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Six Strategies to Tackle Challenging Math Word Problems

Probably the hardest thing about doing word problems is taking the words and translating them into a workable mathematical equation. For this reason many students fear and hate doing them. It can be confusing to know where to start and how to go about figuring out the answer. However, there are ways of breaking down a word problem that makes it clearer and easier to solve. The following is a list of helpful hints and strategies in tackling these challenging word problems. 1. Remember that when you are doing a word problem you are looking to convert the words into an equation, so read through the entire problem first. Don’t try to solve the problem when you’ve only read one sentence. It’s important to completely read the problem in order to get the whole picture and effectively translate and solve the problem. 2. Go back to the beginning. Reread the first sentence. Write down what you know and what you don’t know. Use variables to stand for the unknowns and clearly label... read more

The Importance of S.T.E.M. (Science, Technology, Engineering, Math)

Today, the future depends on you as much as it does on me. The future also depends on educating the masses in Science, Technology, Engineering, and Math, otherwise known as STEM. As a new tutor to WyzAnt, I hope to instill the importance of these subjects in student's lives, as well as, the lives around them.    Besides the fact that,  "the average U.S. salary is $43,460, compared with the average STEM salary of $77,880," (Careerbuilder) these subjects are interesting and applicable to topics well beyond the classroom. Success first starts with you; I am only there to help you succeed along the way. STEM are difficult subjects. Yet when you seek out help from a tutor, like myself, you have what it takes to master them.    Please enlighten me on students looking to achieve and succeed rather than live in the past and think I can't as opposed to I can. We can take the trip to the future together, one question at a time

Summer: Relax your brain or retain your knowledge?

I was a fairly typical young person and, like my peers, counted down the days until summer. My mother was a math professor, so I never stopped doing math during the summer, but felt like other parts of my brain became a little mushy in the summer. Come September, it was difficult to get back into the swing of writing papers and studying history and memorizing diagrams. I was out of practice and lost my routine. As an adult, I have almost continually taken classes, because I enjoy learning and find that from class to class, I need to maintain a routine, i.e. a study area and a time of day that I complete my assignments. I have also found that reviewing material a week or two before the course begins helps me to start the class with more confidence and competence. I am a big believer in confidence fueling success and I wonder if younger students practiced assignments in the week or two prior to return to school, if that confidence would help the transition to the school year... read more

Recommended Statistics Learning Strategies - Experienced Subject Matter Expert

My recommended strategy to Students at all academic levels for learning and successfully passing the course at all modalities (on-line, on-ground) is the culmination of at least ten years of teaching and tutoring statistics at the undergraduate, graduate, and post-graduate levels in business, management, sciences, social studies, and psychology. It consists of the following: 1. The first is to learn how to overcome fear and anxiety from the unknown and look at tutoring as a prudent investment to your immediate future and success. Engage the tutor from the start of the course and don't prolong the decision because of the complexity and quantitative nature of the subject area. This component of the overall strategy is to keep the weekly normal pace and retain basic real life knowledge for ongoing participation in the political and economic process of the National affairs and State-of-the-Union. 2. Academic Reading Materials and Study Guides encompass three distinct sections... read more

Favorite educational quote

It is the mark of an educated mind to be able to entertain a thought without accepting it. (Aristotle) This quote provokes me never to accept the status quo and always challenge assumptions. It is the thought that through education we never stop learning or seeking after truth and knowledge.

Mathematical Journeys: What Does the Function Look Like?

This week's Math Journey builds on the material in The Function Machine. If you have not yet read that journey, I suggest you do so now. In The Function Machine we discussed why graphing a function is possible at all on a conceptual level – essentially, since every x value of a function has a corresponding y value, we can plot those corresponding values as an ordered pair on a coordinate plane. Plot enough pairs and a pattern begins to emerge; we join the points into a continuous line as an indication that there are actually an infinite number of pairs when you account for all real numbers as possible x values. But plotting point after point is a tedious and time-consuming process. Wouldn't it be great if there was a quick way to tell what the graph was going to look like, and to be able to sketch it after plotting just a few carefully-chosen points? Well, there is! Mathematicians look for an assortment of clues that help to determine the shape of a... read more

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

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

The Sum of Two Squares

Do you think is factorable? In general, the sum of two squares is not factorable, such as . However, there are special situations in which the sum of two squares is factorable, like the one in our title. You don't believe it? Let's try it.   The trick here is to add an extra term to this polynomial, with a purpose of completing the square. Usually, when we complete the square, we will add a constant term to a quadratic expression, and subtract that same term at the end of the expression. But this time, we are adding the "middle" term. (Of course, we will need to subtract it at the end so that we don't change our original expression.) + - Here we can group the first three terms of the expression: Write the grouped terms as a perfect square: Now, do you recognize this is the difference of squares? Difference of Squares   To use the difference of two squares formula, we can write... read more

Should I hire a Tutor? - Advice for Parents

Should I get a tutor? Will it help my child? These are some of the most common questions posed to tutors by parents of students struggling in school. Tutoring can be expensive and difficult to schedule so parents must decide whether the time and money will be well spent. Instead of relying on a crystal ball, use these factors to help make the decision. 1. Does the student spend an appropriate amount of time on homework and studies? While it can help with study skills, organization, and motivation, tutoring cannot be expected to keep the student on track unless you plan on having a session every night. If you can make sure the student puts in effort outside of tutoring, she will be more likely benefit from it. 2. Does the student have difficulty learning from the textbook? If this is the case, the student will probably respond to one-on-one instruction that is more personalized. A tutor will help bring the subject to life and engage the student. A good tutor will... 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

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

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

Math - Check your work!!

Whenever you complete a math problem, it is paramount to go back and double check your work. Remember, no one is perfect and mistakes will be made from time to time. The first step is to always ask yourself "Does this answer make sense"? For example, if you're working on a geometry problem and you're trying to calculate an angle of a polygon, and you determine the answer is 110°, look at the angle and ask "Does this answer makes sense, does this angle look like it's greater than a right angle or a 90° angle"? If not, you know you've made an error and can go back to find the mistake. You can do it!!

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

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!

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

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