I am taking from The Official Hunter College High School Test: problem 76 on page 20. We read the following.
In the expression below, each letter represents a one digit number. Where the same letter appears, it represents the same number in each case. Each distinct letter represents a
different number. In order to make the equation true, what number must replace C?
A great start is to decode each AAA, AAB, and ABC. It helps to look at this problem wholly; particularly we look at the leading sum on the left wall (of the same types). We glean that either: (1) A + A + A = 20, (2) A + A + A + 1 = 20 or (3) A + A + A + 2 =
20: its very important to remember that given three numbers each less than ten, the sum of them which is great, is at most 2 in the tens place. This means that each row can only donate a 1 or 2 to the next. We can conclude that our line...
There are several points in grade school that involve a critical shift in the thinking that is required in the school work. Parent's should be aware of these points as they navigate through the abyss of raising a school-aged child and supporting the child
as he/she moves forward through the grades.
3rd Grade - The third grader is transitioning from whole number thinking into understanding the concepts of parts. They are exposed to fractions, decimals and percentages. This is a major paradigm shift. Students are also exposed to
long division at this point. Supporting children in this phase requires an emphasis on helping the child conceptualize whole things being split into parts. In addition to homework support, tutoring, and supplementary work, parents should introduce cooking
chores to children at this time, and make them follow a recipe that has precise measurements. Reading comprehension and writing is also an issue...
Four years ago, I came up with this math trick. Take a look at it, and at the end I'll show you why it works!
Let's play a game. I’m going to let you make up a math problem, and I will be able to tell you the answer from here. I can’t see what you’re doing, I’m not even in the same room as you, but I will still be able to tell you the correct answer.
Trust me. I’m a professional. Ready?
Okay. First, pick a number. It can be any number you wish, large or small. Now add 5 to that number. Got it? Okay, now double your new number (multiply by 2). Alright, now subtract 4 from the double.
Next, divide your new number by 2. Now, finally, subtract your original number from this new quotient. Got it? Okay. Here comes the cool part. Ready?
The answer is 3. Nifty, huh? What’s that? How’d I do it? Oh, magic.
Okay, okay, it’s not magic. The answer will always be 3, no matter what number you pick. Let’s illustrate this by...
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 Introduction (page 23) to Manhattan's Strategy Guides for the Revised GRE. This passage appears in all eight of Manhattan's strategy guides, so it somehow went unnoticed after at least eight rounds of editing by allegedly
"expert" readers and test-takers. See if you can spot the error!
"If ab=|a|x|b| which of the following must be true?
II. a>0 and b>0
A. II only
B. III only
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...
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
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...
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...
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 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
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...
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...
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...
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:
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…
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...
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.
Vi Hart, website: vihart.com
Sal Khan, https://www.khanacademy.org/math/algebra
Mamikon Mnatsakanian, www.its.caltech.edu/.../calculus.html
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...
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...
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...
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...