tag:blogger.com,1999:blog-2796876133858024262024-02-07T00:17:09.770-06:00Math-Magic with Ms. Laster!How is math magical? What are the cool things going on in our classroom?Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.comBlogger25125tag:blogger.com,1999:blog-279687613385802426.post-55139941536659966082015-01-03T17:09:00.002-06:002015-01-03T17:10:38.710-06:00Your Many Intelligences, version 2015<div style="text-align: center;">
<b><span style="color: red;">Happy New Year! Welcome to 2015!! Ready for a new semester?</span></b></div>
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How was your break? Ready to jump into school, learning, and your intelligence? (Of course you are!)<br />
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Have you ever heard of Howard Gardner's theory of <b><i>Multiple Intelligences</i></b>? Instead of just IQ, Dr. Gardner suggested people have a variety of "types" of intelligence. He originally proposed 7 intelligences, then 8, and now some say 9, but here are two video options for you to learn about the different intelligences.<br />
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This video "defines" each intelligence with animated images:<br />
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This video looks like a student project, and there is a bit of narration with the images:<br />
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I know you're anxious to determine your type of intelligence, and here's your opportunity! Please take one of the surveys online found either <a href="http://www.literacyworks.org/mi/assessment/findyourstrengths.html" target="_blank">here</a>, <a href="http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks3/ict/multiple_int/index.htm" target="_blank">here</a> (click "Take the Test") or <a href="http://www.edutopia.org/multiple-intelligences-assessment" target="_blank">here</a>. All three are different formats and offer different type of feedback, but my scores were the same. Did you have one dominant intelligence, or were there several top intelligences? Dr. Gardner's official site is called <a href="http://multipleintelligencesoasis.org/" target="_blank">MI Oasis</a>, and he still teaches at <a href="http://howardgardner.com/" target="_blank">Harvard</a>. You may find additional definitions and more information about intelligences at the websites <a href="http://www.edwebproject.org/edref.mi.th.html" target="_blank">here</a>, <a href="http://www.rubythroat.org/MultipleIntelligencesDefin.html" target="_blank">here</a>, <a href="http://psychology.about.com/b/2013/01/02/gardners-theory-of-multiple-intelligences.htm" target="_blank">here</a>, or <a href="http://teammates.org/postsecondary/multiple-intelligences/" target="_blank">here</a>. <br />
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Next, please submit your findings and reflections in <a href="https://docs.google.com/a/g.risd.org/forms/d/1WyqBM7Mw_g9bwPupYlEyubcw9dUmqJanjyUYrz-MICg/viewform" target="_blank">this Google form</a>. Please complete the surveys and the responses by next Tuesday, January 13, 10 PM.<br />
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<span style="color: red;"><b>Thank you, and as always, I look forward to reading your responses!</b></span><br />
<span style="color: red;"><b>(Don't forget to hit "Submit" at the end of your survey!)</b></span></div>
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<b><span style="color: #38761d;">Did you enjoy learning about multiple intelligences? If you found any other interesting information, videos, or links, please post in the comments below!</span></b>Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-86501410513799823742014-09-01T18:05:00.001-05:002014-09-01T18:05:07.648-05:00Math Is... 2014 VersionIf I didn't teach math, I would love to teach English because I enjoy reading so much! I especially loved reading your Mathographies, and I captured your "Math is..." comments in the wordle below:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiatH-_M1higTuWbsTg3vpWGEM0nm2-hmpkZZ-fwDmjyw7H1_8thyphenhyphenBrbgfQtqukD869uvAG9yyktuthj5zyKnhUA6ACkzD6RpoRDL-j1IjGUO7cqQFKKafnYc9fJ3DKugpE0tZttL79okQ/s1600/math+is.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiatH-_M1higTuWbsTg3vpWGEM0nm2-hmpkZZ-fwDmjyw7H1_8thyphenhyphenBrbgfQtqukD869uvAG9yyktuthj5zyKnhUA6ACkzD6RpoRDL-j1IjGUO7cqQFKKafnYc9fJ3DKugpE0tZttL79okQ/s1600/math+is.PNG" height="297" width="640" /></a></div>
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Please allow me to address some of your questions and concerns here:<br />
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<li>Even though my "other job" carries a lot of responsibilities, when I am with my classes, <u><b>you</b></u> are my priority. If you have questions or need tutoring, I will find time for you, and I have been known to tutor during every period of the day! Talk to me, I'll check my calendar, and we'll work out something that is mutually convenient.</li>
<li>Feel free to email your questions, too. I usually shut down my school email early (8:00 PM) but I begin answering email super early in the morning. Check my website for answer keys and videos that may help, too. Ask a friend or find another math teacher to help! </li>
<li>Some people prefer groups, some people working alone...we'll do both. For those who prefer individual work time, the "collaboration" work time will require you to <i>stretch</i>, I know. I completely get it because I am a huge introvert. I try to accommodate many learning preferences, but I also want you to grow as a learner.</li>
<li>Several people commented that they tend to shut down when they get frustrated or don't understand something, and I plan to help you conquer that mindset. (<a href="http://mindsetonline.com/changeyourmindset/firststeps/" target="_blank">Here are tips</a> to change from a fixed mindset to a growth mindset.) In my class, I hope you will develop a growth mindset about learning, I want you to appreciate the struggle, and learn that making mistakes is OK! I've created a slideshow with my favorite quotes about learning and struggle, and it's on my website homepage. It's so important that I'll add it here, too! </li>
<li>My favorite <i>growth mindset </i>comment was from the person who wrote, "I like to work in groups with people who are smarter than I am." Awesome! What a way to show that you're willing to take risks, stretch yourself, and learn from others.</li>
<li>One of my number one priorities is that our class is <b>SAFE</b>...safe for you to take risks, safe to make mistakes in your learning journey, and safe to ask as many questions as you need!</li>
<li>Your notes will definitely help prepare for your test. I know we have rushed through some notes, but I hope you'll take the time to return to your notes, process the material, and fill in any blanks (steps, definitions, etc.)</li>
<li>A few people were worried about the weight of tests. I will do my part to make certain you're prepared for tests, but you'll have to do your part, too! Find some useful study tips <a href="http://www.coolmath.com/studytip.htm" target="_blank">here</a> and <a href="http://studyskills.com/studying/how-to-study-for-a-math-test/" target="_blank">here</a>.</li>
<li>By the way, we're learning all about reference angles to work right triangle problems (SOHCAHTOA) and vectors, which are also used in physics.</li>
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If you have any questions or other concerns, feel free to leave your questions in the comments below.</div>
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Thanks so much for a great start to PAP pre-calculus!</div>
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<i>Mathmagically Yours,</i></div>
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<i>Ms. Laster</i></div>
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Enjoy some of my favorite mindset quotes!</div>
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<iframe allowfullscreen="true" frameborder="0" height="389" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/1NbODDTzk7Ezg5HBEZzv5JPHeogk5KgeHpwAinxqb1wQ/embed?start=true&loop=true&delayms=3000" webkitallowfullscreen="true" width="480"></iframe>
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Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-48758484058122077022014-08-11T19:44:00.000-05:002014-08-11T19:44:00.160-05:00Welcome to 2014!<div class="" style="clear: both; text-align: left;">
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<span style="color: red;"><i>Welcome to our class! </i></span></h3>
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<span style="color: red;"><i>I know we're going to have a great year together.</i></span></h3>
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<span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">Welcome to another year of math! I hope this year will be a wonderful learning experience for you, and I've accepted the challenge of making it the best year ever for all of us!</span><br />
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<span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">I hope you realize that teachers don't actually have 3 months off during the summer, and I spent a LOT of time doing some great learning by reading, attending conferences, and reflecting. (I think people who love teaching are the ones who love learning!) Thanks to a great idea in a book called <u>Teach Like a Pirate</u>, I decided on 5 words that I hope will describe our class this year:</span><br />
