tag:blogger.com,1999:blog-8399389267815059112Tue, 15 Apr 2014 08:20:49 +0000Math at SchoolMSSunFunMade4Mathlesson planningstudent engagementMyFavFridayAlgebraFree Downloadtechnology#MakeOverMondayLinear equationclassroom environmentfunctionsmath stationsFirst Week Activitiesdesmosproblem situationsslopesolving equationssolving systemsDifferentiated InstructionNumber senseSimultaneous equationsformative assessmenthands-on materialsrational functionsEmbedded Formative AssessmentFoldableGamesNotebookingelementary mathexploringMTBoSgoalsorganizationquestioningtextbook revisionCommon Core Math StandardsReviewerror analysisfunction familieshomeworkmotivationprofessional developmentprojectsrational exponentsstudent ownership of learningtransitionAnchor ChartsBeauty of MathClassroom managementCurriculum/StandardsGlobal MathGratitudeI notice I wonderMTBoSMath MunchSmile FileVocabularyabsolute value unitfavoriteslife of a teachermathematics educationmini-postersobservationscaffoldingsolving quadraticsstudent relationships#howtolearnmathCurrentlyEdmodoGraphing storiesHow to Learn MathLinear equationsMentorMobMy Favorite ThingsNotice/WonderOnline PracticeProblem SolvingTutoringTwitterVolumeWord wallalgebra tilescandy cornchangechoicescreativitydonors choosefactoringflipping the classroomfractionsinterceptslaptop initiativemath dialoguemath enrichmentmath practicemath suppliesmatricesparent functionspolynomialspracticepuzzlesschoolskill-based practicesocial mediastudent reflectionstudy skillsteacher evaluationvirtual filing cabinetwriting across the curriculum"donors choose"#Alg2Chat#EduRead#TXEduChat#efamath#hunterstrong180 day blog2048Analyzing GraphsBackwards DesignCarl SandburgCheckerboard BordersChrome Apps/ExtensionsColorCommon AssessmentsDay in the LifeDigital FramesEric JensenFibonnaci SequenceFlubarooFlyswatter ReviewFour QuartetsGoogle formsGoogle siteGraphic organizerHigh-Stakes TestIcebreakersIndependent LearningLiebster AwardLinky PartyMOOCMath LiteratureMath Teachers at PlayMonday Math MomentsNational Security AgencyNinth gradeOffice DepotOreosPascal TrianglePeer tutorPipe CleanersPlatoPoint-slope formPolygonal NumbersQR codeReal Number SystemReflectionSemesterSierpinski's TriangleSingapore MathSpiral ReviewSurface AreaSyllabusSymbalooTS EliotTeach Like a PirateTeacherWebTic Tac ToeYoutubea day in the lifeblog challengebox methodcantileverscard sortchatsclass websitecollaborationcriteria for successcritical thinkingcuriositydirect instructiondiscoursediscover learningdistrict benchmarkdomain and rangedonorschooseend of yearestimation 180exam reviewexamsexplore mathematicsexponential functionfailurefavorite nofire stationfree math poetry rubricfunction transformationsgrab baggradinggrowth mindsetilluminationsindependent/dependent variablesinnovationsinstructional videoskick itlaws of exponentslearning how to learnlinear transformationslist poetrylogarithmsmath assessmentsmath ideasmath in videomath labmid-yearmoviesmy favorite nonew beginningsparabola projectparent contactpatternsperiodic functionplace valuepreparationproject-based learningproperties of logsquadratic functionsrate of changeresearchreview gamesatisfactionscatter plotsschool lunchessliderssolving inequalitiesspoons gamespring breakstandard formstudent giftsteamworktimed flash cardstransformation of linear equationswhiteboardingwhy blogx-puzzleszapAlgebra's FriendMath is beautiful.http://algebrasfriend.blogspot.com/noreply@blogger.com (Beth Ferguson)Blogger206125tag:blogger.com,1999:blog-8399389267815059112.post-7976075305728755001Tue, 15 Apr 2014 02:42:00 +00002014-04-14T21:42:36.207-05:00writing across the curriculumWriting in Math ClassWriting has been a big topic on our campus this year ... a school initiative. Our math coach has stressed improving upon our short constructed responses more than emphasizing the writing of essays.<br /><br />With that in mind our coach shared a few writing frames from science that can be used in math. <a href="https://drive.google.com/a/roundrockisd.org/file/d/0ByJ71RI_wBc7N2hfNDNualFyaHNJZkxWWUlIeWh5aGp0WEpz/edit?usp=sharing">Here are 3 samples!</a> These samples are simplistic but great for teaching structure of writing short responses!<br /><br />We incorporate writing in many activities and all of our tests. Again, our writing prompts are for short responses. Here are some examples from recent activities:<br /><br /><b>From our rational function unit,</b> What is the horizontal asymptote of this function? Show this on the graph. What does this value represent in terms of the prom tickets? Thinking about the cost of the tickets, why does your value for the horizontal asymptote make sense?<br /><b><br /></b><b>From our exponential unit:</b> You have a rich Uncle that gives you $5000 to invest. You have researched two different banks to see which you want to use to help you make the most money. Describe when it would be better to choose MK Federal Credit Union and when it would be better to choose MCB National.<br /><br /><b>From our square root unit: </b>Does doubling the length of the skid double the speed the driver was going? Justify your response using tables, symbols, and graphs.<br /><br /><b>From a recent project, one choice included:</b> Read an article about mathematics or a mathematician in the New York Times (http://topics.nytimes.com/top/news/science/topics/mathematics/). Create a mini-poster that illustrates the article. Include a “3-Part Source Integration” writing. A “3-Part Source Integration” is a three-sentence statement that includes the title of the text, the author’s name, author information, source material that is either paraphrased or directly quoted, and a brief statement explaining the significance of the paraphrase or quotation.<br /><br />We have also written responses on Edmodo to Math Munch postings. Here is <a href="http://algebrasfriend.blogspot.com/2013/10/math-munching-today.html">a blog post</a> where I share students' thoughts. <br /><br />I find that these short writing opportunities provide windows into students' thinking. How do you use short writing prompts?<br /><br />In the article, <a href="http://www-tc.pbs.org/teacherline/courses/rdla230/docs/session_6_brandenburg.pdf">"Advanced Math? Write!"</a> the author stresses to start small. She emphasizes journal writing. I have not tried journal writing with 150 students. Even when I had considerably fewer students I found keeping up with responses to journals challenging. How could I begin journaling with students without feeling overwhelmed?<br /><br /><br /><br /><br />http://algebrasfriend.blogspot.com/2014/04/writing-in-math-class.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-873780898142118023Thu, 10 Apr 2014 23:03:00 +00002014-04-10T18:03:17.589-05:00lesson planningrational functionsRational Functions ... how do you teach them?I thought I'd write about how we structure our rational functions unit. I'm curious what others do with it.<br /><br />(Background ... we are Texas - a non common core state; we have 90 minute classes <u><b>every other </b></u>day)<br /><br />We split the unit into two parts.<br /><br />Part 1<br />Day 1: Data Collection: How is the resulting graph like others we have studied? How is it different? (We start every function unit with a data collection day). For rational functions we used the spaghetti cantilever activity. <a href="http://180snaps.blogspot.com/2014/03/day-128-spaghetti-cantilevers.html">Find it here.</a> Students work in teams, collect data, answer questions about independent, dependent variables, discrete vs continuous functions, and domain and range. Then they try to find a function that fits their data.<br /><br />Day 2: Transformations: Transformations are a huge part of our curriculum and by this time of the year, students are very familiar with how "a," "h," and "k" affect functions. So we start with the basic rational function in transformation form. Students use Desmos to track transformations and describe them. With this day we talk about asymptotes and how they are a major attribute of this function. (Asymptotes were introduced in our exponential/logarithm unit). Last we express the domain and range of functions!<br /><br />Day 3 & 4: We start this day with a review of factoring and how to use factoring to simplify algebraic fractions. Then we being the work of dissecting the attributes of the rational functions based on the factored forms of functions. We start with discontinuities - the vertical asymptotes and holes. Then we discuss the horizontal asymptote; next we find the intercepts; and last we write the domain and range. <br /><br />Day 5: We review ... presenting the content in various ways. <a href="https://drive.google.com/file/d/0ByJ71RI_wBc7MUVySW1qQ1luSms/edit?usp=sharing">Here is a sample.</a><br /><br />Day 6: We test ... this test is short and could be combined with a introductory activity to the second half of the unit. I chose to give my students time to work on their <a href="http://180snaps.blogspot.com/2014/04/day-140-141-short-test-allows-time-to.html">Desmos Creative Art unit</a>.