach "scholarship" values to graduate students. By "scholarship" values, she means what kind of values students need to embrace and practice in order to become good historians themselves. This includes values like patience in finding sources in the archive, really thinking about how your findings fit in to other people's arguments, and to value silences in the sources—to critically appreciate them. I was drawn to this article, first, by the author. I've read Bynum's Holy Feast and Holy Fast my first year of graduate school in a feminist history and theory class and just loved it. The writing is superb, and the argument intriguing. This article isn't necessarily based on an official "study" but on Bynum's own teaching of graduate students.
I liked this article because it reminded me of what we'd discussed in the theory stream about teaching students to practice "expert" practices and by encouraging metacognition. In Bynum's article, she writes about the assumptions high school students, undergraduates, and even first-year graduate students have about research. Over the years, these students learned to be critical of sources and arguments. This rang true with me. Yes, especially graduate students can be excellent at deconstructing and criticizing other people's arguments and books. But Bynum pointed out that graduate students also need to learn the value of research and of "getting something right." She explains that she used a first-year introductory "methods" class to teach new graduate students these values of scholarship.
Bynum demonstrated "scholarship" values by guiding students through the tasks needed to write a book review. She had this process broken down into concrete parts, like trying to summarize an author's argument in a sentence, by reading other book reviews and thinking about why they "succeed" as a review and by examining footnotes to make sure they were correct and useful to the author's intent. Only after looking at the different parts of a book review and gaining a better grasp of the knowledge and work needed to write one does she have her students write their own book review. She also helped individual students come up with plausible research projects, then let them come up with a second research proposal on their own. There was an emphasis on teaching the practice of reviewing and project creation, and then there was a chance to let students do the work on their own. She had a "hands-on" approach to teaching students how to have a "scholarly stance."
I think this is a valuable lesson and helps me recognize why some classes "worked" for me early on in graduate school. I will be teaching an undergraduate history course soon and ideally I would like my students to learn the material, learn the different interpretations of events, and make a judgment about the interpretations. It would be great if I could also suggest to them the values of historical research as well.
Unfortunately I had a great amount of trouble finding an appropriate article as all of my search terms yielded results about teaching *language* rather than teaching Linguistics (I'm just not sure if this type of work is out there as I am in a pretty 'fringe' field. In the end I decided on an article about how the formal linguistic knowledge that linguists possess can be incorporated into a classroom setting in order to teach first languages to children: "Some aspects of the impact of Linguistics on the teaching of English in disadvantaged children" ( though unfortunately the article doesn't really contain information about how to learn my field but rather how my field can influence the learning of natural languages.
The author points that two that there are two primary groups that enter language classes: proficient speakers of the native language, and those learning it as a second language, but notes that this leaves out an important third group: those who speak a non-standard variety of the language who need additional/modified types of instruction. The author then goes on to discuss, at each linguistic level the types of issues that these students have. In terms of phonology issues such as neutralizing the final sound in /with/ from a /th/ to an /f/, resulting in /wif/ and advocates the use of this type of linguistic information to inform training on standard pronunciations. In terms of grammatical features, she notes that although many students can pronounce the /s/ sound in /verse/ they will omit the /s/ sound in /printer's/, even though one is a simple phoneme and one is a morpheme expressing possession. These linguistic distinctions must be expressed to the student, as well as the importance of 'linking' verbs, and the correct way to form verbal/tense aspect combinations. The author advocates making these distinctions clear by clearly stating/describing the components of a complex VP such as "have been cooking" by explaining the function of each auxiliary verb as well as the /-ing/ morpheme. This runs counter to the lower level approaches that dominate language teaching, informed by linguistically sophisticated terminology that rather than a statement to student such as "no thats wrong, its "have been cooking" not "have be cook" or "have been cook."
Ultimately the author advocates an increase in this type of approach, early exposure to formal texts, and a move away from the piecemeal correction approach that is so often adopted (as well have having the teacher slowly enunciate words for the students as they will never actually hear the form in natural speech). Though this does not quite get at the issue of how students learn the concept of linguistics, I believe it is interesting in that it shows how adopting formal linguistic concepts can result in better language outcomes than traditional teaching practices. |
Project Information
About this project:
This is the
Advanced Trigonometry Calculator
project ("advantrigoncalc")
This project was registered on SourceForge.net on Mar 19, 2011, and is described by the project team as follows:
* You can use functions: all trigonometry, all hyperbolic, logarithm, arithmetic and statistics. And logically the operators "+,-,/,*,^,!,_". * You can enter 4 different numerical systems in the same expression: binary, decimal, octal, hexadecimal. * You may have the answer in 4 different number systems (binary, decimal, octal, hexadecimal) * You can create variables of type "variable name=expression" and use them in the following expressions. * You can standardize the form of calculations (degrees, radians, gradians) or/and if you want you can force a function to be calculated in radians, degrees, and gradians, using "rad", "deg", "gon". Example "radsin(pi/6)" ="degsin(30)". * You can use three types of parentheses "{}" "[,]" "(,)" * You can solve expressions with exponents like "2^_2^3^_4" and using parentheses you can calculate with even more complexity. * You can get the answer in the form of SI prefixes (milli, micro, everyone!) Example "1E-9" = "1n". * And more |
Geometry
Geometry is the branch of mathematics concerned with the measurements and relations of planar figures (segments lines, angles polygons, circles) and solids (rectangular solids, pyramids, cylinders, cones, spheres). The content also includes the development of deductive reasoning and an introduction to basic trigonometry. Due to the challenging nature of geometry, students should expect homework every night in this course. A scientific calculator is recommended for this course. Prerequisite: "C" or better in Algebra I 1 year – 1 credit
Algebra II
This course is a continuation of the study of algebra. The content includes the concepts from Algebra I, synthetic substitution and division, negative and rational exponents, complex numbers, relations and functions, conics, logarithms, and an introduction to trigonometry. This course is strongly recommended for college-bound students. A graphing calculator is recommended for this course. Students should expect homework every night. Prerequisite: "C" or better in Geometry and Algebra I 1 year – 1 credit
Pre-Calculus
This course is a continuation of the study of algebra, a study of trigonometry, and an introduction to calculus. It is designed to prepare the college-bound student for college level mathematics. The content includes concepts from Algebra II, sequences, series, binomial expansion, matrices and determinants, permutations, combinations, probability, trigonometry, and calculus. A graphing calculator is required for this course. Students should expect homework every night. Prerequisite: "B" or better in Algebra II 1 year – 1 credit
Transition to College Mathematics
This course is offered as an alternative for college-bound seniors who have limited experience or success in college preparatory mathematics. It is designed for students who either were not recommended for Pre-Calculus or do not feel confident taking Pre-Calculus. It is the study of the algebra, geometry, basic trigonometry essential for success in an introductory college math course. It will also include topics in statistics and probability. Emphasis is placed on applications. A scientific calculator is required for this course. Prerequisite: Algebra I, Geometry and Algebra II |
The Conference Board
of the Mathematical Sciences ( is an
umbrella organization consisting of sixteen professional societies all
of which have as one of their primary objectives the increase or
diffusion of knowledge in one or more of the mathematical sciences. Its
purpose is to promote understanding and cooperation among these
national organizations so that they work together and support each
other in their efforts to promote research, improve education, and
expand the uses of mathematics.
Student paper sessions are sponsored by the MAA Committee on
Undergraduate Activities and Chapters at MathFest, with travel grants
available to Student Chapter members. The undergraduate student poster
sessions at the Joint Math Meetings offer another opportunity for
students to participate in national meetings. The MAA Undergraduate Mathematics
Conferences ( program provides support for
regional conferences that provide significant opportunities for
students to present their work to their peers. The MAA Student
Chapter (
program is currently under review, as part of the ongoing MAA
strategic planning initiative, and we hope to enhance this
program's
ability to support local faculty effort to involve students in
mathematics activities outside the classroom.
MAA Online
A significant component of MAA Online is the Mathematics Digital Library (MathDL)
( which now encompasses the MAA book
reviews, Classroom Capsules, Journal of Online Mathematics and Its
Applications (JOMA), Digital Classroom Resources and more. Convergence
( the online magazine for the
use of history in the classroom, is also linked from MathDL. MathDL is
also the lead site in the Math Gateways project, which will soon launch
and offer a portal to more than a dozen mathematical sites, providing a
common search engine that we anticipate will enhance mathematics
faculty's ability to locate resources across the web.
The National
Association of Mathematicians ( has always
had as its main objectives, the promotion of excellence in the
mathematical sciences and the promotion of the mathematical development
of underrepresented American minorities. It also aims to address the
issue of the serious under-representation of minorities in the
workforce of mathematical scientists.
Comments? Let us hear from you. We are always looking for ways to
improve the information we make available. |
Secondary Mathematics III [2011]
Understand solving equations as a process of reasoning and explain the reasoning. Extend to simple rational and radical equations.
A.REI.2
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Applying Radical Equations
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
Applying Rational Equations
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
Solving Radical Equations
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
Solving Rational Equations |
For a one-semester course in Mathematical Statistics. This innovative new introduction to Mathematical Statistics covers the important concept of estimation at a point much earlier than other texts (Chapter 2). Thought-provoking pedagogical aids help students test their understandinThis text is intended primarily for a first course in mathematical probability for students in mathematics, statistics, operations research, engineering, and computer science. It is also appropriate for mathematically oriented students in the physical and social sciences. Prerequisite material consi... |
Operations with Real Numbers: Negative Exponents
The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples.
Objectives of this module: understand the concepts of reciprocals and negative exponents, be able to work with negative exponents |
Inductive Reasoning, Part 1 of 3 In this video, Sal Khan uses a simple number pattern to help the viewer understand how to use inductive reasoning to figure out what the next number will be. (Because it is a simple number pattern, the viewer will know what the the next number is, but Mr. Khan explains how to answer the mathematical question using inductive reasoning.)Mr. Khan uses the Paint Program (with different colors) to illustrate his points. Sal Khan is the recipient of the 2009 Microsoft Tech Award in Education. (02:01.77 Water Quality Control (MIT) The course material emphasizes mathematical models for predicting distribution and fate of effluents discharged into lakes, reservoirs, rivers, estuaries, and oceans. It also focuses on formulation and structure of models as well as analytical and simple numerical solution techniques. Also discussed are the role of element cycles, such as oxygen, nitrogen, and phosphorus, as water quality indicators; offshore outfalls and diffusion; salinity intrusion in estuaries; and thermal stratification, eu Author(s): AdamsS34 Problem Solving Seminar (MIT) This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates. Author(s): Rogers, Hartley,Kedlaya, Kiran,Stanley Summing up6.1 Direct proportion Doing and undoingLewis Carroll in Numberland An intriguing biographical exploration of Lewis Carroll, focusing on the author's mathematical career and influences. Author(s): Robin Wilson
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Use Photomerge Exposure in Manual mode Learn how to use the new Photomerge Exposure feature in Photoshop Elements 8 to combine images with different exposures into one perfect image. See why Manual mode is best when combining images that were taken with and without flash.Medieval Rus' Medieval Rus' is a resource designed to support the study of medieval Russian literature, developed by prominent medieval Slavicist David Birnbaum and his graduate students. The site offers: glossaries of church architecture and Christian festivals; external links to historical maps and genealogies; links to relevant associations and mailing lists; but its most useful features are to be found under 'syllabus'. The four unit course (Kievan Rus 988-1240; Mongol Russia 1240-1480; Muscovy 1480-1 Author(s): No creator set |
High School Advantage 2008 was specially developed to supplement classroom
curriculum by including award-winning content that support state standards.
In-depth lessons with sample problems and questions teach, reinforce and track
student progress in the core subjects.
A Complete Student Resource Center now on DVD with 10 core subjects along with
after school extras including PC games and more!
Skills Learned
Algebra II
Geometry and Trigonometry
Composition
Economics
World History
U.S. Government
Foreign Language
Typing
Biology
Chemistry and Physics
Product Features
10 Core Subjects Expanding on Key Academic Areas
1,600+ Lessons Deliver Easy-to-Understand Concepts and Tutorials
2,000+ Exercises Adapt to Different Learning Levels and Styles
Supports State Standards
Student Planner
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After School Extras for today's students include music, PC games, mobile
games, ringtones
Educational Features
Mathematics Over 265 Lessons and 900 Exercises Solidify critical math skills and prepare for College exams or professional
endeavors with lessons and exercises in the key subject areas.
Algebra II
Roots
Functions
Conic Sections
Quadratic Equations
Geometry and Trigonometry
Triangles
Angle Pairs
Parallel Lines
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Reasoning and Equality
Coordinate Geometry
Graphing Sine and Cosine
Trigonometric Functions
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Economics
Practice micro-economics in a simulated environment with 1,000 different company
scenarios
Observe how markets function in a dynamic simulated setting.
Compete in an interactive game that allows you to see the impact of
changing economic conditions through time.
Students are asked to manage a variety of companies in different market
types ranging from single company monopolies to highly competitive markets.
Science Over 180 Lessons and 800 Animations Supplement classroom experience and review Biology, Chemistry and Physics at
your own pace. Interactive multimedia lessons reinforce your understanding
of these subjects and help you make sense of concepts, formulas, reactions and
equations.
Biology
Skeleton
Muscles
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Human Development
Scientific Classification
Matter and Energy
Atomic Structure
Periodic Table
Chemistry and Physics
Acids and Bases
Organic Chemistry
Nuclear Chemistry
Linear Motion
Laws of Gravity
Weight and Mass
Kinetic Theory
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History and U.S. Government Over 300 Lessons and 75 Video Clips Students retrace historical events and review key concepts in American
government form the Declaration of Independence to the role of the Internet in
the 21st century.
World History
Renaissance
Reformation
Thirty Years War
Age of Exploration
Age of Enlightenment
Industrial Revolution
World Wars I and II
Age of Terrorism
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Executive Branch
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The U.S. Constitution
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Political Parties
Foreign Language Over 1,000 Words and Phrases Learn basic vocabulary and sentence structure in Spanish, French, German and
Italian. Each language comes complete with the Native Speak pronunciation
flashcard system. |
A no-nonsense, practical guide to help you improve your algebra skills with solid instruction and plenty of practice, practice, practice. Practice Makes Perfect: Algebra presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations. Inside you will find the help you need for boosting your... more...... more...
Don't be tripped up by trigonometry. Master this math with practice, practice, practice!
Practice Makes Perfect: Trigonometry is a comprehensive guide and workbook that covers all the basics of trigonometry that you need to understand this subject. Each chapter focuses on one major topic, with thorough explanations and many illustrative examples,... more...
Take it step-by-step for pre-calculus success!. The quickest route to learning a subject is through a solid grounding in the basics. So what you won't find in Easy Pre-calculus Step-by-Step is a lot of endless drills. Instead, you get a clear explanation that breaks down complex concepts into easy-to-understand steps, followed by highly focused ASVAB AFQT—without ever breaking a sweat! First, you'll determine exactly how much time you First, you'll determine exactly how much... more...
The easy way to prepare for officer candidate tests Want to ace the AFOQT, ASVAB or ASTB? Help is here! Officer Candidate Tests For Dummies gives you the instruction and practice you need to pass the service-specific candidate tests and further your military career as an officer in the Army, Air Force, Navy, Marine Corps, or Coast Guard. Packed |
Objective 4.02
Objective 4.03
Objective 4.04
Design experiments and list all possible outcomes and probabilities for an event.
Goal 5
Algebra - The learner will demonstrate an understanding of mathematical relationships.
Objective 5.01
Identify, describe, and generalize relationships in which:
Quantities change proportionally.
Change in one quantity relates to change in a second quantity.
Objective 5.02
Translate among symbolic, numeric, verbal, and pictorial representations of number relationships.
Objective 5.03
Verify mathematical relationships using:
Models, words, and numbers.
