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	<title>The Crafty Canvas Learning Library</title>
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	<link>http://thecraftycanvas.com/library</link>
	<description>Lessons Learned and Worth Sharing amongst Students, Tutors, and Parents</description>
	<lastBuildDate>Mon, 13 May 2013 14:18:26 +0000</lastBuildDate>
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		<title>10 Homework Tips to Avoid the 4th Quarter Slump</title>
		<link>http://thecraftycanvas.com/library/10-homework-tips-to-avoid-the-4th-quarter-slump/</link>
		<comments>http://thecraftycanvas.com/library/10-homework-tips-to-avoid-the-4th-quarter-slump/#comments</comments>
		<pubDate>Mon, 29 Apr 2013 14:11:19 +0000</pubDate>
		<dc:creator>ansonwhan</dc:creator>
				<category><![CDATA[Lessons Learned & Worth Sharing Blog]]></category>
		<category><![CDATA[homework made easy]]></category>
		<category><![CDATA[homework tips]]></category>
		<category><![CDATA[motivating kids to do homework]]></category>
		<category><![CDATA[self-motivation]]></category>

		<guid isPermaLink="false">http://thecraftycanvas.com/library/?p=372</guid>
		<description><![CDATA[<table cellpadding='10'><tr><td valign='top' align='left'><p>Categories: <ul class="post-categories">
	<li><a href="http://thecraftycanvas.com/library/category/lessons-learned-shared-blog/" title="View all posts in Lessons Learned &amp; Worth Sharing Blog">Lessons Learned &amp; Worth Sharing Blog</a></li></ul></p><p>Tags: <a href="http://thecraftycanvas.com/library/tag/homework-made-easy/" rel="tag">homework made easy</a><a href="http://thecraftycanvas.com/library/tag/homework-tips/" rel="tag">homework tips</a><a href="http://thecraftycanvas.com/library/tag/motivating-kids-to-do-homework/" rel="tag">motivating kids to do homework</a><a href="http://thecraftycanvas.com/library/tag/self-motivation/" rel="tag">self-motivation</a></p>This recent article explores the new-found insight discovered by one columnist and parent from the Educational Connections&#8217; monthly newsletter.  As spring time and summer weather makes procrastination and slacking more tempting, here are some great tips for parents/educators and students<span class="ellipsis">&#8230;</span><div class="read-more"><a href="http://thecraftycanvas.com/library/10-homework-tips-to-avoid-the-4th-quarter-slump/">Read more &#8250;</a></div><!-- end of .read-more --><table width='100%'><tr><td align=right><p><b>(<a href='http://thecraftycanvas.com/library/10-homework-tips-to-avoid-the-4th-quarter-slump/' title='10 Homework Tips to Avoid the 4th Quarter Slump'>Read more...</a>)</b></p></td></tr></table></td></tr></table>]]></description>
				<content:encoded><![CDATA[<p>This recent article explores the new-found insight discovered by one columnist and parent from the Educational Connections&#8217; monthly newsletter.  As spring time and summer weather makes procrastination and slacking more tempting, here are some great tips for parents/educators and students to avoid slipping in the final stretch of the school year.</p>
<p><a title="Read more..." href="http://www.babble.com/babble-voices/rants-in-my-pants-julie-miner/2013/04/29/10-tips-to-avoid-the-4th-quarter-slump/designated-homework-time?utm_source=Summer+Programs+Newsletter+-+early+May&amp;utm_campaign=Summer+Programs+newsletter&amp;utm_medium=email" target="_blank">Read more&#8230;</a></p>
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		<title>Comparing College Costs with Net Price Calculators</title>
		<link>http://thecraftycanvas.com/library/comparing-college-costs-with-net-price-calculators/</link>
		<comments>http://thecraftycanvas.com/library/comparing-college-costs-with-net-price-calculators/#comments</comments>
		<pubDate>Thu, 18 Apr 2013 14:01:15 +0000</pubDate>
		<dc:creator>ansonwhan</dc:creator>
				<category><![CDATA[Lessons Learned & Worth Sharing Blog]]></category>
		<category><![CDATA[college costs]]></category>
		<category><![CDATA[cost of secondary education]]></category>
		<category><![CDATA[net price calculator]]></category>

		<guid isPermaLink="false">http://thecraftycanvas.com/library/?p=369</guid>
		<description><![CDATA[<table cellpadding='10'><tr><td valign='top' align='left'><p>Categories: <ul class="post-categories">
	<li><a href="http://thecraftycanvas.com/library/category/lessons-learned-shared-blog/" title="View all posts in Lessons Learned &amp; Worth Sharing Blog">Lessons Learned &amp; Worth Sharing Blog</a></li></ul></p><p>Tags: <a href="http://thecraftycanvas.com/library/tag/college-costs/" rel="tag">college costs</a><a href="http://thecraftycanvas.com/library/tag/cost-of-secondary-education/" rel="tag">cost of secondary education</a><a href="http://thecraftycanvas.com/library/tag/net-price-calculator/" rel="tag">net price calculator</a></p>The US Department of Education now requires every college that offers federal financial aid to post a &#8220;net price calculator&#8221; on its website, according to The New York Times article, &#8220;Clarity and Confusion From Tuition Calculators,&#8221; by Richard Pérez-Peña. The<span class="ellipsis">&#8230;</span><div class="read-more"><a href="http://thecraftycanvas.com/library/comparing-college-costs-with-net-price-calculators/">Read more &#8250;</a></div><!-- end of .read-more --><table width='100%'><tr><td align=right><p><b>(<a href='http://thecraftycanvas.com/library/comparing-college-costs-with-net-price-calculators/' title='Comparing College Costs with Net Price Calculators'>Read more...</a>)</b></p></td></tr></table></td></tr></table>]]></description>
				<content:encoded><![CDATA[<p>The US Department of Education now requires every college that offers federal financial aid to post a &#8220;net price calculator&#8221; on its website, according to The New York Times article, &#8220;Clarity and Confusion From Tuition Calculators,&#8221; by Richard Pérez-Peña. The goal is for each school to provide an estimate of the cost of tuition, books, and room and board, subtracting the amount of aid, grants, and scholarships applicable to each student, based on need and merit.</p>
<p>Learn more about this in A+ Test Prep &amp; Tutoring&#8217;s monthly newsletter, <a title="available here" href="http://campaign.r20.constantcontact.com/render?llr=eryhxxbab&amp;v=0019vIjpnfVUZ9Vqh0x4uAoXYOabO5SLxFv03r4Y7Z5Q0boS0o7nqmteTVWCq7A5q410ybqgQdGxA9O4Zsa0Y7iHhoa4QBI8PbhiYtQZz3U3YpyRoU9IZmlL7t3hdq9J8lH" target="_blank">available here</a>.</p>
