tag:blogger.com,1999:blog-812794395259173668Thu, 24 Apr 2014 21:04:11 +0000Teaching_PracticesGeometryPre-CalculusAlgebranixTMCDrawing On MathPonderings of a high school math teacher.http://drawingonmath.blogspot.com/noreply@blogger.com (Tina C)Blogger185125tag:blogger.com,1999:blog-812794395259173668.post-3818292963701255023Wed, 02 Apr 2014 01:31:00 +00002014-04-01T21:33:32.282-04:00Teaching_PracticesInvitations for InterventionsI had a crowd of students after school today. So many, in fact, that some looked around the room and decided they would come back another day. I've decided there are two important ingredients to getting kids to stay after. First, they need to be invited. Second, they need to see that it matters. A third, bonus ingredient, is follow through.<br /><br /><h4>Invitations:</h4>I invite students to stay for what our school calls "dayback" in a variety of ways. The most basic is a calendar in my classroom that shows when I am available after school. It is near the door so hopefully students look at it on the way out and remember to come back at the end of the day.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-6sYVLLDNqlk/UC6aQPDbTHI/AAAAAAAACc0/V_cZkoHkveA/s1600/2012-08-15+14.11.27.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-6sYVLLDNqlk/UC6aQPDbTHI/AAAAAAAACc0/V_cZkoHkveA/s1600/2012-08-15+14.11.27.jpg" height="240" width="320" /></a></div><br />Whenever a student asks if I'm staying after today I refer them to the calendar, but if it's at the end of the period I will also announce to the whole class which days I am available. It never hurts to hear an extra reminder.<br /><br />Throughout the quarter I communicate to students what they need to do to be successful in class. A week or two before a report is sent home, I print a progress report for every student. At mid-quarter the list of assignments isn't overwhelming so I print the whole report. By the end of the quarter there are too many assignments for it to be helpful for most kids. My grade system has a feature where you can print just the category averages which helps kids get a sense of what they need to focus on (projects or tests since those are 80% of their grade combined) so near the end of the quarter I print those (then kids can ask me what they need to fix/hand in after school if they don't have a record of it).<br /><br />At other points I invite particular students to stay after based on particular criteria. Today I gave <a href="http://www.scribd.com/doc/215829505/Dayback-Signup">this note</a> to every kid who was completely missing something (either they were absent or never handed it in). Other times I use <a href="http://www.scribd.com/doc/215825323/Current-Grade-Dayback">this note</a> to tell students (sometimes all, sometimes below a cutoff) where they stand. This quarter the 10th grade team talked about starting mandatory dayback for kids who are failing. I think I'm the only one who followed through, but I decided to start with kids who had a failing average for the year (the goal is to start this much earlier next year so kids will keep up rather than need to catch up) and they would 'graduate' from staying after weekly when their average is over a 65%. Ideally by then they would see that staying after helps them and continue! Once kids received their <a href="http://www.scribd.com/doc/215825333/Mandatory-Dayback">initial notification</a> I asked them every Monday <a href="http://www.scribd.com/doc/215825332/Mandatory-Dayback-Reminder">which day</a> they would stay as a reminder that they needed to continue staying weekly until I said otherwise.<br /><br /><h4>Staying After Matters:</h4>Once you get a kid to show up after school, you need to convince them it's worth their while or they won't come back again. Frequently you need to convince them of this before they even show up. But after sitting down with me to work on something and finally understanding for the first time, they're convinced. The jump in their grade is an added bonus. My grading system allows students to retake any quiz or test and the new grade replaces the old one. They can also correct any project to get full credit. When I explain this to a kid (sometimes for the 50th time in a class) they are somewhat skeptical that doing one assignment will make a big difference. These are often the same kids who decided to go back and make up homework assignments - homework is 10% of the grade and they can only earn half credit for late homework because we go over it. Is is worth doing? Yes. Not because it will impact your grade, but because it will prepare you to retake the quiz and test on that topic. Weighted averages appear to be beyond even my advanced students. Something about attention to detail is missing for many of them.<br /><br />To keep track of what they need to do, but more importantly to have a visual reminder of what they have accomplished, I have kids on mandatory dayback <a href="http://www.scribd.com/doc/215825329/Mandatory-Dayback-Form">fill out a form</a>. This form has been awesome for streamlining. When a kid first shows up we make a list of everything they can correct/retake/do (for Fundamentals of Geometry kids there's a stamp chart they can look at, for PreCalc kids they are supposed to track their own assignments but I'll cross reference with the online gradebook). Then each time they show up they work on the next item on the list and I don't need to tell them what to do. The forms stay in a folder on my desk so kids can grab them when they come, but also so that I can see who has been in each week (all forms are on the left on Monday, when a kid stays after they return the form on the right).