# Blogs

## Algebra 1 Blogs

Factoring can be quite difficult for those who are new to the concept. There are many ways to go about it. The guess and check way seems to be the most common, and in my mind, it is the best, especially if one wants to go further into mathematics, than Calculus 1. But for those just getting through a required algebra course, here is another way to consider, that I picked up while tutoring some time ago:   If you have heard of factor by grouping, then this concept will make some sense to you. Let's use an example to demenstrate how to do this operation:   Ex|   x2 + x - 2   With this guess and check method, we would use (x + 1)(x - 2) or (x + 2)(x - 1). When we "foil" this out, we see that the second choice is the correct factorization. But, instead of just using these guesses, why not have a concrete way to do this.   Let's redo the example, with another method.   Ex| x2 + x - 2   First... read more

I am happy to announce that all my students have passed the NY State Regents examinations, except one student.  The subjects varied from Algebra 1, Algebra 11/Trigonometry, English, US and Global History and Living Environment.  I am so proud of them.  Most of these students are students who struggled quite a bit.  It was a long journey but one I would do again.    I am very proud of them as most of them will be graduating this year.  The NY State Common Core examinations are next.

Several of my current Geometry students have commented on this very distinction.  This has prompted me to offer a few possible reasons.   First, Geometry requires a heavy reliance on explanations and justifications (particularly of the formal two-column proof variety) that involve stepwise, deductive reasoning.  For many, this is their first exposure to this type of thought process, basically absent in Algebra 1.   Second, a large part of Geometry involves 2-d and 3-d visualization abilities and the differences in appearance between shapes even when they are not positioned upright.  Still further, for a number of students, distinguishing the characteristic properties amongst the different shapes becomes a new challenge.   Third, in many cases Geometry entails the ability to form conjectures about observed properties of shapes, lines, line segments and angles even before the facts have been clearly established and stated... read more

As a student, I found that I remembered information a lot easier when the information was in a song.  I learned the 'quadratic formula song' in one of my math classes and have not forgotten the formula since.  Several of my students have also found this song helpful (and catchy!), so I though I'd share:   The 'Quadratic Formula Song' (sung to the lyrics of 'Pop Goes the Weasel') The quadratic formula is negative b plus or minus the square root of b squared minus four a c all over 2a!   (Warning, this will get stuck in your head!)

Here are some of my favorite Math resources. Check back again soon, this list is always growing! I also recommend school textbooks, your local library, and used bookstores. As a note, college-level math textbooks are often helpful for high school math students. Why is that? Isn't that a little counter-intuitive? Yes, it would appear that way! However, many college-level math textbooks are written with the idea that many college students may not have taken a math class in a year or more, so they are written with more detailed explanations. This can be particularly helpful for high school students taking Algebra, Geometry, and Trig. I have a collection of college-level math books that I purchased at a local used bookstore. The most expensive used math book I own cost \$26 used. Books that focus on standardized test prep (such as the SAT, AP, or GED prep) can be helpful for all core subjects, as they summarize key ideas more succinctly than 'normal' textbooks. These are GREAT... read more

Hi,   I would be honored in having the opportunity of working with students and parents. The education and success of students are very important to me and I would love to do what I can to help. I am a math and education major with an Associate's of Arts and Teaching Degree from Lee College and I am seeking a teaching career. I live in the Baytown area and I am not able to provide my own transportation due to the fact that I have a disability which prevents me from driving, so I can only rely on public transportation and I am limited to how far I can travel. Therefor, communication is much needed. I am available until 4:30 p.m. Monday through Friday. Anyone needing a private tutor, please contact me. I would be happy to help you at any time.

Hi All!   In the spirit of giving, starting on 11/29/2013,  I will be offering a few brainteasers/ trivia questions where the first 3 people to email me the correct answer will receive a free, one hour, tutoring session in any subject that I offer tutoring for (via the online platform)!  That's right free!  Get your thinking hats on everyone!   Merry Christmas!!  Andrew L. Profile

Area, Volume and Circumference equations: Area of a Square A=S2 Area of a Triangle A=1/2bh Area of a Rectangle A=LW Right Triangle/Pythagorean Theorem a2+b2=c2 Area of Parallelogram A=bh Area of a Trapezoid A=1/2h(a+b) Area of a Circle A=πr2 Circumference of a Circle c=πd or c=2πr Volume of a Sphere V=4/3πr3 Surface Area of a Sphere SA=4πr2 Volume of a Cube V=s3 Volume of a Rectangular Solid V=lwh Slope of a line Equations Slope-intercept form y=mx+b m is the slope b is the y-intercept y is a y coordinate on the graph (that coincides with the line) x is an x coordinate on the graph (that coincides with the line) Horizontal line y=b Vertical line x=a Finding... read more

