tag:blogger.com,1999:blog-5410562205692621875Sat, 01 Aug 2015 14:00:04 +0000geometrynew TPT sellerfractionsproblem solvingmultiplicationanglesdivisionreducing fractionsmath study skillspatternsscienceAlgebraConceptual Development ModelReadingadditioncountinggraphinglong divisionnumber patternsplace valuequadrilateralsskip countingtrash to treasure ideasBloom's TaxonomyEarth DayFibonacci numbersTen Black Dotsadding fractionsautumndigital rooteven numbersfallglyphsgreatest common factorleast common multipleleavesmanipulativesmathmath humormathphobiaodd numbersparent/teacher conferencespatterns in naturepositive and negative numbersproperties of zerorecyclingright anglescience investigationsspecial educationsubitizingtestingtrapezoid100th Day2 digits times 2 digitsAdding consecutive numbersAlgebraic equationsAnno's Counting BookAnno's Mysterious Counting JarBen FranklinCommon CoreConsumer's ReportFoilFreeGrandparent's DayHalloween activitiesMagic SquaresMath CurseMilk Lid MathMy Side of the MountainNot on the TestOhio StateOrder of OperationsPEMDASPi DayPinterestSpellingTeachers Pay TeachersThanksgivingWolf's Chicken Stewadding and subtracting positive and negative numbersartbase ten systembeginning school activitiesbutterliescard holderscell phoneschanging fractions to decimalschecklistscirclesclassroom managementcoffee filterscomparing numberscomplimentary anglesconcentric circlesconstructing anglesdecimalsdeliberate practicedicedividenddividing by 1/4dividing by zerodividing fractionsdivisibility rulesdivisordominoesdrilldump and divideequivalent fractionsfactorialsfalcon hoodsfive elements of a storyfoodgamesgoal settinggrades 4-5grades PreK-1graphic organizersgreater thangreater than/less than symbolsgritgrouping studentshailhomeworkisosceles trapezoidkiteleap yearlearning math factsleft angleless copiesless thanlesson planslinear equationslinear measurementlowest termsmaking a bookmaking stencilsmath and artmath attitudemath factsmath tipsmathsmeasurementmeasuring anglesmini lessonsmultiple choice testsmultiplying by 11multiplying polynomialsnegative self-talknegative x negativenumber tilesoctagonone unknownpalindromespaperless optionsparabolaparent infopattern stickspercentperegrine falconpipicture graphsplane geometryplateful of ideaspracticeprimary gradesprogressive educationproperties of ninequotientresonancerhombusrhyming wordsshort divisionslopesolving for xsong about testingsortingsound patternsspiderssquare numbersstencils from plastic lidssubtractionsupplementary anglestest anxietytesting constesting prostoilet papertraditional educationusing a protractorvinculumword problemsx as an unknownzero as a divisorzero as an exponentGo Figure!Where "Mathphobics" and Lovers of Math Converge!http://gofigurewithscipi.blogspot.com/noreply@blogger.com (Scipi)Blogger134125tag:blogger.com,1999:blog-5410562205692621875.post-6531646864217687270Sat, 01 Aug 2015 14:00:00 +00002015-08-01T09:00:04.754-05:00Back to School Two Day Sale<div style="text-align: left;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-CWZLEgLUpYE/U9kxGpgPChI/AAAAAAAAFnE/Pn8D9BLiPHs/s1600/School+House+-+Old+Fashioned.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-CWZLEgLUpYE/U9kxGpgPChI/AAAAAAAAFnE/Pn8D9BLiPHs/s1600/School+House+-+Old+Fashioned.png" /></a></div><br />August marks the beginning of school for many teachers - me included. Getting the classroom ready, buying supplies, marking items, attending in-services, etc. is what most teachers are doing. I am sure many of you are looking for new ideas and resources for the new school year.<br /><br /><div style="text-align: right;"></div><div class="separator" style="clear: both; text-align: center;"></div><a href="http://3.bp.blogspot.com/-1mATVSZOCrU/VbkDE4z7pzI/AAAAAAAAGk8/6LYOArAz-AA/s1600/Back%2Bto%2BSchool%2BSale.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://3.bp.blogspot.com/-1mATVSZOCrU/VbkDE4z7pzI/AAAAAAAAGk8/6LYOArAz-AA/s1600/Back%2Bto%2BSchool%2BSale.JPG" /></a><strong><em>Teachers Pay Teachers</em></strong> wants you to be ready for the classroom by having a two day sale, <b><span style="color: blue;">August 3rd and 4th</span></b>. Most TPT sellers will have the items in their stores discounted anywhere from 5% to 20%. In addition, a TPT discount of <strong>10%</strong> will be applied at checkout if you enter the special code of <strong><span style="color: #351c75;"><u style="background-color: orange;">BTS15</u></span></strong>.<br /><br />Of course, my <b><span style="color: #660000;"><a href="http://www.teacherspayteachers.com/Store/SciPi/Products">store</a></span></b> is no exception. Any resource in my <a href="http://www.teacherspayteachers.com/Store/SciPi/Products"><b>store</b></a> that costs <b><span style="color: #990000;">$3.00 or more</span><span style="color: #660000;"> </span></b>will be discounted by 10%. Add the additional 10% at checkout, and you will be saving a total of 19%!<br /><br />So here is your chance to purchase all of the products on your TPT wish list. You don't even have to worry about shipping costs since the majority of items are digital and available for download immediately after purchase. So grab that on-line shopping cart and rush on over to <strong><em>Teachers Pay Teachers</em></strong> to stock up for the new school year.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-83flPQCeEJs/Uo93P0NEPiI/AAAAAAAAE-c/V9FyLAR7lnM/s1600/signature+with+heart.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><br /></a></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/08/back-to-school-two-day-sale.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-9125616176499585165Tue, 28 Jul 2015 12:30:00 +00002015-07-28T08:55:57.664-05:00anglesgeometryright angleFrom A Different Angle<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-vv_jTPoQww8/VX8ocMuvYZI/AAAAAAAAGiU/mxFkLSaRiWQ/s1600/Acorn.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-vv_jTPoQww8/VX8ocMuvYZI/AAAAAAAAGiU/mxFkLSaRiWQ/s1600/Acorn.JPG" /></a></div>Here is a riddle for you. <em>What did the little acorn say when he grew up</em>? Give up? It's <b>Gee-I'm-A-Tree</b> or <strong>Ge-om-e-try</strong>. This is what my students are beginning to study. I absolutely love teaching this part of math, and it is interesting how the students respond. Those that are visual, love it, but usually, those who do better with the abstract aren't so fond of it.<br /><br />I have a beautiful, talented daughter who loves languages. She is fluent in Spanish and loves to write, write, and write. To my chagrin, she always struggled in math, especially in high school, until she got to Geometry. Her math grade changed from a disappointing (let's just say she passed Algebra) to an A. She thought Geometry was wonderful!!<br /><br />I enjoy teaching Geometry because there are so many concrete ways to show the students what you mean. For instance, when introducing angles, (before using protractors) I use my fingers, coffee filters (when ironed, they make a perfect circle), interlocking plastic plates, the clock, etc. to demonstrate what the various angles look like. Here is an example of what I mean. <br /><div class="MsoNormal" style="margin: 0in 0in 10pt;"><span style="font-size: xx-small;"><br /></span>To introduce right angle, I have the students fold a coffee filter (which is ironed flat) into fourths, and we use that angle to locate right angles all around the room.<span style="mso-spacerun: yes;"> </span>We discuss the importance of a right angle in architecture, and what would happen if a right angle didn’t exist. </div><div class="MsoNormal" style="margin: 0in 0in 10pt;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-OUljh01hVYA/Tr1HrOB_2_I/AAAAAAAAAYg/5iDKT5EyqTc/s1600/three+o%2527clock.bmp" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" nda="true" src="http://1.bp.blogspot.com/-OUljh01hVYA/Tr1HrOB_2_I/AAAAAAAAAYg/5iDKT5EyqTc/s1600/three+o%2527clock.bmp" /></a></div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f"><stroke joinstyle="miter"></stroke><formulas><f eqn="if lineDrawn pixelLineWidth 0"></f><f eqn="sum @0 1 0"></f><f eqn="sum 0 0 @1"></f><f eqn="prod @2 1 2"></f><f eqn="prod @3 21600 pixelWidth"></f><f eqn="prod @3 21600 pixelHeight"></f><f eqn="sum @0 0 1"></f><f eqn="prod @6 1 2"></f><f eqn="prod @7 21600 pixelWidth"></f><f eqn="sum @8 21600 0"></f><f eqn="prod @7 21600 pixelHeight"></f><f eqn="sum @10 21600 0"></f></formulas><path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f"></path><lock aspectratio="t" v:ext="edit"></lock></shapetype><shape alt="hour blue clock 03 clip art" href="http://www.pdclipart.org/displayimage.php?album=32&pos=21" id="Picture_x0020_1" o:button="t" o:spid="_x0000_s1026" style="height: 57.6pt; margin-left: 1.5pt; margin-top: -0.3pt; mso-position-horizontal-relative: text; mso-position-horizontal: absolute; mso-position-vertical-relative: text; mso-position-vertical: absolute; mso-wrap-distance-bottom: 0; mso-wrap-distance-left: 9pt; mso-wrap-distance-right: 9pt; mso-wrap-distance-top: 0; mso-wrap-style: square; position: absolute; visibility: visible; width: 57.6pt; z-index: 1;" type="#_x0000_t75"><imagedata o:title="hour blue clock 03 clip art" src="file:///C:\DOCUME~1\VICKYR~1\LOCALS~1\Temp\msohtmlclip1\12\clip_image001.png"></imagedata><wrap type="square"></wrap></shape><span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"></span></div><div class="MsoNormal" style="margin: 0in 0in 10pt;">We then use an analog clock to discover what time represents a right angle. Right away, they respond with 3:00 or 9:00. Some will say 3:30, but when I display 3:30 on a Judy clock (comes in handy even on the college level), they see that the hour hand is not directly on the three which means it is not a 90 degree angle.</div><div class="MsoNormal" style="margin: 0in 0in 10pt;"><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-fjrZniL0j_M/TsE2Xx4es0I/AAAAAAAAAZA/Eq8H7m7HcC0/s1600/right+angle.bmp" imageanchor="1" style="clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" nda="true" src="http://2.bp.blogspot.com/-fjrZniL0j_M/TsE2Xx4es0I/AAAAAAAAAZA/Eq8H7m7HcC0/s1600/right+angle.bmp" /></a></div>I also demonstrate a right angle by using my fingers. What is great about fingers is that they are always with you. I call the finger position you see on the right, <em><strong>Right on, Right angle</strong></em>.</div>So are you ready for another geometry riddle? (I have many!) What is Orville and Wilbur's favorite angle? That’s right; it is a right (Wright) angle.<br /><div><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-gwJsz1QN9Sk/VX8mu_HyP9I/AAAAAAAAGiE/KKJRoXbQUvw/s1600/Angles.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-gwJsz1QN9Sk/VX8mu_HyP9I/AAAAAAAAGiE/KKJRoXbQUvw/s1600/Angles.JPG" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.teacherspayteachers.com/Product/Angles-Geometry-Hands-On-Activities-53956">Angle Resource</a></b></td></tr></tbody></table><div><div>Want more geometry riddles? Check out <b><a href="https://www.teacherspayteachers.com/Product/Geometry-Parodies-Matching-Activity-of-Geometric-Terms-110299">Geometry Parodies</a> </b>by clicking here. Also, if you are interested in many different concrete ways to teach angles, take a look at my product entitled: <b><a href="https://www.teacherspayteachers.com/Product/Angles-Geometry-Hands-On-Activities-53956">Angles: Geometry Hands-On Activities.</a></b></div></div><div><br /><br /></div><div><br /></div><div><br /></div></div><div><br /></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/07/from-different-angle.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-1104140640634127287Tue, 21 Jul 2015 12:30:00 +00002015-07-21T09:01:15.731-05:00base ten systemplace valueA Perfect TenDon't you love tests where you ask a question which you believe everyone will get correct, and then find out it just isn't so? I gave my algebra college students a pretest to see what they knew and didn't know. One of the first questions was: <strong><em>Why is our number system called Base Ten?</em></strong> This is an extremely important concept as it reveals what they know about place value. Below are some of the answers I received.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-uu5_wVoeVPk/TpxR9SvDx0I/AAAAAAAAAQg/mNFi7UK2euM/s1600/ten+fingers.bmp" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="120" oda="true" src="http://3.bp.blogspot.com/-uu5_wVoeVPk/TpxR9SvDx0I/AAAAAAAAAQg/mNFi7UK2euM/s200/ten+fingers.bmp" width="200" /></a></div>1) It is called Base Ten because we have ten fingers. (Yikes! If that is so, should we include our toes as well?)<br /><br />2) It is called Base Ten because I think you multiply by ten when you move past the decimal sign. (Well, sort of. You do multiply by ten when you move to the left of the decimal sign, going from the ones place, to the tens place, to the hundreds place, etc.)<br /><span style="font-size: xx-small;"><br /></span>3) I think it is called Base Ten because it's something we use everyday. (Really????)<br /><br /><strong><span style="color: #990000;">Enough!</span></strong> It is called Base Ten because we use ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to write all of the other numbers. Each digit can have one of ten values: any number from 0 through 9. When the value reaches 9, just before 10, it starts over at zero again. (Notice the pattern below.)<br /><br /><div style="text-align: center;"><div class="separator" style="clear: both; text-align: center;"></div><span style="color: black; font-family: Times, "Times New Roman", serif;"><span style="background-color: yellow;"><strong>0</strong></span>, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1<span style="background-color: yellow;"><strong>0</strong></span>, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2<span style="background-color: yellow;"><strong>0</strong></span>, etc.</span></div><div><div style="text-align: left;"><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-mt-i8KM2I9s/TqbEk-NUEuI/AAAAAAAAASs/AzP2mFFqteg/s1600/Number-line.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="48" ida="true" src="http://1.bp.blogspot.com/-mt-i8KM2I9s/TqbEk-NUEuI/AAAAAAAAASs/AzP2mFFqteg/s640/Number-line.gif" width="640" /></a></div><br />In addition, each place is worth ten times more than the last. Ten is worth ten times more than 1, and 1,000 is ten times more than 100. The pattern continues infinitely both ways on a number line.</div><span style="font-size: xx-small;"></span><br />The decimal point allows for the place value to continue in a consistent pattern with numbers smaller than one. As we move to the right of the decimal point, each place is divided by ten to get to the next place value. One hundredth is one tenth divided by ten, and one thousandth is one hundredth divided by ten. The pattern goes on infinitely. <br /><br /><div style="text-align: center;">100's, 10's, 1's . 0.1, 0.01, 0.001, 0.0001, 0.00001, etc.</div><a href="http://4.bp.blogspot.com/-LaGIM55FQf0/TqRmlY-LQfI/AAAAAAAAASI/NtBZl9vR0vs/s1600/red+arrow+pointing+right.bmp"><img border="0" src="http://4.bp.blogspot.com/-LaGIM55FQf0/TqRmlY-LQfI/AAAAAAAAASI/NtBZl9vR0vs/s1600/red+arrow+pointing+right.bmp" /></a><br />Since all mathematics is based on patterns, this should not be a new revelation. Perhaps on the post-test, my students will omit the fingers and instead rely on patterns to answer the questions!<br /><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; text-align: center;"><div style="text-align: left;"><br /></div></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/07/a-perfect-ten.htmlnoreply@blogger.com (Scipi)1tag:blogger.com,1999:blog-5410562205692621875.post-4812786396462559990Tue, 14 Jul 2015 12:30:00 +00002015-07-14T14:40:32.277-05:00new TPT sellerA Go Figure Debut for a Cavalier Who Is New!<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-VDphE1194GE/VXDEmemi1KI/AAAAAAAAGf4/mUorJ5TH5DM/s1600/Diane%2B-%2BCavalier.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-VDphE1194GE/VXDEmemi1KI/AAAAAAAAGf4/mUorJ5TH5DM/s1600/Diane%2B-%2BCavalier.JPG" /></a></div>You are probably wondering how "cavalier" got into today's title. Well, in the "small" world of <i><b><span style="color: #990000;">Teachers Pay Teachers</span></b></i>, (it has over 89,000 sellers!) I met someone who grew up in the <u>same</u> little town I did, and even graduated from the same high school (our town only has one). She graduated five years after I did; so, we really never knew each other; however, we were both Cavaliers; so, hence the title of today's article.<br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-ii1YPhgyFlk/VXC35IYzFTI/AAAAAAAAGe4/LREphjugmoE/s1600/Diane%2BVogel%2B-%2BPicture.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-ii1YPhgyFlk/VXC35IYzFTI/AAAAAAAAGe4/LREphjugmoE/s1600/Diane%2BVogel%2B-%2BPicture.JPG" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.teacherspayteachers.com/Store/Diane-Vogel">Diane Vogel</a></b></td></tr></tbody></table><br />Diane is a retired teacher of 40 years. She has taught in a resource as well as a self-contained learning disabilities classroom. In addition she has taught 2nd and 3rd graders in a regular education classroom. Towards the end of her teaching career, she taught in a psychiatric hospital, and concluded her final years with teaching 4th-6th grade gifted students.<br /><div><br /></div><div><div style="text-align: left;"></div>Her <a href="https://www.teacherspayteachers.com/Store/Diane-Vogel"><b><span style="color: #990000;"><i>Teachers Pay Teachers</i></span></b> <b>store</b></a> contains 24 resources, three of which are free. They include items from many disciplines, including special education and gifted. Her resources for grades K-10 reflect her multi-disciplinary hands-on approach to teaching which incorporates all modalities. </div><div><br /></div><div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-jeJPdpBZPDU/VXDEJBHpBBI/AAAAAAAAGfw/u6df-J6k0Pg/s1600/Diane%2527s%2BFreebie.