<br /><br />(This is where we are now)<br /><br />Part 2<br />Day 1: Students use their understanding of simplifying algebraic fractions to multiply and divide fractions. This is a skill practice day. We also solve simple rational equations - the factors cancel leaving simple linear equations to finalize. Students play Tic Tac Toe after doing some routine work.<br /><br />Day 2: Students use rational functions in introductory problem solving. This year I am using <a href="http://illuminations.nctm.org/Lesson.aspx?id=1968">Illuminations, "Light It UP" unit</a>. Students will work in groups ... I may help them get started - use leading questions - but then I want them to grapple with the problems themselves as much as possible. I will set up the experiment ... maybe in 2 - 3 stations so that students can do the experiment as well.<br /><br />Day 3: I have to get pumped up for this day ... we will add and subtract algebraic functions and simplify complex fractions. My students are so squeamish about fractions. I would really like to talk with their previous teachers about how fractions were handled in middle school, algebra 1, and geometry. This will be a skills practice day! I'm thinking I will give every student a rational function on an index card. They will partner up with another student - find the sum and difference. Then I'll play a few seconds of music. When the music stops, they partner up again - find the sum and difference again. We may do this 4 or 5 times.<br /><br />Day 4: We solve rational equations. I haven't thought this far yet ... but I'd like to create some form of partner practice that is self-checking.<br /><br />Day 5: We will tackle the more traditional word problems that involve rational functions like rate of work problems.<br /><br />Day 6: I will use this as a catch up day. I know 90 minutes sounds like a long time but it's every other day ... and so often skills that I think we master in our 90 minutes need reviewing.<br /><br />Day 7: This will be our official test review day.<br /><br />Day 8: We will test!<br /><br />This about 5 school weeks! The only other unit that we spend this much time on is the quadratic unit.<br /><br />So ... how do you address rational functions? Do you have any activities that help students with adding and subtracting? What are your favorite application problems for rationals?<br /><br /><br /><br />http://algebrasfriend.blogspot.com/2014/04/rational-functions-how-do-you-teach-them.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-6713802515262562508Tue, 08 Apr 2014 03:15:00 +00002014-04-07T22:15:04.693-05:00creativitydesmosdomain and rangefunction transformationsparent functionsprojectsCreative Art Project Introduced!Yes, some students were ho-hum ... but others ...<br /><br />... explored all the trig functions to see what shapes they would make<br />... imported a picture into Demos to see if he could outline it with equations<br />... discussed the virtues of a single drawing versus a scene<br />... asked if abstract drawings were acceptable<br />... tried a few basic functions and how to limit the domain and range<br /><br />I wish now I hadn't given students 3 whole weeks to complete the project ... I can't wait to see their art!<br /><br />So what is expected and why?<br /><br />Our algebra 2 curriculum is structured around a series of parent functions. We introduce the concept of functions at the beginning of the year. And then we start marching through seven of them! With linear functions we explore systems of equations. Then we look at absolute value functions and how they are related to linear functions. We end our first semester with an intensive study of quadratic functions ... first examining the graph, transformations, and using graphs to solve problems. And then we solve quadratics and problem solve some more.<br /><br />In our second semester we jump into radical equations first since they are inverses of quadratics ... and then we take a detour to study rational exponents. Next up are exponential functions and logarithms. And last we learn about rational functions. That's where we are now. We are finishing our first unit on rationals which is the graphing unit. Then we will simplify, solve, and apply rational functions to word problems.<br /><br />So this creative art project is planned with the purpose of reviewing these seven functions, their transformations, domain, and range. Students must use at least five of the seven studied to create art. Their artwork must have at least 12 equations total but as we discussed today, most will have many, many more.<br /><br />In the past I would have students create this work on paper. BUT oh my, <a href="https://www.desmos.com/">DESMOS</a> to the rescue! How much nicer to have the art online, equations clearly identified, easy to see what students did! Now the focus is on transformations, limiting domain and range ... not on their ability to graph the functions by hand. The thinking process is different ... better from my perspective!<br /><br />Here is <a href="https://drive.google.com/file/d/0ByJ71RI_wBc7bFE0eGlJbGc0VlE/edit?usp=sharing">a link to the handout</a> I gave students. I can't wait to share their work with you all! Check back after April 28!http://algebrasfriend.blogspot.com/2014/04/creative-art-project-introduced.htmlnoreply@blogger.com (Beth Ferguson)2tag:blogger.com,1999:blog-8399389267815059112.post-1419583672536764861Tue, 08 Apr 2014 03:01:00 +00002014-04-08T13:07:35.340-05:00#Alg2Chat#EduRead#TXEduChatchatsTwitterTwitter Chats - getting the hang of them!Last night it was <a href="http://bit.ly/1mWXTY3">#TXEduChat</a> ...<br />Tonight it was <a href="http://bit.ly/1hyuwGf">#Alg2Chat</a> ...<br />On April 23, <a href="http://readchatreflect.blogspot.com/">#EduRead</a> is coming ...<br /><br />First I found the chats overwhelming.<br />Fast scrolling text, words I wanted to read but couldn't quite catch ... <br />Then just being a novice at Twitter ...<br />Figuring out which icon responded, which one retweeted, which one favorited ...<br /><br />Next wanting to jump in ...<br />But feeling intimidated by such engaged professionals ...<br />Not sure if my thoughts are outdated ...<br /><br />And then it came together ...<br />I said something ... someone favorited it, retweeted it, commented back ...<br />I was on my way ...<br /><br />Now I want evenings free for the chats ...<br />How can I accomplish that!?!<br /><br />A benefit of the chats is hearing what others are doing in their math classes.<br /><br />As others talk about their curriculum, I am realizing that I like our Algebra 2 curriculum more and more. While I think it's fast and somewhat crowded, it has a certain rhyme/reason to it. And it's making sense to me ... and hopefully to our students.<br /><br />I'm learning what technology tools others are using ... and feeling validated ... and challenged to explore more!<br /><br />Folks are discussing student engagement, growth mindset, and how these apply to the classroom. How to make them happen. Collaboration, Creativity were recent topics ... great thought provoking discussion!<br /><br />So now to share with my colleagues in the brick and mortar building ... there is a world of engaging, purposeful conversation in our profession ... come join me!<br /><br /><br />http://algebrasfriend.blogspot.com/2014/04/twitter-chats-getting-hang-of-them.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-1249951605641774497Mon, 07 Apr 2014 02:15:00 +00002014-04-07T21:43:30.753-05:002048desmosilluminationsrational functionsExcuses! 2048! Testing! Spring Fever!I have neglected blogging lately! It could be due to playing 2048 too much! A moment of honesty ... my students were winning and I hadn't won yet. I would get frustrated; make wrong moves. So I had to keep playing to win at least once!<br /><br />Second reason for not blogging is the crazy schedule for the past week and a half. Two days of STAAR testing messed with several days of class. Finally I think we are back on a regular schedule - all students should be ready for their unit test on attributes of rational functions on Tuesday.<br /><br />Even with the above excuses and a heavy case of spring fever, I am excited about the <a href="http://algebrasfriend.blogspot.com/2014/03/working-on-instructions-for-project-in.html">Desmos creative art project </a>I just assigned to students. The students seemed excited too. I can't wait to see their creations. The purpose of the project is to review the seven parent functions we have studied, their transformations, as well as the necessary emphasis on domain and range. Projects will be posted towards the end of April.<br /><br />We are about to embark on solving rational equations and applying those skills to word problems. I'm still working on lesson plans but I know we will use <a href="http://illuminations.nctm.org/Lesson.aspx?id=1968">Illuminations problems</a> from the activity Light It Up.<br /><br />If you have good ideas about how to teach students who recoil from factions how to add and subtract algebraic ones, I'd love to hear your thoughts!http://algebrasfriend.blogspot.com/2014/04/excuses.