February 11, 2008 - Monday
1) Quiz #3
2) HW #9 Review PPT; walk around and give credit
3) Lesson: Like and Unlike Radicals; Adding and Subtracting Radicals
4) Classwork - Adding and Subtracting Worksheet D42
HW #10
Simplify Radicals Worksheet
(Mixed) #22-33
_______________________________________________
February 13, 2008 - Wednesday
1) ELM # 23-25
2) HW #10 Review (answers on O/H)
3) Lesson: Rationalizing the Denominator for Single Term Denom. And Multiplying Radicals using FOIL – Students Take Notes, then pass out packet for FOILing Radicals J
4) Classwork - Dividing Radicals without Vars D-43
HW #11
1) Multiplying and Dividing Radicals W.S. (odds)
2) More Mult. Radicals W.S. first part a-d
3) Complete Classwork
_______________________________________________
February 15, 2008 - Friday
1) ELM # 26-28
2) HW #11 PPT
3) Radicals: Lesson 5: Students are to read silently pg. 4 & 5 from packet passed out yesterday and do Problem Set 2 - 4 at the end of the sections – Rationalizing the Denominator using Conjugate
HW #12
Rationalizing the Denominator W.S.
_______________________________________________
multiplying radicals calculator
Tuesday, August 31, 2010
How Algebra is going to help me be or become ...?
Today, a student asked one of the typical questions that students ask in a developmental math course: "How Algebra is going to help me be or become ...?" Unfortunately, today this question irked my normal coolness and patience with students. Why students continue having a narrowed mind about knowledge in general? Why they consider course content as useless when they cannot find an immediate application of this content to their lives? Why shut down the unlimited ramifications of what they are learning to focus it only to the present they live in?
As you can see, I was annoyed by the question since I cannot comprehend how students invest so much in a college education to just come out the same way they got in: with a narrowed mind attitude. I thought the purpose of earning a college education is to come out a better person than when we got in. Anyway, here is my response to my student's discussion post:
Students,
Learning Algebra will help you in the following way:
(1) To earn a college degree since it is part of your degree plan. The college degree diploma will open many opportunities that you may have never expected. Once you earn your degree, employers will see this as a person who is persistent, hard worker, self-disciplined and capable of overcoming whatever challenges s/he may face. Isn't this what you experienced in this course?
(2) To make you think in a structured, logical and critical manner. This is what Algebra is all about! When difficult situations arise in your life, you will methodically think and reflect how to solve it instead of just making wild guesses or reactive decisions that most likely you will regret at a later time.
(3) To develop the habit of working smarter, not harder. I am certain there have been times in your life that you are responsible for com! pleting a task that is tedious and repetitive, and you wonder ! if there is a better way to do it. The ability of analyzing if there is a pattern on what you do and find a better-efficient way of doing it is what Algebra is all about.
In my humble opinion, and with all due respect, it is time to stop seeing Algebra as a manipulation of variables, such as x + y = z, and start realizing that Algebra is about understanding how the world around you works, so you can take control and make it better. Isn't this why you are pursuing a college degree?
help in algebra
As you can see, I was annoyed by the question since I cannot comprehend how students invest so much in a college education to just come out the same way they got in: with a narrowed mind attitude. I thought the purpose of earning a college education is to come out a better person than when we got in. Anyway, here is my response to my student's discussion post:
Students,
Learning Algebra will help you in the following way:
(1) To earn a college degree since it is part of your degree plan. The college degree diploma will open many opportunities that you may have never expected. Once you earn your degree, employers will see this as a person who is persistent, hard worker, self-disciplined and capable of overcoming whatever challenges s/he may face. Isn't this what you experienced in this course?
(2) To make you think in a structured, logical and critical manner. This is what Algebra is all about! When difficult situations arise in your life, you will methodically think and reflect how to solve it instead of just making wild guesses or reactive decisions that most likely you will regret at a later time.
(3) To develop the habit of working smarter, not harder. I am certain there have been times in your life that you are responsible for com! pleting a task that is tedious and repetitive, and you wonder ! if there is a better way to do it. The ability of analyzing if there is a pattern on what you do and find a better-efficient way of doing it is what Algebra is all about.
In my humble opinion, and with all due respect, it is time to stop seeing Algebra as a manipulation of variables, such as x + y = z, and start realizing that Algebra is about understanding how the world around you works, so you can take control and make it better. Isn't this why you are pursuing a college degree?
help in algebra
AP CALCULUS
Dd loved her Calculus learning experiences through a variety of sources. She has read plenty of Calculus books (some are listed below under Reading list) and worked on plenty of Calculus problems. She also liked the latest AOPS Calculus book very much, and there is a wonderfulcourse that goes with the book. She also enjoyed reading Life of Fred Calculus book. I am listing a few resources for AP Calculus preparation.