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://3.bp.blogspot.com/-jeJPdpBZPDU/VXDEJBHpBBI/AAAAAAAAGfw/u6df-J6k0Pg/s200/Diane%2527s%2BFreebie.JPG" width="159" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.teacherspayteachers.com/Product/Common-Core-Math-Grade-2-Just-Ducky-MD2-857234">Free Item</a></b></td></tr></tbody></table>One of Diane's free resources is called <a href="https://www.teacherspayteachers.com/Product/Common-Core-Math-Grade-2-Just-Ducky-MD2-857234" style="font-weight: bold;">Just Ducky</a><b> </b>and is appropriate for grades 1-3. She claims that most workbooks never contain enough measurement activities; so, this resource can serve as a supplement. In it, students count ducks and measure the length of duck calls. In addition, students are encouraged to write about how measuring with ducks is different than measuring with a ruler.<br /><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-iIJgRKvvN94/VXC8jv6PsJI/AAAAAAAAGfM/dtZeEF5BMxM/s1600/Diane%2527s%2BPaid.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://4.bp.blogspot.com/-iIJgRKvvN94/VXC8jv6PsJI/AAAAAAAAGfM/dtZeEF5BMxM/s200/Diane%2527s%2BPaid.JPG" width="161" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="http://she%20has%20used%20it%20with%20gifted%20students%20who%20were%20very%20motivated%20to%20see%20who%20could%20spell%20the%20longest%20word%20using%20the%20periodic%20table./">Only $4.00</a></b></td></tr></tbody></table>Diane's featured resource is entitled <a href="https://www.teacherspayteachers.com/Product/Periodic-Table-Activities-1146060" style="font-weight: bold;">Periodic Table Activities</a><b> </b>which is appropriate for grades 6-10. It is a review activity using the Periodic Table. It consists of seven spelling units, each with an answer key. As an alternative, it might be assigned as homework or as an activity suitable for a substitute teacher. Usually, each activity takes 20-40 minutes to complete depending on the level of your students. Diane has used it with gifted students whom she said were very motivated to see who could spell the longest word using the Periodic Table.<br /><span style="background-color: white; color: #202020; font-family: 'Times New Roman', serif; font-size: 16px; line-height: 18.2000007629395px;"><br /></span><br /><div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-spvL9Rbnl3g/VXC-rSIYtPI/AAAAAAAAGfY/Dy3C_SDdq5M/s1600/Diane%2BVogel%2B-%2Bstore%2Blogo.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="64" src="http://2.bp.blogspot.com/-spvL9Rbnl3g/VXC-rSIYtPI/AAAAAAAAGfY/Dy3C_SDdq5M/s320/Diane%2BVogel%2B-%2Bstore%2Blogo.JPG" width="320" /></a></div>Diane also owns and operates a school supply store, which is up-to-date with the latest trends in education. She attends two buying trips a year which provide her with an exclusive and unique opportunity to interact with all of the educational vendors and to view the newest materials for teachers and their classrooms. <a href="http://gaschoolsupply.com/"><b>GA School Supply</b></a> (GA stands for Georgia/Alabama) offers a full line of educational materials, teaching supplies, classroom decorations and teaching tools to help your students' learning experience.<br /><br />If you are having trouble finding a specific item for your classroom, you might check it out. Also take a minute to visit her <a href="https://www.teacherspayteachers.com/Store/Diane-Vogel"><b>store</b></a> and at least download one of her three free resources. While you are there, take the time to rate the resource and maybe even become one of her followers.<br /><div class="MsoNormal" style="background: white; line-height: 13.65pt; margin-bottom: 26.25pt; margin-left: 0in; margin-right: 0in; margin-top: 11.25pt;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: #313131; font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/07/a-go-figure-debut-for-cavalier-who-is.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-4918214208469059517Tue, 07 Jul 2015 12:30:00 +00002015-07-12T16:58:26.681-05:00comparing numbersgreater thangreater than/less than symbolsless thanSee You Later Alligator<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 10pt; tab-stops: 455.25pt;"><div style="border: currentColor;"><a href="http://4.bp.blogspot.com/-C_4d85hrWzc/VUJhJbfWgYI/AAAAAAAAGXI/9-Qvsx6zm5s/s1600/Alligator%2B-%2Bcrossed%2Bout.PNG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="85" src="http://4.bp.blogspot.com/-C_4d85hrWzc/VUJhJbfWgYI/AAAAAAAAGXI/9-Qvsx6zm5s/s1600/Alligator%2B-%2Bcrossed%2Bout.PNG" width="200" /></a>I originally posted this article back on May of 2011, but as I view products on Pinterest, I feel a need to revisit it. I have seen alligators, fish, movable Popsicle sticks, etc. as ways to teach greater than or less than. Even though these may be good visual tools, to be honest, there are <strong><u>no</u></strong> alligators or even fish in mathematics. <br /><div style="border: currentColor; text-align: left;"></div>Because many students still fail to understand which way the symbol is placed, here is a different method which you might wish to try. First of all, every child knows how to connect dots; so, let’s use that approach. <br /><div style="border: currentColor;"></div><br />Suppose we have two numbers 8 and 3. Ask the students, “Which number is greater?" Yes, 8 is greater. Let’s put two dots beside that number. 8 : Now ask, “Which number is smaller or represents the least amount?" You are right again. Three is smaller. Let’s put one dot beside (in front of) that number. Now have the students connect the dots.....<br /><br /><div style="border: currentColor;"></div></div><div style="border: currentColor;"><div style="text-align: center;"><span style="font-family: 'Times New Roman','serif';"><span style="mso-spacerun: yes;"><strong><span style="font-size: large;"><span style="color: #990000; font-family: Times, "Times New Roman", serif; font-size: x-large;">8 > 3</span> </span></strong></span></span></div><div style="text-align: center;"></div><div style="text-align: left;"><br />It will work every time! When two numbers are equal, put two dots beside each number and connect the dots to make an equal sign.<span style="font-family: Times New Roman, serif;"> </span>What makes this method a little different is that the students can visually see which number is greater because it has the most dots beside it; so when reading the number sentence, most of the time it is read correctly.<br /><br /></div><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-WokUn3XaqY4/VUJeTg3HM5I/AAAAAAAAGXA/1BefUHXGUAc/s1600/Number%2BTile%2BCover%2B-%2BPrimary-Free.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><span style="font-family: 'Times New Roman','serif';"></span></div></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-WokUn3XaqY4/VUJeTg3HM5I/AAAAAAAAGXA/1BefUHXGUAc/s1600/Number%2BTile%2BCover%2B-%2BPrimary-Free.PNG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://1.bp.blogspot.com/-WokUn3XaqY4/VUJeTg3HM5I/AAAAAAAAGXA/1BefUHXGUAc/s1600/Number%2BTile%2BCover%2B-%2BPrimary-Free.PNG" width="154" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="http://www.teacherspayteachers.com/Product/Number-Tiles-FREE-Problem-Solving-Activities-for-the-Primary-Grades">Free Resource</a></b></td></tr></tbody></table><br />In a free handout, entitled <a href="http://www.teacherspayteachers.com/Store/SciPi/Products">Number Tiles - Activities for the Primary Grades</a>, is a greater than and less than activity which can be used over and over again. Just click on the title to download your free copy.<br /><br /><br /><br /><br /><br /></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/07/see-you-later-alligator.htmlnoreply@blogger.com (scipi)1tag:blogger.com,1999:blog-5410562205692621875.post-6686313243798930918Tue, 30 Jun 2015 12:30:00 +00002015-06-30T09:03:05.490-05:00pattern sticksreducing fractionsskip countingReducing Fractions with Pattern Sticks!<div style="border: currentColor;"><br /></div><a href="http://4.bp.blogspot.com/-OXyq4Xs-PnQ/TnO3ycP_82I/AAAAAAAAAMM/Ar1kira6P8o/s1600/mult.+chart+%25232.bmp" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="186" rba="true" src="http://4.bp.blogspot.com/-OXyq4Xs-PnQ/TnO3ycP_82I/AAAAAAAAAMM/Ar1kira6P8o/s1600/mult.+chart+%232.bmp" width="200" /></a>When working with fractions, many of my students seem confident in performing the different operations, but a few are still unsure of how to reduce fractions. <br /><br />Although I have stressed learning the Divisibility Rules for 2, 5, 10, and the digital root for 3, 6, 9, some still have difficulty since they do not know their multiplication tables. As a mathematics tool, I have the students make Pattern Sticks, a visual and kinesthetic aid, similar to a multiplication chart like the one on the left. Notice that an extra column (blue) has been added to the chart. (In this space, a hole is punched so that a 1" ring can be inserted to store all of the sticks in one place.)<br /><div style="border: currentColor;"><br /><a href="http://4.bp.blogspot.com/-TWPEFnilWY8/TnzC4vguQqI/AAAAAAAAANI/-R5iZRzYxs4/s1600/directions+for+pattern+sticks.bmp" imageanchor="1" style="clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" hca="true" src="http://4.bp.blogspot.com/-TWPEFnilWY8/TnzC4vguQqI/AAAAAAAAANI/-R5iZRzYxs4/s1600/directions+for+pattern+sticks.bmp" /></a>On the right are the directions for making the Pattern Sticks using a multiplication chart. <br /><br />(Side note: My students cut out individual Pattern Sticks which I prefer over cutting a multiplication chart apart.)</div><div style="border: currentColor;"><br /><a href="http://3.bp.blogspot.com/-VFm8MucMX9g/VUKDhBdsCTI/AAAAAAAAGXg/EHOybw2WaU0/s1600/Pattern%2BStick.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-VFm8MucMX9g/VUKDhBdsCTI/AAAAAAAAGXg/EHOybw2WaU0/s1600/Pattern%2BStick.PNG" /></a>I then give the students fractions such as 9/36 to reduce. Using the Pattern Sticks, they search for a column where a 9 and a 36 are lined up in the same column. They easily find it on the 1 strip and the 4 strip. They then take the two strips and line them up so that the 9 is over the 36. (see illustration above) By moving to the left, they discover that 9/36 is the same as 1/4. This is 9/36 in its lowest terms. Also notice that all the fractions in the illustration are equivalent fractions - fractions that have the same value. The Pattern Sticks can also be used to determine what number to divide by and to change improper fractions to mixed numbers.</div><div style="border: currentColor;"><strong></strong><br /><div style="text-align: right;"></div><a href="http://4.bp.blogspot.com/-o34Y8BWzDGA/VVO3AytWEeI/AAAAAAAAGcA/YgQBf7cWz_E/s1600/Pattern%2BSticks.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="http://4.bp.blogspot.com/-o34Y8BWzDGA/VVO3AytWEeI/AAAAAAAAGcA/YgQBf7cWz_E/s200/Pattern%2BSticks.JPG" width="160" /></a>If you are interested in learning more about Pattern Sticks and how to use them in your classroom, check out the resource entitled <a href="http://www.teacherspayteachers.com/Product/Pattern-Sticks-A-Math-Tool-for-Skip-Counting-Reducing-Fractions">Pattern Sticks: A Math Tool for Skip Counting & Reducing Fractions</a> at Teachers Pay Teachers.<br /><br /></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/06/reducing-fractions-with-pattern-sticks.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-760796207967160148Tue, 23 Jun 2015 12:30:00 +00002015-06-23T07:30:01.259-05:00Foilmultiplying polynomialsFOIL - It Doesn't Always Work!<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-WPYE1asFETQ/VSwwhDD2BKI/AAAAAAAAGUw/cdA6aoL-WU0/s1600/FOIL%2BDiagram.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-WPYE1asFETQ/VSwwhDD2BKI/AAAAAAAAGUw/cdA6aoL-WU0/s1600/FOIL%2BDiagram.JPG" /></a></div>In more advanced math classes, many instructors happen to hate "FOIL" (including me) because it <b>only</b> provides confusion for the students. Unfortunately, FOIL (fist, outer, inner and last) tends to be taught as <b>THE</b> way to multiply all polynomials, which is certainly not true. As soon as either one of the polynomials has more than a "first" and "last" term in its parentheses, the students are puzzled as well as off course if they attempt to use FOIL. If students want to use FOIL, they need to be forewarned: <b>You can <span style="color: #990000;">ONLY</span> use it for the specific case of multiplying two binomials. You can NOT use it at ANY other time!</b><br /><br />When multiplying larger polynomials, most students switch<br /><div><a href="http://3.bp.blogspot.com/-XQT58hO8BfI/VSwq34P9X2I/AAAAAAAAGUQ/Nn9kyILFfx8/s1600/Clarence%2Bthe%2BClam.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://3.bp.blogspot.com/-XQT58hO8BfI/VSwq34P9X2I/AAAAAAAAGUQ/Nn9kyILFfx8/s1600/Clarence%2Bthe%2BClam.JPG" /></a>to vertical multiplication, because it is much easier to use, but there is another way. It is called the clam method. (An instructor at the college where I teach says that each set of arcs reminds her of a clam. She’s even named the clam Clarence; so, at our college, this is the Clarence the Clam mehod.) <br /><br />Let’s say we have the following problem:</div><div><br /><div><div align="center" class="MsoNormal"><!--[if gte vml 1]><v:shape id="Circular_x0020_Arrow_x0020_32" o:spid="_x0000_s1036" style='position:absolute;left:0;text-align:left; margin-left:433.5pt;margin-top:18.7pt;width:63pt;height:48pt;flip:y;z-index:251708416; visibility:visible;mso-wrap-style:square;mso-width-percent:0; mso-height-percent:0;mso-wrap-distance-left:9pt;mso-wrap-distance-top:0; mso-wrap-distance-right:9pt;mso-wrap-distance-bottom:0; mso-position-horizontal:absolute;mso-position-horizontal-relative:text; mso-position-vertical:absolute;mso-position-vertical-relative:text; mso-width-percent:0;mso-height-percent:0;mso-width-relative:margin; mso-height-relative:margin;v-text-anchor:middle' coordsize="800100,609600" o:gfxdata="UEsDBBQABgAIAAAAIQC75UiUBQEAAB4CAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbKSRvU7DMBSF dyTewfKKEqcMCKEmHfgZgaE8wMW+SSwc27JvS/v23KTJgkoXFsu+P+c7Ol5vDoMTe0zZBl/LVVlJ gV4HY31Xy4/tS3EvRSbwBlzwWMsjZrlprq/W22PELHjb51r2RPFBqax7HCCXIaLnThvSAMTP1KkI +gs6VLdVdad08ISeCho1ZLN+whZ2jsTzgcsnJwldluLxNDiyagkxOquB2Knae/OLUsyEkjenmdzb mG/YhlRnCWPnb8C898bRJGtQvEOiVxjYhtLOxs8AySiT4JuDystlVV4WPeM6tK3VaILeDZxIOSsu ti/jidNGNZ3/J08yC1dNv9v8AAAA//8DAFBLAwQUAAYACAAAACEArTA/8cEAAAAyAQAACwAAAF9y ZWxzLy5yZWxzhI/NCsIwEITvgu8Q9m7TehCRpr2I4FX0AdZk2wbbJGTj39ubi6AgeJtl2G9m6vYx jeJGka13CqqiBEFOe2Ndr+B03C3WIDihMzh6RwqexNA281l9oBFTfuLBBhaZ4ljBkFLYSMl6oAm5 8IFcdjofJ0z5jL0MqC/Yk1yW5UrGTwY0X0yxNwri3lQgjs+Qk/+zfddZTVuvrxO59CNCmoj3vCwj MfaUFOjRhrPHaN4Wv0VV5OYgm1p+LW1eAAAA//8DAFBLAwQUAAYACAAAACEAyvZ4F9kCAACgBgAA HwAAAGNsaXBib2FyZC9kcmF3aW5ncy9kcmF3aW5nMS54bWykVW1P2zAQ/j5p/8Hyd0hS2lIqAuq6 gSYxQHSMz4fjNNEcO7Pdt/36nV/SdtBt0vjS+nx3z52fe+ycX64bQZZcm1rJnGbHKSVcMlXUcp7T x69XRyNKjAVZgFCS53TDDb28eP/uHMZzDW1VM4II0owhp5W17ThJDKt4A+ZYtVyir1S6AYumnieF hhUiNyLppekwaaCW9GIH9REskIWu/wNKKPadF1OQSzAIKdh4fyf2KNjbkWEsl9e6nbX32nXObpf3 mtRFTpE5CQ1SRJPoiGFoJi+y5juAdakbF6/KkqxzOuxnZ6MBYm1wGtlw1E/TgMfXljAMGKVphnuE YcAwPRt2flbd/QOBVZ/+ioFNhmZwsdegaV17cvn6xCe97sjTWrOFAE0mWqsVQUfHgcvqCOgQTOTO VSOlqNtveFavg7eRsD0AjFtt7DVXDXGLnLLYn2/PV4LljbGhsS7WHdMoURdXtRDecELmU6HJEkRO gTEubc+ni0XzRRVh/3SQhiFgfa99l+Jn/huakGSV05PsdODIcbGRBrueeYrt+oMqNq7wM/6jqrTC 1nHUpmVXNZ7jBoy9B403DTfxzto7/CmFQlgVV5RUSv88tO/iUf3opWSFNzen5scCNKdEfJYmp2dZ v4+w1hv9wWkPDb3ved73yEUzVchJ5rvzSxdvRbcstWqelC4mriq6QDKsjZOwujOmFm104QPB+GTi 10w1LdgbOWvxqgZNuPF8XT+BbuMwLV6FWzWroOWHRhlivWbVZGFVWcc5B1adQxg7sxvBvUg991wW jtkHZF2Ae/q4PHqcxUFhBI5rN56F4bP2gbOI283POEgPLx94iW8C3taglq0q9oUUTmcqKHjYdjLy l/2VjoQDdMglKnOLHQEOiTSLncd4l8rLEjveJqeeuj80FvS5zfCVldwlN7VU+hCAsNvKIT4IPRDj JY8bL95mHxK/Je4DsG9f/AIAAP//AwBQSwMEFAAGAAgAAAAhAJxOXiHiBgAAOhwAABoAAABjbGlw Ym9hcmQvdGhlbWUvdGhlbWUxLnhtbOxZT28bRRS/I/EdRntv4/+NozpV7NgNtGmj2C3qcbwe704z u7OaGSf1DbVHJCREQRyoxI0DAiq1EpfyaQJFUKR+Bd7M7K534jVJ2wgqaA7x7tvfvP/vzZvdy1fu RQwdEiEpjzte9WLFQyT2+YTGQce7NRpcWPeQVDieYMZj0vHmRHpXNt9/7zLe8BlNxhyLySgkEUHA KJYbuOOFSiUba2vSBzKWF3lCYng25SLCCm5FsDYR+AgERGytVqm01iJMY28TOCrNqM/gX6ykJvhM DDUbgmIcgfSb0yn1icFODqoaIeeyxwQ6xKzjAc8JPxqRe8pDDEsFDzpexfx5a5uX1/BGuoipFWsL 6wbmL12XLpgc1IxMEYxzodVBo31pO+dvAEwt4/r9fq9fzfkZAPZ9sNTqUuTZGKxXuxnPAsheLvPu VZqVhosv8K8v6dzudrvNdqqLZWpA9rKxhF+vtBpbNQdvQBbfXMI3ulu9XsvBG5DFt5bwg0vtVsPF G1DIaHywhNYBHQxS7jlkytlOKXwd4OuVFL5AQTbk2aVFTHmsVuVahO9yMQCABjKsaIzUPCFT7ENO 9nA0FhRrAXiD4MITS/LlEknLQtIXNFEd78MEx14B8vLZ9y+fPUHH958e3//p+MGD4/s/WkbOqh0c B8VVL7797M9HH6M/nnzz4uEX5XhZxP/6wye//Px5ORDKZ2He8y8f//b08fOvPv39u4cl8C2Bx0X4 iEZEohvkCO3zCAwzXnE1J2PxaitGIabFFVtxIHGMtZQS/n0VOugbc8zS6Dh6dInrwdsC2kcZ8Ors rqPwMBQzRUskXwsjB7jLOetyUeqFa1pWwc2jWRyUCxezIm4f48My2T0cO/HtzxLom1laOob3QuKo ucdwrHBAYqKQfsYPCCmx7g6ljl93qS+45FOF7lDUxbTUJSM6drJpsWiHRhCXeZnNEG/HN7u3UZez Mqu3yaGLhKrArET5EWGOG6/imcJRGcsRjljR4dexCsuUHM6FX8T1pYJIB4Rx1J8QKcvW3BRgbyHo 1zB0rNKw77J55CKFogdlPK9jzovIbX7QC3GUlGGHNA6L2A/kAaQoRntclcF3uVsh+h7igOOV4b5N iRPu07vBLRo4Ki0SRD+ZiZJYXiXcyd/hnE0xMa0GmrrTqyMa/13jZhQ6t5Vwfo0bWuXzrx+V6P22 tuwt2L3KambnRKNehTvZnntcTOjb35238SzeI1AQy1vUu+b8rjl7//nmvKqez78lL7owNGg9i9hB 24zd0cqpe0oZG6o5I9elGbwl7D2TARD1OnO6JPkpLAnhUlcyCHBwgcBmDRJcfURVOAxxAkN71dNM ApmyDiRKuITDoiGX8tZ4GPyVPWo29SHEdg6J1S6fWHJdk7OzRs7GaBWYA20mqK4ZnFVY/VLKFGx7 HWFVrdSZpVWNaqYpOtJyk7WLzaEcXJ6bBsTcmzDUIBiFwMstON9r0XDYwYxMtN9tjLKwmCicZ4hk iCckjZG2ezlGVROkLFeWDNF22GTQB8dTvFaQ1tZs30DaWYJUFNdYIS6L3ptEKcvgRZSA28lyZHGx OFmMjjpeu1lresjHScebwjkZLqMEoi71HIlZAG+YfCVs2p9azKbKF9FsZ4a5RVCFVx/W70sGO30g EVJtYxna1DCP0hRgsZZk9a81wa3nZUBJNzqbFvV1SIZ/TQvwoxtaMp0SXxWDXaBo39nbtJXymSJi GE6O0JjNxD6G8OtUBXsmVMLrDtMR9A28m9PeNo/c5pwWXfGNmMFZOmZJiNN2q0s0q2QLNw0p18Hc FdQD20p1N8a9uimm5M/JlGIa/89M0fsJvH2oT3QEfHjRKzDSldLxuFAhhy6UhNQfCBgcTO+AbIH3 u/AYkgreSptfQQ71r605y8OUNRwi1T4NkKCwH6lQELIHbclk3ynMquneZVmylJHJqIK6MrFqj8kh YSPdA1t6b/dQCKluuknaBgzuZP6592kFjQM95BTrzelk+d5ra+CfnnxsMYNRbh82A03m/1zFfDxY 7Kp2vVme7b1FQ/SDxZjVyKoChBW2gnZa9q+pwitutbZjLVlca2bKQRSXLQZiPhAl8A4J6X+w/1Hh M/sFQ2+oI74PvRXBxwvNDNIGsvqCHTyQbpCWOIbByRJtMmlW1rXp6KS9lm3W5zzp5nJPOFtrdpZ4 v6Kz8+HMFefU4nk6O/Ww42tLW+lqiOzJEgXSNDvImMCUfcnaxQkaB9WOB1+TIND34Aq+R3lAq2la TdPgCj4ywbBkvwx1vPQio8BzS8kx9YxSzzCNjNLIKM2MAsNZ+g0mo7SgU+nPJvDZTv94KPtCAhNc +kUla6rO577NvwAAAP//AwBQSwMEFAAGAAgAAAAhAJxmRkG7AAAAJAEAACoAAABjbGlwYm9hcmQv ZHJhd2luZ3MvX3JlbHMvZHJhd2luZzEueG1sLnJlbHOEj80KwjAQhO+C7xD2btJ6EJEmvYjQq9QH CMk2LTY/JFHs2xvoRUHwsjCz7DezTfuyM3liTJN3HGpaAUGnvJ6c4XDrL7sjkJSl03L2DjksmKAV 201zxVnmcpTGKSRSKC5xGHMOJ8aSGtHKRH1AVzaDj1bmIqNhQaq7NMj2VXVg8ZMB4otJOs0hdroG 0i+hJP9n+2GYFJ69elh0+UcEy6UXFqCMBjMHSldnnTUtXYGJhn39Jt4AAAD//wMAUEsBAi0AFAAG AAgAAAAhALvlSJQFAQAAHgIAABMAAAAAAAAAAAAAAAAAAAAAAFtDb250ZW50X1R5cGVzXS54bWxQ SwECLQAUAAYACAAAACEArTA/8cEAAAAyAQAACwAAAAAAAAAAAAAAAAA2AQAAX3JlbHMvLnJlbHNQ SwECLQAUAAYACAAAACEAyvZ4F9kCAACgBgAAHwAAAAAAAAAAAAAAAAAgAgAAY2xpcGJvYXJkL2Ry YXdpbmdzL2RyYXdpbmcxLnhtbFBLAQItABQABgAIAAAAIQCcTl4h4gYAADocAAAaAAAAAAAAAAAA AAAAADYFAABjbGlwYm9hcmQvdGhlbWUvdGhlbWUxLnhtbFBLAQItABQABgAIAAAAIQCcZkZBuwAA ACQBAAAqAAAAAAAAAAAAAAAAAFAMAABjbGlwYm9hcmQvZHJhd2luZ3MvX3JlbHMvZHJhd2luZzEu eG1sLnJlbHNQSwUGAAAAAAUABQBnAQAAUw0AAAAA " path="m38100,304800c38100,168584,177409,54259,361206,39640,521858,26862,674545,94096,735374,204400r31820,l723900,304800,614794,204400r28099,c583665,140730,473958,106115,362550,115947,220469,128486,114300,209252,114300,304800r-76200,xe" fillcolor="#943634 [2405]" strokecolor="#243f60 [1604]" strokeweight=".25pt"> <v:path arrowok="t" o:connecttype="custom" o:connectlocs="38100,304800;361206,39640;735374,204400;767194,204400;723900,304800;614794,204400;642893,204400;362550,115947;114300,304800;38100,304800" o:connectangles="0,0,0,0,0,0,0,0,0,0"/></v:shape><![endif]--><!