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<span style="background-color: white; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; font-size: 13px; line-height: 18.479999542236328px;"><span style="color: #666666;">I want our class to feel </span><b><span style="color: red;">safe</span></b><span style="color: #666666;">, </span><span style="color: red;"><b>inspirin</b><b>g</b></span><span style="color: #666666;">, and </span><b><span style="color: red;">challenging</span></b><span style="color: #666666;">. During our class, I hope you will feel </span><b><span style="color: red;">accomplished </span></b><span style="color: #666666;">and experience the </span><b><span style="color: red;">joy </span></b><span style="color: #666666;">in learning. </span></span></blockquote>
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<tr><td class="tr-caption" style="text-align: center;">Yes, the pencils say Mathmagical and Growth Mindset!<span style="color: #666666; line-height: 18.479999542236328px; text-align: left;"> </span></td></tr>
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<span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">The purpose of this post is for brief introductions, so a bit more about me...t</span><span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">his summer, I spent a lot of time with my family--here, in Hot Springs, Arkansas, and in Colorado. I also spent time with friends, where we tried new restaurants, talked school stuff, and went to movies. (I finally saw <i>Frozen</i>, and it was my first digital 3D movie, which I loved!) I'm a cat person, I'm a mountain person, and I love reading and buying new school supplies. According to some around LHHS, I coined the phrase <i>mathmagical</i>, and in honor of the new word, I have a whole box of new pencils waiting to give away to students who show something mathmagical or those who exhibit a growth mindset. (You have heard about growth mindset, right??) </span><span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">My </span><i style="color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">other</i><span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; font-size: 13px; line-height: 18.479999542236328px;"> job at school is I am one of two campus "Instructional Specialists," so I did a lot of planning and work for presentations in August. </span><br />
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<tr><td class="tr-caption" style="text-align: center;">Arches National Park--Look at that great parabola!</td></tr>
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<span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">For your first post, please briefly introduce yourself. You may share something from your Mathography, or you may include something new. You only need to write a sentence or two...just please write something that will help us know you a bit better. </span><span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">Please look over the blog rules page before commenting.</span></div>
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<span style="background-color: white; color: #666666; font-family: 'Trebuchet MS', Trebuchet, Verdana, sans-serif; font-size: 13px; line-height: 18.479999542236328px;">My examples were too long, and don't feel obligated to write that much, but I'll be happy with all of your posts.</span><br />
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<b>I look forward to getting to know you, and I'm so excited about the new year! </b><br />
<span style="text-align: start;"><b><span style="color: red;">Get used to hearing about #growthmindset!</span></b></span></div>
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<b>Thank you for your comments! </b><br />
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<b>(By the way, I moderate the comments, so they do not appear until I post them. Sorry for any confusion!)</b><br />
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<span style="color: #444444; font-family: Trebuchet MS, sans-serif;"><i>Mathmagically yours</i>, </span><br />
<span style="color: #444444; font-family: Trebuchet MS, sans-serif;">Ms. Laster</span></div>
Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com3tag:blogger.com,1999:blog-279687613385802426.post-10929896268480893962014-01-04T10:07:00.000-06:002014-01-05T19:17:13.328-06:00Your MANY Intelligences<div style="text-align: center;">
<b><span style="color: red;">Happy New Year! Welcome to 2014!! Ready for a new semester?</span></b></div>
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How was your break? Ready to jump into school, learning, and your intelligence? (Of course you are!)<br />
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Have you ever heard of Howard Gardner's theory of <b><i>Multiple Intelligences</i></b>? Instead of just IQ, Dr. Gardner suggested people have a variety of "types" of intelligence. He originally proposed 7 intelligences, then 8, and now some say 9, but here are two video options for you to learn about the different intelligences.<br />
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Both videos were created by teachers. The first video is straight forward, and includes words, definitions, and pictures. The second video is a made-up song and animation, originally created for young children, but it is cute (like School House Rock cute) in an elementary school way ... choose which one seems better for you!<br />
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<iframe allowfullscreen="allowfullscreen" frameborder="0" height="315" src="http://www.youtube.com/embed/cf6lqfNTmaM" width="420"></iframe><br />
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<iframe allowfullscreen="allowfullscreen" frameborder="0" height="315" src="http://www.youtube.com/embed/RmW_3ZhQZpc" width="420"></iframe><br />
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I know you're anxious to determine your type of intelligence, and here's your opportunity! Please take one of the surveys online found either <a href="http://www.literacyworks.org/mi/assessment/findyourstrengths.html" target="_blank">here</a>, <a href="http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks3/ict/multiple_int/index.htm" target="_blank">here</a> (click "Take the Test") or <a href="http://www.berghuis.co.nz/abiator/lsi/mi_test.html" target="_blank">here</a>. (If another teacher gives you a paper version of an MI survey, feel free to use that quiz, rather than an online version.) All three are different formats and offer different type of feedback, but my scores were the same. Did you have one dominant intelligence, or were there several top intelligences? You may find definitions and more information about intelligences at the websites <a href="http://www.edwebproject.org/edref.mi.th.html" target="_blank">here</a>, <a href="http://www.rubythroat.org/MultipleIntelligencesDefin.html" target="_blank">here</a>, <a href="http://psychology.about.com/b/2013/01/02/gardners-theory-of-multiple-intelligences.htm" target="_blank">here</a>, or <a href="http://teammates.org/postsecondary/multiple-intelligences/" target="_blank">here</a>. There are so many resources, but I tried to pick ones that weren't too teacher-y.<br />
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Next, please submit your findings and reflections in <a href="https://docs.google.com/spreadsheet/viewform?formkey=dDVSUTk0OFJqRmZHMDhlQU9pQzhlYnc6MQ" target="_blank">this Google form</a>. Please complete the surveys and the responses by next Wednesday, January 15, 10 PM.<br />
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<span style="color: red;"><b>Thank you, and as always, I look forward to reading your responses!</b></span><br />
<span style="color: red;"><b>(Don't forget to hit "Submit" at the end of your survey!)</b></span></div>
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<b><span style="color: #38761d;">Did you enjoy learning about multiple intelligences? If you found any other interesting information, videos, or links, please post in the comments below!</span></b>Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com2tag:blogger.com,1999:blog-279687613385802426.post-51607461515137006232013-11-30T07:17:00.000-06:002014-11-30T15:14:11.457-06:00Polar Coordinates and Equations--More than Pretty Pictures!<br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJxW_dsnjzQMe6-5jSuKjUM1yCxuRTltQlg5SB2CJsgTby-aKU3PUqfg5EnirnjjqHExM6ByXQ1u03gVWu7WRpJjAytmOjzNNdc18D90ntzBrzT0hb0sBs5vgZ2N9BjCfQc388nGAi49U/s1600/polor+heart.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJxW_dsnjzQMe6-5jSuKjUM1yCxuRTltQlg5SB2CJsgTby-aKU3PUqfg5EnirnjjqHExM6ByXQ1u03gVWu7WRpJjAytmOjzNNdc18D90ntzBrzT0hb0sBs5vgZ2N9BjCfQc388nGAi49U/s320/polor+heart.PNG" height="213" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;">Great use for cardioid graphs!</td></tr>
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Since our study of polar graphs and coordinates was abbreviated (and we had Thanksgiving in between) I wanted to provide a few resources for you to help with your test review, so here you go:</div>
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<u><b>Written resources:</b></u><br />
<ul>
<li><a href="http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx" target="_blank">Great examples</a> from a professor at Lamar College</li>