<br /><br /><h4>Follow Through:</h4>If a student says they will stay after and then don't, I try my best to ask them what happened the next class. It's hard to do though. That's why I started a spreadsheet for the kids with mandatory dayback. At the end of the week (once kids have had a chance to show up on Friday) I go through the folder and mark who stayed this week. I email the deans a list of the kids who didn't show up (which is why they're divided by grade, we have a dean for grade 9, grade 10 and grade 11/12). Then if the deans see the kids during the week they reinforce the importance of coming to see me.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-1eHRcQzeGWE/UztgsWrMnHI/AAAAAAAAE_A/x9OnAhpjwZ8/s1600/dayback+spreadsheet.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-1eHRcQzeGWE/UztgsWrMnHI/AAAAAAAAE_A/x9OnAhpjwZ8/s1600/dayback+spreadsheet.PNG" height="166" width="320" /></a></div><div style="text-align: center;">(the blanks are kids who were not notified yet, either because they are chronically absent or they didn't fall below the cutoff until a later week)</div><div style="text-align: center;"><br /></div><div style="text-align: left;">I wish students realized from the start that struggling isn't a sign of failure, but a sign of needing extra support. I wish that they knew staying after school is something good students do, not students who are 'in trouble.' But most students don't come to me knowing these things. I don't chase kids and I know I won't remember to talk to students in the middle of class, but I can hand a kid a note that says "I want to see you, I care about you, we can work together and you will improve." </div>http://drawingonmath.blogspot.com/2014/04/invitations-for-interventions.htmlnoreply@blogger.com (Tina C)4tag:blogger.com,1999:blog-812794395259173668.post-7191005299228964255Sat, 15 Mar 2014 00:13:00 +00002014-03-14T20:13:38.866-04:00AlgebraGeometryTeaching_PracticesConfronting the InsanityThe testing pressure in my district is real. The school committee met this week to talk about handing one of our elementary schools over to a private company. The skill deficits my students have are also real. Every time we talk about parallel or perpendicular lines we have to discuss how to find slope and what slopes would show the lines are parallel/perpendicular. When we are trying to find the missing angle of a polygon they struggle both to set up and to solve equations. So, the limited Algebra practice that I naturally incorporate in Geometry class isn't sufficient. I can't send them into an Algebra heavy state test in May like this, and I can't send them into Algebra 2 like this. I'm not going to quit teaching Geometry to teach Algebra, and I'm sick of forcing Algebra into Geometry (today we were identifying quadrilaterals given the four vertices, then writing the equation of the line containing one side... because they need practice writing equations of lines).<br /><br />So my co-teacher and I decided today that we will set aside some time to do Algebra, maybe at the beginning of each class (the glory of 90 minute blocks is we can do this and still have a rich Geometry lesson). In our conversation we thought a good first task would be to have kids practice matching equations to graphs, and then we can work up to writing equations and graphing. But then my last block class had kids in such different places that some kids will be ready to move on from matching after day one while others will need a lot more practice. I think this has to be individualized, each kid could get a chart listing all the skills, quiz on a topic (say 5 questions on a very specific skill) and they either test out of that skill or get assigned related practice problems. If each kid gets an individualized assignment do these have to come in a particular order or can kids choose? Which skills have prerequisites? Maybe I can have kids write practice problems after they master a skill so I'm not making a million?<br /><br />I hate being so skill/test focused so I'm also hoping to mix in Fawn's awesome <a href="http://www.visualpatterns.org/">visual patterns</a> and <a href="http://mathtalks.fawnnguyen.com/">estimation problems</a>. Possible plan: each week every student must complete 2 skill assessments, a pattern and an estimation problem (then I can skip estimation on my skill list!). Patterns and estimation should be written up with a partner, skill assessments must be completed individually (but feel free to discuss practice problems with a partner). If I plan 60 minute lessons then students can work on this at the end of class (plus about half the students - the ones with a math learning disability - have a second block with my co-teacher, she has been trying to set up similar things so this can carry through to the other class).<br /><br />This afternoon I set out to see what skills are important according to the state test. And came up with a list (below) that I can work with. I'm really hoping part of this matches your curriculum, that you do SBG and you have assessments and skill practice sheets that you can share with me. Please??