--[if !vml]--><span style="height: 32px; left: 0px; margin-left: 581px; margin-top: 55px; mso-ignore: vglayout; position: absolute; width: 79px; z-index: 251708416;"></span><!--[endif]--><!--[if gte vml 1]><v:shape id="Circular_x0020_Arrow_x0020_28" o:spid="_x0000_s1035" style='position:absolute; left:0;text-align:left;margin-left:6in;margin-top:-.05pt;width:63pt;height:48pt; z-index:251700224;visibility:visible;mso-wrap-style:square; mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; mso-wrap-distance-bottom:0;mso-position-horizontal:absolute; mso-position-horizontal-relative:text;mso-position-vertical:absolute; mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0; mso-width-relative:margin;mso-height-relative:margin;v-text-anchor:middle' coordsize="800100,609600" o:gfxdata="UEsDBBQABgAIAAAAIQC75UiUBQEAAB4CAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbKSRvU7DMBSF dyTewfKKEqcMCKEmHfgZgaE8wMW+SSwc27JvS/v23KTJgkoXFsu+P+c7Ol5vDoMTe0zZBl/LVVlJ gV4HY31Xy4/tS3EvRSbwBlzwWMsjZrlprq/W22PELHjb51r2RPFBqax7HCCXIaLnThvSAMTP1KkI +gs6VLdVdad08ISeCho1ZLN+whZ2jsTzgcsnJwldluLxNDiyagkxOquB2Knae/OLUsyEkjenmdzb mG/YhlRnCWPnb8C898bRJGtQvEOiVxjYhtLOxs8AySiT4JuDystlVV4WPeM6tK3VaILeDZxIOSsu ti/jidNGNZ3/J08yC1dNv9v8AAAA//8DAFBLAwQUAAYACAAAACEArTA/8cEAAAAyAQAACwAAAF9y ZWxzLy5yZWxzhI/NCsIwEITvgu8Q9m7TehCRpr2I4FX0AdZk2wbbJGTj39ubi6AgeJtl2G9m6vYx jeJGka13CqqiBEFOe2Ndr+B03C3WIDihMzh6RwqexNA281l9oBFTfuLBBhaZ4ljBkFLYSMl6oAm5 8IFcdjofJ0z5jL0MqC/Yk1yW5UrGTwY0X0yxNwri3lQgjs+Qk/+zfddZTVuvrxO59CNCmoj3vCwj MfaUFOjRhrPHaN4Wv0VV5OYgm1p+LW1eAAAA//8DAFBLAwQUAAYACAAAACEAh2AWGKoCAAA4BgAA HwAAAGNsaXBib2FyZC9kcmF3aW5ncy9kcmF3aW5nMS54bWysVN9P2zAQfp+0/8HyOyQtpUBFQF03 0CQEiIB4PhyniebYme2mKX/9zj/SVoB42NaH1Pbdfffd5zufX/aNIB3XplYyo6PDlBIumSpquczo 0+PVwSklxoIsQCjJM7rhhl5efP1yDrOlhraqGUEEaWaQ0cradpYkhlW8AXOoWi7RVirdgMWtXiaF hjUiNyIZp+k0aaCW9GIH9R0skJWu/wJKKPaLFwuQHRiEFGy2fxI5CvbvyDCT3bVu8/ZeO+bstrvX pC4yispJaFAimkRDdMNt8iZquQPoS904f1WWpM/odJKmpylibTJ6dpSOT44DHO8tYWhH28iZGdqn 6dkU1yFddfc5AKt+fAqBFAMVXOzRM60jJ7v39Y6xM0LBi1qzlQBN5lqrNUHDoICLGsofEExU7r8U vmUNs1Ybe81VQ9wioyyS8px8k0F3Y2xgM/i62oQk64wejYLSCDgQtH3ui7f9N1VsnOsL/uNta4X4 eAemZVc1JrsBY+9B4wTgIc6SvcNPKRTCqriipFL69aNz549diVZK1jhRGTW/V6A5JeKnNNgEo8kE Ya3fTI5PxrjR+5aXfYtcNQslcJA9O790/lYMy1Kr5lnpYu6yogkkw9wol9XDZmFxjyYcXMbnc79m qmnB3si8xREaeTmdho/9M+g2Km6xR29VXkHLP9I7+PpuUvOVVWUdLyOo6q/C2NxuBPft47XnsnDK PqDqAtyTxOXBU+76Cy8KPfC7u56V4Xn7wFnEHe7POMhw0w+8xFnFMRp7hv6l4guhSQcoGjDGpQ3V mQoKHo6PU/zFlNsIn1pIBHTIZS3EFjsCuFfwPXZgHv1dKC9LZLwNTj8jFoK3ET6zkrvgppZKfwQg sKqYOfh7+lEY3/J48ObN9C7xjXcP8/7+4g8AAAD//wMAUEsDBBQABgAIAAAAIQCcTl4h4gYAADoc AAAaAAAAY2xpcGJvYXJkL3RoZW1lL3RoZW1lMS54bWzsWU9vG0UUvyPxHUZ7b+P/jaM6VezYDbRp o9gt6nG8Hu9OM7uzmhkn9Q21RyQkREEcqMSNAwIqtRKX8mkCRVCkfgXezOyud+I1SdsIKmgO8e7b 37z/782b3ctX7kUMHRIhKY87XvVixUMk9vmExkHHuzUaXFj3kFQ4nmDGY9Lx5kR6Vzbff+8y3vAZ TcYci8koJBFBwCiWG7jjhUolG2tr0gcylhd5QmJ4NuUiwgpuRbA2EfgIBERsrVaptNYiTGNvEzgq zajP4F+spCb4TAw1G4JiHIH0m9Mp9YnBTg6qGiHnsscEOsSs4wHPCT8akXvKQwxLBQ86XsX8eWub l9fwRrqIqRVrC+sG5i9dly6YHNSMTBGMc6HVQaN9aTvnbwBMLeP6/X6vX835GQD2fbDU6lLk2Ris V7sZzwLIXi7z7lWalYaLL/CvL+nc7na7zXaqi2VqQPaysYRfr7QaWzUHb0AW31zCN7pbvV7LwRuQ xbeW8INL7VbDxRtQyGh8sITWAR0MUu45ZMrZTil8HeDrlRS+QEE25NmlRUx5rFblWoTvcjEAgAYy rGiM1DwhU+xDTvZwNBYUawF4g+DCE0vy5RJJy0LSFzRRHe/DBMdeAfLy2fcvnz1Bx/efHt//6fjB g+P7P1pGzqodHAfFVS++/ezPRx+jP5588+LhF+V4WcT/+sMnv/z8eTkQymdh3vMvH//29PHzrz79 /buHJfAtgcdF+IhGRKIb5Ajt8wgMM15xNSdj8WorRiGmxRVbcSBxjLWUEv59FTroG3PM0ug4enSJ 68HbAtpHGfDq7K6j8DAUM0VLJF8LIwe4yznrclHqhWtaVsHNo1kclAsXsyJuH+PDMtk9HDvx7c8S 6JtZWjqG90LiqLnHcKxwQGKikH7GDwgpse4OpY5fd6kvuORThe5Q1MW01CUjOnayabFoh0YQl3mZ zRBvxze7t1GXszKrt8mhi4SqwKxE+RFhjhuv4pnCURnLEY5Y0eHXsQrLlBzOhV/E9aWCSAeEcdSf ECnL1twUYG8h6NcwdKzSsO+yeeQihaIHZTyvY86LyG1+0AtxlJRhhzQOi9gP5AGkKEZ7XJXBd7lb Ifoe4oDjleG+TYkT7tO7wS0aOCotEkQ/mYmSWF4l3Mnf4ZxNMTGtBpq606sjGv9d42YUOreVcH6N G1rl868flej9trbsLdi9ympm50SjXoU72Z57XEzo29+dt/Es3iNQEMtb1Lvm/K45e//55ryqns+/ JS+6MDRoPYvYQduM3dHKqXtKGRuqOSPXpRm8Jew9kwEQ9TpzuiT5KSwJ4VJXMghwcIHAZg0SXH1E VTgMcQJDe9XTTAKZsg4kSriEw6Ihl/LWeBj8lT1qNvUhxHYOidUun1hyXZOzs0bOxmgVmANtJqiu GZxVWP1SyhRsex1hVa3UmaVVjWqmKTrScpO1i82hHFyemwbE3Jsw1CAYhcDLLTjfa9Fw2MGMTLTf bYyysJgonGeIZIgnJI2Rtns5RlUTpCxXlgzRdthk0AfHU7xWkNbWbN9A2lmCVBTXWCEui96bRCnL 4EWUgNvJcmRxsThZjI46XrtZa3rIx0nHm8I5GS6jBKIu9RyJWQBvmHwlbNqfWsymyhfRbGeGuUVQ hVcf1u9LBjt9IBFSbWMZ2tQwj9IUYLGWZPWvNcGt52VASTc6mxb1dUiGf00L8KMbWjKdEl8Vg12g aN/Z27SV8pkiYhhOjtCYzcQ+hvDrVAV7JlTC6w7TEfQNvJvT3jaP3OacFl3xjZjBWTpmSYjTdqtL NKtkCzcNKdfB3BXUA9tKdTfGvboppuTPyZRiGv/PTNH7Cbx9qE90BHx40Ssw0pXS8bhQIYculITU HwgYHEzvgGyB97vwGJIK3kqbX0EO9a+tOcvDlDUcItU+DZCgsB+pUBCyB23JZN8pzKrp3mVZspSR yaiCujKxao/JIWEj3QNbem/3UAipbrpJ2gYM7mT+ufdpBY0DPeQU683pZPnea2vgn558bDGDUW4f NgNN5v9cxXw8WOyqdr1Znu29RUP0g8WY1ciqAoQVtoJ2WvavqcIrbrW2Yy1ZXGtmykEUly0GYj4Q JfAOCel/sP9R4TP7BUNvqCO+D70VwccLzQzSBrL6gh08kG6QljiGwckSbTJpVta16eikvZZt1uc8 6eZyTzhba3aWeL+is/PhzBXn1OJ5Ojv1sONrS1vpaojsyRIF0jQ7yJjAlH3J2sUJGgfVjgdfkyDQ 9+AKvkd5QKtpWk3T4Ao+MsGwZL8Mdbz0IqPAc0vJMfWMUs8wjYzSyCjNjALDWfoNJqO0oFPpzybw 2U7/eCj7QgITXPpFJWuqzue+zb8AAAD//wMAUEsDBBQABgAIAAAAIQCcZkZBuwAAACQBAAAqAAAA Y2xpcGJvYXJkL2RyYXdpbmdzL19yZWxzL2RyYXdpbmcxLnhtbC5yZWxzhI/NCsIwEITvgu8Q9m7S ehCRJr2I0KvUBwjJNi02PyRR7Nsb6EVB8LIws+w3s037sjN5YkyTdxxqWgFBp7yenOFw6y+7I5CU pdNy9g45LJigFdtNc8VZ5nKUxikkUigucRhzDifGkhrRykR9QFc2g49W5iKjYUGquzTI9lV1YPGT AeKLSTrNIXa6BtIvoST/Z/thmBSevXpYdPlHBMulFxagjAYzB0pXZ501LV2BiYZ9/SbeAAAA//8D AFBLAQItABQABgAIAAAAIQC75UiUBQEAAB4CAAATAAAAAAAAAAAAAAAAAAAAAABbQ29udGVudF9U eXBlc10ueG1sUEsBAi0AFAAGAAgAAAAhAK0wP/HBAAAAMgEAAAsAAAAAAAAAAAAAAAAANgEAAF9y ZWxzLy5yZWxzUEsBAi0AFAAGAAgAAAAhAIdgFhiqAgAAOAYAAB8AAAAAAAAAAAAAAAAAIAIAAGNs aXBib2FyZC9kcmF3aW5ncy9kcmF3aW5nMS54bWxQSwECLQAUAAYACAAAACEAnE5eIeIGAAA6HAAA GgAAAAAAAAAAAAAAAAAHBQAAY2xpcGJvYXJkL3RoZW1lL3RoZW1lMS54bWxQSwECLQAUAAYACAAA ACEAnGZGQbsAAAAkAQAAKgAAAAAAAAAAAAAAAAAhDAAAY2xpcGJvYXJkL2RyYXdpbmdzL19yZWxz L2RyYXdpbmcxLnhtbC5yZWxzUEsFBgAAAAAFAAUAZwEAACQNAAAAAA== " path="m38100,304800c38100,168584,177409,54259,361206,39640,521858,26862,674545,94096,735374,204400r31820,l723900,304800,614794,204400r28099,c583665,140730,473958,106115,362550,115947,220469,128486,114300,209252,114300,304800r-76200,xe" fillcolor="#4f81bd [3204]" strokecolor="#243f60 [1604]" strokeweight=".25pt"> <v:path arrowok="t" o:connecttype="custom" o:connectlocs="38100,304800;361206,39640;735374,204400;767194,204400;723900,304800;614794,204400;642893,204400;362550,115947;114300,304800;38100,304800" o:connectangles="0,0,0,0,0,0,0,0,0,0"/></v:shape><![endif]--><!--[if !vml]--><span style="height: 32px; left: 0px; margin-left: 579px; margin-top: 2px; mso-ignore: vglayout; position: absolute; width: 79px; z-index: 251700224;"></span><!--[endif]--><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/></v:shapetype><v:shape id="Picture_x0020_2" o:spid="_x0000_s1034" type="#_x0000_t75" style='position:absolute;left:0;text-align:left;margin-left:446.45pt; margin-top:6.15pt;width:36pt;height:61.7pt;z-index:-251631616;visibility:visible; mso-wrap-style:square;mso-width-percent:0;mso-height-percent:0; mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; mso-wrap-distance-bottom:0;mso-position-horizontal:absolute; mso-position-horizontal-relative:text;mso-position-vertical:absolute; mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0; mso-width-relative:page;mso-height-relative:page'> <v:imagedata src="file:///C:\Users\Owner\AppData\Local\Temp\msohtmlclip1\01\clip_image003.jpg" o:title="Scallop-Shell-Clam[1]"/> <w:wrap type="square"/></v:shape><![endif]--><!--[if !vml]--><!--[endif]--><b>(x + 2) (2x<span style="font-family: 'Times New Roman', serif; font-size: 14pt;"><sup>2 </sup><o:p></o:p></span> + 3x – 4)</b></div><br />Simply multiply each term in the second parenthesis by the first term in the first parenthesis. Then multiply each term in the second parenthesis by the second term in the first parenthesis.<br /><br />I have my students draw arcs as they multiply. Notice below that the arcs are drawn so they connect to one another to designate that this is a continuous process. Begin with the first term and times each term in the second parenthesis by that first term until each term has been multiplied.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-ypS516IpKFM/VSw1eyZPaBI/AAAAAAAAGVA/cmUtaDnm2T4/s1600/Clarence%2Bthe%2BClam%2B-%2Bexplanation.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="265" src="http://3.bp.blogspot.com/-ypS516IpKFM/VSw1eyZPaBI/AAAAAAAAGVA/cmUtaDnm2T4/s1600/Clarence%2Bthe%2BClam%2B-%2Bexplanation.JPG" width="640" /></a></div>When they are ready to work with the second term, I have the students use a different color. This time they multiply each term in the second parenthesis by the second term in the first while drawing an arc <b><u>below</u></b> each term just as they did before. The different colors help to distinguish which terms have been multiplied, and they serve as a check point to make sure no term has been missed in the process.<br /><div class="separator" style="clear: both; text-align: center;"></div><div style="text-align: center;"><br /></div>As they multiply, I have my students write the answers horizontally, lining up the like terms and placing them one under the other as seen below. This makes it so much easier for them to add the like terms:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-PTJ0-ZwtDFg/VSwru6-l9xI/AAAAAAAAGUg/770Eapz6W0k/s1600/Clarence%2Bthe%2BClam%2B-%2Bvertical.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-PTJ0-ZwtDFg/VSwru6-l9xI/AAAAAAAAGUg/770Eapz6W0k/s1600/Clarence%2Bthe%2BClam%2B-%2Bvertical.JPG" /></a></div><div>This "clam" method works every time a student multiplies polynomials, no matter how many terms are involved.</div><br />Let me restate what I said at the start of this post: "FOIL" only works for the special case of a two-term polynomial multiplied by another two-term polynomial. It does <b><u>NOT</u></b> apply to in ANY other case; therefore, students should not depend on FOIL for general multiplication. In addition, they should never assume it will "work" for every multiplication of polynomials or even for most multiplications. If math students only know FOIL, they have not learned all they need to know, and this will cause them great difficulties and heartaches as they move up in math.<br /><br />Personally, I have observed too many students who are greatly hindered in mathematics by an over reliance on the FOIL method. Often their instructors have been guilty of never teaching or introducing any other method other than FOIL for multiplying polynomials. Take the time to show your students how to multiply polynomials properly, avoid FOIL, if possible, and consider Clarence the Clam as one of the methods to teach. </div><div><br /><div class="MsoNormal"><span style="height: 47px; margin-left: 116px; margin-top: 16px; mso-ignore: vglayout; position: absolute; width: 78px; z-index: 251714560;"><br /></span></div></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/06/foil-it-doesnt-always-work.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-657809575526361495Tue, 16 Jun 2015 12:30:00 +00002015-06-16T07:30:00.045-05:00new TPT sellerA Go Figure Debut for a Buckeye Who's New!<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-DLrJIoBpcEo/VVzRI5Y35uI/AAAAAAAAGdM/cJpU6qNPXiI/s1600/Caffeine%2BQueen%2BBanner.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="236" src="http://3.bp.blogspot.com/-DLrJIoBpcEo/VVzRI5Y35uI/AAAAAAAAGdM/cJpU6qNPXiI/s640/Caffeine%2BQueen%2BBanner.JPG" width="640" /></a></div><div class="MsoNormal" style="background: white; margin-bottom: 0.0001pt;"><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><br /></span></div><div class="MsoNormal" style="background: white; margin-bottom: 0.0001pt;"><span style="background-color: transparent;">The </span><a href="https://www.teacherspayteachers.com/Store/Caffeine-Queen" style="background-color: transparent;"><b>Caffeine Queen</b></a><span style="background-color: transparent;"> is my newest Go Figure Debut. We have a great deal in common, especially when it comes to THE Ohio State University…..Go Bucks! She has taught both regular education and special education. Like most effective teachers, she is always on the lookout for exciting new teaching strategies. She describes herself as a hands-on teacher who enjoys creating items that are kid friendly. </span></div><br />She believes RESPECT should be a two way street in any classroom. She says her shining teacher moment occurs daily when she receives hugs from her students! She thinks a fun and welcoming classroom atmosphere, along with engaging and interesting lessons, is truly the recipe for success. The internet world has really brought her teaching to life, and she desires to share some of those ideas and insights with other teachers.<br /><br />She currently has 54 products in <a href="https://www.teacherspayteachers.com/Store/Caffeine-Queen"><b>her store</b></a>, most priced under $4.00. Her store features many math resources for the elementary as well as for middle school. If you visit <a href="http://caffeinequeenteacher.blogspot.com/"><b>her blog</b></a>, you can read interesting and motivating articles about how she teaches math. I particularly like her May 2nd article about <b><a href="https://www.teacherspayteachers.com/Product/2-Digit-Multiplication-1807459">multiplication</a></b> and how she uses shapes to help those who are struggling with two digit problems that require regrouping. Even I can relate to her April 5th post about fractions because my college students still struggle with them!<br /><div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-ijodaOFITRY/VVzRSLyO-QI/AAAAAAAAGdU/wcug30jpXQE/s1600/Caffeine%2BQueen%2BFreebie.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-ijodaOFITRY/VVzRSLyO-QI/AAAAAAAAGdU/wcug30jpXQE/s1600/Caffeine%2BQueen%2BFreebie.JPG" /></a></div>Her <b><a href="https://www.teacherspayteachers.com/Product/Divisibility-Rules-Poster-Page-and-ISN-notebook-page-1072014">featured free item</a></b> is a one-page divisibility rules poster that can be used during math class when students are working on factoring, simplifying fractions, etc. A smaller version of the poster is included for students to use in their Interactive Student Notebooks (ISN) or binders so that it is always within reach. Finally, a short worksheet for individual students or partners is included so that they can work on the newly learned rules while committing them to memory.<br /><div><br />Her highlighted <b><a href="https://www.teacherspayteachers.com/Product/2-Digit-Multiplication-1807459">paid resource</a></b> is a graphic organizer designed to make teaching the standard multiplication algorithm of two digit multiplication a bit easier to understand. Several different versions of the organizer are included. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-9eFoaWvnUVE/VVzReiv2xfI/AAAAAAAAGdc/Tqq-JADLHe4/s1600/Caffeine%2BQueenPaid.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-9eFoaWvnUVE/VVzReiv2xfI/AAAAAAAAGdc/Tqq-JADLHe4/s1600/Caffeine%2BQueenPaid.JPG" /></a></div>The first three ready-made worksheet pages are multiplication without regrouping, with answer keys included. (The standard algorithm is difficult enough for beginners to conquer without having to immediately worry about regrouping.) Once students are comfortable with multiplying without regrouping, they are ready to begin regrouping. Hopefully, regrouping will go more smoothly because of the time spent solving problems without regrouping, and since the students are now familiar with the process of two digit multiplication. <br /><br />Right now take a few moments to investigate the <a href="https://www.teacherspayteachers.com/Store/Caffeine-Queen"><b>Caffeine Queen’s store </b></a>and <a href="http://caffeinequeenteacher.blogspot.com/"><b>blog</b></a>. Once there, why not become a follower, or download something that is free, or better yet, pick up an educational resource for your classroom?</div><div><br /></div><div><br /></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/06/a-go-figure-debut-for-buckeye-whos-new.htmlnoreply@blogger.com (Scipi)2tag:blogger.com,1999:blog-5410562205692621875.post-3743191245703369782Tue, 09 Jun 2015 12:30:00 +00002015-06-09T07:30:00.613-05:00multiplicationskip countingSkip Counting and Learning How to Multiply<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-Z13jyk5TVYY/VU0aWS7znII/AAAAAAAAGaU/7BZIv7slyyQ/s1600/hundreds%2Bboard.bmp" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="280" src="http://3.bp.blogspot.com/-Z13jyk5TVYY/VU0aWS7znII/AAAAAAAAGaU/7BZIv7slyyQ/s320/hundreds%2Bboard.bmp" width="320" /></a></div>Most elementary teachers use the Hundreds Board in their classroom. It can be used for introducing number patterns, sequencing, place value and more. Students can look for counting-by (multiplication) patterns. Colored disks, pinto beans or just coloring the squares with crayons or colored pencils will work for this. Mark the numbers you land on when you count by two. What pattern do they make? Mark the counting-by-3 pattern, or mark the 7's, etc. You may need to print several charts so your students can color in the patterns and compare them. I usually start with the 2's, 5's and 10's since most children have these memorized.