<li>Another math teacher's <a href="http://mathematicsforstudents.wordpress.com/2012/10/20/polar-coordinates/" target="_blank">resources</a> for students</li>
<li>From the appropriately named "Math is Fun" website - <a href="http://www.mathsisfun.com/polar-cartesian-coordinates.html" target="_blank">examples</a> of converting between coordinates</li>
<li>How to create a polar graph <a href="http://www.analyzemath.com/polarcoordinates/graphing_polar_equations.html" target="_blank">using a table</a></li>
<li><a href="http://mathbits.com/MathBits/TISection/PreCalculus/polargraphs.htm" target="_blank">Using your calculator</a> to create polar graphs</li>
<li>An <a href="http://jwilson.coe.uga.edu/emt668/emt668.folders.f97/anderson/writeup11/writeup11.html" target="_blank">explanation and examples of</a> all of the different polar graphs</li>
<li>Free <a href="http://www.embeddedmath.com/downloads/index.php" target="_blank">graph paper</a> to download</li>
</ul>
<u><b>Video/Interactive Resources (most require Java):</b></u><br />
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<li><a href="http://www.youtube.com/watch?v=r0fv9V9GHdo" target="_blank">Video tutorial</a> of basics of polar coordinates and graphs</li>
<li>Great <a href="http://www.intmath.com/plane-analytic-geometry/8-curves-polar-coordinates.php" target="_blank">interactive site</a> to explain polar</li>
<li>Interactive sites to create polar graphs (like our "web assignment") - found <a href="http://www.shodor.org/interactivate/activities/PolarCoordinates/" target="_blank">here</a> and <a href="http://cs.jsu.edu/~leathrum/Mathlets/polar.html" target="_blank">here</a> </li>
<li>And don't forget my new favorite website for a graphing calculator: <a href="https://www.desmos.com/calculator" target="_blank">Desmos</a>!</li>
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If you find another resource that might help a classmate, please list it in the comments below.Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-50416063857531622692013-09-15T15:49:00.003-05:002013-09-15T15:51:57.868-05:00Test Time!<div class="separator" style="clear: both; text-align: left;">
OK, it's time for our next test, so what changes do you need to make to be ready for test #2? What do you do to prepare for a math test? Can you think of anything that I might do to make the questions more <i>interesting</i>? </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhk7gnOMpckyDz4PhS05Aqy41U5W13kXBuNuj7XsmpxoN41XWihnis68nZELMYOjKl01THPWEVRR0ZCmGvc9ynjsVrzDoi6zpp-M54QLM2quOBeMiXNspF7sldvfa1uX7GKAtljEgzo8kk/s1600/cosine.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhk7gnOMpckyDz4PhS05Aqy41U5W13kXBuNuj7XsmpxoN41XWihnis68nZELMYOjKl01THPWEVRR0ZCmGvc9ynjsVrzDoi6zpp-M54QLM2quOBeMiXNspF7sldvfa1uX7GKAtljEgzo8kk/s320/cosine.jpg" width="320" /></a></div>
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Here is a cool <a href="http://science.kennesaw.edu/~plaval/tools/trig.html" target="_blank">graphing applet</a> to show transformations of sine and cosine graphs. (You will have to allow Java for this applet to run, and click on the links on the left side of the screen.)<br />
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I have a growth mindset about making videos to help you, so here's attempt #2. (I also got a bit of advice from my friend Mr. Gonzales who suggested a "Crash Course" type video.)<br />
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<iframe allowfullscreen="" frameborder="0" height="360" src="//www.youtube.com/embed/x-f6TvHzyvc" width="480"></iframe>
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And here's a lower production <a href="http://www.showme.com/sh/?h=obEinaa" target="_blank">video</a> for a quick review of even and odd functions. (It worked at home, but now it says "converting," so I hope you'll be able to view this video!! Sigh.)<br />
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<b><span style="color: red;">Are these review videos helpful at all? Please let me know! </span></b></div>
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<b><span style="color: red;">What improvements or other suggestions do you have? </span></b></div>
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<b><span style="color: red;">I'm still learning!</span></b></div>
Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-37697950642050009872013-09-08T18:31:00.001-05:002013-09-08T18:38:08.230-05:00Graphs of Sine and Cosine<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBDXYaYS4shvvQvh7pUwwsFepikOAtAKbHR0Q1RGk8v8hKVnRic0jjTq-vmZVGFwgp8oYCeIC1VCyUm5IWAwOZxo6kIZJ8LEVXMGXdxT8zPfDDQutNt3rtA2sGOe6YNh1uXOBHkdlauKw/s1600/sin-cos+graphs.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBDXYaYS4shvvQvh7pUwwsFepikOAtAKbHR0Q1RGk8v8hKVnRic0jjTq-vmZVGFwgp8oYCeIC1VCyUm5IWAwOZxo6kIZJ8LEVXMGXdxT8zPfDDQutNt3rtA2sGOe6YNh1uXOBHkdlauKw/s320/sin-cos+graphs.jpg" width="320" /></a></div>
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For my first absence of the year (several of your teachers will be attending this training) I <i>tried </i>to create a video version of our notes.<br />
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I must admit, the video is pretty terrible, but the instruction is adequate. :) You can hear my pen tap on the screen, I used a couple words wrong (function rather than transformation; stretch rather than shift) I am sometimes too quiet and sometimes too loud, and I think at one point, you hear my cat purring in the back ground! BUT, I have a growth mindset about preparing these types of lessons for you, so I won't give up after my first fail. And I didn't want to learn how to edit because this has already taken me 3 hours to create!<br />
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So please enjoy my version of sine and cosine graphs. The notes for this section are <a href="http://goo.gl/aT6dMg" target="_blank">here</a>, but I'll have copies for you in class.<br />
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If you don't completely understand everything, have patience (and a growth mindset). A classmate may help you and/or I know you can find countless other resources online to help with the topic. I'll return on Wednesday, and we'll continue the discussion about trig graphs, but we'll have even more transformation fun in store.<br />
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<b style="background-color: yellow;">Once you finish the video, please complete the quick survey about </b></div>
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<b style="background-color: yellow;">your learning and understanding.</b></div>
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<iframe frameborder="0" height="1700" marginheight="0" marginwidth="0" src="https://docs.google.com/forms/d/1zc290T4m_5TqEAPG7-vs-Au5EBWTN2PAT6AMB79NnAM/viewform?embedded=true" width="760">Loading...</iframe><br />
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<b><span style="color: red;">If you have any additional suggestions, concerns, or questions, please feel free to leave them in the comments! Thanks, and have a wonderful day.</span></b></div>
Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-33361556419343595022013-08-21T06:00:00.000-05:002013-08-27T20:07:12.380-05:002013-14 Begins NOW!<h3 style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidQ2OfaMWOtYU8nmI5dW2CawGAwzcYJxtUekvcIQfKwu6mmBL1hqYzQOQZYEJcwH5qarkPqD6QopyvKmbc_VswsJ99NywrveTi2uLLotcyNJbG17R7zjhU5tQeT539H4nx1PHaU-XRc5w/s1600/Welcome+Slide.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidQ2OfaMWOtYU8nmI5dW2CawGAwzcYJxtUekvcIQfKwu6mmBL1hqYzQOQZYEJcwH5qarkPqD6QopyvKmbc_VswsJ99NywrveTi2uLLotcyNJbG17R7zjhU5tQeT539H4nx1PHaU-XRc5w/s320/Welcome+Slide.jpg" width="320" /></a></h3>
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<span style="color: red;"><i>Welcome to our class! </i></span></h3>
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<span style="color: red;"><i>I know we're going to have a great year together.</i></span></h3>
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I started this class blog a couple years ago, and I plan to utilize it with our class again this year for both math and non-math posts. Please look over the blog rules page before commenting.<br />
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For your first post, please briefly introduce yourself. You may share something from your Mathography, or you may include something new. You only need to write a sentence or two...just please write something that will help us know you a bit better.<br />
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To help you get to know me, one of my favorite sayings is <b><span style="color: red;">"Whatever worth doing is worth doing well."</span></b> (What does that say about me as a teacher and a person? How could that possibly be a hint about our class? Hmmm...) Another bit about me: last year, we wrote 6-word memoirs and mine was <span style="color: red;"><b>"I love to help find solutions."</b></span> Do you get how that is math-y, teacher-y, and applies to my IS job? I also love technology, so we will experiment with sites and tools I find. I have been known to waste a lot of time looking for the perfect, fun font. <br />