<br /><br /><b>Algebra:</b><br />Simplify algebraic expression (order of operations, exponent rules, factor/distribute)<br /><br />Solving equations (rate, linear, one quadratic-multiple choice)<br />Solving system of linear equations, absolute value inequality<br /><br />Writing linear equation, absolute value inequality<br />Writing and graphing inequalities (one variable)<br /><br /><b>Number Sense</b><br />Estimate percent, square root, with data (total, average, difference)<br />Scientific Notation<br /><br /><b>Geometry:</b><br />Angles of triangles, parallel lines with transversal, parallelogram<br />Similar and congruent triangles<br />Pythagorean Theorem<br />Transformations on coordinate plane<br /><br /><b>Data</b><br />Mean, Median, Mode, Range<br />Box and Whisker Plot, Scatter plot, Line Plot, Circle Graph<br />Probability<br /><br /><b>Measurement:</b><br />Area, Surface Area, Volume<br /><div><br /></div><div>I have a better sense of what I'm hoping to achieve after writing this post, but I still don't know how best to organize this all. It's overwhelming because it seems like an entire Algebra class running on top of my Geometry course. But I'm already overwhelmed so I'd rather be overwhelmed with a purpose and a plan than continue throwing up my hands in despair. Advice greatly appreciated!</div>http://drawingonmath.blogspot.com/2014/03/confronting-insanity.htmlnoreply@blogger.com (Tina C)3tag:blogger.com,1999:blog-812794395259173668.post-7520308129051410908Sat, 08 Mar 2014 23:24:00 +00002014-03-08T18:24:36.417-05:00Pre-CalculusTeaching_PracticesPreCalc Review DayMarch 4th, C Block Honors PreCalculus<br /><br />The bell rings at 11:03, the projected instructions tell students to take out their homework (a concept map, inspired by <a href="http://cheesemonkeysf.blogspot.com/2014/02/building-concept-maps-is-harder-than-it.html">Elizabeth's post</a>) and compare with their neighbors. Which ideas are the same? Which are different? Did you skip those things on purpose or because you decided they weren't important enough to include? Individual students share with me their struggles and successes as I take attendance. A student returns quizzes from last class, most of them remember to record their grades in their chart and students who received perfect scores tape their stars to the "Perfect Score, First Try!" wall. A student tells me she couldn't find the example concept map online; I briefly panicked it hadn't uploaded, then we figured out she didn't realize the files were multi-page and she had to scroll to get to the example. I asked if anyone wanted to share something about their concept map but no one really did. One student said that he thought it was interesting, he had made webs and maps in science and english class before, but never in math. Everyone hands in their concept map in the class inbox.<br /><br />At 11:12 we transition to making observations about the problems they solved last class. Usually we do work and discuss in the same day but last class was short? Maybe? Somehow we are discussing things today but luckily these are my Honors PreCalc kids, they have organized binders and can find the work quickly. I ask them to notice and wonder about solving polynomials of higher degree. A student wants to tell me that the degree of the polynomial tells you how many roots there are, but she says "the exponent is how many solutions there are" For once, I remember to write down exactly what a student says! I then write down the example x^4+x^3+2 and ask her how many solutions. She realizes it's the <b>highest</b> exponent so we add that word in. I tell her that what she said is perfectly clear, and then ask the class if they remember the word for 'the highest exponent' and get a lot of blank stares (could've sworn I just used this term...) but eventually someone clicks in and says "Degree!" I ask them to be even more specific - what kinds of solutions did they get when solving degree 4 polynomials? (I set it up last class so they had one example with 2 real and 2 imaginary, another example with 4 imaginary.) And then push them - is it possible to get one imaginary? Why not? What else did you notice? Someone recognizes that all the imaginary solutions are plus or minus, so I mention the word conjugate and then ask why that matters? We make up an example and I have them multiply out (x-i)(x+i) to see that the resulting polynomial won't have any imaginary coefficients. Several students are totally convinced that there have to be an even number of imaginary solutions, but I'm not so sure about the rest of the class, so I ask if they want to do another example. One student nods so we discuss the number and type of possible roots of degree three polynomials. When I asked if it could have four imaginary roots a couple students are so caught up in the fact that imaginary roots have to be even they say yes. And then smile at their mistake when someone points out that four is greater than three.