]]></content:encoded>
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		<title>Memory Tricks: Mnemonics for the US Cabinet Departments</title>
		<link>http://thecraftycanvas.com/library/memory-tricks-mnemonics-for-the-us-cabinet-departments/</link>
		<comments>http://thecraftycanvas.com/library/memory-tricks-mnemonics-for-the-us-cabinet-departments/#comments</comments>
		<pubDate>Wed, 10 Apr 2013 03:32:48 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Education Mnemonics]]></category>
		<category><![CDATA[Lessons Learned & Worth Sharing Blog]]></category>
		<category><![CDATA[Social Studies]]></category>
		<category><![CDATA[cabinet departments by age]]></category>
		<category><![CDATA[memorize the branches of the cabinet]]></category>
		<category><![CDATA[mnemonic for cabinet departments]]></category>
		<category><![CDATA[United States Cabinet memorization techniques]]></category>

		<guid isPermaLink="false">http://thecraftycanvas.com/library/?p=365</guid>
		<description><![CDATA[<table cellpadding='10'><tr><td valign='top' align='left'><p>Categories: <ul class="post-categories">
	<li><a href="http://thecraftycanvas.com/library/category/education-mnemonics/" title="View all posts in Education Mnemonics">Education Mnemonics</a></li>
	<li><a href="http://thecraftycanvas.com/library/category/lessons-learned-shared-blog/" title="View all posts in Lessons Learned &amp; Worth Sharing Blog">Lessons Learned &amp; Worth Sharing Blog</a></li>
	<li><a href="http://thecraftycanvas.com/library/category/social-studies/" title="View all posts in Social Studies">Social Studies</a></li></ul></p><p>Tags: <a href="http://thecraftycanvas.com/library/tag/cabinet-departments-by-age/" rel="tag">cabinet departments by age</a><a href="http://thecraftycanvas.com/library/tag/memorize-the-branches-of-the-cabinet/" rel="tag">memorize the branches of the cabinet</a><a href="http://thecraftycanvas.com/library/tag/mnemonic-for-cabinet-departments/" rel="tag">mnemonic for cabinet departments</a><a href="http://thecraftycanvas.com/library/tag/united-states-cabinet-memorization-techniques/" rel="tag">United States Cabinet memorization techniques</a></p>While tutoring this week, I had to help a middle school student prepare for a test in his social studies/ US Civics class on the Executive Branch.  One of the requirements for this test was to be able to identify<span class="ellipsis">&#8230;</span><div class="read-more"><a href="http://thecraftycanvas.com/library/memory-tricks-mnemonics-for-the-us-cabinet-departments/">Read more &#8250;</a></div><!-- end of .read-more --><table width='100%'><tr><td align=right><p><b>(<a href='http://thecraftycanvas.com/library/memory-tricks-mnemonics-for-the-us-cabinet-departments/' title='Memory Tricks: Mnemonics for the US Cabinet Departments'>Read more...</a>)</b></p></td></tr></table></td></tr></table>]]></description>
				<content:encoded><![CDATA[<p>While tutoring this week, I had to help a middle school student prepare for a test in his social studies/ US Civics class on the Executive Branch.  One of the requirements for this test was to be able to identify each branch of the US Cabinet.  We both attempted to list them off the top of our heads, but naturally were short a few.  Thus, I decided to search how other teachers and tutors have helped students memorize all the branches; sure enough- there was a mnemonic!  Not only does it provide a way to list each department, but also in the order of their establishment.</p>
<p><strong>S</strong>ee <strong>T</strong>he <strong>D</strong>og <strong>J</strong>ump <strong>I</strong>n <strong>A</strong> <strong>C</strong>ircle; <strong>L</strong>eave <strong>H</strong>er <strong>H</strong>ome <strong>T</strong>o <strong>E</strong>ntertain <strong>E</strong>very <strong>V</strong>isitor <strong>H</strong>ere.</p>
<ul>
<li><span style="font-size: 13px; line-height: 19px;">State</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Treasury</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Defense</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Justice</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Interior</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Agriculture</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Commerce</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Labor</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Health &amp; Human Services</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Housing &amp; Urban Development</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Transportation</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Energy</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Education</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Veterans Affairs</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Homeland Security</span></li>
</ul>
<p>Learn more about the history of this particular mnemonic device <a href="http://www.metaphordogs.org/Dogs/entries/seethedo.html" target="_blank">here</a>.</p>
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		<title>Memory Tricks: Mnemonics for Order of Operations</title>
		<link>http://thecraftycanvas.com/library/memory-tricks-mnemonics-for-order-of-operations/</link>
		<comments>http://thecraftycanvas.com/library/memory-tricks-mnemonics-for-order-of-operations/#comments</comments>
		<pubDate>Wed, 10 Apr 2013 03:20:56 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Education Mnemonics]]></category>
		<category><![CDATA[Lessons Learned & Worth Sharing Blog]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[math mnemonics]]></category>
		<category><![CDATA[middle school math study skills]]></category>
		<category><![CDATA[order of operations]]></category>
		<category><![CDATA[PEMDAS]]></category>

		<guid isPermaLink="false">http://thecraftycanvas.com/library/?p=362</guid>
		<description><![CDATA[<table cellpadding='10'><tr><td valign='top' align='left'><p>Categories: <ul class="post-categories">
	<li><a href="http://thecraftycanvas.com/library/category/education-mnemonics/" title="View all posts in Education Mnemonics">Education Mnemonics</a></li>