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This summer, I spent a lot of time with my family--here, at a friend's lake house, and in Hot Springs, Arkansas. I also spent time with friends, where we tried new restaurants, talked school stuff, and went to movies. I also visited two Presidential Libraries, and I highly recommend visiting any of them around the country! I learned how to grill vegetables, and I enjoy cooking and baking. (I bet you will love the ginger snaps I bring you!) I was kind of "craft-y" this summer, and I made about 100 magnets for different people.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR4sYe9rdyj7ejUaizvWTnoGMc3-APyH7ZC9HovdiVbsUr7r5DvW_ZMjnJ5DMnIhE6is68gVNEY7zP6QDtCbhLnQcqHdk0oGtv8NI_QNOrfCosxg2g0DjlAqDUqGggrkGhuJYOo0UAEr0/s1600/summer+pics.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR4sYe9rdyj7ejUaizvWTnoGMc3-APyH7ZC9HovdiVbsUr7r5DvW_ZMjnJ5DMnIhE6is68gVNEY7zP6QDtCbhLnQcqHdk0oGtv8NI_QNOrfCosxg2g0DjlAqDUqGggrkGhuJYOo0UAEr0/s400/summer+pics.jpg" width="400" /></a></div>
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I also took at least one picture every day this summer, and I plan to continue taking pictures every day during the school year!<br />
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<span style="background-color: white;">Some teachers don't have much time off, and I did a LOT of school work this summer, but it was mostly for fun and just good learning. I took a free online course through Stanford called "How to Learn Math," and I know you will benefit from what I learned there. I love to read pretty much anything, but this summer, I spent most of my time with educational stuff. I enjoy some YA fiction (<i>Allegiant</i> is released on 10/22!) and I am also looking forward to the movie <i>Catching Fire</i> (11/22!)</span><br />
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My examples were too long, and don't feel obligated to write that much, but I'll be happy with all of your posts.<br />
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<b>I look forward to getting to know you, and I'm so excited about the new year! </b><br />
<span style="text-align: start;"><b><span style="color: red;">Get used to hearing about #growthmindset!</span></b></span></div>
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<b>Thank you for your comments! </b><br />
<b>(By the way, I moderate the comments, so they do not appear until I post them. Sorry for any confusion!)</b></div>
Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com29tag:blogger.com,1999:blog-279687613385802426.post-3675803989274762512013-08-18T20:01:00.000-05:002013-08-18T20:01:07.681-05:00Technology SurveyIf you have trouble accessing this survey, please try the link <a href="http://goo.gl/8NtXwc" target="_blank">here</a>.<br />
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While you're here, why don't you <a href="https://twitter.com/klasmath" target="_blank">follow me on Twitter</a> and like our class <a href="https://www.facebook.com/pages/Ms-Laster/490483331045022" target="_blank">Facebook page</a>? ;)<br />
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<iframe frameborder="0" height="1772" marginheight="0" marginwidth="0" src="https://docs.google.com/spreadsheet/embeddedform?formkey=dFZZSW9Wby1NbEtnTzRxZG40MTdtMWc6MA" width="760">Loading...</iframe>
<br />Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-73365618303955190792013-06-02T19:50:00.003-05:002013-07-08T09:40:07.964-05:00Hooray for the End!I can't believe it's already time to end the year! It seems like you were just here last week completing your math-ography and survey.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiXxzUjuU3HHQZVOLKZVdeGfqMMXh7E3RXWmPkBbwbc8kbdHXe__u8-1JEmhqi0RDP60Ag6Uko3cH85v6mi6PaTtgnmB3PWMCssGUeQoRILDCwysv6XONOePTp0T_zbBowTDSryskC3XQ/s1600/pencil.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiXxzUjuU3HHQZVOLKZVdeGfqMMXh7E3RXWmPkBbwbc8kbdHXe__u8-1JEmhqi0RDP60Ag6Uko3cH85v6mi6PaTtgnmB3PWMCssGUeQoRILDCwysv6XONOePTp0T_zbBowTDSryskC3XQ/s1600/pencil.png" /></a></div>
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Here's one last post for you, and I would really appreciate your feedback. I think it is very important to reflect and learn from each experience, so I would like to know what you think about our class and my teaching. In addition, for my "other" job, I think your feedback about teaching in general could help teachers new to LHHS. The last part of the questionnaire asks you to reflect a bit on your own year.<br />
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I have created<span style="font-size: large;"> <a href="https://docs.google.com/forms/d/1h_casBmTdlTOj5w3CB9G788-UgKHxnAuKRqKkIutIuc/viewform" target="_blank">this survey</a> </span>that you may complete at any time this week. Your feedback will help me improve my teaching, but please be considerate about how you respond. (I accept your constructive criticism, but please justify your responses--just like on our tests!) You do not have to include your name, and you do not need to complete every question.<br />
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If you want to share your summer plans, feel free to post in the comments. (My sister will be here in 2 weeks, so for me, summer starts with family fun!)<br />
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A few end of year quotes for you...<br />
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<strong style="background-color: white; color: #333333; line-height: 20.6875px;"><span style="font-family: Times, Times New Roman, serif; font-size: large;">“Believe in your dreams and they may come true; believe in yourself and they will come true.”</span></strong><br />
<span style="font-size: large;"><strong style="background-color: white; color: #333333; line-height: 20.6875px;"><span style="font-family: Times, Times New Roman, serif;"><br /></span></strong>
<strong style="background-color: white; color: #333333; line-height: 20.6875px;"><span style="font-family: Times, Times New Roman, serif;">“Nurture your mind with great thoughts; to believe in the heroic makes heroes.”</span></strong></span><br />
<span style="font-size: large;"><strong style="background-color: white; color: #333333; line-height: 20.6875px;"><span style="font-family: Times, Times New Roman, serif;"><br /></span></strong>
<strong style="background-color: white; color: #333333; line-height: 20.6875px;"><span style="font-family: Times, Times New Roman, serif;">“Even a mistake may turn out to be the one thing necessary to a worthwhile achievement.”</span></strong></span><br />
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<span style="color: red; font-size: large;">Thanks so much for your time!</span></div>
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<span style="font-size: large;">More importantly, thanks for a great year!</span></div>
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Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-69342780264426610802013-05-10T15:30:00.000-05:002013-05-10T15:30:43.047-05:00Math MemoirsNot that anyone is counting or anything, but hooray for the last weeks of school! For an extra credit opportunity I'm "borrowing" <a href="http://mathteachermambo.blogspot.com/2012/01/six-word-memoirs.html" target="_blank">this idea</a> I found on another math teacher's blog. (You can look at her post to see her students' samples.) She actually took the idea from <a href="http://www.npr.org/templates/story/story.php?storyId=18768430" target="_blank">this story</a> on NPR and from <a href="http://www.smithmag.net/">http://www.smithmag.net/</a>, a website where Six Word Memoirs can be shared.<br />
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Using only <u>6</u> words, create a memoir of your year in our PAP Pre-Calculus Class. Your sentence/phrase should make sense, but it does not necessarily need to be a complete sentence. (I'll accept sentence fragments! Don't tell your English teacher!)<br />
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Details...<br />
<ul>
<li>Complete your memoir on a page at least 8.5" x 11".</li>
<li>Include your sentence, and then somehow illustrate your memoir.</li>
<li>You may type or hand-draw your "project."</li>
<li>Please be neat, colorful, and creative.</li>
<li>Your project should fill the page.</li>
<li>Have fun!</li>
</ul>
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Your math memoir will be <span style="color: red; font-weight: bold;">due on Monday, May 20, </span>and it will be worth test points.</div>
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If you would like (need) additional points, either on your HW average or to boost your HW/Quiz category, you may create an additional Six Word Memoir about your "non-math" life. </div>
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Feel free to post your sentence here, but please turn in your projects by next Monday.</div>
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Thanks, and I look forward to reading all of your memoirs!</div>
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By the way, here is my memoir, created while I was proctoring an AP test. :) I think this sentence captures my math and IS jobs. I'm still working on my illustrations, and I'm still working on my personal memoir.</div>
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<span style="color: red; font-size: large;"><i><b>I love to help find solutions.</b></i></span><br />
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Here are a few finished products from last year! I think these memoirs are awesome!</div>
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<tr><td class="tr-caption" style="text-align: center;">Math: Where Conquering Concepts Happens Everyday</td></tr>