Order of operations and the identity, commutative, associative, and distributive properties |
Mathematical Excursions - 3rd edition
Summary: MATHEMATICAL EXCURSIONS, Third Edition, teaches students that mathematics is a system of knowing and understanding our surroundings. For example, sending information across the Internet is better understood when one understands prime numbers; the perils of radioactive waste take on new meaning when one understands exponential functions; and the efficiency of the flow of traffic through an intersection is more interesting after seeing the system of traffic lights represented in a math...show moreematical form. Students will learn those facets of mathematics that strengthen their quantitative understanding and expand the way they know, perceive, and comprehend their world. We hope you enjoy the journey |
Middle School Advantage 2008 delivers the most award-winning content aligned with classroom curriculum. Get the best results with over 9,000 lessons and 2,400 exercises in the core subjects. Take advantage of a premier educational tool that offers state standards-driven content to increase scores in key subject areas.
A Complete Student Resource Center now on DVD with 10 core subjects along with after school extras including PC games and more!
Skills Learned:
Pre-algebra
Algebra I
Geometry
Reading
Vocabulary
Grammar
Earth Science
U.S. History
Foreign Language
Typing
Features:
10 Core Subjects Expanding on Key Academic Areas
9,000+ Lessons Deliver Easy-to-Understand Concepts and Tutorials
2,400+ Exercises Adapt to Different Learning Levels and Styles
Supports State Standards
Student Planner
After School Extras for today's students include music, PC games, mobile games, ringtones
Mathematics
Over 70 Lessons and 200 Exercises
Build a solid math foundation by mastering the fundamentals.
Pre-Algebra
Formulas
Decimals
Percentages
Factorization
Measurements
Scientific Notation
Variables
Word Problems
Calculating Fractions
Ratios and Proportions
Order of Operations
Algebra I
Functions
Radicals
Exponents
Linear Inequalities
Absolute Values
Graphs
Lines and Slopes
Geometry
Pythagorean Theorem
Reasoning
Angles
Triangles
Volumes
Surface Area
English
Over 100 Lessons and 2,000 Exercises
A variety of entertaining interactive activities and lessons strengthen Language Arts aptitude.
Reading
Prefixes and Suffixes
Root Words
Comprehension
Main Ideas
Topic Sentences
Summarizing
Making Predictions
Syllables
Vocabulary
Patterns
Word Definitions
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Grammar
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Punctuation
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Adjectives and Adverbs
Verb Tense
Subject/Verb Agreement
Regular and Irregular Plurals
Science
Over 200 Illustrations and Animations,7,500 Keywords, 800 Cross-References
Explore the origin, structure and development of planet Earth through this fascinating multimedia program. Investigates current issues such as the ozone hole, greenhouse effect, and acid rain.
Earth Science
Weather
Properties of Air
Motion
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Planets
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Over 106 Lessons and 280 Video Clips
Students retrace historical events form the early settlement of North America through the Internet revolution of the late 20th and early 21st century.
U.S. History
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Three Worlds Meet
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Learn basic vocabulary and sentence structure in Spanish, French, German and Italian. Each one comes complete with the Native Speak pronunciation flashcard system |
Use Technology to Explore Symmetry KaleidoMania! lets students dynamically create and analyze symmetric designs and explore the mathematics of symmetry. This CD and book of blackline masters offer a comprehensive unit on transformational geometry and symmetry. Students build important mathematical analysis skills that give them a deeper understanding of, and appreciation for, the patterns they see all around them. KaleidoMania! provides the perfect stage on which to explore these highly visual concepts and encourages the abilities of all students with fun-filled activities. KaleidoMania! gives students the tools for mathematical analysis, helping them to understand how many of the shirt patterns, building friezes, plate designs, and other patterns they see every day can be classified according to their symmetries. In addition to its open-ended symmetry design and analysis tools, KaleidoMania! includes seven software "tours" and six software investigations that correlate with the ten printed activities that are basic to any geometry course. The program also includes two additional activities: Box Net and the 3 Mirror Experiment. With Box Net, students create a source image and a box net, print it, and construct a three-dimensional box. Using 3 Mirror Experiment, students mathematically analyze infinite kaleidoscopic patterns. With its very clear objectives, the activity book is both teacher- and student-friendly. Students quickly move beyond the definitions of symmetry, transformations, and isometries into KaleidoManias interesting investigations and motivating games, where they develop stronger visualization skills and build intuition about these important geometry concepts. They also learn to appreciate the use of symmetry in the art and the crafts of many cultures. Note: KaleidoMania! is available for Windows only. System Requirements 120MHz Pentium-based system (200 MHz recommended) Windows 95 or Windows NT 4 16MB RAM CD drive
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Basic Math for Process Control
Look Inside
About
A practical tutorial on the mathematics essential to the process control field, written by an experienced process control engineer for practicing engineers and students. A quick-and-easy review of the mathematics common to the field, including chapters on frequency response analysis, transfer functions and block diagrams, and the Z-N approximation. A handy desk reference for process control engineers - a helpful aid to students in mathematics courses. |
Real Analysis
e-books in this category
The Foundations of Analysis
by Larry Clifton - arXiv , 2013 This is a detailed introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios, and then define the positive real numbers categorically. (371 views)
Real Analysis
by Martin Smith-Martinez, et al. - Wikibooks , 2013 This introductory book is concerned in particular with analysis in the context of the real numbers. It will first develop the basic concepts needed for the idea of functions, then move on to the more analysis-based topics. (463 views)
Differential Calculus
by Pierre Schapira - Université Paris VI , 2011 The notes provide a short presentation of the main concepts of differential calculus. Our point of view is the abstract setting of a real normed space, and when necessary to specialize to the case of a finite dimensional space endowed with a basis. (629 views)
A Course of Pure Mathematics
by G.H. Hardy - Cambridge University Press , 1921 This classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. Hardy explains the fundamental ideas of the differential and integral calculus, and the properties of infinite series. (2768 views)
Real Analysis for Graduate Students: Measure and Integration Theory
by Richard F. Bass - CreateSpace , 2011 Nearly every Ph.D. student in mathematics needs to take a preliminary or qualifying examination in real analysis. This book provides the necessary tools to pass such an examination. The author presents the material in as clear a fashion as possible. (2637 views)
Orders of Infinity
by G. H. Hardy - Cambridge University Press , 1910 The ideas of Du Bois-Reymond's 'Infinitarcalcul' are of great and growing importance in all branches of the theory of functions. The author brings the Infinitarcalcul up to date, stating explicitly and proving carefully a number of general theorems. (2114 views)
An Introductory Single Variable Real Analysis
by Marcel B. Finan - Arkansas Tech University , 2009 The text is designed for an introductory course in real analysis suitable to upper sophomore or junior level students who already had the calculus sequel and a course in discrete mathematics. The content is considered a moderate level of difficulty. (3032 views)
Elementary Real Analysis
by B. S. Thomson, J. B. Bruckner, A. M. Bruckner - Prentice Hall , 2001 The book is written in a rigorous, yet reader friendly style with motivational and historical material that emphasizes the big picture and makes proofs seem natural rather than mysterious. Introduces key concepts such as point set theory and other. (6200 views)
Elliptic Functions
by Arthur Latham Baker - John Wiley & Sons , 1890 The author used only such methods as are familiar to the ordinary student of Calculus, avoiding those methods of discussion dependent upon the properties of double periodicity, and also those depending upon Functions of Complex Variables. (3473 views)
Theory of the Integral
by Brian S. Thomson - ClassicalRealAnalysis.info , 2012 This text is intended as a treatise for a rigorous course introducing the elements of integration theory on the real line. All of the important features of the Riemann integral, the Lebesgue integral, and the Henstock-Kurzweil integral are covered. (8403 views)
Mathematical Analysis II
by Elias Zakon - The TrilliaGroup , 2009 This book follows the release of the author's Mathematical Analysis I and completes the material on Real Analysis that is the foundation for later courses. The text is appropriate for any second course in real analysis or mathematical analysis. (5779 views)
Basic Analysis: Introduction to Real Analysis
by Jiri Lebl - Lulu.com , 2009 This is a free online textbook for a first course in mathematical analysis. The text covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, and sequences of functions. (9197 views)
Applied Analysis
by J. Hunter, B. Nachtergaele - World Scientific Publishing Company , 2005 Introduces applied analysis at the graduate level, particularly those parts of analysis useful in graduate applications. Only a background in basic calculus, linear algebra and ordinary differential equations, and functions and sets is required. (7055 views)
Analysis: An Introductory Course
by I. F. Wilde - King's College London , 2009 The material is intended to provide a gentle (but nonetheless serious) introduction to some of the concepts of analysis. Contents: Sets; The Real Numbers; Sequences; Series; Functions; Power Series; The elementary functions. (8199 views)
Introduction to Infinitesimal Analysis: Functions of One Real Variable
by N. J. Lennes - John Wiley & Sons , 1907 This volume is designed as a reference book for a course dealing with the fundamental theorems of infinitesimal calculus in a rigorous manner. The book may also be used as a basis for a rather short theoretical course on real functions. (4361 views)
Homeomorphisms in Analysis
by Casper Goffman, at al. - American Mathematical Society , 1997 This book features the interplay of two main branches of mathematics: topology and real analysis. The text covers Lebesgue measurability, Baire classes of functions, differentiability, the Blumberg theorem, various theorems on Fourier series, etc. (5272 views)
Introduction to Real Analysis
by William F. Trench - Prentice Hall , 2003 This book introduces readers to a rigorous understanding of mathematical analysis and presents challenging concepts as clearly as possible. Written for those who want to gain an understanding of mathematical analysis and challenging concepts. (11772 views)
Introduction to Lebesgue Integration
by W W L Chen - Macquarie University , 1996 An introduction to some of the basic ideas in Lebesgue integration with the minimal use of measure theory. Contents: the real numbers and countability, the Riemann integral, point sets, the Lebesgue integral, monotone convergence theorem, etc. (6244 views)
Fundamentals of Analysis
by W W L Chen - Macquarie University , 2008 Set of notes suitable for an introduction to the basic ideas in analysis: the number system, sequences and limits, series, functions and continuity, differentiation, the Riemann integral, further treatment of limits, and uniform convergence. (6770 views)
Set Theoretic Real Analysis
by Krzysztof Ciesielski - Heldermann Verlag , 1997 This text surveys the recent results that concern real functions whose statements involve the use of set theory. The choice of the topics follows the author's personal interest in the subject. Most of the results are left without the proofs. (4775 views)
Mathematical Analysis I
by Elias Zakon - The Trillia Group , 2004 Topics include metric spaces, convergent sequences, open and closed sets, function limits and continuity, sequences and series of functions, compact sets, power series, Taylor's theorem, differentiation and integration, total variation, and more. (8236 views)
Real Variables: With Basic Metric Space Topology
by Robert B. Ash - Institute of Electrical & Electronics Engineering , 2007 A text for a first course in real variables for students of engineering, physics, and economics, who need to know real analysis in order to cope with the professional literature. The subject matter is fundamental for more advanced mathematical work. (7156 views)
Real Analysis
by A. M. Bruckner, J. B. Bruckner, B. S. Thomson - Prentice Hall , 1997 This book provides an introductory chapter containing background material as well as a mini-overview of much of the course, making the book accessible to readers with varied backgrounds. It uses a wealth of examples to illustrate important concepts. (6879 views) |
unique feature of this compact student's introduction is that it presents concepts in an order that closely follows a standard mathematics curriculum, rather than structure the book along features of the software. As a result, the book provides a brief introduction to those aspects of the Mathematica software program most useful to students. The second edition of this well loved book is completely rewritten for Mathematica 6 including coverage of the new dynamic interface elements, several hundred exercises and a new chapter on programming. This book can be used in a variety of courses, from precalculus to linear algebra. Used as a supplementary text it will aid in bridging the gap between the mathematics in the course and Mathematica. In addition to its course use, this book will serve as an excellent tutorial for those wishing to learn Mathematica and brush up on their mathematics at the same time. less |
King Saud University seeks to become a leader in educational and technological innovation, scientific discovery and creativity through fostering an atmosphere of intellectual inspiration and partnership for the prosperity of society.
Contribution Description
We adapted the simulation for pre-calculus and calculus students. The main goal of the activity is to have students construct algebraic equations to generated position, velocity, and acceleration graphs.
ئاست
High School
Type
تاقیگه
Subject
بیرکاری really like this activity. I have not changed it, yet, but I plan to write an activity for Algebra 1 that will include: interpreting graphs and relating slope to velocity.6/11/11Corina Srygley |
0618547185
9780618547180 on how to study math. Special student-success-oriented sections include chapter-opening Strategies for Success; What You Should Learn--and Why You Should Learn It; Section Objectives; Chapter Summaries and Study Strategies; Try Its; Study Tips; and Warm-Up exercises. In addition the text presents Algebra Tips at point of use and Algebra Review at the end of each chapter. A strong support package includes the CL MATHSpace CD-ROM--which further emphasizes algebra review--and Instructional DVDs that allow students to review material outside of class. «Show less... Show more»
Rent Calculus 7th Edition today, or search our site for other Falvo |
pre-algebra course centers on building the foundations of the student?s algebra. They will be introduced to variables, expressions, order of operations and basic problem solving skills. The course also introduces students to absolute value, the coordinate plane and different algebraic properties |
Lesson Plan
Factoring Polynomials
Grade Levels
Commencement
,
9th Grade
Description
In this lesson, students will review multiplying two binomials together (FOIL) in the "Do-Now". Students will then learn how to factor a quadratic equation in the form of x2 + bx + c, when a is equal to 1.
Support Materials
SMART Board
This instructional content was intended for use with a SMART Board. The .xbk file below can only be opened with SMART Notebook software. To download this free software from the SMART Technologies website, please click here. |
Hi everyone! I need some urgent help! I have had many problems with algebra lately. I mostly have difficulties with step-by-step answers to my algebra problems. I can't solve it at all, no matter how much I try. I would be very relieved if someone would give me some help on this matter.
I really don't know why God made math, but you will be happy to know that a group of people also came up with Algebrator! Yes, Algebrator is a program that can help you crack math problems which you never thought you would be able to. Not only does it provide a solution the problem, but it also explains the steps involved in getting to that solution. All the Best!
Yes I agree, Algebrator is a really useful product. I bought it a few months back and I can say that it is the main reason I am passing my math class. I have recommended it to my friends and they too find it very useful. I strongly recommend it to help you with your math homework.
A extraordinary piece of math software is Algebrator. Even I faced similar difficulties while solving adding exponents, simplifying fractions and unlike denominators. Just by typing in the problem from homeworkand clicking on Solve – and step by step solution to my algebra homework would be ready. I have used it through several algebra classes - Algebra 2, Algebra 2 and Basic Math. I highly recommend the program. |
Utilizing the manipulation of complex polynomials, quadratics, systems of equations, and trigonometric functions will help one be more prepared for calculus. Having taken calculus, algebra was a very important component in terms of simplifying equations into baser forms. This also allowed me to work with equations for 3-D drawings, by breaking down given equations into simpler terms. |
" Plain – English explanations and step-by-step guidance." Really? Well actually yes. This book gives a really nice and simple explanation (in human language) covering all the important aspects of this subject. So this is my shor review of this useful book.
Like all of the "For Dummies" books, this one is also written in a very smart and handy style. Even the very first page of the book contains handy and useful information – tables with equations of geometry and trig functions. Furthermore, throughout any chapter of the book, useful tips, warnings (yeah maths can be dangerous), critical concepts and rules are clearly marked with little icons, which are very useful. Funny illustrationsand tiny comics at the start of the chapters are also a nice way to make your journey through the land of maths a little easier. So, in conclusion, the layout is very nice, interesting, handy and especially useful for students, who are revising the subject.
