Prealgebra Articles - Wyzant Tutor Blogshttps://www.wyzant.com/resources/blogs/prealgebraThis is an aggregate of all of the Prealgebra articles in Wyzant.com's Tutors' Blogs. Wyzant.com is your source for tutors and students.Tue, 17 Jan 2017 07:18:32 -0600https://www.wyzant.com/images/logos/wyzant-logo.pngPrealgebra Articles - Wyzant Tutor Blogshttps://www.wyzant.com/resources/blogs/prealgebrahttps://www.wyzant.com/resources/blogs/prealgebra466936https://www.wyzant.com/resources/blogs/466936/all_my_students_grade_3_thru_8_passed_the_new_york_state_common_core_examsGilant P.https://www.wyzant.com/resources/users/view/77505480All my students, grade 3 thru 8, passed the New York State Common Core exams<div> </div>
<div>For the 8th consecutive year, all the students whom I tutored for the New York State Common Core examinations, have passed. All have been promoted to the next grade, and or graduated. Some of the students have received Academic Awards from their schools. Tutoring takes much diligence, patience and determination. There may be good and bad days, depending on how the students feel, but we did it. I could not have done it without the parents, who are committed to their children's success. I am very delighted.</div>Tue, 28 Jun 2016 14:46:39 -05002016-06-28T14:46:39-05:00441082https://www.wyzant.com/resources/blogs/441082/mathematical_journeys_the_three_types_of_symbolsEllen S.https://www.wyzant.com/resources/users/view/75479140Mathematical Journeys: The Three Types of Symbols<div>We're going back to basics today with a Math Journey covering the three broad categories of symbols. I've found this concept very handy when introducing Algebra to middle school students. So let's go!<br /><br />Math is a language, and I find it often helps to think of it as such right from the beginning. Just as there are different parts of speech in a language, so there are different 'parts of speech' in math. Where a spoken language includes parts of speech such as nouns, verbs, and adjectives, math has three major types of symbols: constants, operators, and variables. Let's go over each one in detail.<br /><br /><strong>Constants</strong><br />These would be the equivalent of your nouns. A Constant is a number – it has a single, discrete place on the number line. Even if the number itself is ugly – a non-terminating decimal, for example – it still does exist in a specific spot somewhere on the number line. In addition to the obvious constants, math frequently uses what I refer to as 'special constants' or 'named constants' – ugly numbers that are important enough for some reason or other that mathematicians have given them special names and symbols. Pi is a good example of this; mathematicians figured out that performing a specific calculation on a circle always yields the same number, regardless of which circle is used, and figured that that number was special enough to warrant a name. In much the same way, other constants such as e and i have been given names and special symbols to represent them due to their importance for certain calculations. But the important thing to remember here is that all of these named constants do have specific spots on the number line – they don't change value depending on the situation. Pi will always be approximately 3.14159, no matter what you do to the rest of the problem.<br /><br />But that's not always the case.<br /><br /><strong>Variables</strong><br />Variables also represent constants, however in this case the actual value of the constant is unknown. The variable does have a specific spot on the number line, but we don't know where it is. Its location on the number line can vary from problem to problem, but within a single problem it is always consistent. We generally refer to variables using lowercase letters, traditionally starting with x, y, and z, and then moving to others if necessary. In practice, a variable behaves just like a constant, since it does actually represent a constant. It can be manipulated the same way you would a constant, except of course you don't know the value so you'll have to leave some calculations unfinished until you get to a point where you can identify the mystery number. Funnily enough, many elementary math programs use the concept of variables, but they don't define them as such. If you've ever seen a basic math worksheet with a question mark in a problem, you've seen a variable. All algebra does is change over from using a question mark to a series of lowercase letters.<br /><br />3 + ? = 7</div>
<div>3 + x = 7<br /><br /><strong>Operators</strong><br />All the constants and variables in the world won't help us without an operator. Remember how your grammar teacher was always going on about how every sentence needs a verb? Well, every mathematical sentence or phrase needs an operator. An operator is a symbol that performs an action on a constant or set of constants. Plus signs, minus signs, multiplication and division symbols are all operators, but so are square root bars and fraction bars. In fact, as you may have read in one of my earlier Math Journeys, a fraction is just an indication of the top constant being divided by the bottom constant. The equals sign is also an operator of sorts, though it doesn't perform an action on the constants so much as declare a relationship between them. The greek letter Sigma is an operator as well, used to represent taking the sum of a series.<br /><br />And then there's the special operator known as 'a function.' We've talked about functions multiple times before in my blog, and I usually introduce it as a machine that turns one number into another by applying a set rule. That sounds like an operator to me! The key here is that a function is kind of a general operator, one that you can define within a given problem any way you want or need it to be. Want to indicate a specific sequence of operations performed on a number repeatedly over the course of a single problem? Use a function and define it appropriately!