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Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-25474343899112164252013-04-07T16:19:00.002-05:002013-04-07T19:01:02.955-05:00Math-Magic with Pascal and Fibonacci<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn0uqZWeie0NJBLMDada-eZ-NMWro5kH0YIU4Xmr1iaT5HH1f2ncQLfZqZfYdcVa1FfR9D-wPcST1D2JBjUPXLXHlCgOpNGYQ0mWcY179Des4lIkQQ4e7GZkAzhAjdRLKtMKE2kWO2Rs8/s1600/pascals+triangle.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn0uqZWeie0NJBLMDada-eZ-NMWro5kH0YIU4Xmr1iaT5HH1f2ncQLfZqZfYdcVa1FfR9D-wPcST1D2JBjUPXLXHlCgOpNGYQ0mWcY179Des4lIkQQ4e7GZkAzhAjdRLKtMKE2kWO2Rs8/s1600/pascals+triangle.jpg" /></a></div>
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The purpose of the "web" assignment is to give you time to simply browse. I hope you enjoy exploring different sites to see examples of some true <i>mathmagic</i>! <br />
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Click <a href="https://www.dropbox.com/s/q0kv3xfznu25ci7/Pascal%20Fibonacci%20web%20explore.pdf" target="_blank">here for a link</a> to the document for today's assignment. <br />
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And here's a new web tool I've wanted to try. It's called "<a href="http://thinglink.com/" target="_blank">Thinglink</a>," and you can embed links within the image. Don't know if you'll get to explore Sierpenski triangles and fractals today, but they're very cool and related to Pascal's triangle, too! I've attached a few links, and if you find something else fun, please try adding new links to this image.<br />
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<img class="alwaysThinglink" src="//cdn.thinglink.me/api/image/377560547928834050/1024/10/scaletowidth#tl-377560547928834050;626328886" width="500" /><script async="" charset="utf-8" src="//cdn.thinglink.me/jse/embed.js"></script>
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<span style="color: red;"><b>Please share!</b></span><br />
By Tuesday, April 9, 5 PM, please post (in the comments below) <span style="font-family: 'Times New Roman', serif; font-size: 12pt;">a sentence or two about the most
math-magical thing you discovered about Pascal’s triangle, the Fibonacci
sequence, or Phi. What was fun, interesting, cool, or made you ooh and aah?? Please share!</span><br />
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<span style="color: red;"><b>Thank you, and have fun!</b></span></div>
Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com37tag:blogger.com,1999:blog-279687613385802426.post-36243194062811396732013-03-24T16:40:00.000-05:002013-03-24T16:40:57.306-05:00Let's Hear Your Voice!Thanks again for your willingness to try a new technology tool!<br />
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You must first register with <a href="http://voicethread.com/" target="_blank">Voice Thread</a>. <br />
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Once you register, you may search for our slides, or simply click the links below. Feel free to look at both slide shows, and I will grade your comments left on either presentation. (Sorry about any blurry pictures!)<br />
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<b><span style="color: #cc0000;">1st period's work:</span></b><br />
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<object height="360" width="480"><param name="movie" value="https://voicethread.com/book.swf?b=4342342"></param>
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<b><span style="color: #cc0000;">3rd period's work:</span></b><br />
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If you can think of any ways other ways students/teachers might enjoy using Voice Thread, please leave your comments on the slideshow or post a comment below.<br />
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Thank you!Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-28651245121606329282013-03-17T13:00:00.002-05:002013-03-17T13:00:22.245-05:00A Math Super Power!<span style="font-family: inherit;">Several years ago, Steve Strogatz, an award winning mathematician from Cornell, wrote a series of 15 articles in the <i>New York Times Opinionator</i> blog. He is a professor who really understands </span><i style="font-family: inherit;">math-magic</i><span style="font-family: inherit;">, and he wanted to explain it from the beginning of numbers to advanced calculus. The entire series may be found </span><a href="http://topics.nytimes.com/top/opinion/series/steven_strogatz_on_the_elements_of_math/index.html" style="font-family: inherit;" target="_blank">here</a><span style="font-family: inherit;">, and if you're looking for good math reads, check out all of the articles, in order. I </span><u style="font-family: inherit;">promise</u><span style="font-family: inherit;">, the articles are engaging and entertaining, and in fact, in his first post, he uses a clip from Sesame Street to explain the importance of numbers. How brilliant is that?!?</span><br />
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<span style="font-family: inherit;">In math, we don’t often have opportunities for reading and writing, so when the series was first published, I kep</span><span style="font-family: inherit;">t looking for ways to incorporate it into my classroom...so now you'll get to respond on this blog! :-)</span><br />
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<span style="font-family: inherit;">In your next opportunity to <i>post for points</i>, please read his article called "<a href="http://opinionator.blogs.nytimes.com/2010/03/28/power-tools/" target="_blank">Power Tools</a>," (which I also gave you before the break) and summarize the material using a 20 word <b><span style="color: red;">gist</span></b>. Write a complete sentence (or I’ll even take a coherent phrase) using only 20 words. You may summarize the entire article, one particular piece of the article, or you may draw a conclusion about the article, but you must do so using only twenty words. More importantly, your sentence/phrase must make sense! </span></div>
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<span style="font-family: inherit;">Please don't forget to include either your first name or initials so that you can receive your extra credit points!</span><br />
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<span style="color: red; font-family: inherit;">Once again...your sentence must make sense, relate to the article, and use <u>EXACTLY</u> 20 words.</span><br />
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<span style="font-family: inherit;">Please post your comments by 5 PM on Friday, March 22. </span></div>
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Have fun, and thanks for playing!</div>
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As always, I look forward to reading your responses.</div>
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Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com27tag:blogger.com,1999:blog-279687613385802426.post-28661854383005546672013-01-06T21:32:00.000-06:002013-01-06T06:29:52.528-06:00You're Intelligent in How Many Ways???<div style="text-align: center;">
<b><span style="color: red;">Happy New Year! Welcome to 2013!! Ready for a new semester?</span></b></div>
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How was your break? Ready to jump into school, learning, and your intelligence? (Of course you are!)<br />
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Have you ever heard of Howard Gardner's theory of <b><i>Multiple Intelligences</i></b>? Instead of just IQ, Dr. Gardner suggested people have a variety of "types" of intelligence. He orginally proposed 7 intelligences, then 8, and now some say 9, but here are two video options for you to learn about the different intelligences.<br />
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Both videos were created by teachers. The first video is straight forward, and includes words, definitions, and pictures. The second video is a made-up song and animation, originally created for young children, but it is cute (like School House Rock cute) in an elementary school way ... choose which one seems better for you!<br />
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<iframe allowfullscreen="allowfullscreen" frameborder="0" height="315" src="http://www.youtube.com/embed/cf6lqfNTmaM" width="420"></iframe>
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<iframe allowfullscreen="allowfullscreen" frameborder="0" height="315" src="http://www.youtube.com/embed/RmW_3ZhQZpc" width="420"></iframe><br />
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I know you're anxious to determine your type of intelligence, and here's your opportunity! Please take one of the surveys online found either <a href="http://www.literacyworks.org/mi/assessment/findyourstrengths.html" target="_blank">here</a>, <a href="http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks3/ict/multiple_int/index.htm" target="_blank">here</a> (click "Take the Test") or <a href="http://www.berghuis.co.nz/abiator/lsi/mi_test.html" target="_blank">here</a>. (If another teacher gives you a paper version of an MI survey, feel free to use that quiz, rather than an online version.) All three are different formats and offer different type of feedback, but my scores were the same. Did you have one dominant intelligence, or were there several top intelligences? You may find definitions and more information about intelligences at the websites <a href="http://www.edwebproject.org/edref.mi.th.html" target="_blank">here</a>, <a href="http://www.rubythroat.org/MultipleIntelligencesDefin.html" target="_blank">here</a>, <a href="http://psychology.about.com/b/2013/01/02/gardners-theory-of-multiple-intelligences.htm" target="_blank">here</a>, or <a href="http://teammates.org/postsecondary/multiple-intelligences/" target="_blank">here</a>. There are so many resources, but I tried to pick ones that weren't too teacher-y.<br />