Now a few words about the author. The author, Mark Ryan, has been teaching maths since 1989. He runs the Math Center in Winnetka, Illinois. His natural talent in maths was clearly shown, when he scored 800 (perfect score) on the maths part of the SAT. However, his real talent is explaining maths in plain English. This talent is truly obvious throughout the book, where hard to grasp subjects are explained in plain English with a help of helpful graphs and illustrations.
The book is organized neatly into a couple of parts regarding the most important subjects of calculus – differentiation and integration. In addition, there are a couple of other important subjects like limits, finding areas of various geometrical figures and revision in algebra and trig functions. However, it would be very useful if the book had more problems, with explained and detail answers. Nevertheless, it's still a great book to revise and deeply cover the subject of calculus.
All in all, I had fun reading this book and revising calculus, which is a major part of maths in both late high school and college. Furthermore, the book helped me to understand this subject more deeply. Thus it's a great book with a couple of minor drawbacks. So if you're looking for a great book to revise or learn calculus, look no more.
Score: 8/10
Similar books: "Physics for Dummies", "Chemistry for Dummies", "Maths for Dummies". |
Academic Success Center
"Supporting Academic
Excellence"
MATH
0099--Intermediate Algebra(4 hours institutional credit)
MATH
0099 is the
second of two courses designed for students who are not prepared to
enter a college core curriculum mathematics course. Intermediate Algebra
consists of a study of exponents, polynomials, rational expressions,
equations, inequalities, radicals, graphing, and functions. |
Representing Polynomials
This lesson unit is intended to help educators assess how well students are able to translate between graphs and algebraic representations of polynomials |
Math resources
2
1
A little embarrassed to say this but during unit 1 with the simple conversions of converting the speed of light into nanosticks or whatever I was a bit confused by the simple algebra..Does anyone know any excellent preferably free math resources concerning math you'd find in computer science such as algebra,calculus,trig etc?
The Khan Academy - awesome resource for free videos and brushing up on math, all the way from 1+1 up to Calculus, Linear Algrebra, etc
However, everything that's been needed in this course so far, they didn't expect us to have any math skills. They've given numbers and said "just multiply these" or whatever, but there hasn't been any complicated math anywhere along the way.
You could also check out PurpleMath - They tend to provide a lot of good (and unique) explanations that use easier to grasp concepts. One of my favorites is the magic cubes they use to explain adding and subtracting negative numbers.
I often recommend this site to teachers and students I work with (though Khan Academy is my favorite!). There are others, but let me know if this one works for you.
As I was driving home I thought of something that might be confusing to you, and it's related to the Grace Hopper material too. When people quote CPU speeds they typically say something like my Intel Core i5 core runs at 2.7 [GHz]. If you wanted to compute how far light travels in one clock cycle of this CPU, then it might be helpful to restate the [GHz] units as 2,700,000,000 [clocks/s] or [cycles/s]. Then you might want to solve:
I can't recommend Khan Academy enough. I was able to review probability and statistics as well as linear algebra over there enough for the CS373 class. You can pretty much learn everything through Vector Calculus over there! |
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$166.40Normal 0 false false false MicrosoftInternetExplorer4 Intended for a 2-semester sequence of ElementaryandIntermediate Algebrawhere students get a solid foundation in algebra, including exposure to functions, which prepares them for success in College Algebra or their next math course. Operations on Real Numbers and Algebraic Expressions; Equations and Inequalities in One Variable; Introduction to Graphing and Equations of Lines; Systems of Linear Equations and Inequalities; Exponents and Polynomials; Factoring Polynomials; Rational Expressions and Equations; Graphs, Relations, and Functions; Radicals and Rational Exponents; Quadratic Equations and Functions; Exponential and Logarithmic Functions; Conics; Sequences, Series, and The Binomial Theorem; Review of Fractions, Decimals, and Percents; Division of Polynomials; Synthetic Division; The Library of Functions; Geometry; More on Systems of Equations For all readers interested in elementary and intermediate algebra. |
Grade 11 Mathematics
MBF3C1:Foundations for College Mathematics, Grade 11, College Preparation
This course enables students to broaden their understanding of mathematics as a problem-solving tool in the real world. Students will extend their understanding of quadratic relations, as well as of measurement and geometry; investigate situations involving exponential growth; solve problems involving compound interest; solve financial problems connected with vehicle ownership; and develop their ability to reason by collecting, analysing, and evaluating data involving one and two variables. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. Prerequisite: Foundations of Mathematics, Grade 10, Applied
MCR3U1:Functions, Grade 11, University Preparation
This course introduces the mathematical concept of the function by extending students' experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; and develop facility in simplifying polynomial and rational expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems. Prerequisite: Principles of Mathematics, Grade 10, Academic
MCF3M1:Functions and Applications, Grade 11, University/College Preparation
This course introduces basic features of the function by extending students' experiences with quadratic relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modelling real-world situations. Students will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to financial and trigonometric applications. Students will reason mathematically and communicate their thinking as they solve multi-step problems. Prerequisite: Principles of Mathematics, Grade 10, Academic, or Foundations of Mathematics, Grade 10, Applied |
a barbie world...
Algebra is a fundamental part of a modest education in today's world. It could easily be taught to younger students and leaving it out would be an enormous disservice. It amazes me that many people - even those who claim to be educated - are almost proud when they say they can't do math. This seems to be an American phenomena |
Office hours:
I maintain an open door policy for office hours. I come to the
office early each morning (usually 7:30 to 8:00) and if I am not
tied up in a meeting or talking to another student I am available
to you.
Prerequisites for EMAT 4680/6680: MATH 2210 or 2260. If you have
not studied differential and inferential calculus, discuss the
situation with me.
Objectives
To become familiar with and operational with
using technology tools in doing mathematics.
To solve mathematics problems using application
software.
To create mathematics demonstrations using
application software.
To construct new ideas of mathematics for
yourself using application software.
To engage in mathematical investigations
using software applications.
To engage in some independent investigations
of mathematics topics from the secondary school curriculum or
appropriate for that level.
To communicate mathematics ideas that arise
from applications software.
To communicate mathematics ideas using various
techology tools.
To facilitate mathematics investigations
and communication about mathematics investigations using general
tools such as word processing, paint and draw programs, spreadsheets,
and the Internet.
Course Description.
Look carefully at the objectives: the course is about doing mathematics. Technology is a goal only insofar as it supports doing mathematics. This is a course about mathematics and technolgy is a lens for extending what mathematics we can do and how we approach our mathematics.
This course will concentrate on using various software applications
to solve mathematics problems, to organize pedagogical demonstrations,
and to set up problem explorations. Students on campus will use
application software owned by the Department of Mathematics and Science Education
and will carry out the course using primarily MacIntosh computers.
All materials for the course are maintained by an Internet Web
page site and students will create and use web documents in the
course. Students off campus who have access to their own server
have an option put their web productions on their own server and
link to the course page.
The emphasis is on exploration of various mathematics contexts
to learn mathematics, to pose problems and problem extensions,
to solve problems, and to communicate mathematical demonstrations.
The following software will be used:
Graphing Calculator
3.5,
Graphing Calculator 4.0,
Graphing Calculator Lite
Graphing Calculator 3.5 is an older version of a computer program, Graphing
Calculator, that for many years was bundled with Macintosh computers. It is available on
all machines in our laboratory in Room 111/113. Version 3.5 will graph relations
(implicit functions) as well as functions, and can be used for parametric
equations, polar equations, 3D graphs, and more. See
Graphing Calculator 4.0 is the same version as Graphing Calculator except it is written to run only on computers with Intel Processors. Most newer machines have Intel processors.
Graphing Calculator Lite is a version of Graphing Calculator 4.0 that can be downloaded from the Apple APPstore for a cost of $14.99. It will install only on the machine to which you download but it is fully functional on Intel Processor MacIntosh computers and has all of the capabilities that we use in this course.
A Windows version of Graphing Calculator 4.0 is also available. GC 4.0 is available
for purchase from the web site for either Macintosh computers or Windows computers.
See also for information on purchasing this product as a student. (Scan your student
ID to get $40 price)
Geometer's Sketchpad.
GSP is a dynamic geometric construction package
with features that include construction tools, measurement tools,
transformation tools, and animation tools. Geometer's Sketchpad
is published by Key Curriculum
Press at < We are using version 4.07.
GSP is available for both Macintosh and Windows and files transfer
from one platform to the other. See the web site for information
on purchase of a student version for approximately $40. It is
also available at the UGa Bookstore.
A new version of GSP, 5.0, is now available. If you are purchasing GSP for your own use, you may want to consider GSP5. There is a setting within GSP5 that allows you to save files in the GSP4 format. For our purposes, either version of GSP can be used but GSP5 files should be saved in the GSP4 format for use in our web pages.
A very recent development is the Geometers Explorer. This is an APP that downloads to the iPad or iPhone for reading GSP sketches such as we may embed in web pages in this course.
Java GSP is a tool within Geometers Sketchpad for creating Applets to insert in web pages.
For a GSP with a Script Tool example click
here. When the script screen opens in GSP, open a new
sketch and select two points, as instructed, to "play"
the script.
Patterns formed by concentric pentagons rotating in opposite
ways are shown in Pentamotion.
Excel
Excel is a second generation spreadsheet program
that allows creation and manipulation of a data array and the
immediate graphing of selected subsets of the array. It is a
part of MicroSoft Office that is widely used on both Windows
and MacIntosh platforms.
Tool programs for word processing and drawing.
It is useful to be able to go from any application
program to present output within a discussion and to print that
discussion on the printed page. Microsoft Word is one of several
word processing programs available. Various "paint"
programs provide useful drawing capabilities.
Dreamweaver
Dreamweaver is a utility program for creating and editing web pages.
It is one of the most versitile web editors available and the choice of many
web developers. A verson is on our computers in Rm 111/113.
Firefox or Safari
Browser software for reading internet files. Internet Explorer has not been supported for the Macintosh platform since 2002 but there are still copies of it around. Some students have used Google Chrome as their prefered browser.
Project InterMath.
Project InterMath is a National Science Foundation supported (1999 - 2004) project to introduce
mathematics technology to middle school mathematics teachers
and help them improve their mathematics background. It implements
a similar instructional philosophy to this course but at the
middle school level. Visit this website to see a huge selection
of mathematics investigations in algebra, number, geometry, and
statistics. See also the Interactive
Mathematics Dictionary.
A note on EMAT 4690/6690.
EMAT 4690/6690 is a follow-up course to EMAT 4680/6680 offered
usually Spring semester and it is an extension of EMAT 4680/6680
in two senses. First it allows more advanced use of these software
packages as well as other applications. Second, it emphasizes
the development of units of material (e.g. sequences
of lessons) that might be used with secondary school students.
Course Assignments
There is no textbook.
The class will use wireless networked computers in Room
111/113. All assignments will be given and turned in via the
Web Site at <
or placed on the student's own web server and linked to this
Web Site. We will have access to and learn to use various network
tools.
Time on computers
You can not expect to accomplish what you should from this course
without time on the computers that is in addition to the time
we have in class. The usual expectation of 2 hours study outside
of class for every hour in class is probably a minimum. There
are several MacIntosh laboratories available in this building
and across campus.
A note on computers
We are scheduled to hold this class in Room 111/113 with a laboratory
of Macintosh iMac G5 computers. There are some additional
Macintosh computers in Room 105m (Begle Library), Room 228, Room 615, and
in the EMAT office area.
In general, the application programs we will use in this class
will run on any of the Macintosh computers except the oldest
machines. There are distinctions such as operating systems and
hard disk drives that have to be accounted for. If you have your
own Mac, or access to one, I will help you get set up to run
these programs on it (if it is possible).
Most Macs today run with operating system Mac OS 10.6.8 Snow Leopare. Mac OS 10.7 Lion has been released and is running on some of our computersl. In general, as
operating systems have improved over time, most people move to the newest
system. Our machines in Room 111/113 use System Mac OS 10.6.8. All of the machines in the Rm 111/113 Laboratory are Intel Processor.
Most of our software is also available for Windows machines.
The functionality of some other Windows software is similar to
what we use. Certainly the Windows environment could be used
for implementing this course. Students can work at home on a
Windows computer and transport to these Rm 111/113 machines via
removable media (e.g. CD disks or USB thumb drives) or the network.
It is also possible to set up FTP access to the server so that
your web productions can be implemented from a remote site. Expect
to experience a few hang-ups but it will work. Further, software
or hardware with similar functionality is available on many hand-held
devices. You would need Windows versions of GSP and Graphing
Calculator 4.0 on your computer to fully implement this course.
Grades and Requirements
Grading is a necessary part of what we do and it is my intention
to base grades on performance in meeting the requirements of
the course. This performance includes the following:
1. Attendance
2. Participation
on the computer working with others
class discussions
investigations
3. Write-ups
4. Final Projects
I think # 1 and # 2 are rather obvious. We
will have repeated opportunities to discuss #3 and # 4. But for
the terminally anxious. . .
A. There will be 13 Assignments. These are guides
or suggestions for explorations and participation arranged around
a variety of topics. There will be a "Write-up"
for each assignments except Assignment 0.
No. You do not need to "hand in" each assignment, other than the items you do for a Write-up. You
do not even have to do the assignment items that are not for your Write-up. It is hard to imagine how you could
benefit from the class if you avoid them. . . .
B. Each person will develop a personal Web Page for the
course.
C. There will be a set of "Write-up" projects.
These are the "homework" for the course. The Write-ups
will be prepared as an HTML documents (i.e. a Web Page document)
and linked to your personal web page. I will review any write-up draft if asked. All of them are due in the best form you can do them on the final day of the class. The set of write-ups is an electronic portfolio of your work for the course and should represent your "best work." That means you may want to revisit and revise drafts of your write-ups toward the end of the course.
D. The Final Projects are in lieu of a final examination,
will take considerably longer than an examination, and is due
on the day of our scheduled final examination.
The University of Georgia seeks to promote
and ensure academic honesty and personal integrity among students
and other members of the University Community. A policy on academic
honesty has been developed to serve these goals. All members
of the academic community are responsible for knowing the policy
and procedures on academic honesty. |
If you need to know it, it?s in this book. Cracking the AP Calculus AB and BC Exams, 2013 Edition has been optimized for e-reader viewing with cross-linked questions, answers, and explanations, and includes: ? 5 full-length practice tests with detailed explanations (3 for AB and 2 for BC) ? A comprehensive review of all topics, from derivatives... more...
The P-NP problem is the most important open problem in computer science, if not all of mathematics. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose... more...
If you need to know it, it's in this book. This eBook version of the 2013-2014 edition of Cracking the SAT Math 1 & 2 Subject Tests has been optimized for on-screen viewing with cross-linked questions, answers, and explanations. It includes: · 4 full-length practice tests with detailed explanations (2 each for Levels 1 and 2) · Comprehensive... more...
This book gives an overview of the wide range of spatial statistics available to analyse ecological data, and provides advice and guidance for graduate students and practising researchers who are either about to embark on spatial analysis in ecological studies or who have started but are unsure how to proceed. more...
The learn-by-doing way to master Trigonometry Why CliffsStudySolver Guides? Go with the name you know and trust Get the information you need--fast! Written by teachers and educational specialists Get the concise review materials and practice you need to learn Trigonometry, including: Explanations of All Elements and Principles * Angles and quadrants... more...
Finite Element Analysis is an analytical engineering tool developed in the 1960's by the Aerospace and nuclear power industries to find usable, approximate solutions to problems with many complex variables. It is an extension of derivative and integral calculus, and uses very large matrix arrays and mesh diagrams to calculate stress points, movement... more...
Business intelligence is a broad category of applications and technologies for gathering, providing access to, and analyzing data for the purpose of helping enterprise users make better business decisions. The term implies having a comprehensive knowledge of all factors that affect a business, such as customers, competitors, business partners, economic |
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Foundation Maths Units 1 & 2
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Mathematics is the study of function and pattern in number, logic, space and structure. It provides both a framework for thinking and a means of symbolic communication that is powerful, logical, concise and precise. It also provides a means by which people can understand and manage their environment. Essential mathematical activities include calculating and computing, abstracting, conjecturing, proving, applying, investigating, modelling, and problem posing and solving.