<br /><br />11:24 We transition to independent review. I have sample problems available for each of the topics that will be on the test next week and emphasize that even if students are confident in solving polynomials since we just finished that topic they should read through the problems because they ask for the answer in different forms (real solutions vs. all solutions vs. factored). A student asks if they can retake a quiz and I tell the whole class that now is a great time to do any make up work or retakes they need to do, since any of those tasks results in them practicing the topics that will be on the test. Things get busy as half the class wants me to answer a question about their quiz or the graded assignment from last week. I run around in circles for a while until most people are working on something, then I walk in circles answering questions. Progress reports go out this week but I'm behind in grading so I flip through the assignments in the inbox to make sure that everyone who has resubmitted the graded assignment did so correctly. I spot a few with issues and instruct those students how to complete that section.<br /><br />12:05 All is quiet. Everyone is working. I can breathe for a moment, but only one, someone else has a question.<br /><br />12:15 Most students haven't done the review problems on operations with complex numbers. I really want them to realize that |a|*|b|=|a*b|, which isn't something we discussed in class. I get everyone's attention and tell them to do those problems right now if they haven't yet, then hurry up and notice something. The student who told me at the beginning of class he hadn't done a concept map in math before shared that he didn't feel like it was useful last night, but today as he did all the review problems he felt that he understood everything much better. (YAY!!) I told him I was glad to hear that and we chatted about how your brain works off of connections; the more you access a memory the better you remember it, so the more connections you have to an idea the easier it is to access.<br /><br />12:20 I am about to get everyone's attention to talk about the complex number pattern, but notice one of my students who doesn't participate much is tutoring her partner. I wait.<br /><br />12:23 Attention everyone! Please do this complex number problem that I am writing on the board. A student guesses that the pattern is |a|*|b|=|a*b| and I say yes! I project the journal questions (What did you notice or wonder? How should you study for the test?) and the homework (study, here are the relevant sections in the book). A student goes up to the review problems that she hasn't gotten to and lines them up so she can take a photo with her phone. Smart use of technology!<br /><br />12:28 The bell rings. I experience immediate regret for telling students the pattern after one of them guessed rather than making sure everyone did out the work to see why. That would have been an excellent homework problem. Hindsight...<br /><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/211398908/March-4th" style="text-decoration: underline;" title="View March 4th on Scribd">March 4th</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_67214" scrolling="no" src="//www.scribd.com/embeds/211398908/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />Note: This post is for Day in the Life, Single Class Edition. Read all the <a href="http://ditlife.tumblr.com/">DITLife posts </a>and <a href="https://docs.google.com/spreadsheet/viewform?usp=drive_web&formkey=dGxKYWZmVWJyTEtmYUhQRWdMYmNpcHc6MQ#gid=0">submit your own</a>!http://drawingonmath.blogspot.com/2014/03/precalc-review-day.htmlnoreply@blogger.com (Tina C)2tag:blogger.com,1999:blog-812794395259173668.post-4882571802253511863Mon, 03 Mar 2014 01:57:00 +00002014-03-02T20:57:40.517-05:00DITLife, Single Class Edition<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-9Fm1JW6SFYc/UxPhM6TGTbI/AAAAAAAAEz8/2N9kP-pVCbY/s1600/DITLife.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-9Fm1JW6SFYc/UxPhM6TGTbI/AAAAAAAAEz8/2N9kP-pVCbY/s1600/DITLife.jpg" height="200" width="178" /></a></div>Yesterday <a href="http://www.teachesmath.com/?p=592">Lisa wrote a post</a> about varying the types of instruction she uses in her math classes and put out a call for examples. This sounded like a perfect time to bring back <a href="http://ditlife.tumblr.com/">Day in the Life of an Educator</a>. But this time, instead of sharing your entire day, share a single class period in detail. I'm always curious to hear what happens in other classrooms, but more than that, I'm curious why people make the decisions they do. Why did you make that a whole class activity? How do you get students to work in groups? (I've yet to tackle this goal, let alone accomplish it.) Did students react as you expected? What decisions did you consider ahead of time and what did you have to decide on the fly? ... So many questions!<br /><br />If you're interested in answering some of those questions, write a blog post about one class period this week. Then, <a href="https://docs.google.com/spreadsheet/viewform?usp=drive_web&formkey=dGxKYWZmVWJyTEtmYUhQRWdMYmNpcHc6MQ#gid=0">submit your post</a> and tweet it using #DITLife. I will put all of the posts submitted via form onto the <a href="http://ditlife.tumblr.com/">tumblr</a> (hence the need for a description and tags).<br /><br /><br /><iframe frameborder="0" height="1485" marginheight="0" marginwidth="0" src="https://docs.google.com/spreadsheet/embeddedform?formkey=dGxKYWZmVWJyTEtmYUhQRWdMYmNpcHc6MQ" width="760">Loading...