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-3958322916060569243Sat, 22 Mar 2014 14:03:00 +00002014-03-22T09:05:03.095-05:00creativitydesmosparent functionsprojectsWorking on Instructions for Project in DesmosI'm working on instructions and a rubric for students' project in <a href="https://www.desmos.com/">Desmos</a>. The purpose of the project is to review<a href="http://algebrasfriend.blogspot.com/2013/09/made4math-parent-function-review.html"> the seven parent functions</a> we have studied and to give students an opportunity to demonstrate creativity with those functions. A key skill will be limiting domain and range.<br /><br />I don't have the rubric yet ... it needs to be simple.<br />Here are the instructions for the project. I would love your feedback!<br /><br /><br /><div style="text-align: left;"><br /></div><iframe height="640" src="https://docs.google.com/file/d/0B-1saJM8fLPgNFhNbUU3VkttV0k/preview" width="540"></iframe> http://algebrasfriend.blogspot.com/2014/03/working-on-instructions-for-project-in.htmlnoreply@blogger.com (Beth Ferguson)2tag:blogger.com,1999:blog-8399389267815059112.post-3523310696170140257Fri, 21 Mar 2014 02:50:00 +00002014-03-20T21:50:08.377-05:00desmoslesson planningrational functionsLesson Planning - Rational Functions continuedDay 1 on Rational Function is tomorrow.<br /><br />Students will share their research on cantilevers. That will take only a few minutes. I want students to think briefly about the possible variables in designing a cantilever.<br /><br />Then we will build our own spaghetti cantilevers. Students will measure the deflection in centimeters as they hang a weight on the end of spaghetti. The variable will be the number of spaghetti pieces. We will start with just one piece, then a bundle of 2 pieces, then 3, 4, 5, up to 8 pieces of spaghetti. If our data collection is clean we will get data that creates a rational function curve. This activity will serve as the introduction to the function. <br /><br />As we analyze our data, I want to make a connection to the concept of reciprocals. We will examine the linear parent function and what happens when we graph it's reciprocal.<br /><br />Last, I've prepared a guide for students to <a href="https://drive.google.com/file/d/0B-1saJM8fLPgaTgzYWs1WG5adDg/edit?usp=sharing">examine the transformations</a> - what happens to the parent function when a, h, or k are involved using desmos. I'm hoping students will have time to start the exploration in class and will finish it for homework.http://algebrasfriend.blogspot.com/2014/03/lesson-planning-rational-functions_20.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-5211927137944742355Thu, 20 Mar 2014 02:51:00 +00002014-03-19T21:52:53.351-05:00cantileversprojectsrational functionsMicro-Project: Cantilevers!This semester one of my goals is to give students opportunities to work on mini-projects - mostly one-page explorations of math outside of the typical curriculum. I wrote about the one we did in <a href="http://algebrasfriend.blogspot.com/2014/02/mini-project-and-lesson-planning.html">February here</a>. (I wanted to share some of these but I didn't ask students to leave their last names off of the projects ... learning that if I want to post their work, I have to specify first names only).<br /><br />Today I gave students a "micro" project ... smaller, shorter than even a mini project!<br /><br /><br />We start Rational Functions on Friday. We are going to start our unit with a math lab to collect and analyze data. The lab on Friday uses spaghetti to make a cantilever. We'll measure the deflection as we increase the number of pieces of spaghetti.<br /><br />I suspected that students might not know what a cantilever is. So I asked them to find an interesting example of a cantilever. I created template slides in Google Presentation. Each student puts their fascinating find on a slide with the link to the picture and a short blurb about the cantilever.<br /><br />After a short test today, students had time to begin their work. Already nearly half of my students have created their slide. Here are examples (I haven't proofed these) ... <br /><br /><br /><iframe allowfullscreen="true" frameborder="0" height="480" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/1N1c7IQcJ9tNC0u5W62E8JExI6EfAE3bic09-hw-LdQM/embed?start=false&loop=false&delayms=3000" webkitallowfullscreen="true" width="560"></iframe> <br /><br /><br />A couple of the students as leaving today "made fun" of how easy this homework is. I'm OK with that. Now when we work with our spaghetti on Friday we will have some visual ideas of cantilevers and the variables involved in making them work!<br /><br />Our next project ... using our seven parent functions to create a work of art in Desmos!http://algebrasfriend.blogspot.com/2014/03/micro-project-cantilevers.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-6205430069454884415Tue, 18 Mar 2014 03:08:00 +00002014-03-17T22:08:45.234-05:00lesson planningrational functionsLesson Planning Rational FunctionsI participated tonight in the <a href="http://sfy.co/ccR8">@alg2chat</a>! I often have plans to participate but too often get caught up in evening activities. I'm glad I took the time tonight to visit ... definitely will do so next week as well!<br /><br />In our chat teachers mentioned having just completed the Rationals unit and students having difficulty with it. Since we begin Rational Functions on Friday, I was all ears! It's been several years since I taught Algebra 2 so every unit is a new adventure for me.<br /><br />I know as we get into solving rational equations that students will struggle with the algebraic manipulation. We have a couple of weeks before we get to that part. As if our custom with each parent function we start first with the graph ... <br /><br />As the discussion progressed, <a href="http://www.jensilvermath.com/">Jen Silverman</a> shared a couple of activities from a precalculus class. One of them caught my eye. The document was a discussion starter. It had several graphs and equations with this question: Make as many connections between the equation and the graph as you can.<br /><br />That was just the kind of open ended question I've been looking for as a way to start the thought process about rational functions. The equations on her document were more difficult than the ones we will study. So I simplified ... and scaled down to just one graph, one question, one discussion.<br /><br />Here is <a href="https://drive.google.com/file/d/0B-1saJM8fLPgTzl4VWE2WEIteTA/edit?usp=sharing">my copy of the activity</a>. http://algebrasfriend.blogspot.com/2014/03/lesson-planning-rational-functions.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-1722301690748949783Sun, 16 Mar 2014 22:48:00 +00002014-03-16T17:48:53.373-05:00lesson planningproperties of logsLesson Planning ... spring break is over ...Long breaks spoil me ... can't say I'm ready to go back to school ... I know once I get there I'll be fine :)<br /><br />So this weekend as I was looking over my plans for Monday I was not satisfied with what I had. The topic of the day is properties of logs. I decided to visit math blogs to see what others had done with this topic. I found many ideas. Here are my plans for tomorrow:<br /><br />Lesson Plan March 17<br /><br />1) Opening Activity: We may share spring break stories ... or I might show this <a href="http://youtu.be/CXmxooGQ_Dg">3 minute video</a> on St Patrick's Day little known facts! I also love this infographic - <a href="http://www.history.com/topics/st-patricks-day/history-of-st-patricks-day/interactives/st-patricks-day-by-the-numbers">St. Patrick's Day By the Numbers</a>!<br /><br />2) Warm-Up with<a href="http://algebrasfriend.blogspot.com/2014/02/logarithm-flash-cards-timed-powerpoint.html"> this powerpoint</a> ... practicing just a little bit of mental math related to logs.<br /><br />3) Discovery Discussion of Properties of Logs using <a href="http://function-of-time.blogspot.com/2010/12/log-laws.html">Kate's outline</a>.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-1wBCyajsTco/UyYoVaNGiAI/AAAAAAAAJOE/DgXeg1OpIrc/s1600/IMG_20140316_162424_325.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://2.bp.blogspot.com/-1wBCyajsTco/UyYoVaNGiAI/AAAAAAAAJOE/DgXeg1OpIrc/s1600/IMG_20140316_162424_325.jpg" height="180" width="320" /></a></div>4) For practice I created <a href="https://drive.google.com/file/d/0B-1saJM8fLPgZk5nN2R4RzQ3dG8/edit?usp=sharing">4 sets of problems</a>. In each set there are six problems to condense and six problems to expand. I orchestrated the problems so that the condensing and expanding are the same problems. Students will work the problems on the cards they choose. Then students with the same colors will get together and check their work making sure their answers match the problems on the A and B cards. We will do a second round, so students will swap colors with a classmate and repeat the process.