	<li><a href="http://thecraftycanvas.com/library/category/lessons-learned-shared-blog/" title="View all posts in Lessons Learned &amp; Worth Sharing Blog">Lessons Learned &amp; Worth Sharing Blog</a></li>
	<li><a href="http://thecraftycanvas.com/library/category/math/" title="View all posts in Math">Math</a></li></ul></p><p>Tags: <a href="http://thecraftycanvas.com/library/tag/math-mnemonics/" rel="tag">math mnemonics</a><a href="http://thecraftycanvas.com/library/tag/middle-school-math-study-skills/" rel="tag">middle school math study skills</a><a href="http://thecraftycanvas.com/library/tag/order-of-operations/" rel="tag">order of operations</a><a href="http://thecraftycanvas.com/library/tag/pemdas/" rel="tag">PEMDAS</a></p>When it comes to learning math, memorizing the Order of Operations is probably one of the earliest encounters students have with mnemonics. PEMDAS- or more commonly, Please Excuse My Dear Aunt Sally helps students remember what order to do their<span class="ellipsis">&#8230;</span><div class="read-more"><a href="http://thecraftycanvas.com/library/memory-tricks-mnemonics-for-order-of-operations/">Read more &#8250;</a></div><!-- end of .read-more --><table width='100%'><tr><td align=right><p><b>(<a href='http://thecraftycanvas.com/library/memory-tricks-mnemonics-for-order-of-operations/' title='Memory Tricks: Mnemonics for Order of Operations'>Read more...</a>)</b></p></td></tr></table></td></tr></table>]]></description>
				<content:encoded><![CDATA[<p>When it comes to learning math, memorizing the Order of Operations is probably one of the earliest encounters students have with mnemonics.</p>
<p><strong>PEMDAS</strong>- or more commonly, <strong>P</strong>lease <strong>E</strong>xcuse <strong>M</strong>y <strong>D</strong>ear <strong>A</strong>unt <strong>S</strong>ally helps students remember what order to do their mathematical operations.</p>
<ol>
<li><span style="font-size: 13px; line-height: 19px;">Parentheses</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Exponents</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Multiplication</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Division</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Addition</span></li>
<li><span style="font-size: 13px; line-height: 19px;">Subtraction</span></li>
</ol>
]]></content:encoded>
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		<title>Save the Date for Big Ideas Fest 2013</title>
		<link>http://thecraftycanvas.com/library/save-the-date-for-big-ideas-fest-2013/</link>
		<comments>http://thecraftycanvas.com/library/save-the-date-for-big-ideas-fest-2013/#comments</comments>
		<pubDate>Sat, 06 Apr 2013 18:34:09 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Education News]]></category>
		<category><![CDATA[Big Ideas Fest]]></category>
		<category><![CDATA[Educational Conferences]]></category>
		<category><![CDATA[Educational Conventions]]></category>

		<guid isPermaLink="false">http://thecraftycanvas.com/library/?p=351</guid>
		<description><![CDATA[<table cellpadding='10'><tr><td valign='top' align='left'><p>Categories: <ul class="post-categories">
	<li><a href="http://thecraftycanvas.com/library/category/education-news/" title="View all posts in Education News">Education News</a></li></ul></p><p>Tags: <a href="http://thecraftycanvas.com/library/tag/big-ideas-fest/" rel="tag">Big Ideas Fest</a><a href="http://thecraftycanvas.com/library/tag/educational-conferences/" rel="tag">Educational Conferences</a><a href="http://thecraftycanvas.com/library/tag/educational-conventions/" rel="tag">Educational Conventions</a></p>Save the Date! Big Ideas Fest 2013 December 4th-7th Ritz-Carlton, Half Moon Bay, CA Mark it on your calendar, start gathering your big ideas, and get ready to design the future of education. For more information, checkout the Save the<span class="ellipsis">&#8230;</span><div class="read-more"><a href="http://thecraftycanvas.com/library/save-the-date-for-big-ideas-fest-2013/">Read more &#8250;</a></div><!-- end of .read-more --><table width='100%'><tr><td align=right><p><b>(<a href='http://thecraftycanvas.com/library/save-the-date-for-big-ideas-fest-2013/' title='Save the Date for Big Ideas Fest 2013'>Read more...</a>)</b></p></td></tr></table></td></tr></table>]]></description>
				<content:encoded><![CDATA[<p>Save the Date!</p>
<address>Big Ideas Fest 2013<br />
December 4th-7th<br />
Ritz-Carlton, Half Moon Bay, CA</address>
<p>Mark it on your calendar, start gathering your big ideas, and get ready to design the future of education.</p>
<p style="text-align: center;">For more information, <a href="http://us2.campaign-archive2.com/?u=32177111dabb558fc401595e5&amp;id=81c983dd21&amp;e=73fe84509f" target="_blank">checkout the Save the Date announcement here</a></p>
<p style="text-align: center;">or</p>
<p style="text-align: center;">visit their website, <a href="http://www.bigideasfest.org/" target="_blank">http://www.bigideasfest.org/</a></p>
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		<title>Are High Schoolers Lazy?</title>
		<link>http://thecraftycanvas.com/library/are-high-schoolers-lazy-2/</link>
		<comments>http://thecraftycanvas.com/library/are-high-schoolers-lazy-2/#comments</comments>
		<pubDate>Sat, 06 Apr 2013 07:26:32 +0000</pubDate>
		<dc:creator>admin</dc:creator>
				<category><![CDATA[Education News]]></category>

		<guid isPermaLink="false">http://thecraftycanvas.com/library/?p=347</guid>
		<description><![CDATA[<table cellpadding='10'><tr><td valign='top' align='left'><p>Categories: <ul class="post-categories">
	<li><a href="http://thecraftycanvas.com/library/category/education-news/" title="View all posts in Education News">Education News</a></li></ul></p><p></p>The following was featured in Educational Connections&#8217; March 2013 newsletter&#8230; Hot Topic: Student Disengagement According to a recent Gallup poll, between the grades of five and 12 student engagement follows an alarming, steady decline. At the elementary school level eight<span class="ellipsis">&#8230;</span><div class="read-more"><a href="http://thecraftycanvas.com/library/are-high-schoolers-lazy-2/">Read more &#8250;</a></div><!-- end of .read-more --><table width='100%'><tr><td align=right><p><b>(<a href='http://thecraftycanvas.com/library/are-high-schoolers-lazy-2/' title='Are High Schoolers Lazy?'>Read more...</a>)</b></p></td></tr></table></td></tr></table>]]></description>