<br /><br />On the other hand, the Hundreds Board can also be confusing when skip counting because there are so many others numbers listed which easily create a distraction. I have found that <a href="https://www.teacherspayteachers.com/Product/Pattern-Sticks-A-Math-Tool-for-Skip-Counting-Reducing-Fractions-156778"><b>Pattern Sticks</b></a> work much better because the number pattern the student is skip counting by can be isolated. <b><a href="https://www.teacherspayteachers.com/Product/Pattern-Sticks-A-Math-Tool-for-Skip-Counting-Reducing-Fractions-156778">Pattern Sticks</a> </b>are a visual way of showing students the many patterns that occur on a multiplication table. Illustrated below is the pattern stick for three. As the student skip counts by three, s/he simply goes from one number to the next (left to right).<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-vazzh8et5Kw/VVzVVEKSXOI/AAAAAAAAGdw/m_Q2ExAzBGo/s1600/Pattern%2BStick%2Bfor%2B3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="37" src="http://1.bp.blogspot.com/-vazzh8et5Kw/VVzVVEKSXOI/AAAAAAAAGdw/m_Q2ExAzBGo/s400/Pattern%2BStick%2Bfor%2B3.JPG" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-zKsaPa9mj-g/VU0eBuWiusI/AAAAAAAAGag/tWU1UTfrBHs/s1600/Fingers%2Bfor%2BSkip%2BCounting.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-zKsaPa9mj-g/VU0eBuWiusI/AAAAAAAAGag/tWU1UTfrBHs/s1600/Fingers%2Bfor%2BSkip%2BCounting.JPG" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="http://www.orientaltrading.com/martian-fingers-a2-39_431.fltr"><b>Martian Fingers</b></a></td></tr></tbody></table></div>For fun, I purchase those scary, wearable fingers at Halloween time. (buy them in bulk from <i>The Oriental Trading Company </i>- click under the fingers for the link.) Each of my students wears one for skip counting activities. I call them the <b><span style="color: #990000;">Awesome Fingers of Math</span></b>! For some reason, when wearing the fingers, students tend to actually point and follow along when skip counting.<br /><br />Most students enjoy skip counting when music is played. I have found several CD's on Amazon that lend themselves nicely to this activity. I especially like Hap Palmer's <a href="http://www.happalmer.com/Files/Multiplication%20Mountain.html"><b>Multiplication Mountain</b></a>. My grandchildren think his songs are catchy, maybe too catchy as sometimes I can't get the songs out of my mind!<br /><br />Think about this. As teachers, if we would take the time to skip count daily, our students would know more than just the 2's, 5's and 10's. They would know <b><span style="color: #990000;">all</span></b> of their multiplication facts by the end of third grade. And wouldn't the fourth grade teacher love you?!?<br /><br /><b><u>IMPORTANT:</u></b> If you like this finger idea, be sure that each student uses the same finger every time to avoid the spreading of germs. Keeping it in a zip lock bag with the child’s name on the bag works best. (Believe it or not, when I taught fourth grade, the students would paint and decorate the fingernails!)<br /><br /><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/06/skip-counting-and-learning-how-to.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-551736984829930961Tue, 02 Jun 2015 12:30:00 +00002015-06-02T07:30:01.210-05:00Bloom's TaxonomygeometryUsing Bloom's in Math ClassAs one of their assignments, my college students are required to create a practice test using pre-selected math vocabulary. This activity prompts them to review, look up definitions and apply the information to create ten good multiple choice questions while at the same time studying and assessing the material. Since I want the questions to be more than Level 1 (Remembering) or Level II (Understanding) of Bloom's Taxonomy, I give them the following handout to help them visualize the different levels. My students find it to be simple, self explanatory, easy to understand and to the point. <br /><br /><b><span style="color: #990000;">Level I - Remembering</span></b><br /><br /><a href="http://4.bp.blogspot.com/-OXRztkDwdBM/VVDWedIQyqI/AAAAAAAAGa0/oiRTCvgLCFU/s1600/Trapezoid.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-OXRztkDwdBM/VVDWedIQyqI/AAAAAAAAGa0/oiRTCvgLCFU/s1600/Trapezoid.JPG" /></a><br /> What is this shape called?<br /><br /><br /><br /><b><span style="color: #990000;">Level II - Understanding</span></b><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-bPOrVvNaya8/VVDWiqCpuSI/AAAAAAAAGbM/WFJaGoQ8FxM/s1600/Triangle%2Band%2BSquare.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-bPOrVvNaya8/VVDWiqCpuSI/AAAAAAAAGbM/WFJaGoQ8FxM/s1600/Triangle%2Band%2BSquare.JPG" /></a></div><br /><br />Circle the shape that is a triangle.<br /><br /><br /><br /><b><span style="color: #990000;">Level III - Applying</span></b><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-kslI6sWVDg4/VVDWhdzrJ7I/AAAAAAAAGbE/wWKeGudwWcE/s1600/Circle.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-kslI6sWVDg4/VVDWhdzrJ7I/AAAAAAAAGbE/wWKeGudwWcE/s1600/Circle.JPG" /></a></div><br /> Enclose the circle in a square.<br /><br /><br /><br /><b><br /></b><a href="http://4.bp.blogspot.com/-w5f88ArMke4/VVDWkqzeDqI/AAAAAAAAGbU/xa7R_eQ9rP4/s1600/Truck.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://4.bp.blogspot.com/-w5f88ArMke4/VVDWkqzeDqI/AAAAAAAAGbU/xa7R_eQ9rP4/s1600/Truck.JPG" /></a><b><span style="color: #990000;">Level IV - Analyzing</span></b><br /><br /><br /> What shapes were used to draw this picture?<br /><br /><br /><br /><b><span style="color: #990000;">Level V - Evaluating</span></b><br /><div style="text-align: center;"><br />How is the picture above like a real truck? How is it different?</div><br /><b><span style="color: #990000;">Level VI - Creating</span></b><br /><br /><div style="text-align: center;">Create a new picture using five <u>different</u> geometric shapes.<br />(You may use the same shape more than once, but you must use five different geometric shapes.)<br /><br /></div><div style="text-align: center;"><br /></div>As teachers, we are only limited by our imagination as to the activities we ask our students to complete to help them prepare for a test. However, we still need to teach and provide information so the students can complete these types of tasks successfully. With the aid of the above chart, my students create well written practice tests using a variety of levels of Bloom's. When the task is completed, my students have also reviewed and studied for their next math exam. I consider that as time well spent!<br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-Wn6rXQsH-yw/VVT9qOoJIdI/AAAAAAAAGcQ/XcqKqDjLMfU/s1600/Bloom's%2BWith%2BGeometry.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://1.bp.blogspot.com/-Wn6rXQsH-yw/VVT9qOoJIdI/AAAAAAAAGcQ/XcqKqDjLMfU/s200/Bloom's%2BWith%2BGeometry.JPG" width="155" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.teacherspayteachers.com/Product/Using-Blooms-in-Math-1857721">Using Bloom's in Math</a></b></td></tr></tbody></table><br /><br />If you would like a copy of the above chart in a similar but more detailed format, it is available on <b><i>Teachers Pay Teachers</i></b> as a <b><span style="color: #990000;"><a href="https://www.teacherspayteachers.com/Product/Using-Blooms-in-Math-1857721">FREE</a></span></b> resource.<br /><div><div><br /></div><div><br /><br /></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/06/using-blooms-in-math-class.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-5618775398300124014Tue, 26 May 2015 12:30:00 +00002015-05-26T07:30:01.184-05:00geometrykitequadrilateralsLet's Go Fly A Kite!<br />This was a comment I received from a fourth grade teacher, <em>"Would you believe on the state 4th grade math test this year, they would not accept "diamond" as an acceptable answer for a rhombus, but they did accept "kite"!!!!! Can you believe this? Since when is kite a shape name? Crazy."</em> <a href="http://4.bp.blogspot.com/-ArF_1bJ4e4w/Tgs8FqeMSBI/AAAAAAAAAA0/ajjjqj5D44Q/s1600/kite%2B%25232.bmp" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F4.bp.blogspot.com%2F-ArF_1bJ4e4w%2FTgs8FqeMSBI%2FAAAAAAAAAA0%2Fajjjqj5D44Q%2Fs200%2Fkite%252B%2525232.bmp&container=blogger&gadget=a&rewriteMime=image%2F*" /></a><br /><br />First of all, there are <strong><span style="color: #990000;">NO</span></strong> diamonds in mathematics <em>(see Nov. 20, 2014 post entitled Faux Diamonds),</em> but believe it or not, a kite <strong><u>is</u></strong> a geometric shape! The figure on the right is a kite. In fact, since it has four sides, it is classified as a quadrilateral. It has two pairs of adjacent sides that are congruent (the same length). The dashes on the sides of the diagram show which side is equal to which side. The sides with one dash are equal to each other, and the sides with two dashes are equal to each other.<br /><br /><a href="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F1.bp.blogspot.com%2F-vNegJYn7hdA%2FTgEstablRoI%2FAAAAAAAAAGg%2Fi36B0XEec3M%2Fs1600%2Fkite%2B%2525233.bmp&container=blogger&gadget=a&rewriteMime=image%2F*" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F1.bp.blogspot.com%2F-vNegJYn7hdA%2FTgEstablRoI%2FAAAAAAAAAGg%2Fi36B0XEec3M%2Fs1600%2Fkite%2B%2525233.bmp&container=blogger&gadget=a&rewriteMime=image%2F*" /></a><a href="http://1.bp.blogspot.com/-vNegJYn7hdA/TgEstablRoI/AAAAAAAAAGg/i36B0XEec3M/s1600/kite+%25233.bmp"></a>A kite has just one pair of equal angles. These congruent angles are a light orange on the illustration at the left. A kite also has one line of symmetry which is represented by the dotted line. (A line of symmetry is an imaginary line that divides a shape in half so that both sides are exactly the same. In other words, when you fold it in half, the sides match.) It is like a reflection in a mirror.<br /><br /><a href="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F4.bp.blogspot.com%2F-aCtpfWUbZWU%2FTgs84_nr3fI%2FAAAAAAAAABE%2F9svsRQdF9R0%2Fs200%2Fkite%252B-%252Bright%252Bangle.bmp&container=blogger&gadget=a&rewriteMime=image%2F*" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F4.bp.blogspot.com%2F-aCtpfWUbZWU%2FTgs84_nr3fI%2FAAAAAAAAABE%2F9svsRQdF9R0%2Fs200%2Fkite%252B-%252Bright%252Bangle.bmp&container=blogger&gadget=a&rewriteMime=image%2F*" /></a>The diagonals of the kite are perpendicular because they meet and form four right angles. In other words, one of the diagonals bisects or cuts the other diagonal exactly in half. This is shown on the diagram on the right. The diagonals are green, and one of the right angles is represented by the small square where the diagonals intersect.<br /><br /><a href="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F4.bp.blogspot.com%2F-peqd2iiR16Y%2FTgs8rhAkSrI%2FAAAAAAAAAA8%2Fo5QHCAEm3vo%2Fs200%2Fclip%252Bart.bmp&container=blogger&gadget=a&rewriteMime=image%2F*" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F4.bp.blogspot.com%2F-peqd2iiR16Y%2FTgs8rhAkSrI%2FAAAAAAAAAA8%2Fo5QHCAEm3vo%2Fs200%2Fclip%252Bart.bmp&container=blogger&gadget=a&rewriteMime=image%2F*" /></a><a href="http://4.bp.blogspot.com/-peqd2iiR16Y/Tgs8rhAkSrI/AAAAAAAAAA8/o5QHCAEm3vo/s1600/clip%2Bart.bmp"></a>There you have it! Don't you think a geometric kite is very similar to the kites we use to fly as children? Well, maybe you didn't fly kites as a kid, but I do remember reading about Ben Franklin flying one! Anyway, as usual, the wind is blowing strong here in Kansas, so I think I will go fly that kite!<br /><div><br /></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/05/lets-go-fly-kite.htmlnoreply@blogger.com (scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-4247333460048103866Tue, 19 May 2015 12:30:00 +00002015-05-19T07:30:00.928-05:00digital rootdivisibility rulesreducing fractionsThe ROOT of the Problem<div class="separator" style="clear: both; text-align: center;"></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-SRkNJ1Hc7lw/VTqhtdrGe_I/AAAAAAAAGV4/FBxSeH0Qm-g/s1600/Boy%2BMultiplying.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://2.bp.blogspot.com/-SRkNJ1Hc7lw/VTqhtdrGe_I/AAAAAAAAGV4/FBxSeH0Qm-g/s1600/Boy%2BMultiplying.JPG" height="200" width="178" /></a></div>When students skip count, they can easily say the 2's, 5's, and 10's which translates into easy memorization of those particular multiplication facts. Think what would happen if every primary teacher had their students practice skip counting by 3's, 4's, 6's, 7's, 8's and 9's! We would eradicate the <em><strong><span style="color: #990000;">drill and kill</span></strong></em> of memorizing multiplication and division facts.</div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><br /></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">Since many of my college students do not know their facts, I gravitate to the Divisibility Rules. Sadly, most have never seen or heard of them. I always begin with dividing by 2 since even numbers are understood by almost everyone. (Never assume a student knows what an even number is as I once had a college student who thought that every digit of a number must be even for the entire number to be even.) We then proceed to the rules for 5 and 10 as most students can skip count by those two numbers. </div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><br /></div>Finally, we learn about the digital root for 3, 6, and 9. This is a new concept but quickly learned and understood by the majority of my students. (See the definition below).<br /><div style="text-align: center;"><span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"></span></div><span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-QGB4pqqnduE/VTqklB-VWhI/AAAAAAAAGWM/Z_c_a39f2I0/s1600/Digital%2BRoot%2BDefinition.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-QGB4pqqnduE/VTqklB-VWhI/AAAAAAAAGWM/Z_c_a39f2I0/s1600/Digital%2BRoot%2BDefinition.JPG" height="142" width="640" /></a></div><br />Here are several examples of finding Digital Root:<br /><br /><b>1)</b> <b>123 = 1 + 2 + 3 = 6</b>. Six is the digital root for the number 123. Since 123 is an odd number, it is not divisible by 6. However, it is still divisible by 3.<br /><br /><b>2)</b> <b>132 = 1 + 3 + 2 = 6</b>. Six is the digital root for the number 132. Since 132 is an even number, it is divisible by 6 and by 3.<br /><br /><b>3)</b> <b>198 = 1+ 9 + 8 = 18 = 1 + 8 = 9</b>. Nine is the digital root for the number 198; so, 198 is divisible by 9 as well as by 3. <br /><br /><b>4)</b> <b>201 = 2 + 0 + 1 = 3</b>. Three is the digital root for the number 201; so, 201 is divisible by 3.<br /><br />The first time I learned about Digital Root was about eight years ago at a workshop presented by Kim Sutton. (If you have never been to one of her workshops - GO! It is well worth your time.) Anyway, I was beside myself to think I had never learned Digital Root. Oh, the math classes I sat through, and the numbers I tried to divide by are too munerous to mention! It actually gives me a mathematical headache. And to think, not knowing Digital Root was the ROOT of my problem!<br /><div><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-lqM3OBFK4_A/VTqinkDoanI/AAAAAAAAGWA/8P6LdZ9l_5Q/s1600/Divisibility%2BRules.PNG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://2.bp.blogspot.com/-lqM3OBFK4_A/VTqinkDoanI/AAAAAAAAGWA/8P6LdZ9l_5Q/s1600/Divisibility%2BRules.PNG" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.teacherspayteachers.com/Product/Using-Digital-Root-and-the-Divisibility-Rules-to-Help-Reduce-Fractions-154092">Divisibility Rules</a></b></td></tr></tbody></table><br /><br /><br /><div>A teacher resource on <a href="https://www.teacherspayteachers.com/Product/Using-Digital-Root-and-the-Divisibility-Rules-to-Help-Reduce-Fractions-154092"><b>Using the Divisibility Rules and Digital Root</b> </a>is available at Teachers Pay Teachers. If you are interested, just click under the resource cover on your right.<br /><div><br /></div><div class="separator" style="clear: both; text-align: center;"></div></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/05/the-root-of-problem.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-5249996711964895360Tue, 12 May 2015 12:30:00 +00002015-05-12T10:19:42.302-05:00linear measurementnew TPT sellerA Go Figure Debut for an Ontarian That's New<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-UnL4vccT7WQ/VTqPK5a2FmI/AAAAAAAAGVQ/_6_8ccsRVtQ/s1600/Mrs.%2BTeacher%2BLogo.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://2.bp.blogspot.com/-UnL4vccT7WQ/VTqPK5a2FmI/AAAAAAAAGVQ/_6_8ccsRVtQ/s1600/Mrs.%2BTeacher%2BLogo.JPG" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.teacherspayteachers.com/Store/Mrs-Teacher-8969">Mrs. Teacher's Store</a></b></td></tr></tbody></table>For our Go Figure Debut this month, we head north....way north to Ontario, Canada. Pat has been an active member of <b><i>Teachers Pay Teachers</i></b> for about a year and a half. She states that creating and selling resources on this site has been a steep learning curve but a delightful adventure. Her <span style="background-color: white;">TPT </span>store is called <a href="https://www.teacherspayteachers.com/Store/Mrs-Teacher-8969"><b>Mrs. Teacher</b></a>, and it contains 88 different resources for many grade levels and various disciplines. <br /><br />Pat's background experience is actually in finance, but she has always created her own worksheets to supplement her sons' learning materials from school. When her two sons were in school, she would teach them during the summer months so that there was a minimal "summer slide" before school began again. She discovered that she enjoyed teaching so much that she now volunteers at a literacy center where she teaches basic reading, writing and math skills to adults.