<br /><br />5) Last I have a typical routine worksheet for students to complete.<br /><br />Students will take a short test on properties of logs in their next class.<br /><br />We tried to finish our unit on Exponentials and Logs before spring break but didn't quite make it. This is the last topic in the unit. Rational (or Reciprocal) Functions are up next!http://algebrasfriend.blogspot.com/2014/03/lesson-planning-spring-break-is-over.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-6355539920481362133Thu, 13 Mar 2014 14:54:00 +00002014-03-13T09:54:18.956-05:00rational functionsspring breakSpring BreakThis week is Spring Break - and yes, it's almost over. The tension creeps up my neck as I type those words! Spring Break came a bit early this year, but it was very much needed ... by teachers and students!<br /><br />So this week ...<br /><br /><ul><li>Shopping for furniture for our newly enclosed patio</li><li>Creating a special gift for my niece who is getting married in April</li><li>Discovering the joy (and trials) of Legos as my 4 year old grandson's eyes light up</li><li>Reading - thanks to free books identified by <a href="https://www.bookbub.com/">BookBub</a></li><li>Catching up on MTBoS bloggers and their classroom activities</li><li>Gardening ... putting potatoes and tomatoes in the raised bed boxes</li><li>Eating out ... finding 1/2 price appetizers at Jack Allen's Kitchen to be amazing</li></ul><div>And yes, thinking about our next unit in Algebra 2 ... rational functions. I'll write more about it in a separate post. We'll start with creating spaghetti cantilevers to collect data and analyze. Then we will head over to Desmos to observe rational functions on the graph and identify attributes/transformations. The notes needed seem heavy ... I've been thinking about how to organize them for students. And that's as far as I've gotten!</div><div><br /></div><div>And now to relish the remaining hours of spring break ... </div>http://algebrasfriend.blogspot.com/2014/03/spring-break.htmlnoreply@blogger.com (Beth Ferguson)1tag:blogger.com,1999:blog-8399389267815059112.post-1018983527253815399Thu, 06 Mar 2014 03:28:00 +00002014-03-05T21:34:13.384-06:00desmosdirect instructiondiscover learningWeaving short discovery activities in with direct instructionLisa wrote <a href="http://www.teachesmath.com/?p=592">this blog post</a> recently on using less direct instruction in math class.<br /><br />The math community online often blog about the discovery activities, the explorations, the big activities. But often we don't discuss clearly how direct instruction and those activities are intertwined. We discuss even less the day to day details when we are working on the ordinary, the nitty gritty! I had hoped <a href="http://180snaps.blogspot.com/">my 180 blog</a> would have more depth, be more reflective, even about the ordinary days but I find that really difficult. One of my goals is to learn how to reflect better on those ordinary days!<br /><br />I structure my class typically one of two ways. After our warm-up or knowledge check, I invite students to engage in a short discovery activity. I follow that up with specific notes and then additional practice. The other structure I use is starting with notes first and then group practice that has a self-checking mechanism built in.<br /><br />Finding short discovery activities is a challenge. I am learning to use Desmos as we explore each of the required functions in our curriculum. Setting up an exploratory activity to identify transformations on Desmos is easy and engaging!<br /><br />When introducing exponential functions, we started with a very short activity. I gave students this problem:<br /><br /><i>Each spring, the nation’s top 64 college basketball teams are invited to play in the NCAA tournament. When a team loses, it is out of the tournament. Complete the following on your own.</i><br /><ol><li><i>How many teams are left in the tournament after the first round?</i></li><li><i>Create a table to show the number of rounds and the number of teams left at the end of each round. </i></li><li><i>How many rounds of games must be played?</i></li><li><i>Graph the points from the table on the grid below. </i></li><li><i>Examine the graph. Is the function linear? Quadratic? Other? Be ready to explain.</i></li><li><i>If the table was extended indefinitely, what would happen to the y-value?</i></li></ol><div>After students worked on this activity for just a few minutes, I asked them to share their work with their table groups. I asked students to specifically discuss #5. Then I asked groups to share their description of the graphs they created. Their descriptions were the lead-in to my direct instruction about basic attributes of the exponential function.</div><div><br /></div><div>After basic notes, it was time to explore our work on Desmos. I gave students this basic form:</div><div><br /></div><div><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: inherit;"><i>Use <a href="https://www.desmos.com/calculator">https://www.desmos.com/calculator</a> to explore exponential and log functions</i></span></div><div class="MsoNormal"><br /></div><table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;"> <tbody><tr> <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319"><div align="center" class="MsoNormal" style="text-align: center;"><b><span style="font-size: 12pt;"><span style="font-family: inherit;">What to enter in the calculator<o:p></o:p></span></span></b></div></td> <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 301.5pt;" valign="top" width="402"><div align="center" class="MsoNormal" style="text-align: center;"><b><span style="font-size: 12pt;"><span style="font-family: inherit;">Describe what happens in this column</span><span style="font-family: Verdana, sans-serif;"><o:p></o:p></span></span></b></div></td> </tr><tr style="height: .5in; mso-yfti-irow: 1;"> <td style="border-top: none; border: solid windowtext 1.0pt; height: .5in; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" width="319"><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-size: 12pt;"><span style="font-family: inherit;">Enter b<sup>x</sup>and use the slider “b”<b style="font-style: italic;"><o:p></o:p></b></span></span></div><div class="MsoNormal"><b style="text-align: center;"><i><span style="font-size: 12pt;"><sup><span style="font-family: inherit;"><br /></span></sup></span></i></b></div><div align="center" class="MsoNormal" style="text-align: center;"><b><i><span style="font-size: 12pt;"><span style="font-family: inherit;"><o:p></o:p></span></span></i></b></div></td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: .5in; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 301.5pt;" width="402"><div class="MsoNormal"><br /></div></td> </tr><tr style="height: .5in; mso-yfti-irow: 2;"> <td style="border-top: none; border: solid windowtext 1.0pt; height: .5in; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" width="319"><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-size: 12pt;"><span style="font-family: inherit;">Enter 2<sup>x-h </sup>and use the slider “h”<b style="font-style: italic;"><o:p></o:p></b></span></span></div></td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: .5in; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 301.5pt;" width="402"><div class="MsoNormal"><br /></div></td> </tr><tr style="height: .5in; mso-yfti-irow: 3;"> <td style="border-top: none; border: solid windowtext 1.0pt; height: .5in; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" width="319"><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-size: 12pt;"><span style="font-family: inherit;">Enter 2<sup>x</sup>+ k and use the slider “k”<b style="font-style: italic;"><o:p></o:p></b></span></span></div></td><td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: .5in; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 301.5pt;" width="402"><span style="font-family: inherit;"><br /></span></td></tr><tr style="height: .5in; mso-yfti-irow: 4; mso-yfti-lastrow: yes;"><td style="border-top: none; border: solid windowtext 1.0pt; height: .5in; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" width="319"><div class="MsoNormal" style="text-align: center;"><span style="font-size: 12pt;"><span style="font-family: inherit;">Enter a * 2<sup>x</sup>and use the slider “a”<b style="font-style: italic;"><o:p></o:p></b></span></span></div></td> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: .5in; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 301.5pt;" width="402"><div class="MsoNormal"><br /></div></td> </tr></tbody></table><div class="MsoNormal"><br /></div><div align="center" class="MsoNormal" style="text-align: center;"><i><span style="font-size: 12pt;"><span style="font-family: inherit;">Use this activity to prepare to explain how a, h, and k affect the exponential function. You can also view other bases; I used 2, but you could use any other number! After completing the basic transformations, try creating equations with multiple transformation on your own. Record your work.