<br /><br />Breaking down the world of math symbols in this way helps to clear up some of the confusion that often results from the particulars of traditional naming conventions. Consider, for instance, the following six symbols:<br /><br />e ∏<br />x ?<br />f() ∑<br /><br />All three in the first column are lowercase letters, and all three in the second column are greek symbols. However, their usage in math is better represented by the horizontal rows. The first row are constants, the second variables, and the third operators. And the way they behave differs accordingly. So the next time you're confused, take a look at which type of symbol you're working with!</div>Thu, 17 Mar 2016 08:43:09 -05002016-03-17T08:43:09-05:00371883https://www.wyzant.com/resources/blogs/371883/do_you_like_a_challenge_have_a_go_at_this_calculationGaurav W.https://www.wyzant.com/resources/users/view/85919779Do you like a challenge? Have a go at this calculation...<div>In the calculation below the mathematical symbols have been removed.</div>
<div> </div>
<div>Using only +, -, x and / can you make it correct?</div>
<div> </div>
<div><strong>7 32 6 14 9 12 = 112</strong></div>
<div> </div>
<div>Best regards,</div>
<div>Gaurav</div>Sat, 15 Aug 2015 23:58:41 -05002015-08-15T23:58:41-05:00326477https://www.wyzant.com/resources/blogs/326477/rules_for_integers_in_mathematicsSequoah L.https://www.wyzant.com/resources/users/view/85562724Rules For Integers in Mathematics<div>In mathematics, different functions has different rules and I can see a lot of students are struggling with the rules for integers. So I'll kindly discuss the rules for each operation: + - * /</div>
<div> </div>
<div><strong><span style="text-decoration: underline;">Addition</span></strong></div>
<div> </div>
<div>(-) + (-) = (-)</div>
<div><strong>Ex:</strong> -9+-8=-17</div>
<div> </div>
<div>(+) + (+) = (+)</div>
<div><strong>Ex: </strong>4+6=10</div>
<div> </div>
<div>(+) + (-) [Remember to always take the bigger number sign and use the opposing operation, which is subtraction to solve the equation.]</div>
<div><strong>Ex: </strong>5+-3=2</div>
<div> </div>
<div>(-) + (+) </div>
<div><strong>Ex: </strong>-9+8=-1 [Same rule follow as above]</div>
<div> </div>
<div><span style="text-decoration: underline;"><strong>Subtraction</strong></span></div>
<div> </div>
<div>(-) - (-) </div>
<div><strong>Ex: </strong>-9-(-8) = -9+8<br />[When two negatives are next to each other you change to its opposing operation: addition and change the 8 into a positive integer.]</div>
<div> </div>
<div>(+) - (+) = (+) [Unless the first integer is smaller than the second. <strong>Ex:</strong> 5-8= 5+-8 [Then you follow the rule stated above.]</div>
<div><strong>Ex:</strong> 8-6=2</div>
<div> </div>
<div>(+) - (-) [Follow the rules stated above]</div>
<div><strong>Ex:</strong> 5-(-5)= 5+5</div>
<div> </div>
<div>(-) - (+)</div>
<div><strong>Ex:</strong> -5-6 = -5+-6</div>
<div> </div>
<div><span style="text-decoration: underline;"><strong>Multiplication</strong></span></div>
<div> </div>
<div>(-) * (-) = (+)</div>
<div><strong>Ex: </strong>-9*-8=72</div>
<div> </div>
<div>(+) * (+) = (+)</div>
<div><strong>Ex: </strong>6*7=42</div>
<div> </div>
<div>(+) * (-) = (-)</div>
<div><strong>Ex: </strong>9*-6=-54</div>
<div> </div>
<div>(-) * (+) = (-)</div>
<div>-7*9=-63</div>
<div> </div>
<div><strong><span style="text-decoration: underline;">Division</span> </strong></div>
<div> </div>
<div><em>The rules for multiplication is the same as division but I'll still provide examples.</em></div>
<div> </div>
<div><em>(-) / (-) = (+)</em></div>
<div><strong>Ex: </strong>-64/-8=8</div>
<div> </div>
<div><em>(+) / (+) = (+)</em></div>
<div><strong>Ex: </strong>121/11=11</div>
<div> </div>
<div><em>(-) / (+) = (-)</em></div>
<div><strong>Ex: </strong>-72/8=-9</div>
<div> </div>
<div><em>(+) / (-) = (-)</em></div>
<div><strong>Ex: </strong>36/-6=-6</div>
<div> </div>
<div><em>Feel free to use this as a study guide for test taking purposes, thanks for your time.</em></div>
<div> </div>Sat, 28 Feb 2015 12:33:17 -06002015-02-28T12:33:17-06:00299454https://www.wyzant.com/resources/blogs/299454/how_to_overcome_math_negative_self_talk_part_1Avery A.https://www.wyzant.com/resources/users/view/85292630How To Overcome Math Negative Self Talk - Part 1<div>Purpose: This series shares tips on how to identify, manage, and overcome Mathematics Negative Self Talk (NST). We cannot avoid NST totally because the NST about Math skills in general is a widely accepted habit.<br /><br />So what is Mathematics NST anyway? Mathematics NST is when we speak in our minds or to others about an inability to learn, do, and/or understand Mathematics in general. Focus here is what we cannot do or have never done in Mathematics. For example, "I hate Math." "I can't do Math!" "This is too complicated!" " I could never do Math!" "My parents aren't good at Math either." "What can we use Algebra for anyway?" "The teacher is confusing me." The NST phrases list is endless, but also popular in today’s culture.<br /><br />Downside of NST: NST in Math is simply a bad habit of thinking and attitude. This habit limits learning Math and acts as a source of Math Anxiety. This leads to unproductiveness as far as learning in the classroom. Habits can be broken if we choose to do so. NST in Math is a source of Mathematics Anxiety.<br /><br /> Tip 1: NST in Mathematics is simply a bad habit - respect the power of the habit. Recognize and respect the power of NST in Mathematics. Do not submit to this habit, if you can choose to do otherwise. <br /><br /> Tip 2: Replace the NST habit with Positive Self Talk (PST). Suggest alternative language. Help students determine what they do not understand or have not learned yet that limits their performance on Mathematics assessments. Reinforce the PST habit with recall of how you learned other subjects and skills. If you can learn other disciplines or subjects, you can learn Mathematics too.<br /><br />Comment: The truth is that we like and use general Math. We like to use time, get paid reasonable wages for working, checking stock options, sports scores, labor statistics, etc. all involve Math to enjoy or appreciate. Students and educators alike must realize that general Math is all around us every day. Higher level math like Calculus, Operations Research, Differential Equations, etc.….that’s a completely different story.<br /><br />Grow & Improve<br /><br />**Please share your comments.</div>Sun, 02 Nov 2014 10:49:31 -06002014-11-02T10:49:31-06:00246136https://www.wyzant.com/resources/blogs/246136/i_am_in_need_of_some_studentsAshley M.https://www.wyzant.com/resources/users/view/84377950I am in need of some students. <div>Hi,</div>
