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High School Geometry: For Some, Why Is This More Challenging Than Algebra 1?

Several of my current Geometry students have commented on this very contrast.  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

All my students passed the NY State Regents Exams...

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.

Factoring without the "Guess and Check" method

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

Mathematical Journeys: The Unperformed Operation

Come with me on a journey of division. I have here a bag of M&Ms, which you and I and two of your friends want to share equally. I'm going to pour the bag out on the table and split it into four equal piles. For this example, “one bag” is our whole, and the best number to represent that whole would be the number of M&Ms in the bag. Let's say there were 32. If I split those 32 M&Ms into four equal piles and asked you how many were in one pile, you could certainly just count them. But a quicker way would be to take that 32 and divide it by the number of piles I'd made, which in this case is 4. You'd probably write that as: 32 ÷ 4 = 8 So there are 8 candies in each pile. Seems easy enough with a large number of M&Ms, right? But what if there were less candies – what if our “whole” was less than the entire bag? Well, for a while we'd be okay – if there were 16, for example, we'd do the same thing and come up with piles of 4 instead... read more

Why I Hate FOIL

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

The ordering of algebraic operations

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!

Advice to my younger self- the student

IF I could go back in time and give my younger self some advice on how to be a better student, be more successful in school, life, etc, I would definitely tell myself that being involved in everything comes at a cost. It is better to find a few things that you like to do, do them well and often, than feeling stressed because there is so much on your plate at one time. Being a 'Jack of all Trades' it is natural for me to dip my toes in different waters- all at the same time, but that does not mean that I can give 100% to any of them at that time. While I was able to get good grades (A- average) while in school, I was impressed by how much better I did- and felt about my work- the few times that I scaled back on my activities. Another piece of advice that I wish that I could bestow upon my younger self would be to learn how to speak up in a group setting when someone is not fulfilling their part of an agreement. Now, this said, the best way to do this would be in a tactful... read more

Algebra Word Problems: Rate of Change

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... read more

Things a good tutor should say and discuss with you:

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... read more

How to Teach a Frustrated Student

The first thing to do when teaching a frustrated student is to listen to, and acknowledge, their frustrations. Let him or her vent a little. If you're working with young children, they probably won't even realize or communicate that they are frustrated. Therefore, the first thing to do is say "you're very frustrated with learning ________ aren't you?" If you are in a group situation, take the student aside to talk to him or her about it so he or she doesn't become embarrassed. One of the best things you can do when teaching frustrated students is to watch them one-on-one in academic action and observe every little detail when they think, write, and speak. Often, students are lacking very particular, previous basic skills. By watching them work, you can identify where they are going wrong and notice common patterns. For instance, I have tutored many algebra students whose frustration stemmed from an inability to deal with negative numbers. Once this problem was... read more

Easy way to remember the quadratic formula!

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!) 

A Few Thoughts on Why We Learn Algebra

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... read more

Favorite Math Resources, K-12 + GED

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... read more

A Matter of Perspective

Recently I had the opportunity to meet with a parent/business owner who hires/places tutors for high end families in my area. It was a wonderful opportunity as once again I heard the mantra, "Parents just want the grades to go up." I asked what this meant, how I could measure it (quantitatively and anecdotally) and if this was indeed proof of my skills as a tutor or a momentary 'save' on a reversal of fortune. This parent does not use Wyzant. I was hard pressed to accept from this parent the reason I wasn't being contacted by high end parents for tutoring was my lack of guaranteeing grades would go up, a promise I can not make in good faith as there are too many factors involved. Honesty and integrity should be important, not my sales ability. In my years as a teacher and tutor, I have found once I have parents on board, the rest is EASY. Parents are the elephant in the room and I can run myself ragged (knowing full well very little if anything changes without parental... read more

Why Test Prep Books Aren't Worth Your Money: The Case of Princeton Review

All the major test prep books for the SAT, ACT, and GRE -- published by companies like Kaplan, Princeton Review, Barron's, and Manhattan Test Prep -- are poorly written, conceptually deficient, and, worst of all, riddled with serious errors. Students can't be expected to learn from books that aren't even right! And I don't mean the books are riddled simply with typos, which unfortunately is also true, because they are so poorly edited; I mean they really are riddled with serious conceptual errors. Here's a simple example from the very beginning -- the diagnostic test, of all things! -- of Princeton Review's "1,014 GRE Practice Questions." The problem is on page 24, and the answer key and explanation is on page 38. Not only is their answer wrong; what's worse, their *explanation* is wrong, too! I'll set off the problem by dashes (----) and then add more commentary after. NOTE: The question is a classic GRE "quantitative comparison," so it's hard to... read more

5 Things I've Learned From My Favorite Students

1. No one was born to lose. The best of my students understand this principle like the backs of their hands. No, there is no inherent genetic formula or organic compound you can use to get an A in a class. We are all products of our hardwork and investments. Whoever decides to put in excellent work will definitely reap excellent results. 2. Always aim for gold. Have you heard that there is a pot of gold lying somewhere at the end of the rainbow? It's true! Okay, I'm just joking, but my best students always aim for the gold. The very best. As, not Bs, or Cs, or Ds. Just the very best. The one thing people don't think they are capable of achieving is the best. The top of the class. Or the valedictorian. 3. Never settle for less. My best students are innovative, inquisitive thinkers. They tend to think outside the box, never settling for "just what they got from class." They love to use real life examples and explore how theory comes alive in their personal... read more

Physical Exercise and Nutrition DO affect our brain performance and brain health.

As you may know, I am a big fan of the well-known author and brain specialist, Dr. Daniel Amen. He mentions in several of his books that Physical Exercise is good for the brain. I have read of research studies that showed a clear correlation between IMPROVEMENT in students' test scores in math and science, and their level of physical activity (for example, when math class followed PE class, the students had significantly higher scores). Maybe we should schedule PE before all math classes in our schools. What do you think about that idea? This morning I read an online article on the myhealthnewsdaily site, entitled "6 Foods That Are Good for Your Brain," and another article about how Physical Exercise helps maintain healthy brain in older adults too. The second article, "For a Healthy Brain, Physical Exercise Trumps Mental Workout" was found under Yahoo News. The remainder of this note is quoted from that article: Regular physical exercise appears... read more

I am in need of some students.

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.

Christmas Present!!

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  

Math Equations, Formulas and Vocabulary

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

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