</span></span></i></div></div><div><br /></div><span style="font-family: inherit;">After exploring the effects of a, h, and k, and discussing their results with their partners, I pulled the class together again to emphasize a few key points in the form of direct instruction. Students took notes.</span><br /><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">We ended the class with questions something like these:</span></div><div><span style="font-family: inherit;"><span style="font-size: 12pt; text-indent: -0.25in;">1)<span style="font-size: 7pt;"> </span></span><span style="font-size: 12pt; text-indent: -0.25in;">Given the function 2<sup>(x+4)</sup>-3, write the new equation if this equation were translated up 4 units, left 1 unit and vertically compressed by 2/3.</span></span></div><div><span style="font-family: inherit;"><span style="font-size: 12pt; text-indent: -0.25in;">2)<span style="font-size: 7pt;"> </span></span><span style="font-size: 12pt; text-indent: -0.25in;">Given the function (1/4)<sup>(x-2)</sup> + 5, write the new equation if this equation were translated left 3 units and down 1 unit.</span></span></div><div><span style="font-family: inherit;"><span style="font-size: 12pt; text-indent: -0.25in;">3)<span style="font-size: 7pt;"> </span></span><span style="font-size: 12pt; text-indent: -0.25in;">Given the function -3<sup>(x -7)</sup> – 2, write the new equation if this equation were reflected across the x- axis, translated right 3 units and up 3 units.</span></span></div><div><span style="font-family: inherit; font-size: 12pt; text-indent: -0.25in;"><br /></span></div><div><span style="font-family: inherit; font-size: 12pt; text-indent: -0.25in;">On the next day we started with notes, learning to differentiate between exponential growth and exponential decay. I demonstrated how to solve problem situations involving exponential functions using graphs. The notes were short/sweet. I then gave students problems to solve as partners. </span></div><div><span style="font-family: inherit; font-size: 12pt; text-indent: -0.25in;"><br /></span></div><div><span style="font-family: inherit; font-size: 12pt; text-indent: -0.25in;">We used a similar format to introduce logarithms. Instead of a problem situation to create the first graph as in the March Madness example, we used the concept of inverses to invite students to "discover" the basic attributes of the logarithm function. The process was similar - next we went to Desmos to consider the transformations. And last we worked on problem solving using graphs and tables.</span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">Weaving in and out of short discovery activities, following up with notes and practice seems to be effective. I do have some students who want me to give them notes straight up without having to grapple with the math first. They were quite clear about that in my first semester reflection piece. And I understand that they feel tentative and are fearful of making mistakes. It is for that very reason I don't give up on providing short discovery activities.</span></div><div><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /></div>http://algebrasfriend.blogspot.com/2014/03/weaving-short-discovery-activities-in.htmlnoreply@blogger.com (Beth Ferguson)2tag:blogger.com,1999:blog-8399389267815059112.post-2291706398335319186Wed, 05 Mar 2014 03:25:00 +00002014-03-04T21:25:28.432-06:00Anchor Chartsexam reviewAnchor Charts - Logs<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-wZkY0R3FBLo/UxaYTdy6lMI/AAAAAAAAJDE/-i7Oh85BEyY/s1600/IMG_20140304_163921_384+(1).jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-wZkY0R3FBLo/UxaYTdy6lMI/AAAAAAAAJDE/-i7Oh85BEyY/s1600/IMG_20140304_163921_384+(1).jpg" height="320" width="276" /></a></div><br /><br />We reviewed solving exponential equations with logs today.<br /><br />We haven't created many anchor charts this year - but we created this one today.<br /><br />It makes me wish we had created at least one with each unit.<br /><br />Maybe we will do that as an exam review activity!http://algebrasfriend.blogspot.com/2014/03/anchor-charts-logs.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-2745901693974803690Mon, 24 Feb 2014 17:39:00 +00002014-02-24T14:53:15.517-06:00district benchmarkerror analysismy favorite noAnalyzing Data<div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">We are taking the District Benchmark test today. We are on an A/B schedule … so half of my students took the test on Friday. The answers are mostly multiple choice and can be scanned so I have the results of their tests to think about today while these students test.<span style="font-size: small;"><o:p></o:p></span></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;"><br /></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">The district created the test to address content from November, December, and January. I thought the questions were mostly fair but also challenging. Only one question addressed a topic we have not yet taught.<o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;"><br /></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">We took the test “cold.” Students knew about the test, and they knew the topics it covered. I pointed them to some previous work we had done, a couple of test reviews, but I did not require a review. They also know that our PLC typically records the Benchmark test as a quiz grade.<o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;"><br /></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">The class averages from Friday are OK but not as high as I had hoped they would be. They range from 73 to 79. For advanced students I expected class averages in the 80s. I am wondering what my colleagues’ averages are.<o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;"><br /></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">The scoring machine produces really nice reports. I have an item analysis for the first group of students. Interestingly enough the 4 most missed problems all share some strong similarities and connect geometry with algebra. Here are problems like the ones on the test … </span><span style="font-size: small;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-size: 12.0pt;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="background-color: white; background-position: initial initial; background-repeat: initial initial; font-family: inherit;">The owner of a ranch decides to enclose a rectangular region with 140 feet of fencing. To help the fencing </span></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-Et6YxjWtHvM/UwuDAR21FVI/AAAAAAAAI-c/yAARw_PTYTk/s1600/Q+1.PNG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-family: inherit;"><img border="0" src="http://1.bp.blogspot.com/-Et6YxjWtHvM/UwuDAR21FVI/AAAAAAAAI-c/yAARw_PTYTk/s1600/Q+1.PNG" height="101" width="320" /></span></a></div><span style="font-family: inherit;">cover more land, he plans to use one<span class="apple-converted-space"> </span></span><span style="font-family: inherit;"><a href="https://www.blogger.com/null"><span style="color: windowtext;">side</span></a><span class="apple-converted-space"><span style="background: white;"> </span><span style="background: white;">of his barn as part of the enclosed region. What is the maximum<span class="apple-converted-space"> </span></span></span><a href="https://www.blogger.com/null"><span style="color: windowtext;">area</span></a></span><span class="apple-converted-space"><span style="font-family: inherit;"><span style="background-color: white;"> </span><span style="background-color: white;">the rancher can enclose?</span> Only on our test, students were given the equation and asked for the domain of the problem situation. I’m surprised at these results.</span><span style="font-size: small;"><o:p></o:p></span></span><br /><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-size: 12.0pt;"><span class="apple-converted-space"><br /></span></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-size: 12.0pt; mso-no-proof: yes;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/></v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:271.5pt;height:81pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="file:///C:\Users\e131969\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png" o:title="" croptop="2900f"/></v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span style="font-size: 12.0pt;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-I9EepCLkXLI/UwuDARbfPOI/AAAAAAAAI-g/YDrL4WNoo-w/s1600/Q+2.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-I9EepCLkXLI/UwuDARbfPOI/AAAAAAAAI-g/YDrL4WNoo-w/s1600/Q+2.PNG" height="100" width="320" /></a></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">The second most missed problem is similar in concept: </span><span style="background-color: white;"><span style="font-family: inherit;">A rectangular garden is surrounded by a walk of uniform width. If the dimensions of the garden plus the walk are 16 yards by 24 yards, find an equation to represent the area of the walkway. Again it is clear from these results that students are confused. In this problem the confusion may be more about simplifying the math, keeping negative signs straight, than about setting up the equation. It’s difficult to tell since I don’t have their work to study.