<div> </div>
<div>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.</div>Sat, 23 Nov 2013 19:47:33 -06002013-11-23T19:47:33-06:00242155https://www.wyzant.com/resources/blogs/242155/fractions_decimals_and_percentagesMichael H.https://www.wyzant.com/resources/users/view/80737230Fractions, Decimals and Percentages<div>When working with fractions, I find it effective to require students to convert each fraction that we work with to its decimal equivalent, to convert that decimal equivalent back into the original fraction, to convert that decimal into its percentage equivalent, to work a simple percentage problem using that percentage and finally to work the same problem using the initial fraction.</div>
<div> </div>
<div>This comprehensive method helps students to see the relationships between fractions, decimals and percentages in a holistic way and to promote the necessary skills in each element.</div>
<div> </div>Thu, 24 Oct 2013 08:42:15 -05002013-10-24T08:42:15-05:00234691https://www.wyzant.com/resources/blogs/234691/math_instructor_and_tutorSaundra F.https://www.wyzant.com/resources/users/view/83525530Math Instructor and Tutor<p>Greetings!</p>
<p>I am a very enthusiastic individual when it comes to math! Within my 10+ years of teaching math, I have experienced much success with students. I've been rated a highly effective teacher due to most students showing growth on FCAT. A very high percentage moved up 1 or 2 levels on this high stakes test. The small percentage of students that didn't move up a level still showed a considerable amount of growth within the same level. I credit this to my high level of expertise in the field along with the interpersonal relationships that I have with students. I look forward to working with you and helping you develop a love for math!</p>Sat, 10 Aug 2013 13:52:34 -05002013-08-10T13:52:34-05:00233896https://www.wyzant.com/resources/blogs/233896/proving_proportionsJorge L.https://www.wyzant.com/resources/users/view/83164680Proving Proportions<p><b>DEFINITIONS</b>
<br>When given two ratios (in the form x:y) or two relations (in the form of fractions), if the ratios of each element are the same they're said to be proportionate.
<br>Example: 3/6 and 1/2 are proportionate because 3 out 6 is the same as 1 out of two (half).
<br><b>PROVING PROPORTIONALITY</b>
<br>When given two fractions to prove as proportionate, such as
<table>
<tr><td><u>1</u></td> <td>and</td> <td><u>3</u></td></tr>
<td><td>2</td> <td></td> <td>6</td></tr>
</table>
<br>you solve through cross-multiplication.
<br>Cross multiplication involves multiplying the numerator (number on top) by the denominator (number on bottom) of the other fraction, and then comparing the results. If the values are the same, the fractions are proportionate.
<br>The set-up above will be set-up as such:
<table>
<tr><td>1 * 6</td> <td><u>?</u></td> <td>2 * 3</td></tr>
<tr><td>(6)</td><td> = </td><td>(6).</td></tr>
</table>
<br>Because both values are the same, these fractions are proportionate.</p>
<p>Example 2:
<table>
<tr><td> <td>3/2</td> <td>and</td> <td>18/8</td></tr>
</table>
<br>The cross-multiplication yields:
<table>
<tr><td>3 * 8</td><td><u>?</u></td> <td>18 * 2</td></tr>
<tr><td>24</td> <td><u>?</u></td> <td>36</td></tr>
</table>
<br>Because 24 does not equal 36, these two fractions are not proportionate.</p>
<p>Example 3:
<table>
<tr><td>6/10</td> <td>and</td> <td>9/15</td></tr>
</table>
<br>The cross-multiplication yields:
<table>
<tr><td>6 * 15</td> <td><u>?</u></td> <td>9 * 10</td></tr>
<tr><td>90</td> <td>=</td><td> 90</td></tr>
</table>
<br>Since both multiplications solve as 90, these two fractions are proportionate.</p>Tue, 30 Jul 2013 08:56:33 -05002013-07-30T08:56:33-05:00234225https://www.wyzant.com/resources/blogs/234225/vocabulary_part_1Jehsuamo C.https://www.wyzant.com/resources/users/view/80578160Vocabulary Part 1<p></p><p>When I was studying to be a teacher, one of the classes I had to take was Literacy in Secondary Education. Since the word <em>literacy</em> is associated to reading and writing by most, it would strike many as a surprise that Math teachers have to take courses on literacy. However, literacy is the most practical and crucial aspect of ANY academic discipline, simply because it involves the ability to read and write in said subject. For mathematics, it could not be anymore important. If you cannot understand the words that I am using, then it is almost as if we were communicating to each other in different languages.</p>
<p>So whatever subject you are studying, I suggest you learn its vocabulary.</p>
<p>As the helpful tutor that I am, I will share a list of vocabulary terms that was distributed in my literacy class to all of you so that you can check your own vocabulary. Keep in mind that this is considered to be the Mathematics vocab that one should know by the time they finish high school. If you don't know them all, that is fine (honestly most of us forget terms we do not use consistently). Keep in mind that the goal is to know as much of the list as possible. <em><strong>Parents!!! This is also a good way to see what your children have been learning in school!!!</strong></em></p>