AP Calculus consists of two exams-AP Calculus AB and AP Calculus BC. There are various online and distance courses available to learn Calculus, some of which I have listed below.CollegeBoard has in depth information on the syllabus, learning materials and AP exam information. Read the AP Calculus AB and AP Calculus BC course descriptions to get an idea as to what is involved in doing well on the AP exams. Check out the past AP Calculus AB and AP Calculus BC Free Response(FR) questions.
- Websites, tutorials, lecture notes, cheat sheets and more
Calculus.Org is a wonderful in depth website that has links and resources on AP and General Calculus.
Ask Mr. Calculus is a Calculus help page with past AP exam Free Response questions, interactive Calculus learning pages, Visual Calculus etc.
Visual Calculus nice site with great tutorials.
Karl's Calculus Tutor online tutorials and lessons.
Calculus Lecture Notes from the University of Toronto at Scarborough College. Includes many past exams.
Graphics for the Calculus classroom. Great visual explanations.
Calculus tutorials from The Connected Curriculum Project, Dept of Mathematics, Carroll College, Montana.
Calculus Help.com interactive Calculus help with some humor injected lessons.
Video Calculus from the University of T! ennessee Math Department at Knoxville. It is an excellent reso! urce tha t includes tutorials, drills and programs for pre-calculus and calculus.
Calculus Applets interactive applets for single variable calculus.
PowerPoint lectures of AP Calculus AB and BC.
AP Calculus lessons on PowerPoint lessons and tutorials.
Calculus on the web from Temple University.
MIT AP Calculus courses. Free opencourseware.
Math Forum's Math Tools for Calculus.
Calculus Cheat sheets from Paul's online Math notes.
Calculus course information links, resources on AP Calculus.
SOS Mathematics pages on Calculus.
History of Calculus wonderful site on History of Calculus.
Calculus for Beginners and Artists from MIT.
Free Online Calculus courses from William Smith.
Calculus Page Problems from eCalculus.org.
- Graphing Calculator Resources
Dh ! and I ne ver used a Graphing Calculator in India even though we had to learn much more advanced Calculus than the AP Calculus courses here. There were memorization and manipulations involved in solving advanced Calculus problems without having to resort to a calculator of any sorts. I am not sure if Graphing Calculators are used these days in India by all high school kids. We very much doubt that it would be practiced considering the prohibitive cost of these calculators to be able to afford by all Indian high school kids. We have exposed dd to both the version of learning with and without a graphing calculator, although the latter learning is not necessary to do so here in the US. She loves her Graphing Calculator although she enjoys working without them too.
Dd uses the above pictured Graphing Calculator for advance mathematics, mathematical programming, 3D graphing, along with numerous other tasks. There are numerous resources on the web regarding Graphing Calculators. I have listed a few below.
Check out the Education Technology page in Texas Instruments to learn all about Graph! ing Calc ulators
Graphing Calculator programs various programs.
Online Graphing Calculator from Cool Math.
Graphing Calculator pages check out the various programs, tips and resources.
Calculus Calculator programs yet another site with numerous info.
Calculator pages on various calculators.
Graphing Calculators in Calculus see how it is used for Calculus.
Calculus with the TI-89 by Brendan Kelly
Texas Instruments TI-89 Titanium Graphing Calculator the one which is usable in learning Calculus.
- Articles on Calculus learning.
Tips for successful Calculus course from Harvard.
Learning Calculus Prepared by: Susan Hermiller, Melanie Martin, Eric York.
HOW TO SUCCEED IN CALCULUS: For Calculus Students, By Calculus Students; Dr. Woodland's students from Fall 1998.
How to succeed in Calculus in Georgia Tech tips and pointers.
How to succeed in AP Calculus from a high school site.
Read about The Calculus Trap by Richard Rusczyk, which talks about the best course of path for math learning for the very gifted student.
Why Do We Study Calculus? An interesting article on the importance of Calculus.
- Teacher's sites
- Calculus Course Choices
There are many online free Calculus courses as well as fee based ones. One can also take the Calculus course through the local community college or by hiring a tutor. Dd learned much of her Calculus through self learning by working through Spivak Calculus and Stewart Calculusbooks. She loves the AOPS Calculus book as well. Find the most appropriate course path that fits your child's needs and learning styles.
Art of Problem Solving ! (AOPS) Calculus Course My dd loves AOPS courses and books. This is great for a very mathy kid. It is an intense, challenging course that prepares a student for AP Calculus exam.
Math Archives Calculus courses online. A compiled list of varied Calculus courses available on the web.
Calculus courses from Hippocampus.
AP Calculus courses from UCLA.
Aleks Math review for AP Calculus
Thinkwell Calculus Courses for both AB and BC.
EPGY AP Calculus courses.
Apex AP Calculus AB course.
Chalk Dust Calculus Courses.
Life of Fred Calculus book is a fun way to learn Calculus.
Change and Motion: Calculus Made Clear from the Teaching Company.
- Calculus DVDs
Teaching Company Calculus Lectures in DVD and Audio formats.
The Calculus 1 & 2 Tutor - 2 DVD Set! DVD ~ Jason Gibson.