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Next, please submit your findings and reflections in <a href="https://docs.google.com/spreadsheet/viewform?formkey=dDVSUTk0OFJqRmZHMDhlQU9pQzhlYnc6MQ" target="_blank">this Google form</a>. Please complete the surveys and the responses by next Wednesday, January 16, 10 PM. <br />
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<span style="color: red;"><b>Thank you, and as always, I look forward to reading your responses!</b></span><br />
<span style="color: red;"><b>(Don't forget to hit "Submit" at the end of your survey!)</b></span></div>
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<b><span style="color: #38761d;">Did you enjoy learning about multiple intelligences? If you found any other interesting information, videos, or links, please post in the comments below!</span></b>Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-2859849066618198772012-11-24T10:44:00.000-06:002012-11-25T17:39:23.466-06:00Not Quite the North Pole, but Almost as Fun!When I first mentioned polar coordinates, did you immediately think "North Pole!" and then "Santa?" (I know that's the way my mind works every time I think about polar graphs, especially at this time of year!) <br />
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(And since we're talking North Pole, I'll share some KLas family trivia... I've told you that my sister lived in Alaska for a long time, and her wedding was almost exactly 8 years ago...happy anniversary Allison & Steve! So when our entire family ventured to Alaska for her wedding during Thanksgiving, 2004, we had to go to North Pole, Alaska, shop at the Santa Clause house, and take a picture of the real north pole!)<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmbIUbtCAgCB8jTixMadeXpeOvbSR0nVxpb4BMDFUfer3K9HhEhFwtOytg9d7xOpY-bgwfmtoiVWqFzXZ_KMuze-9UB7xp1AD-SIftGzg_eAwD0Jc4HD_VXAnnhawKiDtaeRQ7i7CPl34/s1600/NP+2.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmbIUbtCAgCB8jTixMadeXpeOvbSR0nVxpb4BMDFUfer3K9HhEhFwtOytg9d7xOpY-bgwfmtoiVWqFzXZ_KMuze-9UB7xp1AD-SIftGzg_eAwD0Jc4HD_VXAnnhawKiDtaeRQ7i7CPl34/s320/NP+2.png" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">That's my dad with me...& yes, there are geocaches close by!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Is that Rudolph, peeking around the corner?</td></tr>
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Visiting the North Pole is oh-so-much fun, but look at the possible graphs you can make...doesn't that look like fantastic fun, too?! ;) And you you will be able to create these graphs by the end of the week...no winter visits to Alaska required!<br />
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<tr><td class="tr-caption" style="text-align: center;">Great use for cardioid graphs!</td></tr>
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Since our study of polar graphs and coordinates will be abbreviated, I wanted to provide a few resources for you to help with your studies, so here you go:</div>
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<u><b>Written resources:</b></u><br />
<ul>
<li><a href="http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx" target="_blank">Great examples</a> from a professor at Lamar College</li>
<li>Another math teacher's <a href="http://mathematicsforstudents.wordpress.com/2012/10/20/polar-coordinates/" target="_blank">resources</a> for students</li>
<li>From the appropriately named "Math is Fun" website - <a href="http://www.mathsisfun.com/polar-cartesian-coordinates.html" target="_blank">examples</a> of converting between coordinates </li>
<li>How to create a polar graph <a href="http://www.analyzemath.com/polarcoordinates/graphing_polar_equations.html" target="_blank">using a table</a></li>
<li><a href="http://mathbits.com/MathBits/TIsection/PreCalculus/polargraphs.htm" target="_blank">Using your calculator</a> to create polar graphs</li>
<li>An <a href="http://jwilson.coe.uga.edu/emt668/emt668.folders.f97/anderson/writeup11/writeup11.html" target="_blank">explanation and examples of</a> all of the different polar graphs</li>
<li>Free <a href="http://www.embeddedmath.com/downloads/index.php" target="_blank">graph paper</a> to download</li>
</ul>
<u><b>Video/Interactive Resources (most require Java):</b></u><br />
<ul>
<li><a href="http://www.youtube.com/watch?v=r0fv9V9GHdo" target="_blank">Video tutorial</a> of basics of polar coordinates and graphs </li>
<li>Great <a href="http://www.intmath.com/plane-analytic-geometry/8-curves-polar-coordinates.php" target="_blank">interactive site</a> to explain polar</li>
<li>Interactive sites to create polar graphs (like our "web assignment") - found <a href="http://www.shodor.org/interactivate/activities/PolarCoordinates/" target="_blank">here</a> and <a href="http://cs.jsu.edu/~leathrum/Mathlets/polar.html" target="_blank">here</a> and <a href="http://webspace.ship.edu/msrenault/ggb/polar_grapher.html" target="_blank">here</a></li>
</ul>
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If you find another resource that might help a classmate, please list it in the comments below. If you create a cool polar graph, take a screen shot and email it to me, and I'll post it here!<br />
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Aren't polar graphs <i>cool</i>? <br />
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<br />Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com1tag:blogger.com,1999:blog-279687613385802426.post-52660274242332850682012-10-21T16:00:00.000-05:002012-10-21T16:00:00.348-05:00I Used to Think... But Now I Know...<br />
Last year, Mrs. Saxon found this quote, which is perfect for our discussion about YET:<br />
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<i>“I may not be there yet, but I’m closer than I was yesterday.” – Author unknown</i></div>
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<span style="font-size: small;">I love </span><span style="font-size: small;">the</span><span style="font-size: small;"> way we've used the phrase YET in class, and I hope we will continue these kinds of reminders.</span><i><span style="font-size: small;"></span></i></div>
<ul>
<li><i>Ms. Laster--my homework isn't finished. YET!</i></li>
<li><i>I don't understand what we're doing in class...YET!</i></li>
<li><i>I don't think I'm ready for the test...YET!</i></li>
<li><i>I don't want to do this assignment...YET!</i></li>
</ul>
<i><br /></i><span style="font-size: small;">I first heard this idea at a presentation by Dr. Carol Dweck, who wrote the book <a href="http://www.amazon.com/Mindset-Psychology-Success-Carol-Dweck/dp/0345472322/ref=sr_1_cc_1?s=aps&ie=UTF8&qid=1329872185&sr=1-1-catcorr" target="_blank">Mindset</a>. </span>(Have you heard me talk about <i><span style="color: red;">growth </span></i>and <i><span style="color: blue;">fixed </span></i>mindsets? Haha! Check out her <a href="http://mindsetonline.com/" target="_blank">blog!)</a> I think this idea is very powerful, and it has changed the way I'm thinking and working, not only at school, but also at home and with family.<br />
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If you're trying to change from a growth to a fixed mindset, Dr. Dweck has these suggestions, taken from her website:<br />
<ol>
<li>Listen and realize when you are "hearing" a fixed mindset voice. (I'll never make a hexaflexagon!)</li>
<li>Realize you have choice--to think with a growth mindset. (...YET!)</li>
<li>Talk back with a growth mindset. (I'll get it if I continue to practice and if Kelly tutors me!)</li>
<li>Take action! (Just do it!)</li>
</ol>
Do you have a growth or fixed mindset? Actually, for some areas, you may have a fixed mindset (mine is sports!) but for others, you may have a growth mindset. What are you doing to change your mindset?<br />
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If you have a fixed mindset about trig identities, what can you do about it? OR what have you done about it? If there is something else about our class that you have learned, please share it below in the comments. Please respond to this post with:<br />
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<span style="color: red; font-size: large;"><b>I used to think_______ but now I know________</b></span></div>
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You may fill in the blanks with something about trig identities or anything else about our class.<br />
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Thank you for your time! I know I'll enjoy reading your comments!Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com38tag:blogger.com,1999:blog-279687613385802426.post-64173535121554008332012-09-25T08:04:00.002-05:002012-09-26T19:20:06.582-05:00Sinusoidal Functions as Math Models HELP<div class="separator" style="clear: both; text-align: center;">