<p>I give the words on level 1 and 2 in this blog, there are four levels in the list.</p>
<p><u><strong>LEVEL 1</strong></u></p>
<p>ABOVE<br>
ADDITION<br>
AREA<br>
BEHIND<br>
BELOW<br>
BETWEEN<br>
CALENDAR<br>
CARDINAL NUMBER<br>
CHANCE<br>
CIRCLE<br>
CLOCK<br>
COIN<br>
CORNER<br>
DAY<br>
DECREASING PATTERN<br>
DIFFERENCE<br>
DIRECTION<br>
DISTANCE<br>
ESTIMATE ANSWER<br>
FOOT (measurement)<br>
GRAPH<br>
GREATER THAN<br>
GROUPING<br>
GUESS AND CHECK<br>
HEIGHT<br>
HOUR<br>
IN FRONT<br>
INCH<br>
INCREASING PATTERN<br>
INSIDE<br>
LEFT<br>
LENGTH<br>
LESS THAN<br>
LISTS<br>
LOCATION<br>
MEASURING CUP<br>
MINUTE<br>
MODEL<br>
MONEY<br>
NEAR<br>
NUMBER<br>
NUMBER LINE<br>
NUMERAL<br>
NUMERIC PATTERN<br>
ORDINAL NUMBER<br>
ORIENTATION<br>
OUTCOME<br>
OUTSIDE<br>
PATTERN<br>
PATTERN EXTENSION<br>
POUND<br>
PREDICTION<br>
RECTANGLE<br>
RIGHT<br>
SECOND (TIME)<br>
SET<br>
SHAPE COMBINATION<br>
SHAPE DIVISION<br>
SHAPE PATTERN<br>
SIMILARITY<br>
SIZE<br>
SOUND PATTERN<br>
SQUARE<br>
STANDARD MEASURES OF TIME<br>
STANDARD MEASURES OF WEIGHT<br>
SUBTRACTION<br>
SUM<br>
TABLE<br>
TEMPERATURE<br>
TEMPERATURE ESTIMATION<br>
TEMPERATURE MEASUREMENT<br>
TIME INTERVAL<br>
TRIANGLE<br>
UNDER<br>
VOLUME<br>
WEEK<br>
WHOLE NUMBER<br>
WIDTH<br>
YEAR<br>
ZERO</p>
<p><u><strong>LEVEL 2</strong></u></p>
<p>2-DIMENSIONAL SHAPE<br>
2-DIMENSIONAL SHAPE COMBINATION<br>
2-DIMENSIONAL SHAPE DECOMPOSITION<br>
2-DIMENSIONAL SHAPE SLIDE<br>
2-DIMENSIONAL SHAPE TURN<br>
2-DIMENSIONAL SPACE<br>
3-DIMENSIONAL SHAPE<br>
3-DIMENSIONAL SHAPE COMBINATION<br>
ACUTE ANGLE<br>
ADDEND<br>
ADDITION ALGORITHM<br>
ANGLE<br>
ANGLE MEASUREMENT TOOL<br>
ANGLE UNIT<br>
AREA<br>
ASSOCIATIVE PROPERTY<br>
BAR GRAPH<br>
BASIC NUMBER COMBINATIONS<br>
CAPACITY<br>
CENTIMETER<br>
CERTAINTY (probability)<br>
CIRCUMFERENCE<br>
CLASSES OF TRIANGLES<br>
CLUSTER<br>
COMMON DENOMINATOR<br>
COMMON FRACTIONS<br>
COMMUTATIVE PROPERTY<br>
CONSERVATION OF AREA<br>
CONSTANT<br>
CORRESPONDING ANGLES<br>
CORRESPONDING SIDES<br>
CUBE<br>
CYLINDER<br>
DATA<br>
DATA CLUSTER<br>
DATA COLLECTION METHOD<br>
DECIMAL<br>
DECIMAL ADDITION<br>
DECIMAL DIVISION<br>
DECIMAL ESTIMATION<br>
DECIMAL MULTIPLICATION<br>
DECIMAL SUBTRACTION<br>
DIAGRAM<br>
DIFFERENT SIZE UNITS<br>
DISTRIBUTIVE PROPERTY<br>
DIVIDEND<br>
DIVISIBILITY<br>
DIVISION<br>
ELAPSED TIME<br>
ENGLISH SYSTEM OF MEASUREMENT<br>
EQUATION<br>
EQUILATERAL TRIANGLE<br>
EQUIVALENT FORMS<br>
EQUIVALENT FRACTIONS<br>
ESTIMATION OF HEIGHT<br>
ESTIMATION OF LENGTH<br>
ESTIMATION OF WIDTH<br>
EVEN NUMBERS<br>
EVENT LIKELIHOOD<br>
EXPANDED NOTATION<br>
EXTREME VALUE<br>
FACES OF A SHAPE<br>
FACTORS<br>
FLIP TRANSFORMATION<br>
FRACTION<br>
FRACTION ADDITION<br>
FRACTION MULTIPLICATION<br>
FRACTION SUBTRACTION<br>
FRACTIONS OF DIFFERENT SIZE<br>
FRONT-END DIGITS<br>
FRONT-END ESTIMATION<br>
FUNCTION<br>
GEOMETRIC PATTERN<br>
GEOMETRIC PATTERNS EXTENSION<br>
GRAM<br>
GREATEST COMMON FACTOR<br>
GROWING PATTERN<br>
HISTOGRAM<br>
IDENTITY PROPERTY<br>
IMPROBABILITY<br>
IMPROPER FRACTION<br>
INEQUALITY<br>
INEQUALITY SOLUTIONS<br>
INTERSECTION OF SHAPES<br>
INVALID ARGUMENT<br>
INVESTIGATION<br>
IRRELEVANT INFORMATION IN A PROBLEM<br>
ISOSCELES TRIANGLE<br>
LEAST COMMON MULTIPLE<br>
LINE GRAPH<br>
LINEAR PATTERN<br>
MASS<br>
MEAN<br>
MEASUREMENT<br>
MEASURES OF CENTRAL TENDENCY<br>
MEASURES OF HEIGHT<br>
MEASURES OF LENGTH<br>
MEASURES OF WIDTH<br>
MEDIAN<br>
METER<br>
METRIC SYSTEM<br>
MIDPOINT<br>
MIXED NUMBERS<br>
MODE<br>
MULTIPLE<br>
MULTIPLICATION<br>
NEGATIVE NUMBER<br>
NUMBER OF FACES<br>
NUMBER PAIRS<br>
NUMBER SENTENCE<br>
NUMBER TRIPLET<br>
OBTUSE ANGLE<br>
ODD NUMBERS<br>
OPEN SENTENCE<br>
ORDER OF OPERATIONS<br>
PARALLEL LINES<br>
PARALLELOGRAM<br>
PARALLELOGRAM FORMULA<br>
PART TO WHOLE<br>
PATH<br>
PATTERN ADDITION<br>
PATTERN SUBTRACTION<br>
PERCENT<br>
PERIMETER<br>
PERPENDICULAR LINES<br>
PIE CHART<br>
POSITIVE NUMBER<br>
PRIME FACTORIZATION<br>
PRIME NUMBER<br>
PRISM<br>
PROBABILITY<br>
PROCESS OF ELIMINATION<br>
PRODUCT<br>
PROOF<br>
PYRAMID<br>
QUOTIENT<br>
RECTANGLE FORMULA<br>
RECTANGULAR PRISM<br>
REDUCED FORM<br>
RELATIVE DISTANCE<br>
RELATIVE MAGNITUDE<br>
RELATIVE MAGNITUDE OF FRACTIONS<br>
RELATIVE SIZE<br>
RELEVANT INFORMATION IN A PROBLEM<br>
REMAINDER<br>
REPEATING PATTERN<br>
RESTATE A PATTERN<br>
REVERSING ORDER OF OPERATIONS<br>
RHOMBUS<br>
RIGHT ANGLE<br>
ROTATION<br>
ROUNDING <br>
RULER<br>
SAME SIZE UNITS<br>
SAMPLE<br>
SCALE<br>
SHAPE SIMILARITY<br>
SHAPE SYMMETRY<br>
SHAPE TRANSFORMATION<br>
SHRINKING PATTERN<br>
SPHERE<br>
STANDARD VS NONSTANDARD UNITS<br>
STUDIES<br>
SUBSET<br>
SUBTRACTION ALGORITHM<br>
SURFACE AREA<br>
SURVEY<br>
SYMBOLIC REPRESENTATION<br>
TALLIES<br>
TIME ZONE<br>
TRIAL & ERROR<br>
TRIANGLE FORMULA<br>
TRUNCATION<br>
UNIT CONVERSION<br>
UNIT DIFFERENCES<br>
UNLIKE DENOMINATORS<br>
VALID ARGUMENT<br>
VARIABILITY<br>
VENN DIAGRAM<br>
VERBAL REPRESENTATION OF A PROBLEM<br>
VERIFICATION<br>
VERTICAL AXIS<br>
VOLUME MEASUREMENT<br>
VOLUME OF IRREGULAR SHAPES<br>
VOLUME OF RECTANGULAR SOLIDS</p>Tue, 02 Jul 2013 22:47:22 -05002013-07-02T22:47:22-05:00234548https://www.wyzant.com/resources/blogs/234548/frustration_a_part_of_the_learning_processDana B.https://www.wyzant.com/resources/users/view/80345340Frustration: a Part of the Learning Process<p>Although learning is awesome, it can be a difficult and frustrating journey for many students. This difficulty, however, is often times quite normal although most feel it means that a child may not be able to learn or that he/she is so frustrated that learning is no longer taking place. This is where the experienced tutor steps in; for frustration in learning is a part of the learning itself.</p>
