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Geometry Blogs

NOTE: For today's Math Journey, please refer to the image file “Image for Math Journey: Road Trip Around A Problem” under my WyzAnt files. Link: https://www.wyzant.com/resources/files/671706/image_for_math_journey_road_trip_around_a_problem Let's go on a road trip! When I teach geometry, especially geometry involving angle measures like this problem, I like to describe the process of solving a problem as taking a little road trip. I describe it this way because this is how I personally feel when solving a problem like this – my eyes rove around the figure from one intersection to the next, and I hop in my little math car and drive along lines and stop at intersections to figure out where I am. Geometry is a very visual discipline, and as a visual learner, I have the most fun when I can trace a physical journey around the problem, solving things as I go. So let's hop in our math car and chase this problem down! The first step in any problem like... read more

A student needed to draw a circle with a 2" diameter, then draw the following angles: 100°, 120º, and 140º. She had her compass but didn't have her protractor.   First she drew the circle, then she drew 2 perpendicular diameters. Since a circle encompasses 360º, each quadrant comprising 90º. We drew the 120º angle first using an entire 90º quadrant plus 1/3 of the adjacent quadrant, erasing the unneeded line, which leaves 60º in that second quadrant.   Then we found the circumference of the circle (C=πD, or 3.14x2"=6.28"). Next we found 1/4 of the circumference (6.28"/4=1.57"). We wanted to be able find the arc length in 10º increments, so we divided the arc of one quadrant by 9 (1.57"/9=0.174"). We converted this into 1/16ths of an inch by multiplying by 16 (0.174"x16=2.79 sixteenths of an inch).   Getting back to our angles, we measured the 100º angle next by taking our remaining 60º and adding 40º of... read more

Math Student's Civil Rights   I have the right to learn Math (Math is learnable like other subjects) I have a right to make mistakes, erase then, and try again (Failure points to what I have not learned yet) I have the right to ask for help (asking for help is a great decision) I have the right to ask questions when I don't understand (understanding is the primary goal) I have the right to ask questions until I understand (perseverance is priceless) I have the right to receive help and not feel stupid for receiving it (asking for help is natural) I have the right to not like some math concepts or disciplines (i.e. trigonometry, statistics, differential equations, etc.) I have the right to define success as learning no matter how I feel about Math or supporters I have the right to reduce negative self-talk & feelings I have the right to be treated as a person capable of learning I have the right to assess a helper's ability to... read more

On Friday my TV broke. Kind of a bummer, but we'd had it for many years and it was time for it to go. Now we needed to get a new one, so we headed out to the store. In the process of our search, we realized that our old TV was at the extreme smaller end of the TVs they now sell, so we were going to need to buy a bigger one. We found one we liked, that was only slightly bigger than our old one. The big question, though, before we plunked down our hard-earned cash, was this: would it still fit on our entertainment center? Our current TV was sold as a 40-inch model, and the one we liked was 43-inch. However, TVs are measured across the diagonal, not the width, so we needed to know what the actual width would be. My hubby got out a tape measure, and I got out a pencil and paper. He measured our 40-inch TV across the diagonal and found that 40 was actually just the screen size; the full diagonal with the frame was 42.5 inches. We knew the new one's frame was no larger... read more

Alegbra: http://www.nysedregents.org/algebraone/   Algebra 2/Trigonometry: http://www.nysedregents.org/a2trig/home.html   Geometry: http://www.nysedregents.org/geometrycc/   Math A, Math B, Integrated Algebra, Other Math: http://www.nysedregents.org/regents_math.html   Chemistry: http://www.nysedregents.org/Chemistry/   Earth Science: http://www.nysedregents.org/EarthScience/   Physics: http://www.nysedregents.org/Physics/

Hello Wzyant Academic Community and welcome to my blog section! This is where I am available for online chit-chat, educational assistance free of charge, business discussions & arrangements, and more! I am always eager to help and love to talk turkey with all realms of academia, so don't be shy and feel free to ask many questions!!!       P.S.  ∫∑∞√−±÷⁄∇¾φΩ

Here are 48 of my favorite math words in 12 groups of 4. Each group has words in it that can be thought of at the same time or are a tool for doing math.   between on over in   each multiply of many   ratio divisions distribution compartments   limit neighborhood proximity boundary   infinite infitesmal mark differentiation   graph width height depth   circle sphere point interval   hyper extra spacetime dimensional   geometry proportion sketch spatial   four table cross squared   target rearrange outcome result   area volume space place   What are your favorite math words? If you aren't sure, search for "mathematical words" and pick a few.