				<content:encoded><![CDATA[<p>The following was featured in Educational Connections&#8217; March 2013 newsletter&#8230;</p>
<h3>Hot Topic: Student Disengagement</h3>
<p>According to a recent Gallup poll, between the grades of five and 12 student engagement follows an alarming, steady decline. At the elementary school level eight out of 10 students qualify as engaged. By high school, the statistic is four out of 10.</p>
<p>What causes this troubling trend and what changes could combat it? Watch this video in which Ann Dolin and former Fairfax County School Board member, Stu Gibson, address the problem faced by many schools across the country: student disengagement.</p>
<p><object id="flashObj" width="486" height="412" classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=9,0,47,0"><param name="movie" value="http://c.brightcove.com/services/viewer/federated_f9?isVid=1" /><param name="bgcolor" value="#FFFFFF" /><param name="flashVars" value="videoId=2146929596001&#038;playerID=180211731001&#038;playerKey=AQ~~,AAAAGuN0bcE~,rS1wzGXkRNnKZBuQ4FRjFM7e28yVdmek&#038;domain=embed&#038;dynamicStreaming=true" /><param name="base" value="http://admin.brightcove.com" /><param name="seamlesstabbing" value="false" /><param name="allowFullScreen" value="true" /><param name="swLiveConnect" value="true" /><param name="allowScriptAccess" value="always" /><embed src="http://c.brightcove.com/services/viewer/federated_f9?isVid=1" bgcolor="#FFFFFF" flashVars="videoId=2146929596001&#038;playerID=180211731001&#038;playerKey=AQ~~,AAAAGuN0bcE~,rS1wzGXkRNnKZBuQ4FRjFM7e28yVdmek&#038;domain=embed&#038;dynamicStreaming=true" base="http://admin.brightcove.com" name="flashObj" width="486" height="412" seamlesstabbing="false" type="application/x-shockwave-flash" allowFullScreen="true" swLiveConnect="true" allowScriptAccess="always" pluginspage="http://www.macromedia.com/shockwave/download/index.cgi?P1_Prod_Version=ShockwaveFlash"></embed></object></p>
<p>For more information, <a href="http://r20.rs6.net/tn.jsp?e=001MF6mwFPRds-uRFLX9b0uk6KK6_9N8rFRXAqoEz7MdRU8AbD5aT-CUSdhSq8MfCrxb9aplnlKMsp4c4wALA__TUDXxXxIzaNRRpeAQhKheVY8l8Pfb6UU8GR5iLP_qrVjFpErKAqkNJR9a4ylPNddO8rkIU1CN31WoWdKtzwA3iE_8uXhwXnAZaSc-vmyvCeHB6s3V11lMFQllnUbZOO_4ctD7i_rMKpyS290P_fGbXpkIz36Nvn31cVLSlsXY7pRGQZfxmLztain4NTUTWNQAS4-_cghEBz2v0Yg3H5kMdaZ3dHtdmxtR_uwgY8Ozu6ieFvwfcVIq4LCN0IbluC66l3YDCGMJW51CurbguS8ub3BNlrPLNyBTJ-WG4Y0lMYni-dlJuWdeeYHrNbe4D6QhiqDaxauvaq5nS5thXXFcg4=" target="_blank">take a look at this recent post on The Gallup Blog</a>.</p>
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		<title>Using Lists &amp; Spreadsheets on a TI-Nspire cx cas Scientific Graphing Calculator</title>
		<link>http://thecraftycanvas.com/library/using-lists-spreadsheets-on-a-ti-nspire-cx-cas-scientific-graphing-calculator/</link>
		<comments>http://thecraftycanvas.com/library/using-lists-spreadsheets-on-a-ti-nspire-cx-cas-scientific-graphing-calculator/#comments</comments>
		<pubDate>Wed, 12 Sep 2012 19:03:23 +0000</pubDate>
		<dc:creator>ansonwhan</dc:creator>
				<category><![CDATA[Chemistry]]></category>
		<category><![CDATA[Lessons Learned & Worth Sharing Blog]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[Physics]]></category>
		<category><![CDATA[Science]]></category>
		<category><![CDATA[creating an X-Y table of values on TI-Nspire CX CAS Scientific Graphing Calculator]]></category>
		<category><![CDATA[evaluating data on TI-Nspire CX CAS]]></category>
		<category><![CDATA[using the TI-Nspire CX CAS spreadsheet]]></category>
		<category><![CDATA[working with lists on TI-NSpire CX CAS]]></category>

		<guid isPermaLink="false">http://www.thecraftycanvas.com/library/?p=164</guid>
		<description><![CDATA[<table cellpadding='10'><tr><td valign='top' align='left'><p>Categories: <ul class="post-categories">
	<li><a href="http://thecraftycanvas.com/library/category/science/chemistry-science/" title="View all posts in Chemistry">Chemistry</a></li>
	<li><a href="http://thecraftycanvas.com/library/category/lessons-learned-shared-blog/" title="View all posts in Lessons Learned &amp; Worth Sharing Blog">Lessons Learned &amp; Worth Sharing Blog</a></li>
	<li><a href="http://thecraftycanvas.com/library/category/math/" title="View all posts in Math">Math</a></li>
	<li><a href="http://thecraftycanvas.com/library/category/science/physics-science/" title="View all posts in Physics">Physics</a></li>
	<li><a href="http://thecraftycanvas.com/library/category/science/" title="View all posts in Science">Science</a></li></ul></p><p>Tags: <a href="http://thecraftycanvas.com/library/tag/creating-an-x-y-table-of-values-on-ti-nspire-cx-cas-scientific-graphing-calculator/" rel="tag">creating an X-Y table of values on TI-Nspire CX CAS Scientific Graphing Calculator</a><a href="http://thecraftycanvas.com/library/tag/evaluating-data-on-ti-nspire-cx-cas/" rel="tag">evaluating data on TI-Nspire CX CAS</a><a href="http://thecraftycanvas.com/library/tag/using-the-ti-nspire-cx-cas-spreadsheet/" rel="tag">using the TI-Nspire CX CAS spreadsheet</a><a href="http://thecraftycanvas.com/library/tag/working-with-lists-on-ti-nspire-cx-cas/" rel="tag">working with lists on TI-NSpire CX CAS</a></p>Below are some step-by-step instructions (with pictures) for programming/saving lists of data and using the spreadsheet capabilities on a TI-NSpire CX CAS calculator. 1. With the calculator on, go to the home screen/main menu by clicking the ON button. 2.<span class="ellipsis">&#8230;</span><div class="read-more"><a href="http://thecraftycanvas.com/library/using-lists-spreadsheets-on-a-ti-nspire-cx-cas-scientific-graphing-calculator/">Read more &#8250;</a></div><!-- end of .read-more --><table width='100%'><tr><td align=right><p><b>(<a href='http://thecraftycanvas.com/library/using-lists-spreadsheets-on-a-ti-nspire-cx-cas-scientific-graphing-calculator/' title='Using Lists &amp; Spreadsheets on a TI-Nspire cx cas Scientific Graphing Calculator'>Read more...</a>)</b></p></td></tr></table></td></tr></table>]]></description>
				<content:encoded><![CDATA[<p>Below are some step-by-step instructions (with pictures) for programming/saving lists of data and using the spreadsheet capabilities on a TI-NSpire CX CAS calculator.</p>