<br /><div><br /></div><div>She enjoys playing the flute and also has a flare for art. She loves doing watercolor painting. In addition, Pat dabbles in creating frames, stationery, etc. although she claims that she still has much to learn in that area. In the future, she would love to create clip art, but right now, she has no clue how to even begin!</div><div><br />She characterizes her teaching style best as <i>facilitating</i> because she leans towards student-centered learning. She likes to allow the students to take the initiative for meeting the demands of the various learning tasks. She believes it is important for learning to be both fun and challenging.<br /><br />In her store, Pat has a variety of math resources. I particularly like her 41 page linear measurement package that I believe would be a wonderful addition to your math centers! It covers both the Imperial System and the Metric System and is appropriate for grades 3-5<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin;"><br /><span style="background: white;"><br /></span></span></div><b><a href="https://www.teacherspayteachers.com/Product/Measuring-Up-Linear-Measurement-History-and-Supplemental-Activities-1066032">Measuring Up</a> </b>contains:<br /><ul><li>a brief history of linear measurement</li><li>a test and answer key<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-pceBgNaMM_M/VTqTAsiWJTI/AAAAAAAAGVc/6t42ErnXBZs/s1600/Mrs.%2BTeacher%2BLinear%2BUnit%2BCover.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://3.bp.blogspot.com/-pceBgNaMM_M/VTqTAsiWJTI/AAAAAAAAGVc/6t42ErnXBZs/s1600/Mrs.%2BTeacher%2BLinear%2BUnit%2BCover.JPG" width="155" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.teacherspayteachers.com/Product/Measuring-Up-Linear-Measurement-History-and-Supplemental-Activities-1066032">Linear Measurement Package</a></b></td></tr></tbody></table></li><li>explanations and worksheets in both Imperial and Metric systems</li><li>measuring worksheets for both non-standardized and standardized units</li><li>worksheets for independent work and activities for working with a partner</li><li>problem solving</li><li>estimating</li><li>rounding off measurements </li><li>working with rulers</li><li>measurement conversions</li><li>blank templates for additional practice </li><li>worksheets using standard units to find the perimeter of shapes </li></ul><b><span style="color: #cc0000;">**</span></b>Spellings are given in both American and Canadian English.<br /><div><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-nZIWoxYAFYs/VTqVnFULXPI/AAAAAAAAGVo/nbEZhDHoND4/s1600/Mrs.%2BTeacher%2BFree.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="http://3.bp.blogspot.com/-nZIWoxYAFYs/VTqVnFULXPI/AAAAAAAAGVo/nbEZhDHoND4/s1600/Mrs.%2BTeacher%2BFree.JPG" width="155" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="https://www.teacherspayteachers.com/Product/Lighthouses-540523">Free Resource</a></b></td></tr></tbody></table><div>Pat also has an unique <a href="https://www.teacherspayteachers.com/Product/Lighthouses-540523"><b>free resource</b></a> about different kinds of lighthouses and their history. The easy-to-understand information makes the content understandable even for a young audience. (appropriate for grades 3-5) Using this resource, a teacher might explore the dangers and challenges of life at sea, the importance of being responsible at work, etc. The students are introduced to new nautical terminology, and the included activity helps them to remember the new words.</div></div><div><br /></div><div>So take a few minutes to check out <a href="https://www.teacherspayteachers.com/Store/Mrs-Teacher-8969">Mrs. Teacher's store</a>. While you are there, become a follower, or download a freebie or better yet, purchase a resource for your classroom.</div><div><br /></div><div><br /></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/05/a-go-figure-debut-for-ontarian-thats-new.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-9194382799454365019Tue, 28 Apr 2015 12:30:00 +00002015-04-28T07:30:00.159-05:00Algebrafractionsgreatest common factorleast common multipleAlgebraic Terms - Finding the Greatest Common Factor and Least Common Multiple Using a Venn Diagram - Continued<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-cLOYpu4NlLw/VSgrsBw81HI/AAAAAAAAGTA/lrNRfBRdgds/s1600/College%2Bstudent%2B-%2Bboy%2B-%2Bneeds%2Bhelp.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-cLOYpu4NlLw/VSgrsBw81HI/AAAAAAAAGTA/lrNRfBRdgds/s1600/College%2Bstudent%2B-%2Bboy%2B-%2Bneeds%2Bhelp.JPG" height="200" width="193" /></a></div>I tutor math at the college where I teach. Many of those students have been confused on how to find the greatest common factor for a set of algebraic terms. Having an elementary background, I introduce them to a factor tree which, believe it or not, many have never seen.<br /><br />When just a rule is given by an instructor, often times, students get lost in the mathematical process. I have found that utilizing a visual can achieve an understanding of a concept better than just a rule. A Venn Diagram is such a visual and helps students to follow the process and understand the connection and relationship between each step of finding the GCF and LCM.<br /><br /><a href="http://1.bp.blogspot.com/-t3Ry5bMRU1A/VSgs8B1bDiI/AAAAAAAAGTI/ie_5SMEMipg/s1600/Factor%2BTree%2Bof%2B42.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-t3Ry5bMRU1A/VSgs8B1bDiI/AAAAAAAAGTI/ie_5SMEMipg/s1600/Factor%2BTree%2Bof%2B42.JPG" /></a>It's important to always begin with the definitions for the<br />words factor, greatest common factor and least common multiple. If a student doesn't know the vocabulary, they can't do the work! I continue by explaining and illustrating what a factor tree is (on your left) and how to construct and use a Venn Diagram as a graphic organizer.<br /><div><br /></div><div class="separator" style="clear: both; text-align: center;"></div><div><a href="http://4.bp.blogspot.com/-0PZ27_nMw5o/VSguoNCqk_I/AAAAAAAAGTU/3LwG1vtph3I/s1600/75xy%2Band%2B45xyz.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-0PZ27_nMw5o/VSguoNCqk_I/AAAAAAAAGTU/3LwG1vtph3I/s1600/75xy%2Band%2B45xyz.JPG" height="85" width="320" /></a>Let's suppose we have the algebraic terms of <b>75<i>xy</i></b> and <b>45<i>xyz</i></b>. I have the students construct factor trees for each of the numbers as illustrated on the left.</div><div><br /></div><div><a href="http://3.bp.blogspot.com/-GmxW0GKo_NE/VSgvlJaaTZI/AAAAAAAAGTc/uLrKBm5-5bI/s1600/Diagram%2Bfor%2B75xy%2Band%2B45xyz.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://3.bp.blogspot.com/-GmxW0GKo_NE/VSgvlJaaTZI/AAAAAAAAGTc/uLrKBm5-5bI/s1600/Diagram%2Bfor%2B75xy%2Band%2B45xyz.JPG" /></a>Then all the common factors are placed in the intersection of the two circles. In this case, it would be the <b style="background-color: yellow;">5</b> and the <i><b style="background-color: yellow;">xy</b></i>.<b style="text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";"><span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal; font-weight: normal;"> </span></span></b><br /><br />The students then put the remaining factors and variables in the correct big circle. Five and three would go in the left hand circle and the three <b>2’s</b> and the <i><b>z</b> </i>would be placed in the right hand circle.<br /><br />The intersection is the GCF; so, the GCF for 75xy and 40xyz is <b style="background-color: yellow;">5xy</b>. To find the LCM, multiply the number(s) in the first big circle by the GCF (numbers in the intersection) times the number (s) in the second big circle.</div><div><br /><div style="text-align: center;"><b>5 × 3 × GCF × 2 × 2 × 2 × z = 15 × 5xy × 8z = 240. <span style="background-color: yellow;">The LCM is 600xyz</span>. </b></div><div style="text-align: center;"><br /></div>This method is applicable and helpful in algebra when students are asked to find the LCM or GCF of a set of algebraic terms such as: 25xy, 40xyz. (LCM = 200xyz; GCF = 5xy) or when they must factor out the GCF from a polynomial such as 6x<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin;"><sup>2</sup></span>y<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin;"><sup>3 </sup></span>+<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin;"> </span>9xy<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin;"><sup>2</sup></span>. Using a Venn Diagram is also an effective and valuable tool when teaching how to reduce fractions. </div><div><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-tmssuBvNSlc/VSgyRW-WdiI/AAAAAAAAGTo/24j45XFoGk8/s1600/GCF%2Band%2BLCM%2B-%2BFree.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-tmssuBvNSlc/VSgyRW-WdiI/AAAAAAAAGTo/24j45XFoGk8/s1600/GCF%2Band%2BLCM%2B-%2BFree.JPG" height="200" width="156" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><span style="color: #783f04;"><a href="https://www.teacherspayteachers.com/Product/Algebraic-TermsFractions-Finding-the-GCF-LCM-Using-a-Venn-Diagram-FREE-1805908">Finding GCF and LCM</a></span></b></td></tr></tbody></table><br />Are you interested in finding out more about this method? Then download my newest <b><u>free</u></b> resource entitled: <b><a href="https://www.teacherspayteachers.com/Product/Algebraic-TermsFractions-Finding-the-GCF-LCM-Using-a-Venn-Diagram-FREE-1805908">Algebraic Terms and Fractions - Finding the Greatest Common Factor and the Lowest Common Multiple Using a Venn Diagram.</a></b><br /><br /><br /><br /><br /></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/04/algebraic-terms-finding-greatest-common.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-2049374288115542208Tue, 21 Apr 2015 12:30:00 +00002015-04-21T07:30:02.644-05:00fractionsgreatest common factorleast common multiplereducing fractionsFinding the Greatest Common Factor and Least Common MultipleThe most common method to find the greatest common factor (GCF) is to list all of the factors of each number, then list the common factors and choose the largest one. Example: Find the GCF of <b style="background-color: yellow;">36 and 54</b>.<br /><div><br /></div><div>1) The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, <b style="background-color: yellow;">18</b>, and 36.<br /><br />2) The factors of 54 are: 1, 2, 3, 6, 9, <b style="background-color: yellow;">18</b>, 27, and 54.<br /><br />Therefore, the common factor(s) of 36 and 54 are: <b>1, 2, 3, 6, 9</b>, <b style="background-color: yellow;">18</b><b style="background-color: white;">. </b>Although the numbers in bold are all common factors of 36 and 54, <b style="background-color: yellow;">18</b> is the greatest common factor.<br /><br />To find the lowest common multiple (LCM), students are asked to list all of the factors of the given numbers. Let's say the numbers are <b>9 and 12</b>. </div><div><br /></div><div>1) The multiples of <b>9</b> are: 9, 18, 27, <b style="background-color: yellow;">36</b>, 45, 54.</div><div><br /></div><div>2) The multiples of 12 are: 12, 24, <b style="background-color: yellow;">36</b>, 48, 60.</div><div><br /></div><div>As seen above, the least common multiple for these two numbers is <b style="background-color: yellow;">36</b>. I have seen this done on a large letter M as illustrated below.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-ZSe5CRgQgS4/VRlvWpvJjDI/AAAAAAAAGRY/BcxaCByoSDI/s1600/GCF%2B%26%2BLCM%2B%233.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-ZSe5CRgQgS4/VRlvWpvJjDI/AAAAAAAAGRY/BcxaCByoSDI/s1600/GCF%2B%26%2BLCM%2B%233.JPG" height="320" width="314" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div><br />We often instruct our students to first list the prime factors, then multiply the common prime factors to find the GCF. Often times, if just this rule is given, students become lost in the process. Utilizing a visual can achieve an understanding of any concept better than just a rule. A two circle Venn Diagram is such a visual and will allow students to follow the process as well as to understand the connection between each step. For example: Let’s suppose we have the numbers <b>18 and 12</b>.<br /><br /><b>1)</b> Using factor trees, the students list all the factors of each number.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-M7m3S6Zx-aY/VRlv3lE8EhI/AAAAAAAAGRg/kmWdi-HlaMw/s1600/GCF%2B%26%2BLCM%2B%231.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-M7m3S6Zx-aY/VRlv3lE8EhI/AAAAAAAAGRg/kmWdi-HlaMw/s1600/GCF%2B%26%2BLCM%2B%231.JPG" height="105" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div><br /><b>2)</b> Now they place all the common factors in the intersection of the two circles. In this case, it would be the numbers 2 and 3. <br /><div style="text-align: center;"><br /></div><b>3)</b> Now the students place the remaining factors in the correct big circle(s).<br /><br /><b>4)</b> That leaves the 18 with a 3 all by itself in the big circle. The 12 has just a 2 in the big circle.<br /><br /><b>5) </b> The intersection is the GCF; therefore, multiply 2 × 3 to find the GCF of <b style="background-color: yellow;">6</b>.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-HxQ8Rjc9Lpw/VRlwBxByLzI/AAAAAAAAGRo/QtTu1qZq_AM/s1600/GCF%2B%26%2BLCM%2B%232.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-HxQ8Rjc9Lpw/VRlwBxByLzI/AAAAAAAAGRo/QtTu1qZq_AM/s1600/GCF%2B%26%2BLCM%2B%232.JPG" /></a></div><div style="text-align: center;"><br /></div><div class="MsoListParagraphCxSpFirst"><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-fareast-font-family: "Times New Roman";">6) </span></b>To find the LCM, multiply the number(s) in the first big circle by the GCF (numbers in the intersection) times the number (s) in the second big circle. <br /><br /></div><div style="text-align: center;"><b>3 × GCF × 2 = 3 × 6 × 2 = 36. The LCM is 36.</b></div><br />This is an effective method to use when teaching how to reduce fractions,<br /><br /></div><div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-x9r2h-kz9RE/VRlyfshjmjI/AAAAAAAAGR0/IUFWQpn8aGE/s1600/GCF%2Band%2BLCM.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-x9r2h-kz9RE/VRlyfshjmjI/AAAAAAAAGR0/IUFWQpn8aGE/s1600/GCF%2Band%2BLCM.JPG" height="200" width="154" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Finding-the-Greatest-Common-Factor-Least-Common-Multiple-Using-a-Venn-Diagram-1777766"><b>Finding GCF and LCM</b></a></td></tr></tbody></table>I have turned this method into a resource for <b><i>Teachers Pay Teachers</i></b>. It is 16 pages and begins with defining the words factor, greatest common factor and least common multiple. What a factor tree is and how to construct and use a Venn Diagram as a graphic organizer is shown. Step-by-step examples are given as well as student practice pages. How to use a three circle Venn Diagram when given three different numbers is explained. Two pages of blank pages Venn Diagrams are included for classroom practice. To learn more, just click on the title under the resource cover on your right.<br /><br /><b>Next week's post - <i><span style="color: #990000;">Finding the LCM and GCF for a set of algebraic terms.</span></i></b><br /><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"><br /><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"><o:p></o:p></span></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/04/finding-greatest-common-factor-and.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-1107703677703206602Tue, 14 Apr 2015 12:30:00 +00002015-04-30T10:55:54.028-05:00Earth DayFreerecyclingHappy Earth Day<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-KydYqNXLTf0/UVSg7NJAp_I/AAAAAAAAEPA/ntpeE6XNGc8/s1600/Earth+-+Smiling.PNG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://2.bp.blogspot.com/-KydYqNXLTf0/UVSg7NJAp_I/AAAAAAAAEPA/ntpeE6XNGc8/s1600/Earth+-+Smiling.PNG" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><strong><span style="color: blue; font-family: Georgia, "Times New Roman", serif;"><em>Happy Earth Day Everyone!</em></span></strong> </td></tr></tbody></table>Earth Day is observed each year on April 22nd. The purpose of the day is to encourage awareness of and appreciation for the earth's environment. It is usually celebrated with outdoor shows, where individuals or groups perform acts of service to the earth. Typical ways of observing Earth Day include planting trees, picking up roadside trash, and conducting various programs for recycling and conservation.<br /><a href="http://2.bp.blogspot.com/-SXBL1-3iRXg/UVSiBRwxmOI/AAAAAAAAEPI/RcV9I5mD1Z4/s1600/Recycle+Symbol.PNG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://2.bp.blogspot.com/-SXBL1-3iRXg/UVSiBRwxmOI/AAAAAAAAEPI/RcV9I5mD1Z4/s1600/Recycle+Symbol.PNG" /></a><a href="http://1.bp.blogspot.com/-C7hlXY44nCI/UVSeWWbGAeI/AAAAAAAAEOg/n2H65NOJNcQ/s1600/Recycle+Symbol.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><br /><div><br /></div><div>Symbols used by people to describe Earth Day include: an image or drawing of planet earth, a tree, a flower or leaves depicting growth or the recycling symbol. Colors used for Earth Day include natural colors such as green, brown, or blue. The universal recycling symbol as seen on your left is internationally recognized and used to designate recyclable materials. It is composed of three mutually chasing arrows that form a Mobius strip which, in math, is an unending single-sided looped surface. (And you wondered how I would get math in this article!?!) This symbol is found on products like plastics, paper, metals and other materials that can be recycled. It is also seen, in a variety of styles, on recycling containers, at recycling centers, or anywhere there is an emphasis on the smart use of materials and products.