This study is designed to provide access to worthwhile and challenging mathematical learning in a way which takes into account the needs and aspirations of a wide range of students. It is also designed to promote students' awareness of the importance of mathematics in everyday life in a technological society, and confidence in making effective use of mathematical ideas, techniques and processes. |
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Detailed description The fun and easy way to learn pre-calculus
Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations.
With this guide's help you'll quickly and painlessly get a handle on all of the concepts -- not just the number crunching -- and understand how to perform all pre-calc tasks, from graphing to tackling proofs. You'll also get a new appreciation for how these concepts are used in the real world, and find out that getting a decent grade in pre-calc isn't as impossible as you thought. * Updated with fresh example equations and detailed explanations * Tracks to a typical pre-calculus class * Serves as an excellent supplement to classroom learning
If "the fun and easy way to learn pre-calc" seems like a contradiction, get ready for a wealth of surprises in Pre-Calculus For Dummies!
From the contents Introduction 1
Part I: Set It Up, Solve It, Graph It 7
Chapter 1: Pre-Pre-Calculus 9
Chapter 2: Playing with Real Numbers 21
Chapter 3: The Building Blocks of Pre-Calc: Functions 33
Chapter 4: Digging Out and Using Roots to Graph Polynomial Functions 67 |
and people considering construction careers, this Essential Skills workbook offers exercises that students can use to refresh their math skills. The curriculum-based exercises are built around typical construction workplace tasks.
It includes sections on measuring; dimension and area; elevation and grade; problems involving the Pythagorean Theorem; and weight-load estimation. Each section is independent of the others, which means that learners will not need information from one section to solve problems in another.
You can purchase a hard copy of this document on the Construction Sector Council's website at |
Excursions in Modern Mathematics, CourseSmart eTextbook, 7th Edition
Description
Exc CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
Part 1. The Mathematics of Social Choice
1. The Mathematics of Voting: The Paradox of Democracy
1.1 Preference Ballots and Preference Schedules
1.2 The Plurality Method
1.3 The Borda Count Method
1.4 The Plurality-with-Elimination Method (Instant Runoff Voting)
1.5 The Method of Piecewise Comparisons
1.6 Rankings
Profile: Kenneth J. Arrow
Key Concepts
Exercises
Projects and Papers
References and Further Readings
2. The Mathematics of Power: Weighted Voting
2.1 An Introduction to Weighted Voting
2.2 The Banzhaf Power Index
2.3 Applications of the Banzhaf Power Index
2.4 The Shapely-Shubik Power Index
2.5 Applications of the Shapely-Shubik Power Index
Profile: Lloyd S. Shapely
Key Concepts
Exercises
Projects and Papers
References and Further Readings
3. The Mathematics of Sharing: Fair-Division Games
3.1 Fair-Division Games
3.2 Two Players: The Divider-Chooser Method
3.3 The Lone-Divider Method
3.4 The Lone-Chooser Method
3.5 The Last-Diminisher Method
3.6 The Method of Sealed Bids
3.7 The Method of Markers
Profile: Hugo Steinhaus
Key Concepts
Exercises
Projects and Papers
References and Further Readings
4. The Mathematics of Apportionment: Making the Rounds
4.1 Apportionment Problems
4.2 Hamilton's Method and the Quota Rule
4.3 The Alabama and Other Paradoxes
4.4 Jefferson's Method
4.5 Adams's Method
4.6 Webster's Method
Historical Note: A Brief History of Apportionment in the United States
Key Concepts
Exercises
Projects and Papers
References and Further Readings
Mini-Excursion 1: Apportionment Today
Part 2. Management Science
5. The Mathematics of Getting Around: Euler Paths and Circuits
5.1 Euler Circuit Problems
5.2 What is a Graph?
5.3 Graph Concepts and Terminology
5.4 Graph Models
5.5 Euler's Theorems
5.6 Fleury's Algorithm
5.7 Eulerizing Graphs
Profile: Leonard Euler
Key Concepts
Exercises
Projects and Papers
References and Further Readings
6. The Mathematics of Touring: The Traveling Salesman Problem
6.1 Hamilton Circuits and Hamilton Paths
6.2 Complete Graphs
6.3 Traveling Salesman Problems
6.4 Simple Strategies for Solving TSPs
6.5 The Brute-Force and Nearest-Neighbor Algorithms
6.6 Approximate Algorithms
6.7 The Repetitive Nearest-Neighbor Algorithm
6.8 The Cheapest Link Algorithm
Profile: Sir William Rowan Hamilton
Key Concepts
Exercises
Projects and Papers
References and Further Readings
7. The Mathematics of Networks: The Cost of Being Connected
7.1 Trees
7.2 Spanning Trees
7.3 Kruskal's Algorithm
7.4 The Shortest Network Connecting Three Points
7.5 Shortest Networks for Four or More Points
Profile: Evangelista Torricelli
Key Concepts
Exercises
Projects and Papers
References and Further Readings
8. The Mathematics of Scheduling: Chasing the Critical Path
8.1 The Basic Elements of Scheduling
8.2 Directed Graphs (Digraphs)
8.3 Scheduling with Priority Lists
8.4 The Decreasing-Time Algorithm
8.5 Critical Paths
8.6 The Critical-Path Algorithm
8.7 Scheduling with Independent Tasks
Profile: Ronald L. Graham
Key Concepts
Exercises
Projects and Papers
References and Further Readings
Mini-Excursion 2: A Touch of Color
Part 3. Growth And Symmetry
9. The Mathematics of Spiral Growth: Fibonacci Numbers and the Golden Ratio
9.1 Fibonacci's Rabbits
9.2 Fibonacci Numbers
9.3 The Golden Ratio
9.4 Gnomons
9.5 Spiral Growth in Nature
Profile: Leonardo Fibonacci
Key Concepts
Exercises
Projects and Papers
References and Further Readings
10. The Mathematics of Money: Spending it, Saving It, and Growing It
10.1 Percentages
10.2 Simple Interest
10.3 Compound Interest
10.4 Geometric Sequences
10.5 Deferred Annuities: Planned Savings for the Future
Key Concepts
Exercises
Projects and Papers
References and Further Readings
11. The Mathematics of Symmetry: Beyond Reflection
11.1 Rigid Motions
11.2 Reflections
11.3 Rotations
11.4 Translations
11.5 Glide Reflections
11.6 Symmetry as a Rigid Motion
11.7 Patterns
Profile: Sir Roger Penrose
Key Concepts
Exercises
Projects and Papers
References and Further Readings
12. The Geometry of Fractal Shapes: Naturally Irregular
12.1 The Koch Snowflake
12.2 The Sierpinski Gasket
12.3 The Chaos Game
12.4 The Twisted Sierpinski Gasket
12.5 The Mandelbrot Set
Profile: Benoit Mandelbrot
Key Concepts
Exercises
Projects and Papers
References and Further Readings
Mini-Excursion 3: The Mathematics of Population Growth: There is Strength in Numbers |
TAKS (Texas Assessment of Knowledge and Skills) 2nd Edition
0738604445
9780738604442 and practice students need to excel. The book's review features all test objectives, including Numbers and Operations; Equations and Inequalities; Functions; Geometry and Spatial Sense; Measurement; Data Analysis and Probability; and Problem Solving. Includes 2 full-length practice tests, detailed explanations to all answers, a study guide, and test-taking strategies to boost confidence. DETAILS:-Fully aligned with the official state exam-2 full-length practice tests pinpoint weaknesses and measure progress- Drills help students organize, comprehend, and practice- Lessons enhance necessary mathematics skills-Confidence-building strategy and tips to boost test-day readiness REA Real review, Real practice, Real results «Show less... Show more»
Rent TAKS (Texas Assessment of Knowledge and Skills) 2nd Edition today, or search our site for other REA |
The Sequoia Math Department teaches a comprehensive series of courses aligned to state standards designed to increase students' understanding and competency in increasingly complex mathematics. Our goals are to improve the success rate of all of our students and support all students in completing a high level of mathematics. We encourage students to go beyond the minimum two year requirement and strive to get the majority of the students to complete required a-g courses. Our highest level of coursework include IB Standard Level and Higher Level mathematics with further courses in Multivariable Calculus, Differential Equations, and Linear Algebra. We also offer additional Support classes for students below grade level in grades 9 and 10 and have an Algebra Readiness course for those students far below grade level upon entering high school.
The teachers in the Mathematics Department work collaboratively in curricular teams to provide consistency and support. All teams meet on a regular basis to discuss pacing, strategies, and assessments. Algebra I and Support classes benefit from a dedicated coach to provide additional leadership on best practices, instructional strategies, multiple assessments and support for testing and data evaluation.
The department adopted the College Preparatory Math (CPM) curricula for Geometry, Algebra II, and Pre-Calculus. This program comes from the University of California at Davis and is a nationally recognized program named as one of five exemplary math programs nationwide by the US Department of Education. CPM is a time-tested program and has been adopted by thousands of schools throughout the U.S. It includes the same curriculum as the traditional math textbooks, but it is presented in a unique fashion. Each unit includes an overriding problem anchored in the real world. Teachers coach, lead students to discovery, pose questions, lecture, monitor learning, clarify, and summarize concepts. The integrated curriculum spirals concepts throughout the course. Mastery is not expected the first time that a student is exposed to a concept; rather, mastery is expected over time as the students come in contact with concepts over and over again. The approach focuses on core concepts throughout the year.
Algebra I curricula is coordinated throughout the district and utilizes the state-adopted Prentice Hall textbook as well as a variety of supplemental materials. Students in Algebra I are required to take a common benchmark assessment each quarter. Algebra II students use the newly district-adopted Glencoe Algebra II textbook. IB courses utilize approved instructional materials in addition to other texts.
There are sixteen fully-credentialed math teachers in our department. We all make ourselves available to tutor individually by posting office hours. Most teachers are available during brunch and lunch and frequently before or after school. In addition, we offer a math support program through our 7th period Learning Center where students can get help on all levels of math. Every Tuesday we offer evening tutorials; one section for our Pre-Calculus and Calculus students and another section for our other courses. Students may drop in during the three hours to get assistance on concepts and assignments from a department math teacher.
Mathematics Courses
Our curriculum currently includes:
Algebra Readiness (elective credit)
Algebra Support (elective credit)
Algebra I
Geometry
Accelerated Geometry/Algebra II Trigonometry
Algebra II, Algebra II/trigonometry
Pre-Calculus
IB Math Studies
IB Math SL (AP AB Calculus)
IB Math HL Year 2 (BC Calculus + IB calculus topics)
Multivariable Calculus
Ordinary Differential Equations
Linear Algebra
If you have any questions about our curriculum or department, please contact the department chair, Laura Larkin, at [email protected]
Algebra Readiness
This is a remedial course for freshmen students who are not ready to take Algebra I. Algebra Readiness includes the study of pre-algebraic skills and concepts described in the Mathematics Framework for California Public Schools. The nine topics are whole numbers, operations on whole numbers, rational number, operations on rational numbers, symbolic notation, equations and functions, the coordinate plane, graphing proportional relationships, and algebra. Students must enroll concurrently in Algebra Readiness support. The two courses function as a single class, meeting a total of 100 minutes daily. Elective credit earned for this course will not count toward the Math graduation requirement.
Algebra Support
This is a course to support freshmen and sophomore students who are concurrently enrolled in Algebra I. The course focuses on the prerequisites and skills needed for Algebra I and preparation for CAHSEE. Alternative methodologies such as hands on manipulatives are used in this class. Elective credit earned for this course will not count toward the Math graduation requirement.
A rigorous college-prep course required by all 4-year colleges. Geometrical concepts are discovered by and taught to students through guided lessons. Topics covered include inductive and deductive reasoning, angles, polygons, congruent triangles, constructions, circles, right triangles, similarity, solids, logic, and introductory trigonometry.
Prerequisite: Completion of Algebra I or department recommendation. Open to 9th-graders who have earned a B or better in a formal full-year algebra course in the 8th grade.</p>
Accelerated Geometry/Algebra II Trigonometry
This course is designed to accelerate advanced students to enable them to take calculus and higher level math (after calculus) in their junior and/or senior years. The material is covered at an honors level, and is accelerated so that two courses are taught in one year. The course is excellent preparation for the analysis and synthesis required in advanced math courses. The course covers geometry from a deductive perspective. Topics include proofs, lines, triangles, polygons, vectors, circles, and 3D geometry. The algebra 2 portion of the course covers functions, graphing, polynomials, transcendental functions, rational expressions and equations, radical expressions and equations, trigonometry, complex numbers, and sequences and series. In addition, some topics in probability and statistics will be included as time allows. Students successfully completing this accelerated course may directly enroll in precalculus the following year.
Prerequisites: Algebra 1 with an B or better, teacher recommendation highly encouraged, and a strong desire to learn mathematics.
Algebra II
A math elective, Algebra 2 is a college-prep class. Algebra 1 concepts are reviewed and are taken to a more sophisticated level. The new topics include the applications of linear, quadratic, exponential, and logarithmic equations, systems of equations, determinants, Cramer's Rule, exponential and logarithmic functions, and introductions to conic sections, probability, and statistics.
Prerequisite: Completion of Algebra 1 and Geometry with C- or better
Algebra II/Trigonometry
A math elective, Algebra II/Trigonometry is a college-prep class. Algebra I concepts are reviewed and taken to a more sophisticated level. New topics include the applications of linear, quadratic, exponential and logarithmic equations, determinants, systems of equations, exponential and logarithmic functions, conic sections, sequences, statistics, and probability. The course also includes trigonometry including sine, cosine, and tangent functions and the Laws of Sine and Cosine. Special emphasis is placed on mathematical modeling, graphical representations, and investigations.
Prerequisite: Completion of Algebra I and Geometry with a C or better.
IB Math Studies
This rigorous, one-year math offering is designed to provide a realistic mathematics course for students with varied backgrounds and abilities Students most likely to select this course are those whose main interests lie outside the field of mathematics. The course develops the skills needed to cope with the mathematical demands of a technological society with an emphasis on the application of math to real-life situations. Some of the topics covered include logic, statistics, introductory calculus, as well as a review of geometry and topics from Algebra II. Students enrolled in this course will take the IB Math Studies exam.
A challenging elective course, whose purpose is to prepare students to take AP Calculus and/or IB Math SL/HL the following year. The first semester covers a wide range of topics, including trigonometry, inverse functions, including circular trig, triangle trig, vector, logarithms, and real world modeling with sinusoidal functions. The emphasis is on integrating graphing into the study of all concepts. The second semester is function theory, rational functions, matrices, probability and statistics, Algebra for college Mathematics, polar functions, and series.
This course covers the Calculus curriculum as set forth by the College Board Advanced Placement program and the International Baccaluareate Programme. The course includes topics such as limits, definition of the derivative, applications of the derivative, the Mean Value Theorum, and integral calculus concepts. In addition, the course reviews vectors, matrices, trigonometry, and other IB topics. Students who successfully complete this course will be prepared to take the APAB Calculus exam and IB Standard Level Math exam. This course is also the first year of the two year higher level IB/AP math
Prerequisite: Successful completion of Pre-Calculus with a C- or better. (B highly recommended)
IB Higher Level (HL) Year 2B Higher Level Year 2, AP Calculus (BC)
This course follows the IB Higher Level Year 1/AP Calculus (AB) course, and is designed for gifted math students. The course covers all of the material from BC calculus that was not covered in AP Calculus (AB), and uses the textbook from UC Berkeley's core calculus for math majors sequence. Additionally, a wide range of other advanced topics are covered including calculus based probability theory, complex analysis, functional analysis, separable and first order nonhomogeneous differential equations, advanced induction proofs, multivariable vector geometry and introductory vector calculus. This course not only provides excellent preparation for the BC calculus AP exam, but it also gives students a big advantage in their college mathematics courses. Students who successfully complete the course will be prepared to take the AP/BC exam and the IB Higher Level exam. Students will also receive transferable college credit from Canada college.