<p>I have taught and tutored many students and have seen first hand how this frustration can leave some students, and their parents, feeling helpless and hopeless. But there is ALWAYS Hope!!! What they have failed to realize is that as the brain learns difficult concepts, it can only take in parts at a time, little parts at a time. So although it may seem no learning is taking place, it actually is, just in smaller segments. In fact, the most frustration comes right before a new concept is achieved. This is when most children become the 'most' frustrated. The may not want to go to school, complain they don't feel well, or just feel down. They may just be coming up on a huge milestone in their learning. If they keep trying, the concept will be learned and the symptoms will disappear. </p>
<p>I NEVER give up on my students. I encourage, praise, reward, assist, etc. until the new concept has been reached. Because I understand that frustration is part of the learning process, I become eager when students experience it...they are on the road to progress!!!</p>Fri, 28 Jun 2013 22:25:05 -05002013-06-28T22:25:05-05:00234169https://www.wyzant.com/resources/blogs/234169/be_like_waterBruce S.https://www.wyzant.com/resources/users/view/78147110Be Like Water...<p>Humans have a tremendous capacity to learn and adapt. However, we consistently build barriers that hinder our natural ability to change and grow. Many people, regardless of age, perceive themselves as not being talented enough to excel at math and science. They view math and science as the realms in which only scientists, engineers, mathematicians, and geniuses truly soar.</p>
<p>Nothing could be further than the truth. Sure, possessing a natural affinity towards these subjects helps. Yet, a supposed lack of talent does not prevent you from learning. The path may be more arduous. The journey may be longer. Nevertheless, you possess within you the fire to endure. Willpower, dedication, self belief, and an open mind can compensate for any lack of ability.</p>
<p>Bruce Lee was a legendary martial artist, actor, and philosopher who continues to inspire millions with the sheer intensity which he pursued his endeavors. Frail, sickly, and small as a child, Bruce Lee overcame many physical limitations to transform himself into a physical specimen that the world had never seen. Although the results are magnificently displayed on the big screen, what remains unseen are the thousand of reps, hours of study, and countless days and nights of trial and error that Bruce logged to reach his goals. He would urge people to adapt to any situation just as water adapts and assumes the shape of any container that holds it. "Be water my friend" was a famous utterance of Bruce Lee.</p>
<p>There are things that you too can do to master the art of learning:</p>
<p><strong>Empty your cup</strong></p>
<p>Get rid of any preconceived notions about learning math or science. Unlike athletics, you don't have to be a physical specimen to perform. Instead, the mind reigns supreme. You need to empty your mind and make it a blank slate. Become childlike and allow your natural inquisitiveness to unfold. Little kids don't judge, they just explore! Tap into your inner child and embrace the new and strange.</p>
<p><strong>Realize your strengths</strong></p>
<p>What do you enjoy doing? Think about what personal attributes are activated whenever you enjoy a hobby. Generalize these traits. Now adapt these traits towards learning math or science. For instance, if you are meticulous and organized in your hobby then be meticulous and organized in your studies. If your pastime requires patience, redirect it towards your studies. Everyone is good at something. Break down those elements and rebuild them towards your learning.</p>
<p><strong>Acknowledge and deal with your weaknesses</strong></p>
<p>Maybe you procrastinate. Maybe you are disorganized. Maybe you avoid difficult situations. Now is the time to be honest with yourself. Address your weak points. When you become injured or sick, you instinctively work around your ailment. Well, to overcome your difficulties in learning math or science, you must consciously stop any attempts to sabotage your progress. You must realize when study time must be increased. You must double down on suppressing bad habits and attitudes.</p>
<p><strong>Be like water</strong></p>
<p>There's an old expression, "fake it until you make it". Your mentality is everything! Envision yourself as greater than what you are. Pretend you are the world's greatest scientist or mathematician and you are unraveling a mystery. Jump in and immerse yourself in the moment. When you play with children, become childlike. When cooking, become a famous chef. When playing sports, become a great athlete. When watching a movie, become the character onscreen. Likewise, when studying math or science become the world's greatest analytical mind.</p>
<p>Everything flows from you mindset. Become the scientist. Become the mathematician. Be like water.</p>Tue, 25 Jun 2013 09:20:36 -05002013-06-25T09:20:36-05:00234410https://www.wyzant.com/resources/blogs/234410/my_summer_continuing_educationNatalie B.https://www.wyzant.com/resources/users/view/77223300My Summer Continuing Education<p>Each summer I have a few students who work on both math and reading to keep the 'flow' and/or prep for the upcoming year. These students and their parents are completely committed to the idea of <i>always</i> learning as opposed to the idea of <strike>only</strike> learning in the classroom or merely learning during the school year... in essence, the parents are setting the foundation for lifelong learning.
<br>I would never ask a student to do work which I would not be willing to do myself or work through with them in tutoring. To this end, I have the opportunity to do reading AND catch up on my practice. This summer I am reading 'The Joy of X-A Guided Tour of Math, from One to Infinity' by Steven Strogatz at Cornell University. I LOVE this book! It is almost as good as being in a lecture or small gathering and has helped me explore how I think about math and how to share these ideas with my students.