<div style="clear: both;width: 100%">1. With the calculator on, go to the home screen/main menu by clicking the ON button.<a href="http://thecraftycanvas.com/library/files/2012/09/0A.TI-Nspire_cx_cas-home-on-button.jpg"><img src="http://thecraftycanvas.com/library/files/2012/09/0A.TI-Nspire_cx_cas-home-on-button-225x300.jpg" alt="The &quot;on&quot; button loads the main menu of apps for the calculator." width="225" height="300" /></a><a href="http://thecraftycanvas.com/library/files/2012/09/0B.TI-Nspire_cx_cas.home-screen.jpg"><img src="http://thecraftycanvas.com/library/files/2012/09/0B.TI-Nspire_cx_cas.home-screen-300x225.jpg" alt="TI-nspire CX CAS's home screen" width="300" height="225" /></a></p>
</div>
<div style="clear: both;width: 100%">2. Then select Lists &amp; Spreadsheets from the apps across the bottom (it should be the 4th icon over).  This will display the general spreadsheet screen (with any previous data reloaded).</div>
<div style="clear: both;width: 100%"><a href="http://thecraftycanvas.com/library/files/2012/09/B.TI-Nspire_cx_cas.home-screen.jpg"><img class="alignleft size-medium wp-image-170" src="http://thecraftycanvas.com/library/files/2012/09/B.TI-Nspire_cx_cas.home-screen-300x225.jpg" alt="Choose the Lists/Spreadsheets app from your TI-NSpire CX CAS" width="300" height="225" /></a><a href="http://thecraftycanvas.com/library/files/2012/09/C.TI-Nspire_cx_cas.spreadsheet-list-screen.jpg"><img class="alignleft size-medium wp-image-171" src="http://thecraftycanvas.com/library/files/2012/09/C.TI-Nspire_cx_cas.spreadsheet-list-screen-300x225.jpg" alt="The spreadsheet screen has two special rows at the top of each spreadsheet." width="300" height="225" /></a></div>
<div style="clear: both;width: 100%">3. Use the top most row to assign variable letter(s) or dataset name(s) to a column.</div>
<div style="clear: both;width: 100%"><a href="http://thecraftycanvas.com/library/files/2012/09/D.TI-Nspire_cx_cas.spreadsheet-list-screen1-titles.jpg"><img class="alignleft size-medium wp-image-172" src="http://thecraftycanvas.com/library/files/2012/09/D.TI-Nspire_cx_cas.spreadsheet-list-screen1-titles-300x225.jpg" alt="Variable Names or DataSet Titles" width="300" height="225" /></a></div>
<div style="clear: both;width: 100%">4. Input your list of values/data in the corresponding column(s) below.</div>
<div style="clear: both;width: 100%"><a href="http://thecraftycanvas.com/library/files/2012/09/E.TI-Nspire_cx_cas.spreadsheet-list-screen3-independent-variable-list-set-values.jpg"><img class="alignleft size-medium wp-image-173" src="http://thecraftycanvas.com/library/files/2012/09/E.TI-Nspire_cx_cas.spreadsheet-list-screen3-independent-variable-list-set-values-300x225.jpg" alt="Type in your data/list of values." width="300" height="225" /></a></div>
<div style="clear: both;width: 100%"></div>
<div style="clear: both;width: 100%">5. If you wish to generate a column of results/manipulate your independent variable with a function, then input the variable or equation in the 2nd (gray) row.  Use the &#8220;VAR&#8221; button on the calculator to pull up a list of your previously defined variables by letter or name.</div>
<div style="clear: both;width: 100%"><a href="http://thecraftycanvas.com/library/files/2012/09/F.TI-Nspire_cx_cas.spreadsheet-list-screen2-formulas.jpg"><img class="alignleft size-medium wp-image-174" src="http://thecraftycanvas.com/library/files/2012/09/F.TI-Nspire_cx_cas.spreadsheet-list-screen2-formulas-300x225.jpg" alt="Input formulas on the 2nd row (displays in gray)" width="300" height="225" /></a><a href="http://thecraftycanvas.com/library/files/2012/09/G.TI-Nspire_cx_cas-var-button.jpg"><img class="alignleft size-medium wp-image-175" src="http://thecraftycanvas.com/library/files/2012/09/G.TI-Nspire_cx_cas-var-button-225x300.jpg" alt="Use the VAR button to select predefined variables." width="225" height="300" /></a></div>
]]></content:encoded>
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		</item>
		<item>
		<title>Graphing Functions on a TI-Nspire cx cas Scientific Graphing Calculator</title>
		<link>http://thecraftycanvas.com/library/graphing-functions-on-a-ti-nspire-cx-cas-scientific-graphing-calculator/</link>
		<comments>http://thecraftycanvas.com/library/graphing-functions-on-a-ti-nspire-cx-cas-scientific-graphing-calculator/#comments</comments>
		<pubDate>Wed, 12 Sep 2012 16:13:29 +0000</pubDate>
		<dc:creator>ansonwhan</dc:creator>
				<category><![CDATA[Lessons Learned & Worth Sharing Blog]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[graphing equations on TI-nspire CX CAS]]></category>
		<category><![CDATA[graphing equations with Texas Instruments npire cx cas]]></category>
		<category><![CDATA[graphing functions on TI-nspire CX CAS]]></category>
		<category><![CDATA[graphing on TI-nspire cx cas]]></category>
		<category><![CDATA[TI-nspire CAS CX step-by-step instructions to graph functions]]></category>
		<category><![CDATA[TI-nspire instructions for graphing equations]]></category>
		<category><![CDATA[using Scientific Graphing Calculators]]></category>

		<guid isPermaLink="false">http://www.thecraftycanvas.com/library/?p=143</guid>
		<description><![CDATA[<table cellpadding='10'><tr><td valign='top' align='left'><p>Categories: <ul class="post-categories">
	<li><a href="http://thecraftycanvas.com/library/category/lessons-learned-shared-blog/" title="View all posts in Lessons Learned &amp; Worth Sharing Blog">Lessons Learned &amp; Worth Sharing Blog</a></li>
	<li><a href="http://thecraftycanvas.com/library/category/math/" title="View all posts in Math">Math</a></li></ul></p><p>Tags: <a href="http://thecraftycanvas.com/library/tag/graphing-equations-on-ti-nspire-cx-cas/" rel="tag">graphing equations on TI-nspire CX CAS</a><a href="http://thecraftycanvas.com/library/tag/graphing-equations-with-texas-instruments-npire-cx-cas/" rel="tag">graphing equations with Texas Instruments npire cx cas</a><a href="http://thecraftycanvas.com/library/tag/graphing-functions-on-ti-nspire-cx-cas/" rel="tag">graphing functions on TI-nspire CX CAS</a><a href="http://thecraftycanvas.com/library/tag/graphing-on-ti-nspire-cx-cas/" rel="tag">graphing on TI-nspire cx cas</a><a href="http://thecraftycanvas.com/library/tag/ti-nspire-cas-cx-step-by-step-instructions-to-graph-functions/" rel="tag">TI-nspire CAS CX step-by-step instructions to graph functions</a><a href="http://thecraftycanvas.com/library/tag/ti-nspire-instructions-for-graphing-equations/" rel="tag">TI-nspire instructions for graphing equations</a><a href="http://thecraftycanvas.com/library/tag/using-scientific-graphing-calculators/" rel="tag">using Scientific Graphing Calculators</a></p>The days of a consistent user interface with Scientific Graphing Calculators from Texas Instruments seem to be waning. While many schools still encourage the use of TI-83/TI-84/TI-89 models, some are pushing the more recent release, the TI-Nspire CX CAS- whose<span class="ellipsis">&#8230;</span><div class="read-more"><a href="http://thecraftycanvas.com/library/graphing-functions-on-a-ti-nspire-cx-cas-scientific-graphing-calculator/">Read more &#8250;</a></div><!