Prerequisite: Completion of IB Math HL Year 1/Advanced Placement Calculus (AB or BC) with a C or better (B is highly recommended)
Multivariable Calculus
This course follows IB Higher Level Year 2/AP Calculus (BC), and covers the traditional university level multivariable calculus curriculum. The course covers parametric equations and polar, spherical, and cylindrical coordinates (calculus based), vectors and the geometry of space, vector functions, the calculus of functions of several variables, multiple integrals, vector calculus, including Green's Theorem and Stoke's Theorem, and second order differential equations and their applications. Additionally, the material from IB Higher Level Year 2 is reviewed to make sure that students are prepared for the IB exam. Students will receive transferable collge credit for this class from Canada college.
Prerequisite: Successful completion of IB HL Y2
Ordinary Differential Equations
This is a standard, top university level introductory course in ordinary differential equations. The textbook we have adopted is the book used for the same course at Stanford University. Topics include, but are not limited to: separable ordinary differential equations (ODEs), first order homogeneous and nonhomogenous linear ODEs, second order homogeneous and nonhomogeneous linear ODE's, higher order linear ODE's, systems of linear ODE's, series solutions, a wide variety of applications to ODE's, numerical methods, computing and ODE's, and nonlinear ODE's based on student interest. Students completing this course will also receive transferable college credit from Canada College.
Linear Algebra
This is a standard, top university level introductory course in linear algebra. The textbook we have adopted is also used by Stanford University and several UC campuses. Course curriculum includes, but is not limited to: matrix computations/matrix algebra, methods of solving systems of linear equations in linear algebra, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality and least squares, symmetric matrices and quadratic forms, a wide variety of applications to linear algebra, and computing in linear algebra and based on student interest. Students completing this course will also receive transferable college credit from Canada College. |
Survey Of Mathmatics With Applications - 9th edition
Summary: In a Liberal Arts Math course, a common question students ask is, ''Why do I have to know this?'' A Survey of Mathematics with Applicationscontinues to be a best-seller because it shows studentshowwe use mathematics in our daily lives andwhythis is important. The Ninth Edition further emphasizes this with the addition of new ''Why This Is Important'' sections throughout the text. Real-life and up-to-date examples motivate the topics throughout, and ...show morea wide range of exercises help students to develop their problem-solving and critical thinking skills.
Angel, Abbott, and Runde present the material in a way that is clear and accessible to non-math majors. The text includes a wide variety of math topics, with contents that are flexible for use in any one- or two-semester Liberal Arts Math course. ...show less
Hardcover Fine Unused copy in pristine condition. Looks brand new. Does not include CD or access code-I'm not sure if it originally came with one or not.
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032175966496.5398.39 |
Boonsboro, MDShipping:Standard, ExpeditedComments:Brand new. We distribute directly for the publisher. This book will help prepare the reader to c... [more] [[ Learning any area of abstract mathematics will involve writing formal proofs, but it is at least as important to learn to think intuitively about the subject and to express ideas clearly and cogently using ordinary English. The author aids intuition by keeping proofs short and as informal as possible, using concrete examples which illustrate all the features of the general case, and by giving heuristic arguments when a formal development would take too long. The text can serve as a possible model on how to write mathematics for an audience with limited experience in formalism and abstraction. Ash presents several expository innovations. He presents an entirely informal development of set theory that gives students the basic results that they will need in algebra. One of the chapters which presents the theory of linear operators, introduces the Jordan Canonical Form right at the beginning, with a proof of existence at the end of the chapter.[less] |
1. Solution of any second-order linear homogeneous equation or system with constant coefficient, and inhomogeneous equation with trig or exponential or constant or periodic rhs, or by variation of parameters.
2. Solution of first order linear ODE by integrating factor.
3. Solution of boundary value problems for y" + ly = 0
4. Knowledge of Euler's formulae for coefficients of Fourier Series (sine, cosine and full range), and ability to compute with these (up to piecewise linear functions)
5. Computation of grad, div, curl
6. Use of Stokes' and divergence theorem in simple explicit cases
7. Ability to derive the heat equation in 3d.
Assessment Information
Coursework (which may include a Project): 15%; Degree Examination: 85%. |
How to Solve It: A New Aspect of Mathematical MethodHow to Solve It: A New Aspect of Mathematical Method Book Description
George Polya was a Hungarian mathematician. He wrote this, perhaps the most famous book of mathematics ever written, second only to Euclid's "Elements." "Solving problems," The method of solving problems he provides and explains in his books was developed as a way to teach mathematics to students.
About the Author :
George Polya has contributed to How to Solve It: A New Aspect of Mathematical Method as an author.
Biography of George Polya Born in Budapest, December 13, 1887, George Polya initially studied law, then languages and literature in Budapest. He came to mathematics in order to understand philosophy, but the subject of his doctorate in 1912 was in probability theory and he promptly abandoned philosophy. After a year in Gottingen and a short stay in Paris, he received an appointment at the ETH in Zurich. His research was multi-faceted, ranging from series, probability, number theory and combinatorics to astronomy and voting systems. Some of his deepest work was on entire functions. He al
Popular Searches
The book How to Solve It: A New Aspect of Mathematical Method by George Polya, Sam Sloan
(author) is published or distributed by Ishi Press [4871878309, 9784871878302].
This particular edition was published on or around 2009-6-1 date.
How to Solve It: A New Aspect of Mathematical Method has Paperback binding and this format has 280 number of pages of content for use.
This book by George Polya, Sam Sloan |
Project Based Learning Pathways - David Graser
A blog about real life projects suitable for college math courses such as algebra, finite math, and business calculus. Most of these applied math projects include handouts, videos, and other resources for students, as well as a project letter. Graser,
...more>>
Public Domain Materials - Mike Jones
A collection of public domain instructional and expository materials from a US-born math teacher who teaches in China. Microsoft Word and PDF downloads include a monthly circular consisting of short problems, "The Bow-and-Arrow Problem," and "Twinkle
...more>>
A Recursive Process - Dan Anderson
Anderson's blog, which dates back to June of 2010, has included posts such as "Robocode & Math," "Standards Based Grading," "Cake:Frosting (A look into a proper ratio of real math:cool tech)," "Paper Towels WCYDWT (What Can You Do With This?)," "TwoShelley Walsh
Syllabi and notes for math courses from arithmetic review to beginning calculus. Download MathHelp a tutorial program with problem sets for Mac or PC, or learn how to use MathHelp to create your own tutorials. Brief Mathematics Articles present concepts
...more>>
Sites with Problems Administered by Others - Math Forum
Problems of the week or month: a page of annotated links to weekly/monthly problem challenges and archives hosted at the Math Forum but administered by others, and to problems and archives elsewhere on the Web, color-coded for the level(s) of the problemsStella's Stunners - Rudd Crawford
More than 600 non-routine mathematics problems named in honor of the Dutch baroness Ecaterina Elizabeth van Heemsvloet tot Schattenberg. Each collection in the Stella Library contains five subsets, one for each course of Pre-Algebra, Algebra I, Geometry,
...more>>
studymaths.co.uk - Jonathan Hall
Free help on your maths questions. See also the bank of auto-scoring GCSE maths questions, games, and resources such as revision notes, interactive formulae, and glossary of terms.
...more>>
Success for All
Curriculum driven by co-operative learning that focuses on individual pupil accountability, common goals, and recognition of team success, all with the aim of getting learners "to engage in discussing and explaining their ideas, challenging and teachingaching Mathematics - Daniel Pearcy
Pearcy has used this blog, subtitled "Questions, Ideas and Reflections on the Teaching of Mathematics," as a "journal of ideas, lessons, resources and reflections." Posts, which date back to October, 2011, have included "New Sunflower Applet: Fibonacci
...more>>
ThinkQuest
An international contest designed to encourage students from different schools and different backgrounds to work together in teams toward creating valuable educational tools on the Internet while enhancing their ability to communicate and cooperate in
...more>>
Ti 84 Plus Calculator
Instructional videos include using the parametric function to construct a pentagram, hypothesis testing, sketching polynomial functions, finding critical points of a function, and using the TVM (Time Value of Money) Solver method. The site also offers
...more>>
TI-89 Calculus Calculator Programs
TI-89 calculator programs for sale. Enter your variables and see answers worked out step by step: a and b vectors, acceleration, area of parallelogram, component of a direction u, cos(a and b), cross product, curl, derivative, divergence of vector field,
...more>> |
The global spatial data model (GSDM) preserves the integrity of three-dimensional spatial data. Combining horizontal and vertical data into a single, three-dimensional database, this text provides a logical development of theoretical concepts and practical tools that can be used to handle spatial data efficiently. more...
This book is designed for grades K–2 instruction and provides step-by-step mathematics lessons that incorporate the use of the TI-10 calculator throughout the learning process. The 30 lessons included present mathematics in a real-world context and cover each of the five strands: number and operations, geometry, algebra, measurement, and data... more...
This book is designed for grades 3–5 instruction and provides step-by-step mathematics lessons that incorporate the use of the TI-15 calculator throughout the learning process. The 30 lessons included present mathematics in a real-world context and cover each of the five strands: number and operations, geometry, algebra, measurement, and data... more...
Maths is enjoying a resurgence in popularity. So how can you avoid being the only dinner guest who has no idea who Fermat was or what he proved, and what Fibonacci?s sequence or Pascal?s triangle are? The more you know about Maths, the less of a science it becomes. 30 Second Maths takes the top 50 most engaging mathematical theories, and explains... more... Alexandrov's treatise begins with an outline of the basic concepts, definitions, and results... more... |
NAS Software Inc. carries a wide variety
of math programs geared towards students of all ages
and levels. Our programs are very user friendly and
aim to answer the students and teachers specific needs.
We also carry programs suitable for independent learning.
The
following is a short description of some of our leading
programs:
Please click on the program of your choice: (or scroll
down)
(If
you can't find the program you are looking for please
E-mail us and we will find it for you.)
Provides links from the applied assessment tasks to
the teaching and practice activities.
MATH-KAL
This educational program is unique in that it is extremely user friendly
and requires no special knowledge of computers. Math-
Kal is geared to students from junior high up to the
first years of university. It can be used by students
of different capabilities as it responds to each individual's
skills and level of knowledge. The program gives students
the option to review specific ideas until they feel
comfortable with them. This windows program can run
on a network and it is conducive to independent learning
and teacher instruction.
FEATURES
Interactive individual tutoring
Coaching through every step of solving a problem
Lessons with unlimited examples
Context-sensitive Help system with unlimited number of examples
Individualized progress: you stay on each lesson as long as you need
to learn it
Interactive utilities for teachers.
The courseware recognizes different ways of solving a problem
Clear explonations, in both the Lessons and the Help modes
LANGUAGES
MATH-KAL
is available in the following languages: English,
Spanish, Portuguese, French, German, Swedish, Turkish
and Hebrew. |
Book
Introduction to Book
The Language of Mathematics
The purpose of any language, like English or Zulu, is to make it possible for people to communicate. All languages have an alphabet, which is a group of letters that are used to make up words. There are also rules of grammar which explain how words are supposed to be used to build up sentences. This is needed because when a sentence is written, the person reading the sentence understands exactly what the writer is trying to explain. Punctuation marks (like a full stop or a comma) are used to further clarify what is written.
Mathematics is a language, specifically it is the language of Science. Like any language, mathematics has letters (known as numbers) that are used to make up words (known as expressions), and sentences (known as equations). The punctuation marks of mathematics are the different signs and symbols that are used, for example, the plus sign (+), the minus sign (-), the multiplication sign (××), the equals sign (=) and so on. There are also rules that explain how the numbers should be used together with the signs to make up equations that express some meaning |
Description
Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.
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VHS Course Catalog
AP® Calculus BC Section PA
Prerequisites Four courses of secondary mathematics designed for the college bound student: courses covering algebra, geometry, trigonometry, analytic geometry, elementary functions and their notations. Students should have graphing calculators, access to a scanner and access to MS PowerPoint or a PowerPoint Viewer.
Description The VHS AP Calculus BC course is a full academic-year course. It is a challenging course designed for high school students who have completed four years of secondary mathematics courses such as Algebra, Geometry, Advanced Algebra, Trigonometry/Pre-Calculus (which includes some Analytic Geometry and elementary functions). Work is comparable to that required in most college and university Calculus courses. Students should plan on taking the AP Calculus BC exam offered in May. Successful completion of the AP Exam may provide students with the opportunity to receive college credit.
Emphasis is on conceptual understanding. However, facility with manipulation and computational skills are important outcomes. Students should expect the course as well as the AP Exam to truly push the depth of their understanding of mathematics generally and calculus specifically. Areas of emphasis From the College Board's online resourse for AP Calculus at -Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations. -Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems. -Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems. -Students should understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
Students will be expected to complete daily/weekly assignments and regular quizzes and exams. Each student will need a graphing calculator such as the TI-83 or equivalent and knowledge on how to work with their calculator. As in most online courses the student will be required to do a significant amount of independent learning. Individual responsibility, good work habits, discipline and organization will be important attributes for success.
Students enrolled in Advanced Placement VHS courses are expected |
For the first
part of the course we will be mainly in the Hersh book and we will also
supplement that with readings from the web and other sources.We want to take an almost historical,
cultural overview of some of the highlights of what occurred in "mathematics"
with some tangential explorations along the way.After this survey, we will discuss again,
what is mathematics.