<br>One of my students recommended 'Hoot' by Carl Hiassen and it is on my list for the library. My student read it at school and just knows I would love it as I enjoy science. I am 1/4 through 'The Wind in The Willows' for another student. In the background I am reading 'The Creators' by Boorstin as his books usually take 12-18 months. 'The Discoverers' by Boorstin took almost two years due to the depth of the book (mostly science and math) and I was able to share with students how it is okay to take time reading a book, especially one with footnotes and even do research about ideas I am learning.
<br>In each and every case, I share what I am reading with students and parents, let students look at the books and ask me questions, explain what I like and/or dislike. This is one portion of my contribution to 'life long learning' by demonstrating it in action.
<br>The crazy part - I really enjoy reading and trying new ideas. It is fun to discuss new ideas with teacher colleagues and friends, apply this knowledge in tutoring and begin to explore new ideas which will help me enjoy other aspects of my life.
<br>The best part: I ABSOLUTELY love what I am reading and continue to learn -which helps me improve my practice as a tutor/teacher. My behavior allows me time to lounge in the library, on the beach and pour through used book stores with no shame.
<br>During the regular school year, when my time is limited, I am addicted to Wired, Popular Science, The New Yorker, National Geographic and other magazines which have shorter pieces. While these are also a portion of my own development, they do not necessarily best represent reading full length books. I live for summer to catch up on all the great writing out in the world.
<br>Check in with your tutor to see what they do over the summer and how they 'instigate' the joy of reading!
<br>As <u>James Patterson</u> stated in his recent NPR interview on why reading is important for young people:
<br><i>"What I'm really addicted to is getting people to understand that if their kids aren't competent readers coming out of middle school, it's really going to be hard for them in high school. They're going to have trouble getting through. Kids don't read as much as you'd like them to, just in terms of seeing the world from different perspectives. I mean, that's the great thing about books, still. Here's television, here are the movies, and it's pretty limited in terms of the perspectives. But books, it's still, there's so many different ways to look at life, so many different stories, and books are still the best place to get that kind of diversity."</i></p>Sat, 22 Jun 2013 14:28:33 -05002013-06-22T14:28:33-05:00234433https://www.wyzant.com/resources/blogs/234433/summer_tutoringTracey M.https://www.wyzant.com/resources/users/view/78672910Summer Tutoring<p>SUMMER OPPORTUNITIES</p>
<p>Now that students, teachers, parents and tutors have had a chance to catch their breath from final exams, it's time to make use of the weeks we have before school starts back. Consider all that could be accomplished in the next few weeks:</p>
<ul>
<li>Areas of math that students <strong>NEVER REALLY GRASPED</strong> could be fully explained. This could be <u>elementary skills</u> like adding fractions, <u>middle school topics</u> like systems of equations, or <u>high school areas</u> like sequences and series.</li>
<li>Students could have a <strong>TREMENDOUS HEAD START</strong>on topics that will be covered in the first few weeks of school. Imagine your son or daughter being able to raise their hand to answer a question in the first week of school because they had worked several problems just like the ones that the teacher is demonstrating.</li>
<li><strong>ENORMOUS PROGRESS</strong> could be made in the area of preparation for the standardized tests (PSAT, SAT, ACT and more) that are so important to getting into a great college.</li>
<li><strong>STUDY SKILLS</strong> could be mastered so that your child excels in ways you've always hoped for and in all subjects, not just math.</li>
<li>Topics in <strong>HOME SCHOOL MATH</strong> could be reviewed so that your daughter or son is ready to start their new curriculum in the fall.</li>
<li><strong>GROUP LESSONS</strong> can be coordinated so that students learn together in small groups of 3 to 5 students and have a competitive component added. I have seen this work wonders in helping boys and girls overcome shyness about raising their hand, taking a chance that their answer may be right or wrong and communicating with each other. There is a vast positive difference in how fast the material is mastered.</li>
</ul>
<p>My <u><strong>hourly rate has been reduced for June and July</strong></u> so that students can get much-needed help during these precious weeks before their heavy class loads start back.</p>
<p>I hope to hear from you and I look forward to helping your child make great progress in the area of math!</p>Tue, 18 Jun 2013 16:56:01 -05002013-06-18T16:56:01-05:00233527https://www.wyzant.com/resources/blogs/233527/greeting_wyzant_communityAdam R.https://www.wyzant.com/resources/users/view/82400370Greeting Wyzant Community<p>Greetings Wyzant community, prospective students, fellow tutors:</p>
<p>I have just returned from my studies abroad and am ready to begin teaching again. Please take a look at my profile. My education ranges from my Masters in Physics, to my undergrad degrees in physics, biology and music. I just completed the coursework for a masters program in peace and conflict resolution as well.</p>
<p>Aside from know knowledge and experience teaching, I think I possess a very good ability to understand the different ways students learn. This helps me to engage with them in a way that is most effective for them. Not only does it help to comprehend the material for the subjects they are learning but it also helps them to develop a wisdom and intuition for further (creative) learning and a strategic approach towards test taking.</p>