</div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-AGrZAidt-v0/UVSe2pcS6_I/AAAAAAAAEOw/8Yxrbysuqho/s1600/Trash+to+Treasure+-+FREE.PNG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-AGrZAidt-v0/UVSe2pcS6_I/AAAAAAAAEOw/8Yxrbysuqho/s200/Trash+to+Treasure+-+FREE.PNG" height="200" width="156" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="http://www.teacherspayteachers.com/Product/Trash-to-Treasure-FREE-Activities-Lessons-Using-Recycled-Items"><strong><span style="font-family: Georgia, "Times New Roman", serif;">Free Handout</span></strong></a></td></tr></tbody></table><span lang="EN" style="mso-ansi-language: EN; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;"></span><br />Inspired by Earth Day, Trash to Treasure is an eight page FREE handout. It features clever ideas, fun and engaging mini-lessons in addition to cute and easy-to-construct crafts, all made from recycled or common, everyday items. Discover how to take old, discarded materials and make them into new, useful, inexpensive products or tools for your classroom. To download the free version, just click under the cover page on your right.<br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/04/happy-earth-day.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-5405187793613226778Tue, 07 Apr 2015 12:30:00 +00002015-04-07T07:30:02.637-05:00grouping studentsRandomly Grouping StudentsMy college students are like charter members of a church. They claim their seat on the first day of class, and from then on, no one else better take it! Since we journal every day, often in groups, the same people were sharing with the same people day after day. This meant the students were not getting to know each other; they were unaware of how others were problem solving, and they were way too comfortable in their group. Things had to change!<br /><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><br />So-o-o I asked my students to make name tents by folding a large file card in half. <em>(I know it sounds elementary, but it does help this "old" teacher to quickly learn who is who).</em> On the outside, they printed their name and on the inside, I placed a variety of stickers. (My students didn't seem to mind.) Based on the sticker I called, the students would group by pairs, threes, fours or groups of eight. Now, the students would divide up into groups based on something other than their preference.</div><br /><div class="separator" style="clear: both; text-align: center;"></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><div style="text-align: left;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-F_7Vy_Zx3ew/VNps1iOw3TI/AAAAAAAAGHM/E7fs7PTuVXo/s1600/Grouping%2BCodes.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-F_7Vy_Zx3ew/VNps1iOw3TI/AAAAAAAAGHM/E7fs7PTuVXo/s1600/Grouping%2BCodes.JPG" height="200" width="320" /></a></div>On Monday, we grouped by 2's according to the color of the dog and cat stickers. Right away I noticed that the dominance of the group had changed, and more dialogue was going on between the partners. We then regrouped to present problems using the order of operations, only this time I used the stars to make groups of 3's. <em>(I used this same idea when I taught math in middle school and high school only the stickers were put directly onto the students' journals which always stayed in the room with me.) </em></div><br />I also used this strategy when I taught elementary (back in Noah's Day, <strong><u>after</u></strong> the flood), but there was always one or two "sticker pickers" in my class which seemed, in some magical way, to remove the sticker from their desk. To alleviate this problem, I placed the stickers on the desks and then covered them with clear packing tape or contact paper which was not easily removed. If a student moved away, I simply gave the new student the vacant desk or grouped the remaining students according to a different number.<br /><br />Want to give this a try this in your classroom? Just purchase a variety of stickers. Then decide on the size of the groups you want such as 2's, 3's, 4's, 5's etc. and get to work!<br /><br /><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/04/randomly-grouping-students.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-3737353679141707682Tue, 24 Mar 2015 12:30:00 +00002015-03-24T07:30:01.712-05:00deliberate practicegritHow Gritty Are You?<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-J7fm68WsdUc/VNpmBlsTuWI/AAAAAAAAGGk/M3bO65vvm0A/s1600/Girl%2BStudying.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-J7fm68WsdUc/VNpmBlsTuWI/AAAAAAAAGGk/M3bO65vvm0A/s1600/Girl%2BStudying.JPG" height="166" width="200" /></a></div>What are the causes of success? My college students in my Math Study Skills class have been researching this topic since each one of them desires to be successful at math. We watched a six minute video by Angela Lee Duckworth: <a href="https://www.youtube.com/watch?v=H14bBuluwB8">The Key to Success? Grit </a>on <b><i>You Tube</i></b>. She relates how she left a top paying job in consulting, to teach math to seventh graders in a New York public school. She soon realized that IQ wasn't the only thing separating her successful students from those who struggled. In the video, she describes her theory of "grit" as a predictor of success. Below is a summary of what she says.<br /><div><br /></div><div>At first glance, the answer is easy: success is about talent. It’s about being able to do something – hit a baseball, play chess, write a blog – better than most anyone else. But what is talent? How did that person get so good at hitting a baseball or playing chess? For a long time, talent seemed to be about inheritance, about the blessed set of genes that gave rise to some particular skill. Einstein had the physics gene, Beethoven had the symphony gene, and Tiger Woods (at least until his car crash) had the golf swing gene. The outcome, of course, is that you and I can’t become chess grandmasters or composers or golf pros because we don’t have the necessary anatomy. Endless hours of hard work won’t compensate for our biological limitations. <br /><br />But think about this - Beethoven wasn’t born Beethoven. He had to work extremely hard to become Beethoven. <b>Talent is about practice. Talent takes effort. Talent requires a good coach.</b> But these answers only raise more questions. What, for instance, allows someone to practice for so long? Why are some people so much better at deliberate practice? If talent is about hard work, then what factors influence how hard we can work?<br /><br /><a href="http://2.bp.blogspot.com/-2epmJJOpMQk/VNprXvOZvmI/AAAAAAAAGHE/PsvkFOrFkFU/s1600/Math%2B-%2BHard%2BWork.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://2.bp.blogspot.com/-2epmJJOpMQk/VNprXvOZvmI/AAAAAAAAGHE/PsvkFOrFkFU/s1600/Math%2B-%2BHard%2BWork.JPG" height="162" width="200" /></a>It is deliberate (conscious, intentional, planned) practice that spells success. In other words, deliberate practice works. People who spend more time in deliberate practice mode perform much better. The bad news is that deliberate practice isn't fun and is consistently rated as the least enjoyable form of self-improvement. Nevertheless, as golfers, musicians, etc. gain experience, they devote increasing amounts of time to deliberate practice, and consistent, deliberate practice is done by grit. Not surprisingly, those with grit are more single-minded about their goals – they tend to get obsessed with certain activities – and also more likely to persist in the face of struggle and failure. Woody Allen famously declared that "<i>Eighty percent of success is showing up."</i> Grit is what allows you to show up again and again<br /><br />While grit has little or nothing to do with intelligence (as measured by IQ scores), it often explains why an individual is successful. Thomas Edison was right: "<i>Even genius is mostly just perspiration."</i><br /><br />Our most important talent is having a talent for working hard, for practicing even when practice isn't fun. It’s about putting in the hours when we’d much rather be watching TV, or drilling ourselves with note cards filled with obscure words instead of getting quizzed by a friend. Success is never easy. That’s why talent requires grit.<br /><br /><i>--------------------------------------------------------------------------------</i><br /><div style="text-align: center;"><i>Duckworth, A.L., & Gross, J.J. (2014). Self-control and grit: Related but separable</i></div><div style="text-align: center;"><i>determinants of success. Current Directions in</i></div><div style="text-align: center;"><i>Psychological Science, 23(5), 319-325</i></div><i>--------------------------------------------------------------------------------</i></div><div><br /></div>How does your grit compare with others? I had my students take the 12 point <span style="color: blue;"><a href="https://upenn.app.box.com/12itemgrit">survey</a> </span>developed by Duckworth to see how they rated. Some were surprised while others were well aware of their grit level. I even took it! Want to give it a try or have your students see how gritty they are? Just click on the word "<a href="https://upenn.app.box.com/12itemgrit">survey</a>." When you have completed the survey, fill in the score grid below to find out just how gritty you truly are.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-Idlfx0krFGg/VNppGPP8cXI/AAAAAAAAGGw/l-NU5SCBYM0/s1600/Grid%2BScores.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-Idlfx0krFGg/VNppGPP8cXI/AAAAAAAAGGw/l-NU5SCBYM0/s1600/Grid%2BScores.JPG" height="308" width="640" /></a></div><br /><br /><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/03/how-gritty-are-you.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-3154092987640194552Tue, 17 Mar 2015 12:30:00 +00002015-03-17T07:30:00.307-05:00linear equationsslopeSlope for Vertical and Horizontal Lines<a href="http://3.bp.blogspot.com/-QsdgONo0Mvk/VOOqeoZHAnI/AAAAAAAAGJo/BlU9SRJEp8Y/s1600/y%2Bis%2Bmx%2Band%2Bb.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://3.bp.blogspot.com/-QsdgONo0Mvk/VOOqeoZHAnI/AAAAAAAAGJo/BlU9SRJEp8Y/s1600/y%2Bis%2Bmx%2Band%2Bb.JPG" height="82" width="200" /></a>I tutor at the community college where I also teach. Last week, I had two College Algebra students who were having difficulty with slope. They knew the equation <b>y = m<i>x</i> + b</b>, but were unsure when it came to horizontal or vertical lines. By the way, they were using their graphing calculators which I made them put away. (The book said no calculators.) I feel that if they construct the lines themselves, it puts a visual image into their brain much better than if the calculator does it for them. Sure enough, one of the sections in their math books gave the picture of the line from which they had to write the equation. They were amazed that I could just look at a graph and know the slope, give the equation, etc. When I taught high school math, my students couldn't use a graphing calculator until the middle of this particular chapter as I wanted them to physically draw the lines.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-jrUsmslWEiw/VOOiSEl1T8I/AAAAAAAAGI8/64LQmn6jDMs/s1600/rise%2Bover%2Brun.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-jrUsmslWEiw/VOOiSEl1T8I/AAAAAAAAGI8/64LQmn6jDMs/s1600/rise%2Bover%2Brun.JPG" /></a></div>First, for those who have no idea what I am talking about, slope is rise over run. Rise is how far a line goes up, and run is how far a line goes along. At the right, the line goes up 3 and has a run 5; therefore, the slope is 3/5. Rise/Run (Rise divided by Run) gives us the slope of the line.<br /><br /><a href="http://4.bp.blogspot.com/-vXDGypMJUCc/VOOj7-n02kI/AAAAAAAAGJI/vxIgNAiLgX8/s1600/Slope%2Bof%2Bzero.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://4.bp.blogspot.com/-vXDGypMJUCc/VOOj7-n02kI/AAAAAAAAGJI/vxIgNAiLgX8/s1600/Slope%2Bof%2Bzero.JPG" height="147" width="200" /></a><br />When a line is horizontal, it has no rise, only a run. So the numerator would be zero (for no rise) and the denominator would be a number such as 5 for the run. <b>0 ÷ 5 = 0 </b>This is true for any horizontal line.<br /><br /><a href="http://2.bp.blogspot.com/-lc_o2rcCBH8/VOOktZYTuPI/AAAAAAAAGJQ/gvXRdUnuEqE/s1600/Slope%2Bis%2BUndefined.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-lc_o2rcCBH8/VOOktZYTuPI/AAAAAAAAGJQ/gvXRdUnuEqE/s1600/Slope%2Bis%2BUndefined.JPG" height="161" width="200" /></a>A vertical line is different. It has rise, but no run; therefore there would always be a number in the numerator, but always a zero in the denominator. Since we cannot divide by zero, the slope is considered undefined. (I do use rise over run stating that a horizontal line might have 0/5 which is equal to 0 and that a vertical line might have 3/0 is undefined because we can't divide by zero. Our college algebra book uses O/K for okay and K/O for knock out which I like, but I still think the students need to know why.)<br /><br />I wanted these two students to have a picture that would help them remember the difference. I thought of a table for the horizontal line and asked them what would happen if the legs of the table were uneven. They agreed that the table would have slope. Therefore, the table would have a slope of zero if the legs were even.<br /><br />I then went blank. In other words, by creative juices stopped working, and I could not think of a picture that would help them visualize undefined. Since <b><i>Teachers Pay Teachers</i></b> has a forum,, I asked my fellow math teachers if they had any ideas. Here is what some of them came up with.<br /><br /><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><b><span style="color: #073763;"><a href="https://www.teacherspayteachers.com/Store/The-Enlightened-Elephant">The Enlightened Elephant</a></span> </b>suggested using a ski slope. She talks about skiing down a "cliff", which would not be possible (although some students try to argue that they <b><u>could</u></b> ski down a vertical cliff) and so the slope is "undefined" because it doesn't make sense to ski down a cliff. Skiing on a horizontal line is possible so it's slope is zero, She also talks about uphill (positive slope) and downhill (negative slope). </div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div><b><span style="color: #741b47;"><a href="https://www.teacherspayteachers.com/Store/Math-On-The-Mountain">Math on the Mountain</a></span> </b>likes to explain the concept of steepness of slope as a matter of effort. He tells his students to imagine riding a bike along a sloped line. If they already have some velocity, then a zero slope (horizontal) would take no additional effort. A small slope would require small effort and a greater slope would require much more effort (i.e. the slope/rate is analogous to "effort"). When students consider the amount of effort required to ride a bike up a vertical wall, they can see that it would essentially require an infinite or undefined amount of effort to do so.<br /><div><a href="http://3.bp.blogspot.com/-S8aSJZZ5pYk/VOOndxTwbFI/AAAAAAAAGJc/MW3SDks3yKU/s1600/Hoy%2BVux.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://3.bp.blogspot.com/-S8aSJZZ5pYk/VOOndxTwbFI/AAAAAAAAGJc/MW3SDks3yKU/s1600/Hoy%2BVux.JPG" height="320" width="235" /></a></div><b></b><br /><div><b><b><br /></b></b></div><b><a href="https://www.teacherspayteachers.com/Store/Math-By-Lesley-Elisabeth">Math by Lesley Elisabeth</a></b> tells her students to use "HOY VUX" (rhymes with 'toy bucks')<br /><div><br /><div><b style="text-align: center;"><span style="color: #660000;"> H</span></b><span style="text-align: center;">orizontal - Zero (</span><b style="text-align: center;"><span style="color: #990000;">0</span></b><span style="text-align: center;">) slope - </span><b style="text-align: center;"><span style="color: #990000;"><i>y =</i></span></b><span style="text-align: center;"> ? </span></div><div><span style="text-align: center;"><b><span style="color: #990000;"> </span><span style="color: #660000;">V</span></b></span><span style="text-align: center;">ertical - </span><span style="color: #660000; text-align: center;"><b>U</b></span><span style="text-align: center;">ndefined slope - </span><b style="text-align: center;"><span style="color: #990000;"><i>x =</i></span></b><span style="text-align: center;"> ?</span><br /><div><div style="text-align: center;"><br /></div><div>All horizontal lines are <i>y </i>=7 or <i>y </i>= -3 etc., and all vertical lines are <i>x </i>=1 or <i>x </i>= 6, etc. Students forget this so the acronym <b><span style="color: #990000;">HOY VUX</span></b> helps them to remember. Once they've mastered the slope concept in Algebra I, for the rest of the school year, for Algebra II (especially equations of asymptotes - a line that continually approaches a given curve but does not meet it at any finite distance) and even in calculus classes for tangent lines, <b><span style="color: #990000;">HOY VUX </span></b>is just faster and more practical. </div><div><br /><div><br /></div><span style="color: #274e13;"><b><a href="https://www.teacherspayteachers.com/Store/Animated-Algebra">Animated Algebra</a></b> </span>created a video lesson on the <a href="http://www.teacherspayteachers.com/Prod%20%E2%80%A6%20eo-1538596">Slope Intercept </a> ($5 on TPT). She has a boy skateboard down a negative slope, literally right on the graph line. Karen then shows the same boy taking an escalator up on a line that has a positive slope. Later in the lesson, she rotates the line clockwise, each movement with a click, to show the corresponding slope number to link the line to the slope. She includes lots of other visual cues to help students focus on and pay attention to the concepts.<br /><br />I did find a video on Pinterest that might help us all. It's called <a href="https://www.youtube.com/watch?v=avS6C6_kvXM"><b>Slope Dude</b></a>. My students thought it was corny, but it did help them to remember.<br /><div><br /></div></div></div></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/03/slope-for-vertical-and-horizontal-lines.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-7317031723886379052Tue, 03 Mar 2015 13:30:00 +00002015-03-03T07:30:00.786-06:00piPi DayThe Life and Art of Pi<a href="http://3.bp.blogspot.com/-KQ6TEuzjOzQ/VPCJUVwP9rI/AAAAAAAAGM4/wmyom3ePSfM/s1600/Corinne%2B-%2BImage%2B%235.