-- end of .read-more --><table width='100%'><tr><td align=right><p><b>(<a href='http://thecraftycanvas.com/library/graphing-functions-on-a-ti-nspire-cx-cas-scientific-graphing-calculator/' title='Graphing Functions on a TI-Nspire cx cas Scientific Graphing Calculator'>Read more...</a>)</b></p></td></tr></table></td></tr></table>]]></description>
				<content:encoded><![CDATA[<p>The days of a consistent user interface with Scientific Graphing Calculators from Texas Instruments seem to be waning. While many schools still encourage the use of TI-83/TI-84/TI-89 models, some are pushing the more recent release, the TI-Nspire CX CAS- whose screen resembles many apps for iPhones and Android phones.</p>
<table style="width: 100%">
<tbody>
<tr valign="top">
<td style="width: 33%"><a href="http://thecraftycanvas.com/library/files/2012/09/TI84plus.jpg"><img class="alignleft size-medium wp-image-146" style="width: 98%" src="http://thecraftycanvas.com/library/files/2012/09/TI84plus-180x300.jpg" alt="TI-84 plus is similar to the TI-83 and TI-89" /></a>TI-84 plus</td>
<td style="width: 33%"><a href="http://thecraftycanvas.com/library/files/2012/09/TI-nspire_CAS.png"><img class="alignleft size-medium wp-image-147" style="width: 98%" src="http://thecraftycanvas.com/library/files/2012/09/TI-nspire_CAS-176x300.png" alt="TI-Nspire CAS models have even more buttons and a dynamically different user interface than those of the TI-83 family." /></a>TI-nspire CAS</td>
<td style="width: 33%"><a href="http://thecraftycanvas.com/library/files/2012/09/0.TI-Nspire_cx_cas.jpg"><img class="alignleft size-medium wp-image-148" style="width: 98%" src="http://thecraftycanvas.com/library/files/2012/09/0.TI-Nspire_cx_cas-225x300.jpg" alt="The TI-Nspire CX CAS is a happy medium between the two drastic lines of Calculators" /></a>TI-nspire CX CAS</td>
</tr>
</tbody>
</table>
<p>Below are some step-by-step instructions (with pictures) of how to graph equations on a TI-Nspire CX CAS calculator (as shown in the far right image above).</p>
<div style="clear: both;width: 100%">
<p>1. With the calculator on, go to the home screen/main menu by clicking the ON button.</p>
<p><a href="http://thecraftycanvas.com/library/files/2012/09/0A.TI-Nspire_cx_cas-home-on-button.jpg"><img class="alignleft size-medium wp-image-150" src="http://thecraftycanvas.com/library/files/2012/09/0A.TI-Nspire_cx_cas-home-on-button-225x300.jpg" alt="The &quot;on&quot; button loads the main menu of apps for the calculator." width="225" height="300" /></a></p>
<p><a href="http://thecraftycanvas.com/library/files/2012/09/0B.TI-Nspire_cx_cas.home-screen.jpg"><img class="alignleft size-medium wp-image-151" src="http://thecraftycanvas.com/library/files/2012/09/0B.TI-Nspire_cx_cas.home-screen-300x225.jpg" alt="TI-nspire CX CAS's home screen" width="300" height="225" /></a></p>
</div>
<div style="clear: both;width: 100%">
<p>2. Then select option B to GRAPH from the left column.  This will display the general graphing screen (with any previous graphs of equations/functions reloaded)</p>
<p><a href="http://thecraftycanvas.com/library/files/2012/09/1.TI-Nspire_cx_cas.home-screen.jpg"><img class="alignleft size-medium wp-image-153" src="http://thecraftycanvas.com/library/files/2012/09/1.TI-Nspire_cx_cas.home-screen-300x225.jpg" alt="Select Graph from the home screen" width="300" height="225" /></a></p>
<p><a href="http://thecraftycanvas.com/library/files/2012/09/3.TI-Nspire_cx_cas.graph-screen.jpg"><img class="size-medium wp-image-154 alignleft" src="http://thecraftycanvas.com/library/files/2012/09/3.TI-Nspire_cx_cas.graph-screen-300x225.jpg" alt="The general graphing screen shows the coordinate plane" width="300" height="225" /></a></p>
</div>
<div style="clear: both;width: 100%">
<p>3. Tap the &#8220;tab&#8221; button to load the function editor.  This is similar to pressing the &#8220;Y=&#8221; button on the TI-83 line of calculators.</p>
<p><a href="http://thecraftycanvas.com/library/files/2012/09/4.TI-Nspire_cx_cas.tab-button-to-graph.jpg"><img class="alignleft size-medium wp-image-155" src="http://thecraftycanvas.com/library/files/2012/09/4.TI-Nspire_cx_cas.tab-button-to-graph-300x225.jpg" alt="Push TAB to edit a function for graphing (like the old Y= button)" width="300" height="225" /></a><a href="http://thecraftycanvas.com/library/files/2012/09/5.TI-Nspire_cx_cas.graph-input-function-screen.jpg"><img class="alignleft size-medium wp-image-156" src="http://thecraftycanvas.com/library/files/2012/09/5.TI-Nspire_cx_cas.graph-input-function-screen-300x225.jpg" alt="The function editor is a single line at the bottom of the graphing window" width="300" height="225" /></a></p>
</div>
<div style="clear: both;width: 100%">
<p>4. To clear any existing function/equation in the editor, hold down &#8220;CTRL&#8221; and tap &#8220;del&#8221;. Otherwise, type in your equation or function and hit &#8220;enter&#8221; to graph.  *Remember, all functions must be solved for the dependent variable (ie. y = &#8230;.).</p>
<p><a href="http://thecraftycanvas.com/library/files/2012/09/7.TI-Nspire_cx_cas.ctrl-del-button-to-clear-graphed-functions.jpg"><img class="alignleft size-medium wp-image-160" src="http://thecraftycanvas.com/library/files/2012/09/7.TI-Nspire_cx_cas.ctrl-del-button-to-clear-graphed-functions-300x225.jpg" alt="Use CTRL del to erase any previously input equations." width="300" height="225" /></a><a href="http://thecraftycanvas.com/library/files/2012/09/6.TI-Nspire_cx_cas.graphed-function-screen1.jpg"><img class="alignleft size-medium wp-image-159" src="http://thecraftycanvas.com/library/files/2012/09/6.TI-Nspire_cx_cas.graphed-function-screen1-300x225.jpg" alt="After inputting your function, hit enter to graph it." width="300" height="225" /></a></p>