Next, we move
on to exploring the particular mathematical problem that was birthed soon after
the French Revolution and is unsolved (and worth a whole lot of money) still
today.We examine some of the
mathematics behind this problem in an attempt to understand the significance of
the problem.As we are doing this we
will also participate in more tangential explorations of mathematical topics
that are either related by content or by chronology.In this portion of the course we will be
using the Derbyshire book as well as supplemental readings. |
Description
Algebra 2 is made up of five instructional components: Introduction of the New Increment, Examples with Complete Solutions, Practice of the Increment, Daily Problem Sets and Cumulative Tests. Algebra 2 not only treats topics that are traditionally covered in second-year algebra, but also covers a considerable amount of geometry. Time is spent developing geometric concepts and writing proof outlines. Students completing Algebra 2 Will have studied the equivalent of one semester of informal geometry. Applications to other subjects such as physics and chemistry, as well as real-world problems, are covered, including gas laws, force vectors, chemical mixtures, and percent markups. Set theory, probability and statistics, and other topics are also included. |
Saxon's Math Intermediate 3 is a perfect transition into Saxon Math 5/4! Incremental lessons provide daily practice and assessment; mathematical concepts are taught through informative lessons, diagrams, interactive activities, and investigations that build critical thinking as well as real-world problem solving skills. Saxon Intermediate 3 includes 11 sections, 110 lessons and 11 "investigation" activities. Concepts cover patterns; addition; subtraction; money; fractions; measurement; multiplication; arrays; angles; congruent shapes; symmetry; geometric solids; division; capacity; estimation; sorting; and more. Textbook lessons are divided into three sections. The first section is "power-up practice," which covers basic fact and mental math exercises which improve speed, accuracy, the ability to do mental math, and the ability to solve complicated problems. The second part of the lesson is the "New Concept," which introduces a new math concept through examples, and provides a chance for students to solve similar problems. Thirdly, the "Written Practice" section reviews previously taught concepts. One "Investigation" per session is included; "Investigations" are variations of the daily lesson and often involve activities that take up an entire class. The included Power Up Workbook provides consumable pages for students to complete the Power Up exercises from the textbook, including the Facts Practice, Jump Start, Mental Math, and Problem Solving sections. The textbook may refer students to problems within this Power Up workbook, or the text may contain necessary problems and instructions (such as the mental math problems), which students will need to complete the exercises in this workbook. The Solutions Manual arranges answers by section and lesson, and includes complete step-by-step solutions to the Lesson Practice, Written Practice, and Early Finishers questions, as well as the questions and practice items in the Investigations. It does not contain the answers to the Power-Up Workbook. The Homeschool Testing Book features reproducible cumulative tests which are available after every five lessons after lesson 10. Tests are designed to let students learn and practice concepts before being tested, helping them build confidence. Tests, a testing schedule, test answer forms, test analysis form, and test solutions are included. The three optional Test Solution Answer Forms provide the appropriate workspace for students to "show their work." The answer key shows the final solution only, not the steps taken to arrive at the answer. This Kit Includes: Saxon Intermediate 3 Textbook, 623 indexed pages, hardcover. Pages are two-tone and don't include any distracting illustrations. Power-Up Workbook; 110 non-reproducible, newsprint-like pages, three-hole-punched, perforated pages. Softcover. Testing Book, 63 reproducible, perforated, newsprint-like pages, softcover. Solutions Manual, 123 pages, softcover. |
2000 Solved Problems in Discrete Mathematics
9780070380318
ISBN:
0070380317
Pub Date: 1991 Publisher: McGraw-Hill
Summary: Master discrete mathematics with Schaum'sNthe high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! I...f you don't have a lot of time but want to excel in class, use this book to: Brush up before tests;Study quickly and more effectively; Learn the best strategies for solving tough problems in step-by-step detail. Review what you've learned in class by solving thousands of relevant problems that test your skill. Compatible with any classroom text, SchaumOs Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to rememberNfast! And SchaumOs are so complete, theyOre perfect for preparing for graduate or professional exams. Inside you will find: 2000 solved problems with complete solutionsNthe largest selection of solved problems yet published in discrete mathematics; A superb index to help you quickly locate the types of problems you want to solve; Problems like those you'll find on your exams; Techniques for choosing the correct approach to problems. If you want top grades and thorough understanding of discrete mathematics, this powerful study tool is the best tutor you can have!Chapters include: Set Theory; Relations; Functions; Vectors and Matrices; Graph Theory; Planar Graphs and Trees; Directed Graphs and Binary Trees; Combinatorial Analysis; Algebraic Systems; Languages, Grammars, Automata; Ordered Sets and Lattices; Propositional Calculus; Boolean Algebra; Logic Gates |
Note: ClickScholar Nancy Hogan discovered this website and helped write the review. Her husband, Ron, is a prolific singer/songwriter, and you can read more about him at the end of this review.
"Need help with Algebra? You've found the right place!" That's the claim of this website that offers an amazing algebra resource in the form of free lessons and links to an array of helpful resources for math students.
When you get to the site read the introductory paragraphs that explain what the site has to offer including:
*Lessons - You'll find everything from beginning algebra to word problems to advance algebra topics like "Solving Logarithmic Equations" and "Rational Expressions." The Appendix in this section includes recommendations for calculators and a wonderful article entitled, "Why Do I Have to Take Algebra?"
*Site Reviews - PupleMath has reviewed numerous math websites - so you don't have to, and recommends their faves for:
1) Free Online Tutoring & Lessons 2) Quizzes and Worksheets 3) Other Useful Sites and Services (Note: This explores careers in math, earliest use of math and it's symbols, handouts from University of Texas' Learning Center, and so much more!)
Many of the sites they recommend have been featured on ClickSchooling in the past.
*Homework Guidelines - While homeschoolers may not need the advice in the article "How to Suck Up to Your Teacher" - it's a great read and provides homework guidelines that are wonderful for those who may supplement their learning in classroom environments or enroll at community college, etc.
*Study Skills Self-Survey - Use this terrific feature to determine if you have the study habits needed to learn algebra. |
Book details
Book description
The goal of this book is to teach undergraduate students how to use
Scientific Notebook
(SNB
) to solve physics problems. SNB
software combines word processing and mathematics in standard notation
with the power of symbolic computation. As its name implies, SNB
can be used as a notebook in which students set up a math or science
problem, write and solve equations, and analyze and discuss their
results.
Written by a physics teacher with over 20 years experience,
this text includes topics that have educational value, fit within the
typical physics curriculum, and show the benefits of using SNB. |
Summary: This manual is organized to follow the sequence of topics in the text, and provides an easy-to-follow, step-by-step guide to help students fully understand and get the most out of their graphing calculator. The popular TI-83/84 Plus and the TI-84 Plus with the new operating system, featuring MathPrint'', are covered1575 +$3.99 s/h
VeryGood
Bookbyte-OR Salem, OR
Manual. Has minor wear and/or markings. SKU:9780321744968-3-0
$22 |
MA Mathematics Domains of Study
Areas of Study Within the
M.A. in Mathematics Education Degree
The WGU Master of Arts in Mathematics Education (K-6, 5-9 or 5-12) program content is based on research on effective instruction as well as national and state standards. It provides the knowledge and skills that enable teachers to teach effectively in diverse classrooms. The M.A. in Mathematics Education program content and training processes are consistent with the accountability intent of the No Child Left Behind Act of 2001. The degree program is focused on the preparation of highly qualified teachers. As described in the federal legislation, a highly qualified teacher is one who not only possesses full state certification, but also has solid content knowledge of the subject(s) he or she teaches.
The following section includes the larger domains of knowledge, which are then followed by the subject-specific subdomains of knowledge.
Elementary Mathematics Education Domain (for the K-6 program)
This domain focuses on the following mathematics content, as well as central issues related to the teaching of these topics in grades K–6:
Mathematics (K-6) Content
This subdomain focuses on the following mathematics content with integrated mathematics pedagogy: Introduction to Number Sense; Patterns and Functions; Integers and Order of Operations; Fractions, Decimals, and Percentages; Coordinate Pairs and Graphing; Ratios and Proportional Reasoning; Equations and Inequalities; Geometry and Measurement; and Statistics, Data Analysis, and Probability.
Finite Mathematics
This subdomain focuses on the real number system, symbolic logic, number theory, set theory, graph theory and their applications.
Middle School Mathematics Content Domain (for the 5-9 program)
This domain focuses on the following areas of mathematics: Finite Mathematics, College Algebra, Pre-calculus, Probability and Statistics I, College Geometry and Calculus I.
Finite Mathematics
This sub-domain focuses on the real number system, symbolic logic, number theory, set theory, graph theory and their applications.
College Algebra
This sub-domain focuses on equations, inequalities, polynomials, conic sections, and functional analysis including logarithmic, exponential, and inverse functions in problem solvingComprehensive Exam
The CYV1 is a comprehensive exam assessing the student's knowledge of the subdomains listed above.
High School Mathematics Content Domain (for the 5-12 program)
This domain focuses on the following areas of mathematics: This domain focuses on the following areas of mathematics: Pre-Calculus, Probability and Statistics, College Geometry, Calculus and Analysis, Linear Algebra, Abstract Algebra, and Mathematical Modeling and ConnectionsCalculus II
This sub-domain focuses on integration techniques and applications, the solution of differential equations, and the analysis of sequences.
Research Fundamentals Domain (for the K-6 and 5-9 programs)Capstone Project (for the K-6 program)
The Capstone Project is the culmination of the student's WGU degree program. It requires the demonstration of competencies through a deliverable of significant scope that includes both a written capstone project and an oral defense.
Students will be able to choose from two areas of emphasis, depending on personal and professional interests. These two areas include instructional design and research. If carefully planned in advance, the individual domain projects may serve as components of the capstone. For capstones with the instructional design emphasis, students will design, manage, and develop an instructional product for which there is an identified need. The product can be delivered via the medium of choice (e.g., print-based, computer-based, video-based, web-based, or a combination of these), but you must provide a rationale for the medium selected. The instructional product you develop for your capstone should be an exportable form of instruction designed to bring your target audience to a mastery of predetermined knowledge and skills.
For capstones with the research emphasis, students will design and conduct a data-based investigation of a conclusion-oriented question (decision-oriented investigations are most generally considered to be evaluation projects). The project report should be of publishable quality and may be submitted to an appropriate professional journal at the completion of the project. At the minimum you should plan to share your results with your school or organization questions covering the mathematics content domain. The purpose of the exam is a checkpoint to ensure that you have acquired the critically required skills and knowledge specified in the program competencies.
Teacher Work Sample Written Project (for the 5-9 and 5-12 programs)
The Teacher Work Sample Written Project is the culmination of the student's WGU degree program. It requires the demonstration of competencies through a deliverable of significant scope that includes both a written project and an oral defense.
The Teacher Work Sample is a written project containing a comprehensive, original, research based curriculum unit designed to meet an identified educational need. It provides direct evidence of the candidate's ability to design and implement a multi-week, standards-based unit of instruction, assess student learning, and then reflect on the learning process. The WGU Teacher Work Sample requires students to plan and teach a multi-week standards-based instructional unit consisting of seven components: 1) Contextual factors, 2) learning goals, 3) assessment, 4) design for instruction, 5) instructional decision making, 6) analysis of student learning, and 7) self-evaluation and reflection a presentation (typically PowerPoint) and defense of the Teacher Work Sample (TWS). Candidates will be asked to reflect upon the TWS, note its strengths and weaknesses, discuss its impact on student learning, and suggest future improvements. The purpose of the exam is a checkpoint to ensure that you have acquired the critically required skills and knowledge specified in the program competencies.
NBC News Reports on WGU
"The dreams of 19 governors have become [WGU Grad Angie Gonzalez's] dream fulfilled." |
Fundamentals of Piecewise Polynomial Interpolation, used in graphics, that takes you from linear interpolation to all the common curve drawing methods used in graphics. It uses only Algebra and avoids more complex mathematic notations as much as possible. It also includes a reference with all the common methods used for graphics curves. |
Introduction to Mathematical Modeling
1. COURSE DESCRIPTION.Mathematical modeling uses graphical, numerical,
symbolic, and verbal
techniques to describe and explore real-world data and phenomena. Emphasis is on
the use of elementary
functions to investigate and analyze applied problems and questions , on the use
of appropriate supporting
technology, and on the effective communication of quantitative concepts and
results. THIS COURSE IS
NOT AN APPROPRIATE PREREQUISITE FOR PRECALCULUS OR CALCULUS. Students who must
take precalculus must understand the implications of taking MATH 1101 (See the
instructor immediately if
you have any questions).
2. PREREQUISITE. Knowledge of high school algebra II , or equivalent. This
includes algebraic
expressions, first degree equations and inequalities, exponents, radicals,
solving and graphing linear
equations, factoring quadratic expressions, and other topics.
3. COURSE OBJECTIVES.
Algebra. Students will demonstrate the ability to:
a. Graph points.
b. Graph linear, piecewise linear, exponential, logarithmic, and quadratic
equations and
functions. and identify horizontal asymptotes.
c. Determine the equation of a line given two points or one point and the slope.
d. Determine the absolute value of a quantity.
e. Solve and estimate solutions to linear, quadratic, exponential, and
logarithmic equations,
including use of the properties of exponents and common and natural logarithms.
f. Solve linear systems of two equations by substitution and elimination,
including systems
that have a unique solution, no solution, or many solutions.
g. Simplify expressions using the laws of exponents and logarithms.
h. Calculate average rate of change of any function.
i. Perform arithmetic calculations to answer questions regarding two-variable
data
presented in tabular, graphical, or equation form.
j. Express and compare very large and very small numbers using scientific
notation and
orders of magnitude.
k. Factor quadratic expressions .
l. Complete the square of quadratic expressions.
m. Express the square root of negative numbers in terms of the imaginary unit, i.
n. Given conversion factors, convert units of measure.
o. Use the quadratic formula to solve quadratic equations
Functions. Students will demonstrate:
a. The understanding of the definitions of function, domain, range, independent
and
dependent variables, and input and output.
b. The ability to determine if tables, graphs, and equations represent
functions.
c. The ability to determine the domain and range of functions as mathematical
abstractions
or in a physical context.
d. The ability to determine from the graph of a function the values of the
independent
variable for which the function increases, decreases, or remains constant.
Linear and piecewise linear functions. Students will demonstrate the
ability to:
a. Determine when two real-world variables are related by a linear or piecewise
linear
function.
b. Calculate, and interpret average rate of change as slope.
c. Model the behavior of two real-world variables that are directly proportional
or are
related by a linear or piecewise linear function using tables, graphs,
equations.
d. Evaluate linear and piecewise linear functions.
e. Use a linear function to approximate the value of a non-linear function.
f. Interpret the intersection of the graphs of linear functions as equilibrium
points.
Exponential Functions. Students will demonstrate the ability to:
a. Determine when two real-world variables are related by an exponential
function.
b. Model the behavior of two real-world variables that are related by an
exponential
function using tables, graphs, equations, or combinations thereof including such
applications as population growth and decay, radioactive decay, simple and
compound
interest, inflation, the Malthusian dilemma, musical pitch, and the Rule of 70.
c. Change the base of an exponential function to determine rate of growth/decay,
growth/decay factor, and effective and nominal interest rate .
d. Express continuous growth/decay in terms of the number e.
e. Evaluate exponential functions.
f. Determine the exponential equation model from the table or graphical model.
g. Compare linear to exponential growth.
Logarithmic Functions. Students will demonstrate:
a. The ability to determine when two real-world variables are related by a
logarithmic
function.
b. The ability to model the behavior of two real-world variables that are
related by a
logarithmic function using tables, graphs, equations, or combinations thereof
including
such applications as pH and the decibel system.
c. The understanding of the natural logarithm.
d. The ability to graph logarithmic functions.
Quadratic Functions. Students will demonstrate the ability to:
a. Estimate horizontal intercepts of quadratic functions from their graphs.
b. Determine the horizontal intercepts of quadratic functions in factored form.
c. Determine the vertex, axis of symmetry, and horizontal and vertical
intercepts of
quadratic functions in either the a-b-c or a-h-k forms.
d. Convert quadratic functions from the a-b-c form to the a-h-k form and vice
versa.
e. Determine when two real-world variables are related by a quadratic function
by
calculating the average rate of change of the average rates of change.
f. Model the behavior of two real-world variables that are related by a
quadratic function
using tables, graphs, equations, or combinations thereof including such
applications as
maximum area for fixed perimeter, minimum perimeter for fixed area, free fall ,
maximum profit, and break-even analysis.
4. COURSE COVERAGE. We will cover the following sections from the text:
IMPORTANT NOTE: Georgia State University and its faculty are not responsible for
outcomes due to
individual technical issues, nor scheduled WileyPlus downtimes. It is expected
that the students will be
responsible for completing their work in a timely fashion as to alleviate any
pressures these scheduled
downtimes occur. All students will be notified of these downtimes by WileyPlus
through the
announcements page of the course.
7. Makeup Policy: Your final exam grade will replace your missed exam
grade. No make-up exams will
be given unless in some extreme situations. Absence from the final exam will
result in a grade of F for the
course unless arrangements are made PRIOR (at least one week before the final
exam) to its administration.
8. CALCULATOR Policy . You are recommended to have a scientific calculator
or agraphing calculator .
If you are not strong in mathematics, I strongly recommend you obtain a graphing
calculator. You are not
allowed to share calculator with any other party in your class during any in
class quiz or exam, unless
permitted by your instructor.
5. A private tutor list is available at Math Assistance Complex and Math
Department
Arithmetic and Problem Solving
Brief description: A deep examination of topics in
mathematics that are
relevant for elementary school teaching. Problem solving . Number systems:
whole numbers, integers, rational numbers (fractions) and real numbers (dec-
imals) and the relationships between these systems. Understanding multipli-
cation and division, including why standard computational algorithms work.
Properties of arithmetic. Applications of elementary mathematics.