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-KQ6TEuzjOzQ/VPCJUVwP9rI/AAAAAAAAGM4/wmyom3ePSfM/s1600/Corinne%2B-%2BImage%2B%235.JPG" /></a>Today I welcome <a href="https://alternatetutelage.wordpress.com/">Corinne Jacob</a> as my guest blogger. She is a fan of <i><span style="color: #990000;"><b>Go Figure</b></span></i> who contacted me via e-mail, and as a result we began corresponding. Since she spells her first name just like my granddaughter does, we had an immediate connection. <br /><br />Corinne is a wannabe writer who is convinced that kids learn best when they are having fun. She is constantly on the lookout for new and exciting ways to make learning an enjoyable experience. She loves all things that scream out un-schooling, alternative education and holistic learning.<br /><br /><span style="color: #990000;">----------------------------------------------------------------------------</span><br /><br />Math, after years of being relegated to the role of a heartless monster, has slowly begun to get an image makeover and is getting cooler by the day with fun <a href="https://apps.facebook.com/mathblasters">math games</a> and even days that are dedicated to math concepts like Pi Day, which is celebrated on March 14 of every year. It is especially significant this year as the date format is 3/14/15 (mm/dd/yy) and at the time 9:26:53, we got the pi (<b>π</b>) sequence – 3.141592653!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-rZDNmthTQNs/VPCC7DDN_CI/AAAAAAAAGMI/iJpikhtymbY/s1600/Corinne%2B-%2BImage%2B%231.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-rZDNmthTQNs/VPCC7DDN_CI/AAAAAAAAGMI/iJpikhtymbY/s1600/Corinne%2B-%2BImage%2B%231.JPG" /></a></div><div style="text-align: center;"><span style="font-size: x-small;">“<a href="https://www.flickr.com/photos/myklroventine/3355106480">Happy Pi Day (to the 69th digit)!</a>” by <a href="https://www.flickr.com/photos/myklroventine/">Mykl Roventine</a> is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/2.0/">CC by 2.0</a></span></div><br /><div><b><u>Life of Pi</u></b><br /><br />Students will be excited to learn about the mathematical constant Pi, which is represented by the Greek letter <b>π</b>. It is defined as the ‘ratio of the circumference of any circle to the diameter of that circle.’ What is it that sets <b>π</b> apart from the rest? The value does not change even if the size of the circle does. Though it is not a recurring decimal, its decimal form does not end; that is, it is an infinite decimal. Did you know that so far <a href="http://www.numberworld.org/misc_runs/pi-5t/details.html">10 trillion digits</a> have been discovered?<br /><br />Students will meet <b>π</b> when they start learning to calculate the area and circumference of a circle. It makes an appearance in the formula: A= <b style="text-align: justify;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">πr<sup>2</sup></span></b><br /><div class="MsoNormal" style="text-align: justify;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></b></div><img border="0" src="file:///C:/Users/Owner/AppData/Local/Temp/msohtmlclip1/01/clip_image004.jpg" /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-oo40QUQGnSw/VPCC9brPChI/AAAAAAAAGMQ/GE_soZ0m7jQ/s1600/Corinne%2B-%2BImage%2B%232.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-oo40QUQGnSw/VPCC9brPChI/AAAAAAAAGMQ/GE_soZ0m7jQ/s1600/Corinne%2B-%2BImage%2B%232.JPG" /></a></div><div style="text-align: center;"><span style="font-size: x-small;">“<a href="https://www.flickr.com/photos/djwtwo/6835022968">073/365 - Pi Day Pies, 2012</a>” by <a href="https://www.flickr.com/photos/djwtwo/">Dennis Wilkinson</a> is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/2.0/">CC by 2.0</a></span></div><br /><b><u>Art of Pi</u></b><br /><br />Once students learn about this old stalwart of the math world, they can have fun creating art around <b>π</b>.<br /><br /><b><u>Pi Woods</u></b><br /><br />In this activity, students can represent the <b>π</b> sequence with colored Popsicle sticks and decorate it like the woods. Ask your class to take the first 10 numbers of <b>π</b> = 3.141592653. Paint ten sticks in different colors but assign one color for each number. For instance, 3 is blue, 1 is orange, and so on. Students can then glue these sticks in the correct <b>π</b> sequence. Using their thumbs and some green paint, they can create leaves around these sticks. They can also collect small leaves from the garden and glue them around.<br /><br /><img border="0" src="file:///C:/Users/Owner/AppData/Local/Temp/msohtmlclip1/01/clip_image006.jpg" /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-WsA9yzEfKoM/VPCC_gMtPtI/AAAAAAAAGMY/pVNUJKW_XF0/s1600/Corinne%2B-%2BImage%2B%233.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-WsA9yzEfKoM/VPCC_gMtPtI/AAAAAAAAGMY/pVNUJKW_XF0/s1600/Corinne%2B-%2BImage%2B%233.JPG" /></a></div><div style="text-align: center;"><span style="font-size: x-small;">“<a href="https://www.flickr.com/photos/47738026@N05/8476624791">Pi number</a>” by <a href="https://www.flickr.com/photos/47738026@N05/">J.Gabás Esteban</a> is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/2.0/">CC by 2.0</a></span></div><br /><b><u>Pi Poem</u></b><br /><br />Taking the first few digits of <b>π</b>, say 3.1415, students can write a poem in this order:</div><div><br /><div style="text-align: center;"><b><i>3 word word word</i></b></div><div style="text-align: center;"><b><i>1 word</i></b></div><div style="text-align: center;"><b><i>4 word word word word</i></b></div><div style="text-align: center;"><b><i>1 word</i></b></div><div style="text-align: center;"><b><i>5 word word word word word</i></b></div><br />Or they can also rearrange an existing poem or rhyme to fit the <b>π</b> sequence such as:<br /><div style="text-align: center;"><b><i>3 hey diddle diddle</i></b></div><div style="text-align: center;"><b><i>1 the</i></b></div><div style="text-align: center;"><b><i>4 cat and the fiddle</i></b></div><div style="text-align: center;"><b><i>1 the</i></b></div><div style="text-align: center;"><b><i>5 cow jumped over the moon</i></b></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-NHnv78qM2fg/VPCDCOwxv4I/AAAAAAAAGMg/WrxPjsDtIMM/s1600/Corinne%2B-%2BImage%2B%234.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-NHnv78qM2fg/VPCDCOwxv4I/AAAAAAAAGMg/WrxPjsDtIMM/s1600/Corinne%2B-%2BImage%2B%234.JPG" /></a></div><div style="text-align: center;"><span style="font-size: x-small;">“<a href="https://www.flickr.com/photos/fdecomite/4562063329">Pi</a>” by <a href="https://www.flickr.com/photos/fdecomite/">fdecomite</a> is licensed under <a href="https://creativecommons.org/licenses/by-nc-sa/2.0/">CC by 2.0</a></span></div><br /><b><u>Pi Collage</u></b><br /><br />Students can create a collage with the <b>π</b> numbers. They can take as many as they want; here are <a href="http://www.ilikepi.com/10-000-digits-of-pi/">10,000</a> of them! They can cut them out from magazines, newspapers, drawings and glue them onto construction paper in any order they like to create a colorful collage of <b>π</b> numbers. <br /><br />These are just a few of the ways in which students will retain this number. And don’t forget to mark your calendar so that you can plan something cool for Pi Day! <br /><br /><br /></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/03/the-life-and-art-of-pi.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-6371798944241539518Thu, 19 Feb 2015 13:30:00 +00002015-04-30T10:51:21.489-05:00new TPT sellerA Go Figure Debut for a Math Person Who's New (to me, anyway)!<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-_rsfn3khL50/VM0z87EW1jI/AAAAAAAAGFc/yogrFHguBsc/s1600/Brittany%2B-%2BStore%2BLogo.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-_rsfn3khL50/VM0z87EW1jI/AAAAAAAAGFc/yogrFHguBsc/s1600/Brittany%2B-%2BStore%2BLogo.JPG" /></a></div>Today, I debut a math teacher who is new to me, but through TPT has become a colleague. Brittany is from Colorado; so, she named her store <a href="https://www.teacherspayteachers.com/Store/Brittany-Naujok-The-Colorado-Classroom">The Colorado Classroom</a> - a very fitting name in my opinion.<br /><br />Brittany shares that when she was eight years old, her second grade teacher had a remarkable effect on her. This teacher showed her how a teacher could truly inspire students. Ever since then, her desire has been to be a teacher and to try to emulate her.<br /><div><br /></div>She has taught 6th grade for almost her entire teaching career, but in two very distinct ways. Her first teaching position was at a charter school where she taught 6th grade for eleven years; however, at this school sixth grade was considered an elementary grade. This meant she taught all the disciplines. Seeking a new challenge, she moved to teaching sixth grade math at a local middle school.<br /><div><br /></div>Overall, she tends to use a variety of teaching styles based on the goals and objectives for each individual lesson. These vary from direct instruction and journaling, to student led creations, games, cooperative learning, and more. She really enjoys getting her students involved in their learning and making classroom activities hands-on.<br /><div><br /></div><div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-VyumR9ZHBRw/VM-1zY8Ve3I/AAAAAAAAGFs/UPs5mvpxVZI/s1600/Brittany%2B-%2BFree.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-VyumR9ZHBRw/VM-1zY8Ve3I/AAAAAAAAGFs/UPs5mvpxVZI/s1600/Brittany%2B-%2BFree.JPG" height="200" width="151" /></a></div>You will find more than 200 resources in Brittany's <b><i>Teachers Pay Teachers</i></b> store. Many are math activities, but her store also showcases various resources for social studies. I especially like <a href="https://www.teacherspayteachers.com/Product/Overall-Average-1682606">Overall Average,</a> one of her free math resources since finding the average can be a tricky concept to master. It includes teacher notes and six practice problems as well as two complete example problems with a full answer key.<br /><br /><a href="https://www.teacherspayteachers.com/Product/Ratio-Equivalent-Ratio-Task-Cards-with-Mini-Lesson-1653266">Ratios and Equivalent Ratios</a> is a paid resource that includes a 12 page mini-lesson on ratios and equivalent ratios. Also contained in this package are 32 task cards so that the students can work on and practice their skills. Some of the tasks students are asked to do are....<br /><ol><a href="http://4.bp.blogspot.com/-o__tVyR0AGo/VM-3u00ItrI/AAAAAAAAGF4/LhWSzkzsqi4/s1600/Brenda%2B-%2BPaid.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://4.bp.blogspot.com/-o__tVyR0AGo/VM-3u00ItrI/AAAAAAAAGF4/LhWSzkzsqi4/s1600/Brenda%2B-%2BPaid.JPG" /></a><li>Write ratios in various forms – part:part; part:whole; whole:part</li><li>Use tables to write ratios</li><li>Find the ratio that doesn't belong</li><li>Solve word problems</li><li>Extend their problem by applying the ratio to a real word situation</li><li>Complete ratio tables</li></ol><div>I hope you will take the time to check out <a href="https://www.teacherspayteachers.com/Store/Brittany-Naujok-The-Colorado-Classroom">Brittany's store</a> and the numerous resources she has to offer for grades 4-8. While you are there, why not download one of her free items and then become a follower?</div><div><br /></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/02/a-go-figure-debut-for-math-person-whos.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-3394483319362108634Thu, 12 Feb 2015 13:30:00 +00002015-02-12T07:30:01.539-06:00manipulativesmathMilk Lid Mathprimary gradesMilk Lid Math<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-GL99CYlWowQ/VLaZErlo-yI/AAAAAAAAGD8/mtGP6oAsRCU/s1600/Milk%2BJug.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-GL99CYlWowQ/VLaZErlo-yI/AAAAAAAAGD8/mtGP6oAsRCU/s1600/Milk%2BJug.JPG" /></a></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/></v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_s2058" type="#_x0000_t75" style='position:absolute;margin-left:-17.45pt;margin-top:-.35pt;width:122.55pt; height:127.45pt;z-index:-251657216;visibility:visible;mso-wrap-style:square; mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; mso-wrap-distance-bottom:0;mso-position-horizontal:absolute; mso-position-horizontal-relative:text;mso-position-vertical:absolute; mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0; mso-width-relative:page;mso-height-relative:page'> <v:imagedata src="file:///C:\Users\Owner\AppData\Local\Temp\msohtmlclip1\01\clip_image001.wmz" o:title="MCj02900580000[1]"/> <w:wrap type="tight"/></v:shape><![endif]--><!--[if !vml]--><!--[endif]--><span style="font-family: Subway; font-size: 24.0pt;"><o:p></o:p></span></div><br /><div style="text-align: center;">Start saving those milk jug lids because there are countless math activities you can do in your classroom using this free manipulative</div><div style="text-align: center;">Here are just four of those ideas.</div><div style="text-align: center;"><br /></div><div style="text-align: center;"><br /></div><br /><b>1) Sort the lids by various attributes such as</b>:<br /><ul><li>Color</li><li>Snap-on or Twist-on </li><li>Label or No Label</li><li>Kind of edge (smooth or rough)</li></ul><br /><b>2) Let the students grab one handful of lids.</b> <br /><ul><li>Ask the students to count the lids.</li><li>See if the students can write that number.</li></ul><br /><b>3)</b> <b>Make a pattern using two different colors of lids.</b><br /><div> <br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-d9LT4RzXxa0/VLaZntUwSKI/AAAAAAAAGEE/T-Fgi_Pa4c8/s1600/Milk%2BLid%2BPattern.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-d9LT4RzXxa0/VLaZntUwSKI/AAAAAAAAGEE/T-Fgi_Pa4c8/s1600/Milk%2BLid%2BPattern.JPG" height="80" width="320" /></a></div><ul><li>Identify the pattern using letters of the alphabet or numbers. The pattern above would be an A, A, B pattern or a 1, 1, 2 pattern.</li></ul><ul><li>Now ask the students to use more than two colors to make a pattern</li></ul><ul><li>Once more, have the students identify the pattern using alphabet letters or numbers.</li></ul><br /><b>4) Decide on a money value for each color of lid.</b> (Example: Red lids are worth a nickel, blue lids are worth a dime, and white lids are worth a penny.) Put all of the lids into a bag and have the students draw out four lids. Have the students add up the total value of these four lids.<br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-ky2wq91hr3k/VLabHn0YyKI/AAAAAAAAGEQ/9m11NxvYl90/s1600/Mile%2BLid%2BMath.PNG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-ky2wq91hr3k/VLabHn0YyKI/AAAAAAAAGEQ/9m11NxvYl90/s1600/Mile%2BLid%2BMath.PNG" height="200" width="152" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="http://www.teacherspayteachers.com/Product/Milk-Lid-Math-Hands-On-Activities-for-Math-49288"><b>Milk Lid Math</b></a></td></tr></tbody></table><ul><li>Use play money (coins) to have the students show the value of the lids. </li></ul><ul><li>Have the students practice writing money as either a part of a dollar or as cents.</li></ul><ul><li>Another idea is to have the students find all the combinations of lids that would equal a nickel or a dime or a quarter.</li></ul><div><br /></div>On the original download you will receive 15 ideas with numerous subtopics listed under each one. These may be used with a whole group, small groups, or as center activities.<br /><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;"><o:p></o:p></div><div><br /></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/02/milk-lid-math.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-2499241994784701097Thu, 05 Feb 2015 13:30:00 +00002015-02-05T07:30:01.415-06:00changing fractions to decimalsdivisiondump and divideDump and Divide or Converting Fractions to Decimals<div class="separator" style="clear: both; text-align: center;"></div>When working with fractions, my remedial math college students are never quite sure which number to divide by. This same thing often occurred when I taught middle school and high school. So the question I had to answer was, "How can I help my students remember what number goes where?"<br /><div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-NInBn_CiTfs/T3IYisVzW4I/AAAAAAAAA8M/jOoXg_-8nqA/s1600/division+problem+for+article.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-NInBn_CiTfs/T3IYisVzW4I/AAAAAAAAA8M/jOoXg_-8nqA/s1600/division+problem+for+article.bmp" /></a></div><br />First, the student must understand and know the vocabulary for the three parts of a division problem. As seen in the problem above, each part is correctly named and identified. <br /><br /><b><u>Side Note:</u></b> The symbol separating the dividend from the divisor in a long division problem is a straight vertical bar with an attached vinculum (you might have to look this word up) extending to the left, but it seems to have no established name of its own. Therefore, it can simply be called the "long division symbol" or the division bracket. I wish it were named something fancier, but sometimes plain and straight forward is the best! <br /><a href="http://1.bp.blogspot.com/-p0rRobFZmLI/T3WnIaVEM2I/AAAAAAAAA90/DmZakcWJvWo/s1600/2-5%2527s+with+arrow.bmp"><img border="0" src="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F1.bp.blogspot.com%2F-p0rRobFZmLI%2FT3WnIaVEM2I%2FAAAAAAAAA90%2FDmZakcWJvWo%2Fs1600%2F2-5%252527s%2Bwith%2Barrow.bmp&container=blogger&gadget=a&rewriteMime=image%2F*" /></a>Now let's look at a fraction that the student is asked to rewrite as a decimal. The fraction on your right is two-fifths and is read from top to bottom as two divided by five. That's easy enough, but when my students enter this into their calculators, many will put in the 5 first, and then press the<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-TncJmpbf4to/VGYM6jnf49I/AAAAAAAAF5Q/6NYc-LIx150/s1600/Dump%2Band%2BDivide.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://4.bp.blogspot.com/-TncJmpbf4to/VGYM6jnf49I/AAAAAAAAF5Q/6NYc-LIx150/s1600/Dump%2Band%2BDivide.JPG" /></a></div>division sign, followed by the 2. Of course, they get the wrong answer. Now let's look at the <b>dump and divide</b> method.