</div>
]]></content:encoded>
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		<title>Finding Forces Acting Upon Objects on an Inclined Plane or Ramp with Free Body Diagrams</title>
		<link>http://thecraftycanvas.com/library/finding-forces-acting-upon-objects-on-an-inclined-plane-or-ramp-with-free-body-diagrams/</link>
		<comments>http://thecraftycanvas.com/library/finding-forces-acting-upon-objects-on-an-inclined-plane-or-ramp-with-free-body-diagrams/#comments</comments>
		<pubDate>Fri, 09 Mar 2012 00:29:16 +0000</pubDate>
		<dc:creator>ansonwhan</dc:creator>
				<category><![CDATA[Lessons Learned & Worth Sharing Blog]]></category>
		<category><![CDATA[Physics]]></category>
		<category><![CDATA[force needed for movement up ramp at a constant speed]]></category>
		<category><![CDATA[force needed for sliding down ramp at constant speed]]></category>
		<category><![CDATA[force needed to prevent object from sliding down incline]]></category>
		<category><![CDATA[forces on a hill]]></category>
		<category><![CDATA[Free-body diagrams]]></category>
		<category><![CDATA[friction on a ramp]]></category>
		<category><![CDATA[frictional forces along an inclined plane]]></category>
		<category><![CDATA[inclined plane force calculator]]></category>
		<category><![CDATA[kinetic friction on an inclined plane]]></category>
		<category><![CDATA[normal force of block on ramp]]></category>
		<category><![CDATA[physics block on ramp free body diagram]]></category>
		<category><![CDATA[physics block on ramp problem solver]]></category>
		<category><![CDATA[resolving force due to gravity into components for an inclined plane]]></category>
		<category><![CDATA[static friction on an inclined plane]]></category>

		<guid isPermaLink="false">http://www.thecraftycanvas.com/library/?p=132</guid>
		<description><![CDATA[<table cellpadding='10'><tr><td valign='top' align='left'><p>Categories: <ul class="post-categories">
	<li><a href="http://thecraftycanvas.com/library/category/lessons-learned-shared-blog/" title="View all posts in Lessons Learned &amp; Worth Sharing Blog">Lessons Learned &amp; Worth Sharing Blog</a></li>
	<li><a href="http://thecraftycanvas.com/library/category/science/physics-science/" title="View all posts in Physics">Physics</a></li></ul></p><p>Tags: <a href="http://thecraftycanvas.com/library/tag/force-needed-for-movement-up-ramp-at-a-constant-speed/" rel="tag">force needed for movement up ramp at a constant speed</a><a href="http://thecraftycanvas.com/library/tag/force-needed-for-sliding-down-ramp-at-constant-speed/" rel="tag">force needed for sliding down ramp at constant speed</a><a href="http://thecraftycanvas.com/library/tag/force-needed-to-prevent-object-from-sliding-down-incline/" rel="tag">force needed to prevent object from sliding down incline</a><a href="http://thecraftycanvas.com/library/tag/forces-on-a-hill/" rel="tag">forces on a hill</a><a href="http://thecraftycanvas.com/library/tag/free-body-diagrams/" rel="tag">Free-body diagrams</a><a href="http://thecraftycanvas.com/library/tag/friction-on-a-ramp/" rel="tag">friction on a ramp</a><a href="http://thecraftycanvas.com/library/tag/frictional-forces-along-an-inclined-plane/" rel="tag">frictional forces along an inclined plane</a><a href="http://thecraftycanvas.com/library/tag/inclined-plane-force-calculator/" rel="tag">inclined plane force calculator</a><a href="http://thecraftycanvas.com/library/tag/kinetic-friction-on-an-inclined-plane/" rel="tag">kinetic friction on an inclined plane</a><a href="http://thecraftycanvas.com/library/tag/normal-force-of-block-on-ramp/" rel="tag">normal force of block on ramp</a><a href="http://thecraftycanvas.com/library/tag/physics-block-on-ramp-free-body-diagram/" rel="tag">physics block on ramp free body diagram</a><a href="http://thecraftycanvas.com/library/tag/physics-block-on-ramp-problem-solver/" rel="tag">physics block on ramp problem solver</a><a href="http://thecraftycanvas.com/library/tag/resolving-force-due-to-gravity-into-components-for-an-inclined-plane/" rel="tag">resolving force due to gravity into components for an inclined plane</a><a href="http://thecraftycanvas.com/library/tag/static-friction-on-an-inclined-plane/" rel="tag">static friction on an inclined plane</a></p>In both high school physics and general college physics, Free Body (Force) Diagrams are critical in understanding how forces act upon objects that are on an incline. On a flat horizontal surface, such diagrams are pretty straightforward showing that: Gravity<span class="ellipsis">&#8230;</span><div class="read-more"><a href="http://thecraftycanvas.com/library/finding-forces-acting-upon-objects-on-an-inclined-plane-or-ramp-with-free-body-diagrams/">Read more &#8250;</a></div><!-- end of .read-more --><table width='100%'><tr><td align=right><p><b>(<a href='http://thecraftycanvas.com/library/finding-forces-acting-upon-objects-on-an-inclined-plane-or-ramp-with-free-body-diagrams/' title='Finding Forces Acting Upon Objects on an Inclined Plane or Ramp with Free Body Diagrams'>Read more...</a>)</b></p></td></tr></table></td></tr></table>]]></description>
				<content:encoded><![CDATA[<p><a href="http://thecraftycanvas.com/library/files/2012/03/free-body-force-diagram.png"><img class="alignright size-medium wp-image-133" alt="" src="http://thecraftycanvas.com/library/files/2012/03/free-body-force-diagram-212x300.png" width="212" height="300" /></a>In both high school physics and general college physics, Free Body (Force) Diagrams are critical in understanding how forces act upon objects that are on an incline.</p>
<p>On a flat horizontal surface, such diagrams are pretty straightforward showing that:</p>
<ol>
<li>Gravity exerts a downward force</li>
<li>The surface exerts an equal and opposite upward force (the Normal force)</li>
</ol>
<p>For objects on a ramp, the diagram can become cluttered and confusing fairly quickly.  The key is to understand the fundamental concepts of gravity, friction, and applied forces.  Each type of force when exerted upon the object can result in movement up or down the hill, as well as stop the object altogether.  Additionally, an object moving up or down the inclined plane at a constant speed might exhibit an overall Net Force of 0 Newtons, but that does not mean that an external force need not apply.  Free-body diagrams for objects on an incline must (at the minimum) depict:</p>