</span><span style="font-size: small;"><o:p></o:p></span></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">The third most missed problem is similar yet again but not. This one requires them to remember and apply</span></div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-tTYzWZzc9Lw/UwuDAerT-YI/AAAAAAAAI-k/4WmkkgvJ9tI/s1600/Q+3.PNG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-family: inherit;"><img border="0" src="http://2.bp.blogspot.com/-tTYzWZzc9Lw/UwuDAerT-YI/AAAAAAAAI-k/4WmkkgvJ9tI/s1600/Q+3.PNG" height="103" width="320" /></span></a></div><span style="font-family: inherit;">the Pythagorean Theorem as well as the target skill of squaring binomials. Suppose a rectangle has a length of 3x – 4 and a width of x + 2. Which expression best describes the length of the diagonal of the rectangle? These results are more polarized … may be easier to correct the error in thinking on this one.</span><o:p></o:p><br /><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-size: 12.0pt; mso-no-proof: yes;"><!--[if gte vml 1]><v:shape id="Picture_x0020_7" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:270pt; height:84.75pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="file:///C:\Users\e131969\AppData\Local\Temp\msohtmlclip1\01\clip_image005.png" o:title=""/></v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span style="font-size: 12.0pt;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-size: 12.0pt;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-NAuWlJto3NE/UwuDAwxnzYI/AAAAAAAAI-s/iiOeuU_arK8/s1600/Q+4.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-NAuWlJto3NE/UwuDAwxnzYI/AAAAAAAAI-s/iiOeuU_arK8/s1600/Q+4.PNG" height="100" width="320" /></a></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">The last problem involves the area of a triangle. The base of a triangle is 3 inches more than twice its height. If the area of the triangle is 64 square inches, which of the following equations can be used to find h, the height of the triangle? Again as in the previous problem the answers selected are polarized and I can see that students forgot to multiply “64” by 2 in finishing up the problem. </span><span style="font-size: small;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-size: 12.0pt; mso-no-proof: yes;"><!--[if gte vml 1]><v:shape id="Picture_x0020_10" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:264.75pt; height:84pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="file:///C:\Users\e131969\AppData\Local\Temp\msohtmlclip1\01\clip_image007.png" o:title=""/></v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span style="font-size: 12.0pt;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-size: 12.0pt;"><br /></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit; font-size: 12.0pt;">I’ll use these problems on our next “My Favorite No” activity although I won’t have student work for students to examine. I plan to use the graph though … and ask students to discover what mistakes were made that would cause their classmates to choose the incorrect answers that were chosen.<o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;"><br /></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-size: 12.0pt;"><span style="font-family: inherit;">Taking the time to reflect on these four problems this morning while my students are testing has been a beneficial use of my time. Now I need to finish up tomorrow’s lesson plans!</span><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div><br /><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div>http://algebrasfriend.blogspot.com/2014/02/analyzing-data.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-6279680381004230416Mon, 24 Feb 2014 02:42:00 +00002014-02-23T21:43:55.041-06:00logarithmstimed flash cardsLogarithm Flash Cards - timed powerpointIn preparation for teaching students how to solve log equations, I know they have to simplify basic logs. I saw this Log War Game <a href="http://oldmathdognewtricks.blogspot.com/2012/05/my-version-of-log-wars.html">here</a> and <a href="http://function-of-time.blogspot.com/2009/03/this-game-really-is-worth-1000.html">here</a>. I am making the Log War Game cards but decided to also create a timed powerpoint for students to practice on their own. So I used the cards I found online to create this activity ... hope someone else finds it useful! Thankful for the online community that shares so much!<br /><br />Here is a <a href="https://drive.google.com/file/d/0ByJ71RI_wBc7YmE2VFBiM1lyN0E/edit?usp=sharing">link</a> for ease in downloading.<br /><br /><br /><iframe height="480" src="https://docs.google.com/a/roundrockisd.org/file/d/0ByJ71RI_wBc7MzZZYk5JOVV1bXc/preview" width="480"></iframe>http://algebrasfriend.blogspot.com/2014/02/logarithm-flash-cards-timed-powerpoint.htmlnoreply@blogger.com (Beth Ferguson)4tag:blogger.com,1999:blog-8399389267815059112.post-1599785963420323996Mon, 24 Feb 2014 02:17:00 +00002014-02-23T20:18:21.670-06:00explore mathematicsmini-postersMini-Project and Lesson PlanningThis week I want to get back into my blogging routine.<br /><br />I gave a unit test last Wednesday and Thursday on the attributes of exponential and logarithm functions. Friday and Monday are are given to the district benchmark test.<br /><br />Then TUESDAY .... we just into solving exponential and logarithm functions. I am working on last minute plans for the unit!<br /><br />So with the long testing sequence, I decided to assign a mini-project. I borrowed ideas from <a href="http://fawnnguyen.com/2013/09/04/20130903.aspx">Fawn </a>and from <a href="http://samjshah.com/2014/02/12/explore-mathematics/">Sam</a> to create a very similar mini-project assignment.<br /><br /><br /><iframe height="480" src="https://docs.google.com/a/roundrockisd.org/file/d/0ByJ71RI_wBc7bWVyNWZRaW1rTDg/preview" width="480"></iframe> <br /><br /><iframe height="480" src="https://docs.google.com/a/roundrockisd.org/file/d/0ByJ71RI_wBc7azVDTmFSSHU4dm8/preview" width="480"></iframe><br /><br />This is a very specific homework assignment ... requiring students to explore some math beyond our typical curriculum. <br /><br />Already a few students have sent their work via email. A couple of them worked on a post from <a href="http://mathmunch.org/2013/04/30/ted-bridges-and-silk/">Math Munch</a> and explored the app called <a href="http://weavesilk.com/">Silk</a>. Oh what fun! Because students talked about it, I had to go to Silk ... I <a href="http://r.weavesilk.com/?v=4&id=gapi4snive">created a flower </a>and loved it!<br /><br />Tuesday is coming fast ... I know I'm starting with <a href="http://www.mathalicious.com/">Mathalicious</a>, iPod dPreciation! From there ... hmmm ...http://algebrasfriend.blogspot.com/2014/02/mini-project-and-lesson-planning.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-3698639585671881460Thu, 30 Jan 2014 04:06:00 +00002014-01-29T22:06:47.089-06:00exponential functionobservationPlanning ... again and again!The icy blast messed with my observation lesson. Maybe just as well since I am not pleased with the results of flipping this short unit on rational exponents. I am still reflecting on the process. What did I do that I could have done better? What didn't I do that I should have done? Flipping lessons is not an easy process to be sure!<br /><br />And so now ... I am planning the next unit ... and the lesson that will be observed! The lesson to be observed is our introductory lesson to the exponential function. Typically in our course of study, we introduce each function with a data collection day. My PLC has chosen an M and M activity that simulates the growth of cancer cells as well as the loss of cells when in therapy. I will use that activity as well but I want to set the stage for students before we jump into the counting (and eating) of M and Ms.<br /><br />I'm thinking about leading with this question, "What do a feature film, talent scout, disease and mythbuster share in common? What do they have to do with math?"<div><br /></div><div>More tomorrow ... as I ponder the details, how to order my ideas, how to engage students in meaningful work, and how to demonstrate to my administrator that I "get" the school initiatives!</div>http://algebrasfriend.blogspot.com/2014/01/planning-again-and-again.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-3612346479281328654Tue, 28 Jan 2014 01:30:00 +00002014-01-27T21:56:36.005-06:00card sorterror analysismath stationsrational exponentsRational Exponents - continued sagaMaybe I'm expecting too much.<br /><br />Most students did take notes from videos or a powerpoint that I provided before coming to class. But then in class today, they struggled quite a bit understanding how to use the Laws of Exponents. Some students persevered but others were so ready to give up!