<p>I'm looking forward to working with all of you. Don't hesitate to contact me for any reason...</p>Thu, 06 Jun 2013 12:44:37 -05002013-06-06T12:44:37-05:00233948https://www.wyzant.com/resources/blogs/233948/how_to_maximize_your_mathematics_tutoring_experienceWendy T.https://www.wyzant.com/resources/users/view/81633830How to maximize your mathematics tutoring experience<p>Hi math students :)</p>
<p>When preparing for a mathematics tutoring session, try to have the following things at hand...</p>
<ul>
<li>Textbook (online or e-text)</li>
<li>Syllabus, assignment, tips/hints/suggestions, answer sheet/key</li>
<li>Class notes</li>
<li>Pencils, pens, erasers, paper (graph paper, ruler, protractor)</li>
<li>All necessary formulas, laws, tables, constants, etc.</li>
<li><strong>Calculator that you will use on tests</strong></li>
</ul>
<p>Do I really need my calculator? I can do most of my work in my head.</p>
<p>Having your calculator is just as important as paper and a pencil in most cases. You'll be using it on your test and if you don't know how to input what you want, you won't do very well. Have your tutor teach you about your calculator's functions beforehand. Learn how to check your simple math and how to input exponents, logarithms, or trigonometric functions before your test.</p>
<p>Why do I need my book, notes, or answer key? Isn't the tutor supposed to know everything?</p>
<p>Yes :), but even the most experienced tutor may want to see what level of material your textbook covers, keeping the session within established parameters. Answer keys can show formatting options preferred by an instructor. For example, should fractions be reduced or not, should answers be provided in radians or degrees, and should solutions be factored out or not after simplification? Class notes can often provide examples of particular homework questions worked out using the instructor's preferred method, and with a solution given in the instructor's preferred format. Many methods in mathematics provide options and tutors want you to get as much credit as possible. You should never be missing points when you know the material.</p>
<p> </p>Sun, 02 Jun 2013 22:17:52 -05002013-06-02T22:17:52-05:00234122https://www.wyzant.com/resources/blogs/234122/5_characteristic_of_online_software_for_mathLee L.https://www.wyzant.com/resources/users/view/791918105 characteristic of online software for math<p>5 characteristic of online software for math</p>
<p>Appearance<br>When I first look at a computer screen or a new web design, I first look at the ease of reading the text. The best is a light grey or white cream color with a dark grey or black as the background. I have come across sites that will have a dark color with dark text. If you have ever seen an image with dark colors in it and the image had dark imposed lettering you know what I mean. The dark lettering disappears against the dark backdrop of the image. You almost have to guess what the hidden text is saying. It is far too much work.<br>Another factor in color is too much. Clown colors are out unless you are dealing with children. Sound should also be limited. I do not like circus music unless you are dealing with smaller students.<br>Thus, interest and appearance should be age appropriate. All you have to do is look at a kid site and you will know what I mean. Fat letters, bright colors, circus music in the background although there are some good games out there that are seriously challenging.</p>
<p>Immediate feedback<br>There should be an option for the student to have immediate feedback on the answer and how the answer is processed. I call it teaching without error. It is not a good idea to have the student continue on the same error. Once it is established, then it is hard to break.<br>Thus, the software should not allow the student to move on unless there is a correct reinforcement of their work.</p>
<p>Limited questions<br>The software should not be overhead with endless rows of problems. If you have ever taken a test and had a worksheet place in front of you with an endless row of problems then you know what I mean. The eye focuses on the next problem or the next one and so on. That is a time waster. Just take the first problem first and dont worry about the coming future. It is too overwhelming.</p>
<p>Break between solutions<br>When a student is struggling with math, I think it is a good idea to be able to walk away from the computer after a limited amount of time. I have been in classes where the professor has droned. Sitting there was worse than a root canal. The advantage of listening to a lecture is you can check out and go the happy place in your mind. When dealing with math interaction assessments and practice, there needs to be a stopping and starting place. Something it is just one problem after another, but after 15 or 20 minutes of work, students struggling with math need a break.<br>Another way to handle this issue is a set of 5 or 7 problems on the same subject matter, and then the student is done with that session. Of course, with online math, a student can walk away anytime they want, but the roll is to keep them focused for a time and then give a break.</p>
<p>Ease of changing level of difficulty<br>I always look for the level of difficulty when the online system first starts out. It should be below the students level, even when engaged in mathematical equations taking up half a page of notes.<br>The user should be able to pick the type of equations on which to practice, but the level of difficulty should be based on what the student can actually accomplish. If the student cannot find a solution, then the software should go over the same concept before allowing the more extensive processes. However, again, the new set of problems should always begin with the easiest for the user to manage.</p>