<ol>
<li>Gravity&#8217;s downward force and the corresponding translated downhill force parallel to the surface.</li>
<li>The surface exerts a Normal force that is perpendicular to the surface and both equal and opposite to gravity&#8217;s perpendicular surface component.</li>
<li>An Applied Force acts uphill/against the gradient.</li>
</ol>
<p>Optionally, if the conditions exist, the free body diagram can also show:</p>
<ul>
<li>Static friction  acts uphill/against the gradient.</li>
<li>Kinetic friction can act either way depending on the desired motion of the object.</li>
</ul>
<h1 style="font-size: 16px;"><a title="Forces along an Incline: Applied Forces, Normal Forces, and Frictional Forces – A Vector Based Problem Solver, Calculator, &amp; Component Resolver" href="http://thecraftycanvas.com/library/online-learning-tools/physics-homework-helpers/incline-force-calculator-problem-solver/">This <strong><em>inclined plane force calculator and problem solver</em></strong> helps solve the problem, while showing all the steps in the various calculations and displaying a fully labeled free body diagram.</a></h1>
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		<title>Identify All Possible Rational Roots for a Polynomial with the Rational Root Theorem</title>
		<link>http://thecraftycanvas.com/library/identify-all-possible-rational-roots-for-a-polynomial-with-the-rational-root-theorem/</link>
		<comments>http://thecraftycanvas.com/library/identify-all-possible-rational-roots-for-a-polynomial-with-the-rational-root-theorem/#comments</comments>
		<pubDate>Wed, 07 Mar 2012 22:59:18 +0000</pubDate>
		<dc:creator>ansonwhan</dc:creator>
				<category><![CDATA[Lessons Learned & Worth Sharing Blog]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[algebra]]></category>
		<category><![CDATA[find real solutions to polynomial]]></category>
		<category><![CDATA[Finding all possible rational roots for a polynomial]]></category>
		<category><![CDATA[Rational Root Theorem]]></category>
		<category><![CDATA[solve polynomial equations]]></category>

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		<description><![CDATA[<table cellpadding='10'><tr><td valign='top' align='left'><p>Categories: <ul class="post-categories">
	<li><a href="http://thecraftycanvas.com/library/category/lessons-learned-shared-blog/" title="View all posts in Lessons Learned &amp; Worth Sharing Blog">Lessons Learned &amp; Worth Sharing Blog</a></li>
	<li><a href="http://thecraftycanvas.com/library/category/math/" title="View all posts in Math">Math</a></li></ul></p><p>Tags: <a href="http://thecraftycanvas.com/library/tag/algebra/" rel="tag">algebra</a><a href="http://thecraftycanvas.com/library/tag/find-real-solutions-to-polynomial/" rel="tag">find real solutions to polynomial</a><a href="http://thecraftycanvas.com/library/tag/finding-all-possible-rational-roots-for-a-polynomial/" rel="tag">Finding all possible rational roots for a polynomial</a><a href="http://thecraftycanvas.com/library/tag/rational-root-theorem/" rel="tag">Rational Root Theorem</a><a href="http://thecraftycanvas.com/library/tag/solve-polynomial-equations/" rel="tag">solve polynomial equations</a></p>Much of Algebra I and Algebra II is spent learning how to solve polynomial equations- in particular, finding solutions / roots / zeroes of an equation. This process can be very tedious, but fortunately, there are some theorems and techniques<span class="ellipsis">&#8230;</span><div class="read-more"><a href="http://thecraftycanvas.com/library/identify-all-possible-rational-roots-for-a-polynomial-with-the-rational-root-theorem/">Read more &#8250;</a></div><!-- end of .read-more --><table width='100%'><tr><td align=right><p><b>(<a href='http://thecraftycanvas.com/library/identify-all-possible-rational-roots-for-a-polynomial-with-the-rational-root-theorem/' title='Identify All Possible Rational Roots for a Polynomial with the Rational Root Theorem'>Read more...</a>)</b></p></td></tr></table></td></tr></table>]]></description>
				<content:encoded><![CDATA[<p>Much of Algebra I and Algebra II is spent learning how to solve polynomial equations- in particular, finding solutions / roots / zeroes of an equation.</p>
<p>This process can be very tedious, but fortunately, there are some theorems and techniques that can be used to streamline the process.</p>
<div style="border: 1px solid #ccc; font-size: 12px; font-family: arial,sans-serif;">
<p>In algebra, the <strong>rational root theorem</strong> (or <strong>rational root test</strong>) states a constraint on rational solutions (or roots) of the polynomial equation:</p>
<p><img alt="a_nx^n+a_{n-1}x^{n-1}+cdots+a_0 = 0,!" src="http://upload.wikimedia.org/wikipedia/en/math/8/5/f/85f82fc9b65cf11b7ab01b6d672b0788.png" />    with integer coefficients.</p>
<p>If <em>a</em><sub>0</sub> and <em>a</em><sub><em>n</em></sub> are nonzero, then each rational solution <em>x</em>, when written as a fraction <em>x</em> = <em>p</em>/<em>q</em> in lowest terms (i.e., the greatest common divisor of <em>p</em> and <em>q</em> is 1), satisfies</p>
<ul>
<li><em>p</em> is an integer factor of the constant term <em>a</em><sub>0</sub>, and</li>
<li><em>q</em> is an integer factor of the leading coefficient <em>a</em><sub><em>n</em></sub>.</li>
</ul>
<p>Thus, a list of possible rational roots of the equation can be derived using the formula <img alt="x = pm frac{p}{q}" src="http://upload.wikimedia.org/wikipedia/en/math/a/1/f/a1f942d209cd7f499535e3ee60890537.png" />.</p>
<p style="font-size: 10px; margin: 0;"><sup>*</sup>Definition and explanation of the Rational Root Theorem from Wikipedia.com</p>
</div>
<h1 style="font-size: 16px;">You can use my custom <a title="Rational Root Finder" href="http://thecraftycanvas.com/library/online-learning-tools/math-homework-helpers/rational-root-finder/">Rational Root Finder</a> to identifies all possible factors of p and q for a given equation and then the <a title="Synthetic Division of Polynomials" href="http://thecraftycanvas.com/library/online-learning-tools/math-homework-helpers/synthetic-division-of-polynomials/">synthetic division step-by-step homework solver </a>to test whether a value is in fact a solution/root to the function.</h1>
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