Course Objectives: To strengthen and deepen knowledge and understand-
ing of arithmetic, how it is used to solve a wide variety of problems, and
how it leads to algebra. In particular, to strengthen the understanding of
and the ability to explain why various procedures from arithmetic work.
To strengthen the ability to communicate clearly about mathematics, both
orally and in writing. To promote the exploration and explanation of mathe-
matical phenomena. To show that many problems can be solved in a variety
of ways.
Topical Outline:
Problem solving: Polya's principles. Writing explanations.
Numbers: The natural numbers, the whole numbers, the rational numbers
(fractions), and the real numbers (decimals). The decimal system and place
value. Representing decimals with bundled objects. Representing decimals
on a number line. Comparing sizes of decimals. Finding decimals in between
decimals. Rounding decimals. The meaning of fractions. The importance
of the whole associated with a fraction. Improper fractions . Equivalent
fractions. Simplest form of a fraction . Fractions as numbers on number
lines. Comparing sizes of fractions: by giving them common denominators,
by converting to decimals , and by cross-multiplying. Using other reasoning to
compare sizes of fractions. Solving fraction problems with the aid of pictures.
Percent. Benchmark percentages and their common fraction equivalents.
Solving percentage problems with the aid of pictures. Solving percentage
problems numerically.
Addition and subtraction : Interpretations of addition and
subtraction. The
relationship between addition and subtraction. Explaining why the standard
algorithms for adding and subtracting whole numbers and decimals work.
Using regrouping in situations other than base 10, for example in calculating
elapsed time by replacing 1 hour with 60 minutes. Adding and subtracting
fractions. Explaining why we add and subtract fractions the way we do.
The importance of the whole when adding and subtracting fractions, espe-
cially in story problems. Recognizing and writing story problems for fraction
addition and subtraction. Recognizing story problems that are not solved
by fraction addition or subtraction. Mixed numbers. Understanding when
percentages should and should not be added. Calculating percent increase
and decrease with the aid of pictures. Calculating percent increase and de-
crease numerically. Percent of versus percent increase or decrease. The
commutative and associative properties of addition and their use in mental
arithmetic. Using properties of addition to aid the learning of basic addition
facts. Other (mental) methods for adding and subtracting : rounding and
compensating, subtracting by adding on. Writing equations that correspond
to a mental method of calculation (to demonstrate the connection between
mental arithmetic and algebra).
Multiplication: The meaning of multiplication. Ways of showing multiplica-
tive structure: with groups, with arrays, and with tree diagrams. Using the
meaning of multiplication to explain why various problems can be solved by
multiplying. Explaining why multiplication by 10 is easy in the decimal sys-
tem. Why the commutative and associative properties of multiplication and
the distributive properties make sense and how to illustrate them with arrays,
areas of rectangles, and volumes of boxes. Using properties of arithmetic in
solving arithmetic problems mentally. Writing equations that correspond
to a mental method of calculation (to demonstrate the connection between
mental arithmetic and algebra). Using properties of arithmetic to aid in the
learning of basic multiplication facts. The distributive property and FOIL.
Using multiplication to estimate how many. The partial products multiplica-
tion algorithm. Using pictures and the distributive property to explain why
the standard and partial products procedures for multiplying whole numbers
are valid. Explaining why non-standard strategies for multiplying can be
correct or incorrect, such as explaining why 23 × 23 ≠ 20 × 20 + 3 × 3
and explaining why 32 × 28 = 30 × 30 − 2 × 2. The meaning of multi-
plication for fractions. Recognizing and writing story problems for fraction
multiplication. Recognizing story problems that are not problems for frac-
tion multiplication. Explaining why the procedure for multiplying fractions
works. Powers. (Optional: scientific notation.) Multiplication of decimals:
explaining why the procedure for the placement of the decimal point is valid.
Multiplication of negative numbers. Understanding that multiplication does
not always "make bigger."
Division: The meaning of division (two interpretations, with or without re-
mainder). Understanding when the answer to a story problem solved by
whole number division is best expressed as a decimal, as a mixed number,
or as a whole number with a remainder. Why dividing by zero is unde-
fined. The scaffold method of division. Explaining why the scaffold and
standard longhand procedure for dividing whole numbers works. Explaining
why some non-standard methods of division are valid. The relationship be-
tween fractions and division: explaining why .
Calculating decimal
representations of fractions. Explaining the relationship among remainder,
mixed number, and decimal answers to division problems .
Math 7001: for graduate credit, students must complete an additional
course project. The project could consist of several essays, or a longer paper,
in which the student discusses some aspect of the course material in depth,
or in which the student relates the course material to their future teaching
(e.g., with a collection of lesson plans or with a discussion of some lesson
plans). However, other creative ideas could also be acceptable. For example,
students might think of a creative way to tie their course project for math
7001 to something they will be doing for one of their other courses.
Students will learn the geometric characteristic
and features
of the ellipse equation. Some of the characteristics will be
the elliptical focus points, eccentricity, and extremities.
Specific Objectives
Students will learn that when the eccentricity
(e) is between
0 and one, it is an ellipse. If e = 0, it is a circle.
The student will learn to convert an elliptical quadratic
formula to a more visual equation by completing the square.
The student will see the minor differences of the equation
from a circle equation. The student will also learn about the
other parameters of the elliptical polynomial equation. For a
real life application, the student will go through an exercise
of determining the Mars' elliptical orbit.
The teacher will give a string that is longer
than the width of
the focus points. Students are to pair up and use the string
and a writing instrument to draw an elliptical shape.
Students will write down objects have the elliptical shapes
Teacher will review the quadratic equation. The
teacher will
review how to represent it with polynomials by completing
the square. The teacher will review the quadratic equation of
a circle and parabola. The teacher will show a picture of
ellipse. The teacher will squeeze a circle to an elliptical
shape. The teacher will give the quadratic equation (using
the polynomial format) of an ellipse and its characteristics:
eccentricity, focus, and extremities.
The students will break into groups of three to
four and work
on textbook problems . They will work on exercises to
convert elliptical quadratic equations to its polynomial
format. They will identify the focus, extremities of the minor
axis, and vertices. They will draw the elliptical shape. They
will work as a group to determine the elliptical polynomial
equation on the orbital path of Mars. They should seek
assistance from their peers first. If they need help outside of
their group, the teacher can assist or an advanced student
will be asked to help. If they finish early, they can start on
their homework assignments.
Assessment (based on
objectives)
The student will be given equations, eccentricity
numbers,
and geometric figures in a test. The student will be asked to
determine which are associated to an ellipse. Quadratic
formulas will be given. The student will be asked to translate
it to the quadratic polynomial equation of an ellipse. The
student will be asked what the eccentricity, the foci, and
other elliptical parameters are. The students will be asked to
derive the orbital path of Mars given different orbital
parameters that differ from its real parameters..
Adaptations (ELL
students or special
populations)
Students will enter in their journal the
definition(s) of
eccentricity, axis, axes, focal point, focus, and other words
they don't know. They are to write down their questions.
The teacher or their peers will answer the questions . They
will write down the answers in their journal . They are advise
to use the free tutoring classes or come in early or after
school for sessions with the teacher
Extensions (for gifted
students)
Students will go on the Internet and research
Kepler 's
discovery that the Mars orbital path was elliptical with the
Sun being at one of the focus. Students will investigate the
orbits of Halley's comet which has a more elongated
elliptical orbit. The students will determine when we will
see Halley's comet again. The students can also determine
the intercontinental orbit used for a space vehicle to travel
from Earth to Mars |
Learn More About Media4Math+:
Sign up for a Webinar to get an Overview of Media4Math+!
Media4Math produces video tutorials, TI Nspire Graphing Calculator Tutorials, PowerPoint presentations, Promethean Flipcharts, and other media content for algebra, geometry, and technology-based math instruction. Our materials can be used for classroom instruction, homework help, or independent tutorials. Our goal is to provide the highest-quality video-based materials that can be used in today's math classroom. In particular, these are the resources we offer:
Math in the News. On of our most popular features, we take current events news stories and explore them from the math perspective. Our goal is to show that math is everywhere, even in the day-to-day news. Looked at another way, Math in the News is a great application of algebra and geometry concepts in the real world. Our math news stories cover topics in science, sports, art & architecture, technology, and more. Have a good math news story to share? Let us know! Purchase the Math in the News Year in Review. Includes PowerPoint and Flash video formats.
Math Tutorials. Most textbooks are limited to a handful of math examples to get across key concepts. As a result, students will like need additional tutorials to supplement the textbook. We have no such limitation. Our Math Tutorials page includes hundreds of worked-out solutions to key concepts in Algebra. And these Math Tutorials clearly explain a myriad of different examples. From Algebra Tiles, to the slope formula, quadratic formula, to more advanced topics in algebra, we identify key concepts and show a multitude of tutorials. This wealth of tutorials provide opportuntities to see patterns in the solutions and learn key algorithm through systematic repitition. Use these materials for enrichment, tutorials, algebra help, and other applications. We also provide a Flash video overview of each batch of math tutorials.
Promethean Flipcharts. Do you have Promethean Interactive Whiteboards in your math classroom? Are you looking for math resources? We have an extensive library of video-based Promethean Flipcharts for Algebra, Geometry, and the new TI Nspire CX graphing calculator. These video-based Flipcharts provide real-world applications of math in a highly-engaging format for students.
PowerPoint Slideshows. Do you use PowerPoint presentations? Are you looking for PowerPoint presentations for math? We have a growing library of PowerPoint presentations for Algebra, Geometry, and graphing calculators, including some video-based presentations. Also, our Math in the News archive is available in PowerPont and Flash video formats.
TI Nspire Graphing Calculator Tutorials. Are you new to the TI Nspire graphing calculator? Do you have the original TI Nspire Graphing Calculator Clickpad or the newer TI Nspire Graphing Calculator Touchpad or the newest TI Nspire CX? We have video-based TI Nspire Graphing Calculator tutorials that highlight key functions of the TI Nspire Graphing Calculator, but also in the context of teaching key concepts from Algebra and Geometry. Ready to take your knowledge of the TI Nspire Graphing Calculator to the next level to teach key concepts from Algebra? Try our downloadable video tutorials for the TI Nspire Graphing Calculator CX. This 10-part video series covers all the key topics from a full-year Algebra course and contains many hands-on tutorials using the TI Nspire Graphing Calculator. Whatever your knowledge of the TI Nspire Graphing Calculator, our video-based tutorials will increase your knowledge base.
Math Labs. Video-based critical thinking activities—the Math Labs—provide students opportunities to deepen their knowledge about key concepts in Algebra. These short video clips challenge students to think critically about their understanding of these concepts. Each Math Lab includes a worksheet for gathering data or answering questions.
Print Resources. Providing print support for our video-based TI Nspire Graphing Calculator Tutorials, this section includes a PDF worksheet for these videos. All TI Nspire Graphing Calculator key strokes are clearly shown on every worksheet. We currently have worksheets for the TI Nspire Graphing Calculator Clickpad and TI Nspire Graphing Calculator Touchpad. We will also be adding worksheets for our upcoming Multimedia Algebra Library, launching in 2012.
DVD Products. Expand your video library with our DVD libraries for Algebra, Geometry, and the TI Nspire graphing calculator. Our Algebra Applications and Geometry Applications video series bring math to life with amazing real-world applications of algebra and geometry topics from these courses. Each DVD video is available as a single title or the full library. We also have a downloadable video series for algebra for users of the TI Nspire Graphing Calculator.
Math Solvers. As a complement to our Math Tutorials page, our Math Solvers provides you with tools for solving specific Algebra problems. We have equation solvers and other calculation tools that not only provide an answer to a specfic problem, but also a worked-out solution that can be used for instruction.
Social Media. Our blog provides an informal way to provide you additional information about our video resources. You can follow our blog directly through this site, or you can subscribe to our blog on Wordpress. We also include links to our social media channels.
Library++. Available now, the Library++ subscription service will provide complete curricular support for Algebra and Geometry. Each library includes lesson plans, video lessons, solvers, assessments, and more. Register for the Multimedia Algebra now. |
Mathematics at Hills Road
Maths students enjoy the subject and find it interesting - nearly half the students at Hills Road take one of the maths courses as part of their overall programme. Maths complements other subjects, supporting and enhancing understanding in the physical or social sciences or providing breadth and balance to an arts- or languages-based programme. Maths is a good training for the mind, helping to develop logical thinking and problem-solving skills – the kind of analytical processes that have helped solve problems of all kinds for thousands of years. Students with maths qualifications are numerate and highly employable in a variety of areas as diverse as computing, engineering, finance, data analysis and mathematical modelling.
Entry with:
GCSE grade A in Mathematics.
• Opportunities to use graphical calculators and computers to help you develop your mathematical understanding
• Extra-curricular programme including trips, competitions and talks
• No coursework
• Range of courses allowing some choice in applied modules:
Decision maths develops a variety of approaches to problem-solving and decision-making in industry and commerce
. Statistics analyses situations where outcomes are uncertain and takes probability as its starting point.
Mechanics investigates the way in which objects move and how they are affected by forces. It also appears in physics courses and would be particularly useful for potential engineers.
• The possibility of following a Further Maths AS course as an option in Year 13.
Awarding body:AQA
AS Level Units
Unit 1: Core 1 Unit 2: Core 2 These two units form the "tools of the trade" – the information and set of techniques used to solve problems. They cover topics such as algebra and trigonometry, which appear in GCSE courses, and develop them further. They also cover some new topics, most notably calculus. Unit 3: Applied Unit 1 (either Mechanics, Statistics or Decision depending on the course option chosen)
• A purpose-built Mathematics Centre with teaching rooms grouped around a resource area containing 12 networked computers with access to the Internet and College Intranet and also a library area.
• Stocks of text books and other materials
• A large teaching team of dedicated and enthusiastic subject specialists.
• Additional individual tuition in the lunchtime workshop, as well as other support schemes.
• Advice and preparation for further study in mathematics and related disciplines.
"The topics we have covered are very varied, so the lessons are always interesting. You do not repeat the same material for weeks on end! The teaching styles are also varied which helps people to grasp the new concepts. The different learning styles and classroom activities help us to remember the techniques taught. If you have a problem with anything there is always a member of staff around to help, as well as specific lunchtime surgeries. A highlight of the course was encountering new areas of maths and discovering topics I really enjoy." Pippa Cadd
"I enjoy maths because its challenging, the simplicity of either right or wrong, and the buzz you get when you get a hard question right. It's not just textbook work and this also makes it more interesting and enjoyable." George Proctor |
Summary: Updates the original, comprehensive introduction to the areas of mathematical physics encountered in advanced courses in the physical sciences. Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded |
A study of the properties of real numbers, the properties of exponents and radicals, the arithmetic of polynomial and rational expressions, linear and quadratic equations and inequalities, systems of linear equations, and an introduction to functions. Problem-solving skills and critical-thinking skills are emphasized. Meets 4 hours per week. 3 lecture hours, 1 lab hour.
PREREQUISITES:
Place into MATH 105 with approved and documented math placement test scores or by completing MATH 101 with a grade of S.
NOTES:
COURSE OBJECTIVES / GOALS:
The student should be able to do the following:
Be able to learn and apply algebraic processes to problems, and be able to write math in exact symbolic forms. Students must have the ability to do basic arithmetic by hand. Therefore, calculator usage and other technology is not allowed on quizzes and tests in Math 105 "with the exception of students with disabilities who have an approved accommodation." Students with a calculator exception will take quizzes and tests in the Assessment Center.