<br /><br />Their classwork involved progressively more difficult practice. <br /><br />They started with Manga High to engage them in the basics about rational exponents. With a little work, most students mastered the work on Manga High.<br /><br />Then I created a card sort - <a href="https://drive.google.com/file/d/0B-1saJM8fLPgYXlZWk9UWEw1dUU/edit?usp=sharing">here is a copy</a>. After students got over the shock of having to add/subtract fractions with different denominators, they were able to sort the cards into groups. My advanced students really stress over the concept of fractions!<br /><br />Last, we made a huge leap to more difficult problems - requiring multiple simplifying steps. I used Kuta to develop a practice worksheet, transferred those problems to a "search and shade" activity that I found online. The shading/coloring is optional but offered for those who like that sort of thing. It was at this point that students were ready to give up. Did I go too deep too soon?<br /><br />I am not satisfied that students can do this work on their own. We get one more class day before the test. On that day I have to be sure they can solve equations with rational exponents. It's a lot for such a short teaching time.<br /><br />I plan to use these error analysis activities to reinforce solving skills ... <a href="http://exponentialcurve.blogspot.com/2009/09/algebra-2-error-analysis.html">here</a>, <a href="http://www.carlisleschools.org/webpages/wolfer/files/activity%20exponents%20error%20analysis.pdf">here</a>, and also Regents Prep which seems to be down today!<br /><br />Hopefully in our next class I'll see more growth.<br /><br />I am often at odds with our curriculum calendar that expects students to master challenging concepts in short amounts of time!http://algebrasfriend.blogspot.com/2014/01/rational-exponents-continued-saga.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-7986033401641191516Fri, 24 Jan 2014 23:40:00 +00002014-01-24T17:40:56.375-06:00flipping the classroomlesson planningobservationrational exponentsRational Exponent Unit - preparation for observationI am going to be observed on this short skills unit that I have chosen to flip. I asked for the observation - our administrators let us choose the day and time.<br /><br />The videos I created are OK ... they aren't perfect. I need to work on that skill some.<br /><br />This notes booklet should be helpful to students.<br /><br /><a href="http://www.scribd.com/doc/202053657/Rational-Exponents-Booklet-Notes-Pages-1-and-8" style="font-family: Helvetica, Arial, sans-serif; font-size: 14px;" title="View Rational Exponents Booklet Notes Pages 1 and 8 on Scribd">Rational Exponents Booklet Notes Pages 1 and 8</a><span style="font-family: Helvetica, Arial, sans-serif; font-size: 14px;"> by </span><a href="http://www.scribd.com/algebrasfriend" style="font-family: Helvetica, Arial, sans-serif; font-size: 14px;" title="View Beth Ferguson's profile on Scribd">Beth Ferguson</a><br /><iframe class="scribd_iframe_embed" data-aspect-ratio="1.29411764705882" data-auto-height="false" frameborder="0" height="600" id="doc_72144" scrolling="no" src="//www.scribd.com/embeds/202053657/content?start_page=1&view_mode=scroll&access_key=key-pyr89qz0v6ulhwp5ztq&show_recommendations=true" width="100%"></iframe> <br /><div style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;"><a href="http://www.scribd.com/doc/202053658/Rational-Exponents-Booklet-Pages-2-and-7" style="text-decoration: underline;" title="View Rational Exponents Booklet Pages 2 and 7 on Scribd">Rational Exponents Booklet Pages 2 and 7</a> by <a href="http://www.scribd.com/algebrasfriend" style="text-decoration: underline;" title="View Beth Ferguson's profile on Scribd">Beth Ferguson</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="1.29411764705882" data-auto-height="false" frameborder="0" height="600" id="doc_59727" scrolling="no" src="//www.scribd.com/embeds/202053658/content?start_page=1&view_mode=scroll&access_key=key-1fpzpooyl6cjoe7rrlhn&show_recommendations=true" width="100%"></iframe> <br /><div style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;"><a href="http://www.scribd.com/doc/202053663/Rational-Exponents-Booklet-Pages-3-and-6" style="text-decoration: underline;" title="View Rational Exponents Booklet Pages 3 and 6 on Scribd">Rational Exponents Booklet Pages 3 and 6</a> by <a href="http://www.scribd.com/algebrasfriend" style="text-decoration: underline;" title="View Beth Ferguson's profile on Scribd">Beth Ferguson</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="1.29411764705882" data-auto-height="false" frameborder="0" height="600" id="doc_35164" scrolling="no" src="//www.scribd.com/embeds/202053663/content?start_page=1&view_mode=scroll&access_key=key-1keaj3g92y1hojz6b6po&show_recommendations=true" width="100%"></iframe> <br /><div style="-x-system-font: none; display: block; font-family: Helvetica,Arial,Sans-serif; font-size-adjust: none; font-size: 14px; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal; margin: 12px auto 6px auto;"><a href="http://www.scribd.com/doc/202053669/Rational-Exponents-Booklet-Pages-4-and-5" style="text-decoration: underline;" title="View Rational Exponents Booklet Pages 4 and 5 on Scribd">Rational Exponents Booklet Pages 4 and 5</a> by <a href="http://www.scribd.com/algebrasfriend" style="text-decoration: underline;" title="View Beth Ferguson's profile on Scribd">Beth Ferguson</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="1.29411764705882" data-auto-height="false" frameborder="0" height="600" id="doc_1261" scrolling="no" src="//www.scribd.com/embeds/202053669/content?start_page=1&view_mode=scroll&access_key=key-srsg318jjpqhtmo1m0i&show_recommendations=true" width="100%"></iframe> <br />In each of these lessons I am highlighting three initiatives at our school, formative assessment, technology, and writing. <br /><br />The writing we will do is short ... to the point. We have done some lengthier explanatory writing. But the reflection and short explanations in this booklet fit the expectation ... and of course are worthwhile to student learning.<br /><br />The use of technology is not transformative. I am using technology in its simplest forms ... for taking notes, for routine online practice, and for quizzing.<br /><br />The formative assessments I have planned now are the individual stations and a wrap up activity at the end of each lesson. I'm looking back through the book on formative assessment for a strategy I might like to employ other than ticket out of the door or show me your whiteboard work.http://algebrasfriend.blogspot.com/2014/01/rational-exponent-unit-preparation-for.htmlnoreply@blogger.com (Beth Ferguson)8tag:blogger.com,1999:blog-8399389267815059112.post-888452815936117487Thu, 23 Jan 2014 13:38:00 +00002014-01-23T08:37:04.197-06:00rational exponentsskill-based practiceThe "boring" bitI read Dan Meyer's post on <a href="http://blog.mrmeyer.com/?p=18314">Teaching the Boring Bits</a> this week. Our topic beginning Friday is rational exponents. We will spend just 2 class days on the skills of simplifying and solving with fraction exponents. This is in preparation for delving into the exponential and logarithmic functions.<br /><br />The focus on manipulating algebraic expressions - skill only - has the potential to fall under that category some call the boring bits. I decided to flip the two lessons ... partly because of the non-interesting factor ... a way to shake up the classroom. That alone of course isn't enough necessarily to make the task any more interesting. (I also work in a 1:1 environment and look for ideas and structure to use the technology we have more fully).<br /><br />So I re-read Dan's post. I have a couple of thoughts.<br /><br />I can engineer an argumentative discussion around the question, "Is 0 to the 0 power equal to 1?"<br /><br />And/Or ... in the stations I am setting up, I can structure my feedback to be just enough at just the right time so that they "grapple" with challenging problems.<br /><br />I'm looking for a few challenging problems that will stretch my students' thinking in this skill-based unit. Unit starts tomorrow ... still working out the kinks!http://algebrasfriend.blogspot.com/2014/01/the-boring-bit.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-3293216135258595247Wed, 22 Jan 2014 02:40:00 +00002014-01-21T20:40:15.096-06:00flipping the classroommath stationsrational exponentsskill-based practiceFlipping the classroomIn the midst of our study of functions we will take a two-day detour to learn how to manipulate rational exponents.<br /><br />I decided that this 2-day unit would be the perfect time to try flipping the classroom. The unit is skill-based, and I want students to have as much class time to practice as possible. The notes are simple to give via video.<br /><br />The preparation for the unit is huge. I'm spending a lot of time preparing the stations we will use in class as well as planning the examples I want to put in the videos.