<p>Thats it for now. Happy hunting, I will be covering a few of the free math online software I use with my students in the near future with the criteria outlined above. In the meantime, please leave some feedback on the online software you use so our community can be informed.</p>
<p>Happy tutoring.</p>
<p>Lee</p>Fri, 31 May 2013 18:02:44 -05002013-05-31T18:02:44-05:00227913https://www.wyzant.com/resources/blogs/227913/the_importance_of_algebraKeisha K.https://www.wyzant.com/resources/users/view/82190290The IMPORTANCE of ALGEBRA!<p>To My Future and Current Students,</p>
<p>I can't stress enough the IMPORTANCE of ALGEBRA! Of all the mathematics I have taken in my lifetime...BELIEVE ME IT'S BEEN A LOT, ALGEBRA is the only course that is WOVEN into every single course. I was lucky enough that my first mathematics teacher in High School (Mr. Large), turned me from a B student into an A student such that I graduated High School with a 4.0 in mathematics. The one piece of advice he gave me that I will share with you is that...I NEED TO CHECK, DOUBLE CHECK AND TRIPLE CHECK ALL OF MY ANSWERS!</p>
<p>Algebra is a required course (prerequisite) for many of your other math courses, but most importantly in your High School career it is MANDATORY in order to be successful in Algebra 2. It may seem silly to learn and master Algebra, however, it is an integral part of every math course you will take after that except some geometry courses. Algebra teaches you how to think, be organized and how to prove your answers by checking them. It makes use of all of those math principles you thought were useless before it like...adding, subtracting, multiplying and dividing signed numbers. It makes use of solving quadratic equations by solving single variable equations.</p>
<p>While taking your ALGEBRA course this year or next, focus on truly understanding the following concepts to be transferred into math you will later encounter:</p>
<p>1. Solving Single Variable Equations that require Combining Like Terms.<br />
2. Understanding the how sign changes work with Addition, Subtraction, Multiplication and Division WITHOUT A CALCULATOR!<br />
3. Factoring Polynomials by finding the Roots/Zeros.<br />
a. Quadratics<br />
b. Difference of Squares<br />
c. Quadratic Formula <br />
4. Completing the Square<br />
5. Solving Systems of 2 equations<br />
6. Performing Mathematical Operations on Polynomials<br />
a. Multiplying and Dividing Monomials (e.g. x^2 * x^3 = x^5; (x^7) / (x^2) = x^5)<br />
b. Multiplying Bionomials using FOIL.<br />
c. Multiplying Polynomials (e.g. [(x + 7)(x^2 + 2x + 1)] = x^3 + 9x^2 + 15x + 7)<br />
d. Dividing Monomials and Polynomials<br />
e. Adding/Subtracting Monomials and Polynomials (e.g. x^2 + 2x = x^2 + 2x because the exponent on the variables are not the same though the variable is the same.</p>
<p>Each of these topics will be revisited in your remaining courses and thus should be MASTERED in Algebra if at all possible. Please note mastery does not mean you earned an A in the class. You can master a subject and have a B or even a C for a final grade. It takes some of us longer to learn material than others and that is all fine and well. Some teachers don't believe that your final exam grade if the exam is cumulative should trump your previous performance in the course. When I speak of MASTERY of a subject I am speaking of understanding the concepts and restrictions well enough to know when you can use the things you have learned and when you can not...MASTERY IS NOT PERFECTION, but it is the road that lead to NEAR PERFECTION.</p>
<p>Thanks for Reading!<br />
--Keisha</p>Sun, 24 Mar 2013 05:40:32 -05002013-03-24T05:40:32-05:00227425https://www.wyzant.com/resources/blogs/227425/advice_to_my_younger_self_the_studentLisa B.https://www.wyzant.com/resources/users/view/81951870Advice to my younger self- the student<p>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.</p>
<p>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.</p>
<p>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 manner- not spreading rumors, belittling, or forming a grudge against someone. There are so many times in life when 'life' gets in the way of a group project and if you can learn how to help each other out in a group setting from an early age, you are bound to be a better co-worker. However, to be truly successful you need to be able to decipher when someone is truly going through something and needs assistance and when he/she is just being lazy- the latter requiring a different skill set to handle the situation.</p>
<p>Other than that, be confident in your abilities and don't be afraid to acknowledge the things that you need help with from others. We all have things that we are good at- we all have things that we are not good at, but if we work to the best of our ability no matter what that is and in what form- we can be the success that we were meant to be.</p>Tue, 19 Mar 2013 20:54:44 -05002013-03-19T20:54:44-05:00226605https://www.wyzant.com/resources/blogs/226605/your_child_s_success_is_my_successNeemisha M.https://www.wyzant.com/resources/users/view/80780250Your Child's Success is My Success<p>A parent told me recently that her son scored a near 100% on his last test. I was so proud. I feel proud when all my students succeed. The question is what does it mean for a student to be successful. I think it's a mix between the student having more confidence than when I begin working with the student, as well as an increase in the student's grades.</p>
<p>Depending on the student and his or her own situation grades may increase immediately and with others it may take a bit of time. I want my students to feel confident about their abilities and also be able to show the world and themselves that they understand what's going on in class. I make a commitment when I take on a student, which is, I will work my hardest to be available and flexible. Your child's success is my success.</p>Mon, 11 Mar 2013 12:05:45 -05002013-03-11T12:05:45-05:00