The Advanced Calculus 2 Tutor - 4 DVD Set DVD ~ Jason Gibson.
Calculus
Instructional DVDs by Ron Larson.
The Standard Deviants - Calculus DVD Pack (Conquer Calculus 1 & 2) ~ Standard Deviants.
II SYMBOLS AND SPECIAL TERMS
| II | SYMBOLS AND SPECIAL TERMS |
Mathematical Symbols
Mathematics employs many symbols to describe numerical operations and relationships. This activity defines some common symbols and gives examples of their uses.
The symbols of algebra include numbers, letters, and signs that indicate various arithmetic operations. Numbers are constants (values that do not change), but letters can represent either unknown constants or variables (values that vary). Letters that are used to represent constants are taken from the beginning of the alphabet; those used to represent variables are taken from the end of the alphabet. See also Mathematical Symbo! ls.
| A | Operation Symbols |
The basic operational signs of a! lgebra are familiar from arithmetic: addition (+), subtraction (-), multiplication (×), and division (÷). The multiplication symbol × is often omitted or replaced by a dot, as in a · b. A group of consecutive symbols, such as abc, indicates the product (the result of multiplication) of a, b, and c. Division is commonly indicated by a horizontal bar (also called a vinculum), as in: a/c
A virgule, or slash (/), may also be used to indicate division: a/c.
A power is th! e product of a number multiplied by itself. The notation 4
A number whose nth power is equal to x is an nth root of x. When n is 2 the term “square root” is used and when n is 3 the term “cube root” is used. For example, 3 and -3 are both square roots of 9 since 32 = 9 and (-3)2 = 9; 2 is a cube root of 8 since 23 = 8; -2 is a cube root of -8; y is a cube root of ˆ. The square root of x is denoted like this:
The number of times the root is multiplied by itself is called the index. The index is usually omitted for square roots, but appears as a small raised number just before the root symbol for higher roots:
|
|
The two possible values of square roots, one positive and one negative, are often written using the plus or minus symbol: ±. The equ! ation = 2 or -2, for instance, can be abbreviated = ±2.
| B | Order of Operations and Grouping |
1 + 2 · 3
equals 7 because 2 and 3 are multiplied first and then added to 1. Exponents and roots have even higher priority than multiplication:
3 · 22 = 3 · 4 = 12
Grouping symbols override the order of operations. All operations within a group are carried out first. Grouping symbols include parentheses ( ), brackets [ ], braces { }, and horizontal bars that are used most often for division and roots. Adding parentheses to a previous example:
(1 + 2) · 3
indicates that 1 should be added to 2 first, and then the result multiplied by 3 for a total of 9 rather than 7. Brackets and braces are used in more complicated combinations that require multiple nested (one inside the other) groups. Operations within the innermost group are carried out first:
{2[5 + 3(1 + 4)]} =
{2[5 + 3 · 5]} =
{2[5 + 15]} =
{2 · 20} = 40
When a slash is used to indicate division, care must be taken to group the terms appropriately. For example,
|
|
cannot be written ax + b/c – dy. The second notation indicates that b should be divided by c before b is added to ax. Grouping symbols can be used to correctly represent the fraction when using a slash: (ax + b)/(c - dy).
| Special Definitions |
Any statement that contains the equality relation (=), such as 3x = 9, is called an equation
An expression containing one term, such as 2x3, is called a monomial. An expression involving the addition or subtraction of two terms, as in 2x2 + 3x, is called a binomial, while an expression with three terms, such as 4x5 – x4 ! + 7x, is known as a trinomial. Polynomial is the! general name for expressions in which any number of terms are added or subtracted. The degree of a polynomial refers to the largest exponent of the variables in the polynomial. For example, if the largest exponent of a variable is 3, as in ax3 + bx2, the polynomial is said to be of degree 3. Similarly, the expression xn + xn-1 + xn-2 is of degree n.
A linear equation with one variable is a polynomial equation of degree one—that is, of the form ax + b = 0. These are called linear equations because graphing these equations results in straight lines. A quadratic equation in one variable is a polynomial equation of degree two—that ! is, of the form ax2 + bx + c = 0.
An indeterminate equation, such as x2 + y2 = z2, involves multiple unknowns.
A prime number is any integer (the counting numbers: 1, 2, 3, …; their negatives; and zero) that can be evenly divided only by itself and by the number 1 or the number -1. Thus, 2, 3, 5, 7, 11, 13, 17, and 19 are all prime numbers.
A factor of a number is any integer by which the number can be divided evenly, with no remainder. The factors of 6, for example, are 1, 2, 3, and 6, because 6 ÷ 1 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2, and 6 ÷ 6 = 1. The prime factors of any number are those factors to which it can be reduced such that the number is expressed only as the product of primes and their powers. For example, the prime factors of 6 are 2 and 3. Similarly, because 60 = 22 × 3 × 5, the prime factors of 60 are 2, 3, and 5.
algebra expression
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