The student should obtain a 60% competency as measured by examination to receive a passing grade. A student who is taking this course as a prerequisite for another math course should receive a 70% competency before taking the succeeding course. TOPICAL OUTLINE
Sets - 2%
Definition of set
Symbols used in set notation
Union, intersection, and subset
Real number system - Assigned to student as homework
Definition of real numbers and subsets of the real numbers
Basic operations on the set of real numbers
Properties of the real numbers
Evaluating expressions using the properties of real numbers<\/li>
Integer exponents - 6%
Definition of positive, negative, and zero exponents
Product rule
Quotient rule
Power rule
Scientific notation - Assigned to student as homework
Definition of scientific notation
Using scientific notation on the calculator
Problem solving using scientific notation
Linear equations in 1 variable - 7%
Solving linear equations in one variable using the properties of equality, including those which are identities and those that are inconsistent. |
How To Solve Math Word Problems On Standardized Tests 1st Edition
0071376933
9780071376938 and language skills. It focuses on the category of test question that students dread the most and in which they do least well: mathematics word problems. Written by a national expert in mathematics education, it takes the fear and frustration out of mathematics word problems by providing a simple, step-by-step approach that emphasizes the mechanics and grammar of problem solving and that is guaranteed to make solving all types of math word problems a breeze, even for math-phobic students.Covers all types of mathematics word problems found on standardized tests and identifies the value of each type on the testsFeatures dozens of examples and practice problems, with step-by-step solutions and key mathematics concepts clearly explainedIncludes a 50-question drill using problems drawn from actual tests, with answers provided at the back of the book «Show less... Show more»
Rent How To Solve Math Word Problems On Standardized Tests 1st Edition today, or search our site for other Wayne |
Incorporating Technology into Today's Mathematical Curriculum
Dr. Belinda Wendt
June 11, 1999
Abstract
To adequately prepare students for advanced scientific and engineering courses and applications, PSEs (Problem-Solving Environments) such as MAPLE, MATLAB, and advanced scientific calculators have become essential to a scientific curriculum. Within these environments, students can better visualize mathematical problems and approaches. They can tackle more complicated problems that would be very tedious without such a automated tool, opening the door for more creativity and a more thorough understanding of mathematics. Furthermore, the implementation of software code enhances the theoretical understanding of mathematical approaches. The logical process of software development forces the student to completely understand the procedures being implemented. This can result in increased confidence, which is typically a stumbling block for teaching mathematics. Moreover, the experience the students derive from the PSEs is essential since industrial companies, government agencies, and academic institutions now commonly use these and other similar tools.
An overview of MAPLE and MATLAB will be presented. A method for integrating PSEs within a calculus curriculum will be discussed. Samples will be provided that elicit the benefits listed above. |
What''s Calculus all about?
Does Calculus have any relevance to our daily lives? Or is it just another conglomeration of mathematical symbols hardly making sense to most? This is a presentation to remove the 'fear' of Calculus among students and introduce the subject to a anyone who is a total stranger to the subject but not a stranger to Mathematics. The presentation starts with the nature and scope of Calculus and the type of problems solved using Calculus. Mention is also made of the mathematicians who 'invented' the subject. Some interesting curves are also shown in the end. |
what is pre-algebra?
At least, he's taking the same course I took in 9th grade lo these many years ago. IIRC
Ed seems to remember it all better than I do, and he says the same thing. Christopher is studying the stuff he studied as a freshman in high school.
What is pre-algebra, anyway?
Do we know?
There wasn't any pre-algebra when I was a kid, and I remember Carolyn expressing skepticism about the whole concept back when we first met.
These days I think pre-algebra is simply Year One in a 3-year Algebra Spiral. You teach Algebra 1 in 6th grade, calling it Pre-Algebra; then you teach Algebra 1 again in 7th grade; then you teach it again in 8th.
That's the fast track.
For the slow track you start teaching Algebra 1 in 7th or 8th, calling it Pre-Algebra; then you teach it again for the next two years running.
algebra without the story problems
My other theory is that Pre-Algebra is Algebra 1 without the story problems.
Algebra 1 without the story problems is, IMO, a REALLY bad idea, but that's a subject for another post.
Pre-algebra is simply arithmetic with one new feature: we use letters to represent numbers. Because the letters are simply stand-ins for numbers, arithmetic is carried out exactly as it is with numbers. In particular, the arithmetic properties (commutative, associative, distributive) hold because we are still doing arithmetic with numbers. Thus the identity
3(x + 1) = 3x + 3
holds because we know that it is true when x = 2, when x = 5, and in fact when x is any number at all.
That's it — that's all there is to prealgebra from a purely mathematical standpoint. Later, when students progress to Algebra, this basic idea is used to define functions; as algebra continues it becomes increasingly focused on functions. The purpose of prealgebra is to prepare students for variables and functions without actually mentioning them. It is a crucial topic in the middle grades.
*This is the 'grade A' review for SRA Math, the series Irvington abandoned for TRAILBLAZERS, on mathematicallycorrect. There's a dissenting review by David Klein & Jennifer Marple, (pdf file) also on mathematically correct, saying Saxon is better. Speaking of confusion, I had a memory of mathematicallycorrect reporting that Prentice-Hall Pre-Algebra had been adopted by CA; then a week ago I found a page there saying it had been rejected. Apparently I was right the first time. Was it accepted in one cycle & rejected in another? Don't know.
Algebra is a branch of mathematics which studies structure and quantity. It may be roughly characterized as a generalization and abstraction of arithmetic, in which operations are performed on symbols rather than numbers. It includes elementary algebra, taught to high school students, as well as abstract algebra which covers such structures as groups, rings and fields. Along with geometry and analysis, it is one of the three main branches of mathematics.
So the pre-algebra course overlaps with algebra to the extent that operations are performed on symbols rather than numbers.
I think pre-algebra is just a name that's been stuck on a course regardless of whether it makes perfect logical sense or not.
The LA Times is running a story about the high rate of High School dropouts in the LAUSD.
Below are excerpts from their second article -- on the algebra requirement.
The whole series is avaailable at but may require site registration.
January 30, 2006
THE VANISHING CLASS
A Formula for Failure in L.A. Schools
By Duke Helfand, Times Staff Writer
Each morning, when Gabriela Ocampo looked up at the chalkboard in her ninth-grade algebra class, her spirits sank.
Gabriela failed that first semester of freshman algebra. She failed again and again — six times in six semesters. And because students in Los Angeles Unified schools must pass algebra to graduate, her hopes for a diploma grew dimmer with each F.
"It triggers dropouts more than any single subject," said Los Angeles schools Supt. Roy Romer. "I think it is a cumulative failure of our ability to teach math adequately in the public school system."
In the fall of 2004, 48,000 ninth-graders took beginning algebra; 44% flunked, nearly twice the failure rate as in English. Seventeen percent finished with Ds.
Among those who repeated the class in the spring, nearly three-quarters flunked again.
The school district could have seen this coming if officials had looked at the huge numbers of high school students failing basic math.
Discouragement, Frustration
Birmingham High in Van Nuys......has a failure rate that's about average for the district. Nearly half the ninth-grade class flunked beginning algebra last year.
In the spring semester alone, more freshmen failed than passed. The tally: 367 Fs and 355 passes, nearly one-third of them Ds.
Like other schools in the nation's second-largest district, Birmingham High deals with failing students by shuttling them back into algebra, often with the same teachers.
Last fall, the school scheduled 17 classes of up to 40 students each for those repeating first-semester algebra.
The strategy has also failed to provide students with what they need most: a review of basic math.
Teachers complain that they have no time for remediation, that the rapid pace mandated by the district leaves behind students like Tina Norwood, 15, who is failing beginning algebra for the third time.
Tina, who says math has mystified her since she first saw fractions in elementary school, spends class time writing in her journal, chatting with friends or snapping pictures of herself with her cellphone.
Her teacher, George Seidel, devoted a class this fall to reviewing equations with a single variable, such as x -- 1 = 36. It's the type of lesson students were supposed to have mastered in fourth grade.
"I got through a year of Vietnam," he said, "so I tell myself every day I can get through 53 minutes of fifth period…. I don't know if I am making a difference with a single kid."
Eager to close this competitive chasm, education and business leaders in California sought to re-engineer the state's approach to math. They produced new math standards they believed would foster a "rising tide of excellence."
This meant teaching algebra earlier, as soon as eighth grade for some students, even if instructors questioned whether younger students could handle abstract concepts.
'I Give Up'
Whether requiring all students to pass algebra is a good idea or not, two things are clear: Schools have not been equipped to teach it, and students have not been equipped to learn it.
Secondary schools have had to rapidly expand algebra classes despite a shortage of credentialed math teachers.
The Center for the Future of Teaching & Learning in Santa Cruz found that more than 40% of eighth-grade algebra teachers in California lack a math credential or are teaching outside their field of expertise; more than 20% of high school math teachers are similarly unprepared.
High school math instructors, meanwhile, face crowded classes of 40 or more students — some of whom do not know their multiplication tables or how to add fractions or convert percentages into decimals.
Birmingham teacher Steve Kofahl said many students don't understand that X can be an abstract variable in an equation and not just a letter of the alphabet.
Birmingham math coach Kathy De Soto said she was surprised to find something else: students who still count on their fingers.
High school teachers blame middle schools for churning out ill-prepared students. The middle schools blame the elementary schools, where teachers are expected to have a command of all subjects but sometimes are shaky in math themselves.
At Cal State Northridge, the largest supplier of new teachers to Los Angeles Unified, 35% of future elementary school instructors earned Ds or Fs in their first college-level math class last year.
Some of these students had already taken remedial classes that reviewed high school algebra and geometry.
"I give up. I'm not good at math," said sophomore Alexa Ganz, 19, who received a D in math last semester even after taking two remedial courses. "I think I've been more confused this semester than helped."
Ganz, who wants to teach third grade, thinks the required math courses are overkill. "I guarantee I won't need to know all this," she said, perhaps not realizing that if she were to teach in a public school, she could be bumped as a newcomer to upper grade levels that demand greater math knowledge.
Administrators in L.A. Unified say they are trying to reverse the alarming failure rates of high school students by changing the way math is taught, starting in elementary schools.
The new approach stresses conceptual lessons rather than rote memorization, a change that some instructors think is wrong. New math coaches also are training teachers and coordinating lesson plans at many schools.
The simplest algebraic concepts are now taught — or are supposed to be taught — beginning in kindergarten.
Searching for a solution in its secondary schools, L.A. Unified is investing millions of dollars in new computer programs that teach pre-algebra, algebra and other skills.
Officials are considering other costly changes, including reducing the size of algebra classes to 25, launching algebra readiness classes for lagging eighth-graders and creating summer programs for students needing a kick-start before middle school or high school.
Go figure
Algebra test
A majority of ninth-graders in Los Angeles fail algebra or pass with a D grade.
A copy of the LAUSD pacing plan for "Algebra I: Structure and Method" is included at the end of this letter. It undermines the organization of ideas in this textbook, and it undermines the California Mathematics Framework and Standards. We illustrate with some examples.
The two year pacing plan for "Structure and Method" calls for the quadratic formula together with completing the square of quadratic polynomials (in Chapter 12 of the textbook) to be explained to students before basic factoring techniques for polynomials (in Chapter 5), and before an introduction to radicals, including techniques for simplifying radicals (in Chapter 11). This choice of ordering of topics is so mathematically unsound that it will most likely seriously undermine the ability of LAUSD math teachers to teach algebra in a coherent and meaningful way. It will reduce the learning of algebra to memorizing meaningless formulas without understanding. In the words of the chairman of the Math Department of San Pedro High School (in LAUSD), Richard Wagoner:
"First and foremost among the problems with the Pacing Plan is that
it renders the textbook and all support materials useless and obsolete.
The sequence is so seemingly random that students must jump back and
forth between sections of chapters through most of the course.
Therefore, all review materials, diagnostic tests, supplementary
materials and enriched materials -- all of which are tied to the
sequence as designed by the authors -- can no longer be used."
Teacher George Seidel left a 25-year law career two years ago, hoping to find fulfillment as a teacher at Birmingham High in Van Nuys. "I got through a year of Vietnam," he says, "so I tell myself I can get through 53 minutes of period five.... I don't know if I am making a difference with a single kid."
Officials are considering other costly changes, including reducing the size of algebra classes to 25, launching algebra readiness classes for lagging eighth-graders and creating summer programs for students needing a kick-start before middle school or high school. Go figure
Seems like they're trying everything but what works -- teaching elementary math to mastery before teaching algebraic concepts. It is exeedingly difficult to be this wrong accidentally.
After viewing the photo gallary, I just want to say OMG. This article should be sent to every school board member pushing for "fuzzy" math.
I am a homeschooler, so I don't have a dog in this fight, but ISeeing students in these photos who have been academically-abused for the first 8 years of their school lives just floors me. Really, this country doesn't need to worry about terrorist, we are destroying our country from the inside out.
I look at those pictures and captions and everything points to how grades K-8 failed these kids. Lower schools do not want to hold kids back. One reason given for this is some study showing a higher drop-out rate for those kids who were held back. Duh! Keep passing them right along and you will have a 100% graduation rate.
At our public schools, they use the concepts of developmentally appropriate, full inclusion, and spiraling to justify this approach. They don't want classes/subjects to be filters. However, the filters are delayed until high school so they never see the product of their work. It's easy enough to blame the child, the parent, or society. By eighth grade many kids will decide that they are just not good in math, thereby completely letting the lower schools off the hook. High schools let the lower schools off the hook. They should be yelling and screaming at the lower schools.
My reaction is to tell people to look at the state tests and tell me what is so difficult that schools cannot succeed for most kids no matter what their parents or society does.
I(I'M WRITING COMMENT TO POST AS A KEY WORD SO I CAN FIND THIS AGAIN)
I had no idea homeschoolers didn't struggle over finding a math curriculum.
Of course, I didn't struggle.
There were two choices (that I knew of at the time), and I made the choice quickly once I saw both.
Here are all these teachers AND students saying 'He still counts on his fingers' — how can anyone NOT take seriously the absolute need to learn the procedures and algorithms of elementary math COLD.
My kindergarten aged son gets embarrassed when he has to resort to counting on his fingers to solve an addition or subtraction problem. You think these kids don't know that thye're not supposed to be counting on their fingers in high school? I'm sure this is all part of the low self-esteem problem you get when you you can't do math.
When you're working efficiently at your child's pace, rather than at the pace of the class & the school with its many holidays & moments of lost instructional time, I think it would be easy to get through one Saxon book & two Singapore books each school year K-5 or even K-8.
Because these kids - these young adults - really are suffering. You can see it in their body language.
This didn't need to happen aren know.
Because we are looking at pain.
These young people break my heart.
Every one of these young people can solve an equation like
3x + 2 = 32
Christopher may be able to do that now.
IF CHRISTOPHER WERE USING SAXON MATH HE'D BE ABLE TO DO THIS WITH EASE.
The only reason Christopher has found equations like this one hard is that the course moves way too fast with way too little practice.
I suppose the crafty teacher could secretly teach elementary math in class instead of algebra. It's not like these kids are in any condition to pass algebra anyway. Of course, thne this teacher looks bad since his students are all failing algebra and some other teacher will get all the glory when they ultimately pass algebra arenBut what is it?
................
My MIL taught math to middle school kids for 25 years. She.
She
"Most students who enter my eighth-grade Algebra I or Honors Algebra I classes in September each year are ill-prepared to learn algebra because most of them have not fully mastered arithmetic. To make matters worse, I have too few class periods to teach them the entire rigorous course when one adds up the drug education activities, annual class trips, report card day, vacations, snow days, exams, and parent-teacher conferences. These restrictions demand that the students put in extensive quality time outside of class grappling with difficult problems and practicing for accuracy.
They really should only count full days with the teacher when they're adding up the 180 days of school required. It would probably shock parents how few days in the year are actually spent with their teacher learning about core subjects.
"It would probably shock parents how few days in the year are actually spent with their teacher learning about core subjects."
Even with the teacher instructional time is a shrinking commodity. The first activity of the day is handing out meal ticket. That often takes half an hour of prime time. I've known teachers who schedule an hour of SSR in the morning. More prime time lost. Then you have the dogma of non-instruction under the constructivist regime. Time filled with often trivial activities and projects |
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