Although I enjoy geometric constructions, as in solving geometric problems with the equivalent of a string, I find that many students have little to no interest in them. I particularly like learning about how ancient cultures such as the Egyptians used them to design Pyramids where the error in the corners are about 1/300 of one degree, much more accurate than can be seen and even more accurate than almost all houses built today. Although learning about their history is interesting there is not a lot of places to apply this knowledge in the modern world, i've solved some problems in surveying with geometric constructions but there are always more advanced CAD methods which can also do the trick; which is why I was happy to find Euclid The Game.      This is a straightforward game that applies all the basic principles of geometric constructions into a fun little game. Although it doesn't require the attention to detail the Egyptians would have... read more

Reading Formulas can make or break how a student comprehends the formula when alone - outside the presence of the teacher, instructor, tutor, or parent. Formula For Perimeter of Rectangle:  P = 2l + 2w How To Read:  The Perimeter of a Rectangle is equal to two (2) times the Length of the longer side of the rectangle (L) plus two (2) times the Width of the shorter side of the rectangle (W). When is reading formulas like this necessary?  At three particular moments, reading this formula in this manner can be effective.  When students are initially learning what the formula means When student are learning what it means when they should already know (remediation).  When students want to remind themselves (basics learning study skill habit) Remember, Formulas at their introduction are complete statements or thoughts.  Students cannot and will not recall complete thoughts or statements... read more

Hello Students!   Start this year off strong with good organizational and note taking skills. Make sure you understand the material and are not just taking notes aimlessly. Try to take in what your teacher is saying and don't be afraid to ask questions!! If you start taking the initiative to learn and understand now, college will be a much more pleasant experience for you. Trust me!   Stay organized and plan your homework and study schedule!   Quiz yourself!   Study with friends!   READ YOUR TEXTBOOK! :)    Remember, homework isn't busy work and a chance to copy down your notes, it is part of the learning process. This is especially important with math, as it builds on itself and understanding the basics will make the other subjects easier!   Have a fantastic and fun year!

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

The majority of the students that I have often have the same problem -- they aren't grasping the information fast enough or they aren't really able to follow the lessons a teacher gives.   Sometimes, teachers aren't adaptive to every learning style for each student in their classroom.  However, know that each student has the capability to learn math on their own.  It is just necessary to have key characteristics to make it successful.   Every math student should have: patience motivation adaptability organizational skills open communication between themselves and their teacher (inside and outside the classroom) breaks!! :)   Study Tips Always try to study outside of your home or dorm room. In our minds, those are places that we relax at and it can be difficult to turn your mind off from the distractions to study. Public libraries, universities, coffee shops, and bookstores are the way to go. Some... read more

Nailing an 800 on the math portion of the SAT can be a tricky feat, even if you are steadfastly familiar with all of the requisite formulas and rules. A difficult problem can overwhelm even the most prepared individual come test day. Time constraints, test surroundings, and the overall weight of the exam can unnerve the most grounded students. So what do you do when panic strikes and your mind draws a blank? How do you re-center yourself and charge forward with ferocity and confidence? What you do is this: write everything down from the problem. This is the most important part of the problem solving process. As you peruse the question, write down the pertinent data and establish relationships by setting up equations. This exercise will help you see solutions that were previously difficult to decipher. As you work on practice tests and sample problems, you must work diligently to form a solid habit of writing down important bits of information as you plow through the... read more

I hear a lot about math teachers from my students, and while every teacher is unique, some comments are repeated over and over. By far the most common one I hear is that their teacher didn't really explain something, or was incapable of elaborating when questioned and simply repeated the same lecture again. As a tutor, my first priority is to make sure the student understands the material, and if they're still confused, to find another way to explain it so that it makes sense. In order to do that, I need to have a thorough understanding of the concepts myself, so that I am not simply reading from a textbook but actually explaining a concept. In my years of tutoring math, I've developed a point of view and approach to math that I refer to as “teaching the concept, not the algorithm.” An algorithm is a step-by-step procedure for calculation. The term is used in math and computer science, but the concept of an algorithm is universal. I could tell you that I have an algorithm... read more

Willpower is unique to humanity. It is the keystone characteristic that is directly responsible for our technological advancement over the last several hundred thousand years. Willpower can be defined as the capacity to restrain our impulses and resist temptation in order to maximize our long-term success. It is the expulsion of energy to fight off innate survival based urges to exponentially increase future advantages and benefits. It is the driving force behind all civilizations, and it is what prods humankind forward to learn and grow. When we turn down a bite of cheesecake, step away from a mind numbing reality sitcom, or push off a nap to get some work done, the credit goes to willpower. It is this ghost like aura of control and discipline that we rely on to extend our existence and maximize our accomplishments. When we watch highly successful individuals exercise routinely, read voraciously, and work tirelessly, we are impressed with their ability to resist instant gratification... read more

This week in geometry one of my students is learning about the different "centers" in a triangle (orthocenter, circumcenter, incenter, etc), as well as the midsegments theorem and triangle inequalities.  To help him visualize why all of these things are true, I had him cut out an acute triangle, an obtuse triangle, and a right triangle and use these to illustrate the concepts.  For triangle inequalities, we worked with different lengths of string to see why some combination of leg lengths and some do not. These are both quick, easy ways that help students understand beyond the words and definitions what we are talking about!

I've found that most students have little to no difficulty understanding the difference between parallel and perpendicular lines when only one plane is involved. Either they never touch, or they intersect at a 90 degree angle, or they just plain intersect. This concept is relatively easy to visualize because it is completely 2 dimensional.  Where the difficulty lies, is visualizing these same types of lines when different planes are involved, since it is 3d. To help, I utilize flash cards, or small pieces of paper. Have students draw a series of lines on each flash cards, making sure there is at least a set of parallel lines, perpendicular lines, and intersecting lines on each, and give each line a name. Then move the flashcards in different ways, either stacking them or making parallel planes, and quiz them about the new relationships between the lines.

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