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OK, I know you can do these problems, but it definitely takes some practice! I've watched several videos and found a few links to help you. I also created a tiny "video" using the <a href="http://itunes.apple.com/us/app/educreations-interactive-whiteboard/id478617061?ls=1&mt=8" target="_blank">Educreations</a> app. You should be able to watch my videos just fine from your computer, but if you're on an iPad, you have to download the free app. Unfortunately, this video does not work on an iPhone. :-(<br />
<ul>
<li><a href="http://edcr8.co/VuHDA5" target="_blank">My video</a> on solving a sinusoidal equation algebraically involving a cosine.</li>
<li>When is Fiona an ogre vs. a princess? Use <a href="http://www.youtube.com/watch?v=G62GOVBOiV8" target="_blank">this video</a> to find out!</li>
<li>Here's an <a href="http://www.emathguy.com/instruction/trigonometry/applications/models" target="_blank">explanation</a> of a water wheel problem. Thanks, emathguy!</li>
<li>This <a href="http://www.scasd.org/cms/lib5/PA01000006/Centricity/Domain/1289/sin_model_ans.pdf" target="_blank">PDF</a> shows several problems worked completely. The problems are even some of the same ones I've assigned, and at a quick glance, they look good, but I haven't checked all of the work.</li>
<li>One more <a href="http://schools.bvsd.org/p12/broomfieldhigh/Teachers/masse/Lists/Calendar/Attachments/98/SinCosApplWS1Key.pdf" target="_blank">PDF</a> of some similar problems worked. I like this one because it shows a few distinct steps (looking for a max/min point, writing an equation as a sine or cosine, etc.) But again, I didn't work through all of the problems for correctness, so use at your own risk! :-)</li>
<li>The answers to the "Practice Test" are the photos below, and all steps are shown for the algebraic equations:</li>
</ul>
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The answers to your two practice worksheets are posted on EdLine.<br />
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Most of these problems (and the ones from the video) were taken from the green trig book (Foerster) section 2.12. The odd answers are in the back of the book, of course!</div>
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If you find any other great hints, please share in the comments below!<br />
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From your comments on your exit ticket: one person asked for problems worked out completely, so I posted those equations above. Another specific question asked about how do you determine whether your graph is a sin x or cos x (or -sin x or -cos x).<br />
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<ul>
<li>If the first point you plot is a <span style="color: purple;"><b>maximum point</b></span>, your graph is most likely a <span style="color: purple;"><b>cosine</b></span> because your point is ABOVE the shifted x-axis.</li>
</ul>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1SARnrbGhO9KS3M2Ozth2RibAEHcTlYT5eDAq8W7eJDioDOJMybFutInldT8S8FfORgIiTngyTw-MIDbrVXEa2sjFzD0al7g0LFXPFTNFqflxuHfgDqvTWSuRUIlUava5I7Go4rFsbJk/s1600/cos+graph.jpeg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="167" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1SARnrbGhO9KS3M2Ozth2RibAEHcTlYT5eDAq8W7eJDioDOJMybFutInldT8S8FfORgIiTngyTw-MIDbrVXEa2sjFzD0al7g0LFXPFTNFqflxuHfgDqvTWSuRUIlUava5I7Go4rFsbJk/s320/cos+graph.jpeg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">positive cosine--starts at a MAX</td></tr>
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<ul>
<li>If the first point you plot is a <span style="color: blue;"><b>minimum point</b></span>, your graph is most likely a <span style="color: blue;"><b>negative cosine</b></span> because your point is ABOVE the shifted x-axis.</li>
</ul>
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<tr><td class="tr-caption" style="text-align: center;">negative cosine--1st point is a MIN</td></tr>
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<ul>
<li>If the first point says something about "<span style="color: red;"><b>the middle</b></span>" (or the average, equilibrium, at rest, etc.) your graph is most likely a <b><span style="color: red;">sine</span></b> graph. If the object then is pulled down (or something similar) your function is a negative sine. If the object then moves upward, the function is a positive sine.</li>
</ul>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy-L2Mvv8wSMArKo_K3ups8pp_QA6GDZdo6S9NVHVb_BmzuTD75eo6z229_I6QltJHg6A3lDg0AHBElZQX7WwDY0oHQ9FUrT7YzlimIWbCcWiXFzPiHaxGJnNFK0q5Fb2dpB3rl64f9ts/s1600/neg+sin.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="167" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy-L2Mvv8wSMArKo_K3ups8pp_QA6GDZdo6S9NVHVb_BmzuTD75eo6z229_I6QltJHg6A3lDg0AHBElZQX7WwDY0oHQ9FUrT7YzlimIWbCcWiXFzPiHaxGJnNFK0q5Fb2dpB3rl64f9ts/s320/neg+sin.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">negative sine--"middle and down"</td></tr>
</tbody></table>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiK8pjJAPddsUc9u2J04frJqQAolC4WYxX0kYftBqMtj5gGOIHHvQh-SrxDmjSVZZ6te_goRYEmx6QZZtRu7KlIXp5foiU2U1SQOO3mXeaf8U45SGUMn2kGXoXHpclIg5FWiCdqoOwa2IA/s1600/pos+sine.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="167" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiK8pjJAPddsUc9u2J04frJqQAolC4WYxX0kYftBqMtj5gGOIHHvQh-SrxDmjSVZZ6te_goRYEmx6QZZtRu7KlIXp5foiU2U1SQOO3mXeaf8U45SGUMn2kGXoXHpclIg5FWiCdqoOwa2IA/s320/pos+sine.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">positive sine--"middle and up"</td></tr>
</tbody></table>
<div>
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</div>
Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-66530446234806136352012-09-13T21:13:00.003-05:002013-03-27T18:43:06.617-05:00Cool Math Stuff<div class="separator" style="clear: both; text-align: center;">
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<span style="color: red; font-size: large;"><b>A cool thing to watch...</b></span><br />
Vi Hart's work is <i>amazing</i>, and I bet she would approve of the word "mathmagical!" Check out this great video that applies to our trig graphs. What do you think...is pi wrong? Should we use Tau?<br />
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<iframe allowfullscreen="allowfullscreen" frameborder="0" height="315" src="http://www.youtube.com/embed/jG7vhMMXagQ" width="420"></iframe>
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I could spend hours watching all of her videos, but I know you'll love her <a href="http://vihart.com/doodling/" target="_blank">Doodling in Math Class</a> series. Check 'em out!<br />
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<b><span style="color: red; font-size: large;">A cool series to read...</span></b><br />
A modern math superhero and professor, Steven Strogatz, wrote an incredible series a couple years ago called "<a href="http://topics.nytimes.com/top/opinion/series/steven_strogatz_on_the_elements_of_math/index.html" target="_blank">The Elements of Math.</a>" He includes a clip from Sesame Street, compares logarithms to power tools, and had the best titles for each post. Each one of those articles brought my day to at least an 8! :-)<br />
<br />
He just started another series, and the first article, <a href="http://opinionator.blogs.nytimes.com/2012/09/10/singular-sensations/" target="_blank"><i>Singular Sensations</i></a>, was published this week. I'm looking forward to reading the rest of his essays!<br />
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Do you know any other cool math videos, facts, trivia, posts, or links?<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2aTv-SHS9GXVOvfXeCGhlHitsNWpA4D_HO38xDyWSmBJdWamT2ik-aKV0y-pWiWLyHOsb1EmmVLOJBBKAM5ORTRHDg6bBpa1AQNivDm25lRD79sdhtwSMQfPIM-0ZYFtxkDY-BpZ8GE8/s1600/mathmagic.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2aTv-SHS9GXVOvfXeCGhlHitsNWpA4D_HO38xDyWSmBJdWamT2ik-aKV0y-pWiWLyHOsb1EmmVLOJBBKAM5ORTRHDg6bBpa1AQNivDm25lRD79sdhtwSMQfPIM-0ZYFtxkDY-BpZ8GE8/s1600/mathmagic.PNG" /></a></div>
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<br />Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com3tag:blogger.com,1999:blog-279687613385802426.post-3808949196794342432012-09-09T20:53:00.000-05:002012-09-09T20:53:45.956-05:00I Have Learned...<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3z2qj1iqW-LizUDSTw-jwNJ1OOG2Dh-groeRtNFwf2SOnriAG_hg-7j7PJWVaGh7XOKB7cD3UFtZ_yR-65vPWE17SVpP6rfWWYufP1oI2mYy7tHJZQewW4R0XWG54lOzp6RfluYSR2-k/s1600/Lessons+Learned.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br /><img border="0" height="238" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3z2qj1iqW-LizUDSTw-jwNJ1OOG2Dh-groeRtNFwf2SOnriAG_hg-7j7PJWVaGh7XOKB7cD3UFtZ_yR-65vPWE17SVpP6rfWWYufP1oI2mYy7tHJZQewW4R0XWG54lOzp6RfluYSR2-k/s320/Lessons+Learned.jpg" width="320" /></a></div>
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After two weeks of school, what have you learned so far? Thinking specifically about our math class, what have you learned about how our class works, how to prepare for the class, how to complete homework, and how to prepare for a test? What can you do differently this week? How will you prepare for our next test?<br />
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Don't panic if your grade is not what you want at this point. It's OK to make mistakes! Learn from your mistakes! Make new mistakes. :) Do you have any favorite "failure quotes?"<br />
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<h3>
<div style="text-align: center;">