<br /><br />First, dump the 2 into the calculator. Then press the division sign; then divide by 5. The answer is 0.4.<br /><a href="http://2.bp.blogspot.com/-jDXy8IsfYbo/T3Inf7Yk6SI/AAAAAAAAA9U/wY0FHZtRG4E/s1600/Dump+and+Divide+with+Rules.bmp"><img border="0" src="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F2.bp.blogspot.com%2F-jDXy8IsfYbo%2FT3Inf7Yk6SI%2FAAAAAAAAA9U%2FwY0FHZtRG4E%2Fs400%2FDump%2Band%2BDivide%2Bwith%2BRules.bmp&container=blogger&gadget=a&rewriteMime=image%2F*" /></a><br />I am aware that many of students are not allowed to use calculators; so, let's look at how this method would work using the division bracket. We will use the same fraction of 2/5 and the same phrase, dump and divide.<br /><br /><a href="http://4.bp.blogspot.com/-rpY4gTMgyf0/T3IpRW9C4PI/AAAAAAAAA9k/4o_4a3jH5cc/s1600/2+divided+by+5+in+house.bmp"><img border="0" src="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F4.bp.blogspot.com%2F-rpY4gTMgyf0%2FT3IpRW9C4PI%2FAAAAAAAAA9k%2F4o_4a3jH5cc%2Fs1600%2F2%2Bdivided%2Bby%2B5%2Bin%2Bhouse.bmp&container=blogger&gadget=a&rewriteMime=image%2F*" /></a><a href="http://2.bp.blogspot.com/-WAq0HgO2bRY/T3IiycZJVCI/AAAAAAAAA9M/ImAK8xprM3k/s1600/N+side.bmp"><img border="0" src="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F2.bp.blogspot.com%2F-WAq0HgO2bRY%2FT3IiycZJVCI%2FAAAAAAAAA9M%2FImAK8xprM3k%2Fs1600%2FN%2Bside.bmp&container=blogger&gadget=a&rewriteMime=image%2F*" /></a>First, take the numerator and dump it inside the division bracket. (Note: Use N side instead of inside so that numerator and N side both start with "N".) Now place the 5 outside of the long division bracket and divide. The answer is still .4.<br /><br /><b>Dump and Divide </b>will also work when a division problem is written horizontally as a number sentence such as: 15 ÷ 3. First, reading left to right, dump 15 into the division bracket. Now place the 3 on the outside. Ask, "How many groups of three are in 15?" The answer is 5.<br /><br />Try using <b>Dump and Divide </b>with your students, and then let me know how it works. You can e-mail by clicking on the page entitled Contact Me or just leave a comment.<br /><br /><br /><b><u>Something Else to Think About:</u> </b>Since many students do not know<br /><div>their multiplication tables, reducing fractions is almost an<br /><div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-DtPHRL0o2R8/VGYOej3hQHI/AAAAAAAAF5c/z0AySL08rXg/s1600/Divisibility%2BRules.PNG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-DtPHRL0o2R8/VGYOej3hQHI/AAAAAAAAF5c/z0AySL08rXg/s1600/Divisibility%2BRules.PNG" height="200" width="156" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="http://www.teacherspayteachers.com/My-Products/Edit/Step-1/Using-Digital-Root-and-the-Divisibility-Rules-to-Help-Reduce-Fractions"><b>Divisibility Rules</b></a></td></tr></tbody></table>impossible task. The divisibility rules, if learned and understood, can be an excellent math tool. The resource, <a href="http://www.teacherspayteachers.com/My-Products/Edit/Step-1/Using-Digital-Root-and-the-Divisibility-Rules-to-Help-Reduce-Fractions">Using Digital Root to Reduce Fractions</a>, contains four easy to understand divisibility rules as well as the digital root rules for 3, 6, and 9. A clarification of what digital root is and how to find it is explained. Also contained in the resource is a dividing check off list for the student. Download the preview to view the first divisibility rule plus three samples from the student check off list.<br /><div class="MsoNormal"><span class="apple-converted-space"></span></div><div><br /></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"></div></div></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/02/dump-and-divide-or-converting-fractions.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-2876052588845488850Thu, 29 Jan 2015 13:30:00 +00002015-01-29T07:30:00.859-06:00math attitudemathphobiaIs Math Really the Enemy?<div class="MsoNormal" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; margin: 0in 0in 10pt;"><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-pxCMgV8aC7s/VKhnhaTmfPI/AAAAAAAAF-0/cE6XexCosiY/s1600/Math%2BYeller.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-pxCMgV8aC7s/VKhnhaTmfPI/AAAAAAAAF-0/cE6XexCosiY/s1600/Math%2BYeller.jpg" /></a></div>Last week was the start of spring semester at the college where I teach. (I teach Mathphobics who aren't always thrilled to be in my math class.) As the students were entering and finding seats, I was greeted with, <i>“Math is my worst enemy!”</i> I guess this particular student was waiting for an impending Math Attack. But then I began thinking, “Should this student wait to be attacked or learn how to approach and conquer the enemy?” Since winning any battle requires forethought and planning, here is a three step battle plan for Mathphobics.<br /><br /><b> 1)</b> <b><span style="color: #990000;">Determine why math is your enemy</span></b>. Did you have a bad experience? Were you ever made to feel stupid, foolish, or brainless? Did your parents say they didn’t like math, and it was a family heredity issue? (One of the curious characteristics about our society is that it is now socially acceptable to take pride in hating mathematics. It’s like wearing a badge of honor or is that dishonor? Who would ever admit to not being able to read or write?) Math is an essential subject and without math, not much is possible...not even telling time!<br /><br /><b>2)</b> <b><span style="color: #990000;">Be optimistic.</span></b> Suffering from pessimism when thinking of or doing math problems makes it impossible to enjoy math. Come to class ready to learn. At the end of class, write down one thing you learned or thought was fun. I realize math teachers are a big part of how a student views math. In fact, one of the most important factors in a student’s attitude toward mathematics is the teacher and the classroom environment. Just using lecture, discussion, and seat work does not create much interest in mathematics. You've been in that class. Go over the homework; do samples of the new homework; start the new homework. Hands-on activities, songs, visuals, graphic organizers, and connecting math to real life engage students, create forums for discussion, and make math meaningful and useful. <br /><br /><div style="text-align: right;"></div><b>3)</b> <b><span style="color: #990000;">Prove Yourself.</span></b> Take baby steps, but be consistent. Faithfully do the homework and have someone check it. Don’t miss one math class! You can’t learn if you aren't there. Join in the discussions. Think about and write down your questions and share them with your teacher or with the class. Study for an upcoming test by reviewing 15 minutes each night a week before the test. Get help through tutoring, asking your instructor, or becoming a part of a study group. Keep in mind, no one is destined for defeat!<br /><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-vxdns1DTKQ8/VKloeiKypgI/AAAAAAAAF_Y/QLaxhxDSpKo/s1600/Study%2BTips.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-vxdns1DTKQ8/VKloeiKypgI/AAAAAAAAF_Y/QLaxhxDSpKo/s1600/Study%2BTips.JPG" height="200" width="158" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="http://www.teacherspayteachers.com/Product/Math-Study-Tips-You-Wont-Forget">Free Resource</a></b></td></tr></tbody></table>So don’t just sit there and wait for the dreaded Math Attack. This semester, meet it head on with a three step battle plan in hand!<br /><br />---------------------------------------------------------<br /><br />Math courses are not like other courses. To pass most other subjects, a student must read, understand, and recall the subject matter. However, to pass math, an extra step is required: a student must <b>use</b> the information they have learned to solve math problems correctly. Special math study skills are needed to help the student learn more and to get better grades. To receive 20 beneficial math study tips, just download this free resource.</div><div class="MsoNormal" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; margin: 0in 0in 10pt;"><br /></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/01/is-math-really-enemy.htmlnoreply@blogger.com (Scipi)0tag:blogger.com,1999:blog-5410562205692621875.post-769832360208060601Thu, 22 Jan 2015 13:30:00 +00002015-06-15T14:54:09.076-05:00progressive educationtraditional educationA Go Figure Debut for a Guest Author Who's New<div class="separator" style="clear: both; text-align: center;"><br /></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-ElMr4OTLUwU/VKw4-RjdSDI/AAAAAAAAGCY/OKWxhCpIQwM/s1600/SamizdatMath%2BLogo.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-ElMr4OTLUwU/VKw4-RjdSDI/AAAAAAAAGCY/OKWxhCpIQwM/s1600/SamizdatMath%2BLogo.JPG" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><a href="http://www.teacherspayteachers.com/Store/Samizdatmath">Robert's TPT Store</a></b></td></tr></tbody></table><div><br /></div><div>The following article is by Robert M. Berkman who has worked in mathematics and science education since 1984. He publishes educational materials under the name <a href="http://www.teacherspayteachers.com/Store/Samizdatmath"><span style="color: #351c75;">SamizdatMath</span></a>, which can be found on <b>Teachers Pay Teachers</b>. His also has a blog is entitled <a href="http://bltm.com/blog/">Better Living Through Mathematics</a>. He currently lives in Brooklyn, New York.</div><div><br /></div><div>I've always found Robert's forum posts and blog articles interesting because they contain a great deal of depth along with a bit of humor. He was kind enough to agree to write an article as a guest blogger for my blog. I think you will find the following article (it's part of a full day workshop called “Wiring the Brain for Mathematics Neuroscience and Numeracy") very thought provoking. </div><div style="text-align: center;"><b><span style="color: #990000;"><br /></span></b></div><div style="text-align: center;"><b><span style="color: #990000; font-family: Georgia, Times New Roman, serif; font-size: large;"><u>Thinking About Skills, Context and Neuroscience</u></span></b></div><br />Many years ago I was hired to coordinate a mathematics program at a private school in Manhattan: I had been a classroom teacher for the previous 15 years, and my views definitely tilted towards the “progressive” end of the educational philosophical spectrum. I had no choice: I had seen the results of both “traditional” and “progressive” educational practices, and while neither was perfect, I definitely saw that progressive practices aligned better with what I wanted to see happen in the classroom. I remember the “sage on the stage” practices from my own school years, and while I responded to well to them (I was that kind of learner), many of my classmates were left in the dust. At the same time, I was familiar with the criticisms of progressive math practices, and was ready to modify practices in the classroom to address them.<br /><br />Of course, although I had a thorough understanding of what progressive math looked like, this did not mean that everyone with whom I worked shared that same comprehension. I had two “bosses” at this school: the first was the head of my division, which spanned from kindergarten through 4th grade; she was impressed by both my philosophy and how I intended to translate it into practice.<br /><br />My other “boss” was the chair of the math department, who was ten years my junior and lacked any kind of experience or understanding of what a K - 4 mathematics program looked like. She held some very ignorant views of progressive education, including the idea that using these methods, students would not be required to learn “basic facts.”<br /><br />This came to a head during a meeting where “Jen” (I changed her name to protect those with similar names) described a situation where a 7th grade student she was tutoring for several months had forgotten the answer to 6 x 8. She recounted how she prompted the student to figure out the answer for himself and then watched in dismay as the student made 6 rows of 8 dots per row, and counted them one by one. Initially, I wanted to say the following: “Jen, you must be a pretty cruddy tutor if the parents are paying you all this money to help their son, and you wasted 10 minutes watching him draw and count out all these dots. Why didn't you just tell him that 6 x 8 is 48?”<br /><br />However, Jen was my boss, so I activated my internal editor and I sadly shook my head and agreed that this was a sad state of affairs. But I also understood that this colleague was inadequately informed about many aspects of educational philosophy, especially the difference between “practice” and “outcomes.” Unfortunately, engaging her in discussions to tease out the difference inevitably led her to recount yet another story of a “progressive education failure.”<br /><br />So let’s begin at the beginning: progressive education, in which I firmly believe, has nothing to do with the outcomes of that practice. There is nothing in the practice of progressive education that states that students don’t have to learn how to add, subtract, multiply or divide. This is because progressive education has nothing to do with outcomes: it has to do with methodology. As a progressive educator, my goals are fairly anodyne: I want my students to master mathematics with a balance of conceptual understanding factual knowledge (like computational facts) as well as the application of the latter to problem solving. This doesn’t sound particularly “radical” to me, and I would expect that it probably sounds reasonable to even the most traditional mathematics educator.<br /><br />I’ll repeat this again: <b>progressive and traditional mathematics educators seek exactly the same outcomes</b>. Where we part ways is in the methodology: when I think of “progressive,” I don’t long for some long-lost 60’s era where students wrestled with “new math” or counted on their fingers in 5th grade. As a “progressive,” I’m sensible enough to understand that the “good old days” never really existed, and that students of today struggle with the same learning issues that they did in bygone years. I also don’t buy into the fact that students today are “different” from those of 10, 20 or even 100 years ago: students are students, and except for the fact that they’re more likely to come from economically impoverished households, I haven’t really seen much of a change in my three decades of teaching.<br /><br />As a progressive educator, I do believe in one thing: scientific research. As a progressive, I’m interested in what advancements have been made in understanding how the brain comprehends the world and how it learns new things. My particular interest is in the neuroscience of numeracy, which has led to great insights into the learning of mathematics during the last two decades. <br /><br /><div class="separator" style="clear: both; font-weight: bold; text-align: center;"><a href="http://1.bp.blogspot.com/-w57hDPkvEZU/VKw9hhcm9eI/AAAAAAAAGCk/GWTlcENuuZY/s1600/SamizdatMathBook.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-w57hDPkvEZU/VKw9hhcm9eI/AAAAAAAAGCk/GWTlcENuuZY/s1600/SamizdatMathBook.JPG" /></a></div><div><span style="font-weight: normal;">One of the best books on the subject is Brian Butterworth’s book,</span><span style="color: #351c75;"><b style="font-weight: bold;">What Counts: How Every Brain </b><b style="font-weight: bold;">is Hardwired for Math</b></span><b style="font-weight: bold;">. </b>Although this book is 15 years old, it presents the basics of how the brain works with numbers quite clearly and with a minimum of jargon. My favorite chapter is where Butterworth demolishes “neuromyths” like the idea that the ability to work with numbers is localized to the left side of the brain. How this pernicious piece of factual idiocy got indoctrinated into our educational culture is beyond me, but it still remains pervasive, perhaps because some people make a living perpetuating it as a “fact.”</div><br />In the course of his book, Butterworth describes a finding which would have helped Jen’s student who had forgotten the solution to 6 x 8. As it happens, multiplication facts are stored in a particular part of the brain that works with language, particularly words that are remembered as associations. This would include things like song lyrics, nursery rhymes and prayers. In essence, they are linguistic phrases that we repeat over and over again with little thought. The remedy was not to ask the student to “figure it out,” but to teach him the fact and help him create a “linguistic hook” that would help remind him of the answer when it appeared again (such as “6 x 8 is really great because the answer is 48....”) To me, this is what progressive education is about: I too want that student to have factual knowledge, but I want to use what science has shown me to help troubleshoot and correct the student’s deficit.<br /><div><br />Of course, this brief treatise does not begin to cover the complete belief system of the progressive educator, but it should give you a better understanding of its depth and complexity. In fact, you may be using the technique I described in the previous paragraph, in which case, congratulations and welcome to our ranks!<br /><br /><div class="MsoNormal"><b><span style="font-family: 'Cooper Black', serif; line-height: 115%;"><i><span style="font-size: x-large;">-Robert Berkman</span></i><span style="font-size: 14pt;"><o:p></o:p></span></span></b></div><br /><br /><div><br /></div></div><div class="blogger-post-footer"><br />
<br />
<br />
<a href="javascript:void((function(){var%20e=document.createElement('script');e.setAttribute('type','text/javascript');e.setAttribute('charset','UTF-8');e.setAttribute('src','http://assets.pinterest.com/js/pinmarklet.js?r='+Math.random()*99999999);document.body.appendChild(e)})());"><img alt="Pin It!" style='border: none;' src="http://i1209.photobucket.com/albums/cc390/scipiatgofigure/PinterestImage.png"/></a></div>http://gofigurewithscipi.blogspot.com/2015/01/a-go-figure-debut-for-guest-author-whos.htmlnoreply@blogger.com (Scipi)0