Let's use our imagination a bit. Picture yourself in math class (Algebra I to be exact), minding your own business, having fun playing with the axioms (aka rules) of algebra, and then one day your teacher drops this bomb on you: "Expand (x+3)(x-1)" And you might be thinking, "woah now, where did come from?" It makes sense that this would shock you. You were just getting used to the idea of expanding 3(x-1), and you probably would have been fine with x+3(x-1), but (x+3)(x-1) is a foreign idea all together. Well, before you have much time to think about it on your own and discover anything interesting, your teacher will probably tell you that even though you don't know how to solve it now, there is a "super helpful", magical technique that will help you… FOIL For those of you lucky enough never to have heard of FOIL, I will explain. FOIL stands for First Outside Inside Last and is a common mnemonic... read more

One of the major differences between algebraic equations and algebraic expressions consist of the equal sign because the equal sign consitutes for a solution that can be checked to verify that it is the solution. Expressions are meant to be simplified so common factors are important in simplifying expressions. Equations give a way to actually check the answer by subsitution for the variable while expressions are normally checked by multiplication or another type of operation.

I recently responded to a question on WyzAnt's “Answers” page from a very frustrated student asking why he should bother learning algebra. He wanted to know when he would ever need to use it in the “real world” because it was frustrating him to tears and “I'm tired of trying to find your x algebra, and I don't care y either!!!” Now, despite that being a pretty awesome joke, I really felt for this kid. I hear this sort of complaint a lot from students who desperately want to just throw in the towel and skip math completely. But what bothered me even more were the responses already given by three or four other tutors. They were all valid points talking about life skills that require math, such as paying bills, applying for loans, etc., or else career fields that involve math such as computer science and physics. I hear these responses a lot too, and what bothers me is that those answers are clearly not what this poor student needed to hear. When you're that frustrated about... read more

How to be Successful In Mathematics Math is a complicated subject. Students struggle with it, parents don’t feel comfortable helping with homework, and teachers find it impossible to “re-teach” every year. It is for these reasons that I feel having a good foundation in math is imperative. Students that have a great foundation feel confident and are not afraid of tackling a problem until they figure it out.   What do students need to know to have a good foundation? Well, I think the most basic concepts they need to master are the concepts learned in pre-algebra. Most parents would be shocked to hear that students begin to learn these concepts as early as second grade. Some are those concepts include properly using the order of operations; being able to add, subtract, multiply and divide negative numbers, fractions and decimals; and working problems with more than one variable. I encounter students “freezing” all the time when they encounter fractions,... read more

When both writing down and reading the algebraic expressions, the binary operation (including addition+, subtraction-, multiply*, divide/, exponential^) follow a conventional order: 0) Parenthesis, including {}, [], () 1) Exponent, multiply and divide 2) Addition and subtraction The ordering is 0)>1)>2). Then there is no ordering within each group, eg multiply and divide are at the same level of priority except that 0) comes in such as a parenthesis. Let's take a look at one quick example: 3+(8-2)*6. First compute (8-2)=6; Then compute (8-2)*6=6*6=36; Finally compute 3+(8-2)*6=3+36=39. Another example: 3^2+3/(5-2) First compute (5-2)=3; Then do 3/(5-3)=3/3=1; Next compute 3^2=3*3=9; Finally add 3^2+3/(5-2)=9+1=10. Hope it helps!

My worst school years were when I did not keep up because I didn't care for the subject.  Get over it.  If the course is required you have to take it and do well.  Putting off studying and keeping up with the curriculum will only make getting ready for tests more difficult and you will not have as good understand of the subject.  This can rub off on other subjects as well while you cram for exams.     The semesters I got a jump on all subjects, especially the ones I did not think I would like, I did much better.  Whether it was by reading text book ahead, ready to ask questions in class or understand the lecture and making sure my class notes were well done and I reviewed them after class to fill in gaps, it all helps build the foundation for the subject matter.  Generally if I did this, by the time the semester was 60% complete, the remainder was a breeze.  Made all the difference for me.