<span style="background-color: white; font-family: Times, 'Times New Roman', serif;"><span style="color: #3d85c6;">“Success is not final, failure is not fatal: </span></span></div>
<span style="color: #3d85c6; font-family: Times, Times New Roman, serif;"><div style="text-align: center;">
<span style="background-color: white;">it is the
courage to continue that counts.”</span><span class="apple-converted-space"> </span></div>
</span><span style="font-family: Times, Times New Roman, serif;"><div style="text-align: center;">
<span style="background-color: white;"><span style="color: #3d85c6;">~Winston Churchill</span></span></div>
<div style="color: red; text-align: center;">
<span style="background-color: white;"><br /></span></div>
<div style="text-align: center;">
<span style="background-color: white;"><span style="color: #e69138;">"If you fell down yesterday,</span></span></div>
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<span style="background-color: white;"><span style="color: #e69138;">stand up today."</span></span></div>
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<span style="background-color: white;"><span style="color: #e69138;">~H.G. Wells</span></span></div>
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Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com44tag:blogger.com,1999:blog-279687613385802426.post-33966811594067549412012-09-02T20:18:00.000-05:002012-09-02T20:18:55.692-05:00Math Is...I loved reading all of your Mathographies! I will re-read them at the end of the six-weeks, at the beginning of the 2nd semester, and probably several other times throughout the year. Thank you for all of your responses! I'm looking forward to a great year with you all as my students.<br />
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Here's a <a href="http://wordle.net/" target="_blank">wordle</a> of your "Math Is..." responses. Some of you created great similes and metaphors, by the way. :)<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEJIvUVBmpf5rFE08K-U8frckOOaA19_0hg4-7uyVcOECFd4Zu1YI6GsbWNzTw43OM1HX94ieIUVQdvlVqCUQ_HvxSDHTVdh5dsoDK1G_KPsR54SoXv7VSO8NXGWrhZc_QoVY-XFyRits/s1600/math+wordle.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="215" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEJIvUVBmpf5rFE08K-U8frckOOaA19_0hg4-7uyVcOECFd4Zu1YI6GsbWNzTw43OM1HX94ieIUVQdvlVqCUQ_HvxSDHTVdh5dsoDK1G_KPsR54SoXv7VSO8NXGWrhZc_QoVY-XFyRits/s400/math+wordle.png" width="400" /></a></div>
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By the way, in our two classes, I think we have student representatives from every organization and sport. I think you were about split 50-50 between which you enjoyed more: algebra and geometry. (I'm more of an algebra person, myself.) I loved seeing this comment in numerous papers: "Math is like a puzzle!" I agree!<br />
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YES, I offer LOTS of tutoring, but you sometimes have to specifically get on my calendar...but I WILL find time for you. And YES, I do offer some extra credit, but I'm still trying to work on my details and changing my philosophy about that.<br />
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I know we're going to have a wonderful year learning from each other! I'm so glad you're in my math class!Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-46661660508266068492012-07-10T16:22:00.000-05:002012-07-10T17:09:22.031-05:00My WHY!<span style="background-color: white;">This is what it is all about...this is why I teach!</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUw4FjUXmvhHSDrEIJa6xWYi-DCPRY-C-HSc06L5P3X0p5y1eXdE4yo7d1ApEmfKqX3A2KjlsJaPTt-nZDYZr4OxDLCYMnZrMtnjYG1lZzRDZVsQktLMOEe6_pjTFxZMW-D8K-VXDQv6w/s1600/Graduation!_010.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="161" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUw4FjUXmvhHSDrEIJa6xWYi-DCPRY-C-HSc06L5P3X0p5y1eXdE4yo7d1ApEmfKqX3A2KjlsJaPTt-nZDYZr4OxDLCYMnZrMtnjYG1lZzRDZVsQktLMOEe6_pjTFxZMW-D8K-VXDQv6w/s320/Graduation!_010.JPG" width="320" /></a></div>
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Check out all of <a href="http://tinyurl.com/lhhs2012grad" target="_blank">these</a> graduation pictures, submitted by our faculty and staff. <br />
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<span style="color: red; font-size: x-large;"><i>Congratulations, Class of 2012!</i></span></h2>
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<span style="color: red; font-size: x-large;"><i><br /></i></span></div>
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P.S.--hope you're enjoying your summer!</div>Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com0tag:blogger.com,1999:blog-279687613385802426.post-11113142472691172492012-04-29T08:57:00.000-05:002013-07-08T10:19:02.800-05:00Learning About LimitsHere's opportunity #2 for test corrections to <i>post for points</i>...and remember, it's all about the learning!<br />
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<div style="text-align: center;">
<span style="font-size: large;">"I am always doing that which I can not do, </span></div>
<div style="text-align: center;">
<span style="font-size: large;">in order
that I may learn how to do it."</span></div>
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</ul>
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<div style="text-align: left;">
Take Picasso's belief to heart when you look over your test and make the corrections. Please address the following in your post:</div>
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</div>
<ol>
<li>For <u>each</u> question where points were deducted, what mistakes did you make? Were the mistakes arithmetic (added, subtracted, simplified etc. incorrectly); algebraic (made a mistake with solving an equation or simplifying); conceptual (missed an idea about limits); or careless? Please be specific, i.e. on #11, I didn't know that <i>indeterminate </i>meant evaluate the limit and get 0/0, so I left that problem blank. OR I made an algebraic mistake on #4 (d) and #9 because I didn't know how to factor those polynomials.</li>
<li>From the problems listed above, please summarize what you have learned from making the corrections. How does Picasso's quote relate to making test (or HW or quiz) corrections? How will this beliefs help you during the last month of school?</li>
<li>When is a time in our math class (any time this year) that you have been proud about your learning? </li>
</ol>
<div>
As always, I look forward to reading your posts! Thanks for taking the time to work and comment. </div>
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<div style="text-align: center;">
<span style="color: red;"><b>All posts are due by Monday, May 7, 9 AM.</b></span><br />
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Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com19tag:blogger.com,1999:blog-279687613385802426.post-21490721464101780122012-03-28T21:11:00.002-05:002012-03-28T21:11:55.392-05:00Kinder Than Necessary<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAhd03SKMcwSkjNk1jRZt17tHqqZayYhVZWXg8F8CKE05i9NfK_6iM7oEP_N8Z5pPWBgU5QvFR0iHP982Ug9fQpq7yEHyBbhRUMYps-X_2Rlmk1MgiaZOWftb8aZ17Ns6bMXVugcpnTxk/s1600/heart.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="132" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAhd03SKMcwSkjNk1jRZt17tHqqZayYhVZWXg8F8CKE05i9NfK_6iM7oEP_N8Z5pPWBgU5QvFR0iHP982Ug9fQpq7yEHyBbhRUMYps-X_2Rlmk1MgiaZOWftb8aZ17Ns6bMXVugcpnTxk/s200/heart.jpg" width="200" /></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"></span><br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: large;"><b>No act of kindness, no matter how small, is ever wasted.</b></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">Ah, that is one of my favorite quotes, attributed to Aesop in his fable, <i>The Lion and the Mouse</i>.</span><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;"></span><span style="font-family: Arial, Helvetica, sans-serif;"></span><span style="font-family: Arial, Helvetica, sans-serif;">Here's an opportunity to post about kindness, but not for points...just to share favorite quotes on kindness, acts of kindness you've seen or initiated, or thoughts about being kind. (Another great quote: Real kindness seeks no return.) Feel free to comment anonymously, since this post is just about happiness, kindness, and positive-stuff. </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">I'm already feeling the love. Pass it on, and don't miss any opportunity to be kind!</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"></span><br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-size: x-large;">Wherever there is a human being, there is an opportunity for a kindness.</b></span></div>
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<o:p></o:p></div>Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com6tag:blogger.com,1999:blog-279687613385802426.post-69762540673280733812012-02-21T17:46:00.000-06:002012-02-21T20:56:15.400-06:00The Importance of Being BilingualStudents in my ESL class are ahead of me...they're bilingual, so they could have helped Lucy!<br />
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<iframe allowfullscreen="" frameborder="0" height="315" src="http://www.youtube.com/embed/Xtbbo_lHqAs" width="420"></iframe><br />
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How has knowing another language helped you? How many languages do you speak?Kathryn Lasterhttp://www.blogger.com/profile/17378376328389008590noreply@blogger.com2