<br /><br />The outline of the stations looks like this:<br /><br />Day 1 ... simplifying expressions with rational exponents<br /><br /><ul><li>Manga High </li><li>Card Sort</li><li>Search 'n Shade practice</li></ul><div>Day 2 ... solving equations with rational exponents</div><div><ul><li>Edmodo challenge problems (EOC style)</li><li>Error Analysis</li><li>Solving Practice</li></ul></div><br /><br />I'll share the bits and pieces soon. I left most of the work today on my school computer. The unit starts Friday ... so I need to step up the preparation!http://algebrasfriend.blogspot.com/2014/01/flipping-classroom.htmlnoreply@blogger.com (Beth Ferguson)2tag:blogger.com,1999:blog-8399389267815059112.post-6344014439687656576Thu, 16 Jan 2014 02:40:00 +00002014-01-15T20:41:14.326-06:00review gamestudent engagementzapZAP!! Review Game I saw this game called ZAP on a couple of websites ... <a href="http://5thgraderocks5thgraderules.blogspot.com/2012/02/zap.html">here </a> and <a href="http://mathtastrophe.wordpress.com/2012/07/23/made-4-math-monday-4/">here</a> and <a href="http://www.livinglaughingandloving.com/2012/08/zap-student-review-game-fave.html">here</a>! <br /><br />I decided to create my own ZAP board ... in preparation for review day.<br /><br /><a href="http://2.bp.blogspot.com/-1sBR7QvNEwU/UtdDy0Dr8II/AAAAAAAAIyA/45TTFdx1R54/s1600/IMG_20140114_163851_248.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-1sBR7QvNEwU/UtdDy0Dr8II/AAAAAAAAIyA/45TTFdx1R54/s1600/IMG_20140114_163851_248.jpg" height="180" width="320" /></a><br />At the end of the last semester I asked students for feedback on our class and our activities. One activity they said they liked was playing games to review for tests. BUT I was tired of the football and basketball games. So I started hunting for a new way to play!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-zSH7URE5Dpc/UtdDsnA8ZmI/AAAAAAAAIx4/kvXF3gDsGDg/s1600/IMG_20140114_163934_629.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://4.bp.blogspot.com/-zSH7URE5Dpc/UtdDsnA8ZmI/AAAAAAAAIx4/kvXF3gDsGDg/s1600/IMG_20140114_163934_629.jpg" height="197" width="320" /></a></div>I didn't have library pockets and didn't want to go out to buy them. So I used half size index cards and tape to create pockets. I found some old construction paper already cut into strips ... about 2 x 4 inches. I also found stickers that I had purchased over the summer. So ... it took just a few minutes to create pockets and cards. Then I wrote varying number of points on the cards along with a few silly actions, and the word, "ZAP."<br /><br />We play on Friday! Maybe I'll have a great learning experience to report!<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"></div><br />http://algebrasfriend.blogspot.com/2014/01/zap-review-game.htmlnoreply@blogger.com (Beth Ferguson)4tag:blogger.com,1999:blog-8399389267815059112.post-9077446781902871021Fri, 03 Jan 2014 22:19:00 +00002014-01-03T16:19:43.687-06:00function familieslesson planningThinking out loud - in planning modeSo building off <a href="http://algebrasfriend.blogspot.com/2014/01/how-to-frame-work.html">yesterday's post</a> about how to frame the work next week ...<br /><br /><div class="MsoNormal">I don’t want to start with direct instruction … my students are able and need more time grappling with math.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">What if I start with the <a href="https://drive.google.com/file/d/0B-1saJM8fLPgZzJsc2FHbVprems/edit?usp=sharing">data collection lab</a>? Students have enough background knowledge to do it justice without explanation. And if they get stuck I can give them some help.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">After the lab and after working through the attached problems, I’d like students to create the notes they need for analyzing a square root function. Maybe if I create a list, better yet, a graphic organizer for the information they must know … but leave it to them to fill it out. Then they can compare information among their classmates. After they have done that work, then I could fill in gaps if needed or structure a conversation for them to fill in the gaps.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">I like this plan better than my typical daily plan of setting up the work for them. <o:p></o:p></div><div class="MsoNormal"><br /></div><br /><div class="MsoNormal">Now I just need to create that graphic organizer and determine what specific practice students might need.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">Where are you in planning for the first days back? How do you engage students in critical thinking?</div>http://algebrasfriend.blogspot.com/2014/01/thinking-out-loud-in-planning-mode.htmlnoreply@blogger.com (Beth Ferguson)1tag:blogger.com,1999:blog-8399389267815059112.post-9078354713758815133Fri, 03 Jan 2014 02:54:00 +00002014-01-02T20:54:44.894-06:00critical thinkingfunction familieslesson planningHow to frame the work?Second semester is looming. Fortunately, we get one work day on Monday before students arrive on Tuesday. I want to plan and I don't want to plan ... it's a strange conundrum! I am enjoying this time away from the constant thinking/planning/creating! But second semester is looming.<br /><br />Our Algebra 2 curriculum is based around functions. We started with linear functions and systems, next absolute value functions, and then quadratics. With each function we explore the key characteristics, transformations, how to solve, and applied problems.<br /><br />In second semester we will start with square root functions. But before we jump into those completely, we will review the concept of inverse functions. We discussed inverses in the very first unit in which we explored a variety of parent functions. At that time we mostly looked at using a table to determine the inverse. We didn't discuss composition of functions.<br /><br />So our unit plan looks like this:<br />Day 1: Inverse Functions<br />Day 2: Data Collection and Key Characteristics of Square Root Functions<br />Day 3: Transformations of Square Root Functions<br />Day 4: Solving Square Root Equations<br />Day 5: Applied Problems<br /><br />Since we have studied 3 functions already with this same pattern, students should be able to generalize from previous functions to the square root functions the basic concepts - especially key characteristics and transformations.<br /><br />So ... that brings me to this thought ... how can I frame our work for the coming week to maximize student independence and critical thinking?<br /><br />Any ideas?http://algebrasfriend.blogspot.com/2014/01/how-to-frame-work.htmlnoreply@blogger.com (Beth Ferguson)0tag:blogger.com,1999:blog-8399389267815059112.post-7900591344660313368Sun, 15 Dec 2013 05:07:00 +00002013-12-14T23:07:18.502-06:00#hunterstrongEncouraging Hunter!A week ago, Hunter Garstin, young teenage son of a teacher friend, broke his neck in a wrestling match. <br /><br />After surgery, a stay in the hospital, he has been accepted at the Shepherd Center in Atlanta. He arrived there Friday.<br /><br />He has a long journey of rehabilitation ahead of him.<br /><br />I would love for you to join me in praying for Hunter and encouraging him in his journey. It won't matter that you don't know him personally.<br /><br />You can read about his story on Facebook: <a href="https://www.facebook.com/pages/Prayers-for-Hunter-Garstin/1394077424172673">Prayers for Hunter Garstin</a><br /><br />Give him a shout on Twitter, email an encouraging word, or mail a Christmas card!<br /><br /><i><span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;">TWITTER: Give Hunter a shout out to @huntergarstin </span><br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" /><br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" /><span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;">EMAIL: Send messages to prayersforhuntergarstin@gmail.</span><wbr style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;"></wbr><span class="word_break" style="background-color: white; color: #333333; display: inline-block; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;"></span><span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;">com </span><br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" /><br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" /><span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;">MAIL: With Christmas right around the corner we would love to paper his rehab room walls with cards. Please send cards, letters and well wishes for Hunter as well as any other correspondence to Hunter Garstin PO Box 680249 Franklin, TN 37068 </span><br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" /><br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" /><span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;">PHONE: Please feel free to text Hunter at (678)929-8090. </span></i><br /><i><span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;"><br /></span></i><span style="background-color: white; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;"><b>#hunterstrong</b></span><br /><br /><br />http://algebrasfriend.blogspot.com/2013/12/encouraging-hunter.htmlnoreply@blogger.com (Beth Ferguson)0