Well, there are two exceptions to this question. X cannot be 0 or 1 because 0*0=0, and 1*1=1. No matter how many times you multiply 0 by itself, you will always get 0, and no matter how many times you multiply 1 by itself, you will always get 1. That's why the power of x will never change its value if x is 0 or 1. Now that we realize the two exceptions of 0 and 1 for x, x would have to be in one of two certain ranges: 0<x<1 or x>1. If 0<x<1, then that would mean that x is a proper fraction when the numerator is smaller than the denominator (e.g. 5/6). Let's use the easiest fraction value for x, 1/2, and the easiest power of x, x^2. Plug in the value of x, and you will get x^2=(1/2)^2. This will multiply the fraction of 1/2 twice by itself: (1/2)*(1/2). Now, since any number times 1 is that number, (1/2)*1=1/2 so that 1/2 remains the same. So if the second term is less than 1, it will make the first term smaller than itself as (1/2)*(1/2)=1/4. Therefore, the power... read more

As the school year ramps up again, I wanted to put out a modified version of a Memo of Understanding http://en.wikipedia.org/wiki/Memo_of_understanding for parents and students. It seems each year in the rush to get through the first weeks of school parents and students forget the basic first good steps and then the spiral downwards occurs and then the need for obtaining a tutor and then the ‘wish for promises’ from a tutor. Pay attention to your child’s folder or agenda book. A student is generally not able to self regulate until well into high school. Some people never quite figure it out. Be the best person you can be by helping your child check for due dates, completeness, work turned in on time. Not only will this help your child learn to create and regulate a schedule, it prevents the following types of conversations I always disliked as a teacher ("Can you just give my child one big assignment to make up for the D/F so they can pass"; "I am going to talk to... read more

Solving Word Problems with Proportions and Relative Comparisons These word problems are set-up where the dependent variable is not provided as is, but rather as a part of an operation. You will have to set-up each side of the equality with its own operations. Example 1: “Shelley finished x number of her math homework problems before dinner. Had she finished 3 more, she would have finished half her math homework. Write an equation which represents the relationship between y, total problems and x, number of problems Shelley completed.” This isn’t set-up in the same way as problems presented in previous entries because there isn’t a defined rate of change right away. So, it will be set-up this way with one variable on each side of the equality. You're already given the variables to use in the problem. Proportion of completed problems = proportion of total problems. “3 more than completed problems” = “half her math homework” (half total problems) (x... read more

Word Problems with Multiple Variables and Given Values This type of problem will be presented such that you'll have to set-up the equation or relation between the variables. Additionally, you will be given the value of one or more variables. On all of these problems you are not asked to solve the problem, only set-up the equation. Example 1: “A weather balloon is launched from a height of 100 meters above sea level. The balloon rises at a constant rate of 27 meters per minute. Write an equation that can be used to determine the time in minutes it will take the balloon to reach a height of 2889 meters above sea level.” Start with the relationship of variables: Dependent Variable = Fixed Value + Rate of Change * Independent Variable. “Height of balloon” = “Initial height” + “27meters per minute” h = 100m + 27m For the final step, substitute the given height of 2889: 2889 = 100 + 27m. Example 2: “The perimeter of a rectangle... read more

Writing Expressions Involving Rate of Change These real-world problems can be best translated when broken down into their components (variables and operations). When you see the words “is” or “are”, this is the points where you set-up the equality. Whenever you see the word “per”, “each” the implication is a multiplication. This indicates the rate of change between the variables. The general format for these problems is: Dependent Variable = Fixed Value + Rate of Change * Independent Variable. The fixed value is generally a fixed value which does not change. Most commonly, it will be the initial value in a situation. Example 1: “Mark is purchasing a new computer. The cost of the computer is \$2400 after tax. He will make monthly payments of \$150. Write an equation which describes the balance on the account after any given number of months” Variables present: balance and number of months. The rate of change in this case is the \$150 per month... read more

The most obvious answer is cost. If a tutor charges the same rate for one or four students, it becomes cheaper per hour as you increase students and share the costs with other families. It is often believed a tutor is best when working 1:1 with a student. In some instances it is well worth the time and money to have 1:1 tutoring and sometimes it is appropriate for students to study and do school work in small groups. What is not obvious is the dynamics of small group tutoring. In a variety of circumstances it is invaluable for students to learn how to study “what needs to be studied”. The acts of independence and self regulating behavior have far reaching benefits. Groups need to learn to share and take turns. This seems simple and yet there is the underlying tendency to allow the ‘smart one’ in the group to carry the burden of work. Assuming each student is in the class and has a different point of view/observation about what is happening in class, they should share their... read more