</iframe>http://drawingonmath.blogspot.com/2014/03/ditlife-single-class-edition.htmlnoreply@blogger.com (Tina C)1tag:blogger.com,1999:blog-812794395259173668.post-1265201139593629796Sun, 02 Mar 2014 23:43:00 +00002014-03-02T19:31:12.450-05:00Teaching_PracticesClarifying ExpectationsOne day a few weeks ago when the bell rang to signify the end of school, my co-teacher and I looked at each other and each collapsed into the nearest chair in exhaustion. Class had not gone well (understatement of the year) and we were totally worn out. That evening, when I had regained some energy, I thought through what exactly had gone wrong. A big part of it was that we were returning to an idea that students had learned, but between vacation, snow days, midterm projects and the quarterly exam it had been a month since we had studied that concept. I did not adjust for the month gap because I had no idea it had been so long. This has been the year of interruptions and it's really taking a toll. However, if I write a lesson that is a reach for students, they don't have the right to terrorize us. They have notes, examples, each other and respectful ways to communicate to the adults that they were lost. Students don't always know how to appropriately act when faced with a difficult task, so I decided to create a stamp chart to remind them of their options and reward students who are successful.<br /><br />Every other week students <a href="http://drawingonmath.blogspot.com/2011/10/reflection-and-self-assessment.html">self assess</a> their work in class; sometimes two weeks is too long though. So, in an effort to make it exceedingly clear what behaviors I value, I made a chart (based on that self assessment rubric) that students get as they enter class each day. Then, throughout class, my co-teacher and I stamp boxes corresponding to their behaviors. There’s no grade attached, just the satisfaction of a smiley face or star. (A few students have asked why they get a smiley face for being off task, one even drew in a frown, but carrying more than one stamp in my pocket is way too complex for me.)<br /><div><br /></div><div><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/210145875/Daily-Stamps" style="text-decoration: underline;" title="View Daily Stamps on Scribd">Daily Stamps</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_375" scrolling="no" src="//www.scribd.com/embeds/210145875/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /></div><div><br /></div><div>I've been using the charts for a few weeks now and they are working well. The other day I had two students race down the hall to my classroom, grab their binders and pull out a pencil as they collapsed into their seats to earn the “ready for class” stamp. Another (rather quiet) student participated in the discussion and called my co-teacher over to stamp her paper before I had even finished recording her comment. When I catch a break between conversations with students I will make a quick sweep of the room stamping either 'on task' or 'off task' for each student. I asked students to leave the chart in the top right corner of their desk, so usually this process goes quickly. I have also used it as a way to check off who has completed a task - "Everyone make a parallelogram that is not a rectangle." and then I circulate, stamping 'on task' for each student who has successfully created one (circling back to the students who got a "not yet" comment since it's not about speed). </div><div><br /></div><div>I feel a bit bad about using so much paper, but we use the back for the exit ticket and it really is making a difference in classroom behavior so I think it's worth the cost in paper and ink. The Spanish teacher who saw me copying the charts one morning said two things: “It seems so elementary school. My AP students need this.” Do I wish my students knew how to be ready for class? Sure. But since they don’t, I've given them a daily reminder with clear instructions, along with clues to the other behaviors that make me proud. Bonus: the system reminds me to thank my students for being awesome throughout class, and that’s always a good thing.</div>http://drawingonmath.blogspot.com/2014/03/clarifying-expectations.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-2865345960971160853Mon, 27 Jan 2014 00:36:00 +00002014-01-26T19:36:31.161-05:00AlgebraTen Divided by HalfWhat question would you ask to prompt students to think about 10 divided by 1/2?<br /><br />I'm reading <a href="http://www.amazon.com/Problem-Math-English-Language-Focused-Understanding/dp/1118095707">The Problem With Math Is English</a> and the author says “How many times does half go into 10?” is the only question most teachers have. Which is a problem since that has very little meaning to most students. I posed the question to Twitter and offered “How many half units fit into ten whole units?” as the only context free alternative I could come up with. Luckily, my tweeps came through with plenty more!<br /><br /><blockquote class="tr_bq">Bridget Dunbar: how many groups of 1/2 are in l0?<br /><br />Teresa Ryan: Yes. I like using the groups idea.<br /><br />Tina C: but what is a group of 1/2?<br /><br />Teresa Ryan: Yeah, guess I should have thought about that longer. I was picturing groups of numbers, and 1/2 doesn't quite work. I guess what I'm thinking is breaking the 10 into individual pieces, then counting how many 1/2's there are<br /><br />Tina C: that’s exactly what this book is about. Falling back on our ingrained language which doesn’t always help kids.<br /><br />Kathryn Freed: how many groups of 1/2 an orange could be made from 10 oranges?<br /><br />Tina C: ooh An orange is interesting. This reminds me of @TriangIemancsd's post on partitioning<br /><br />Teresa Ryan: I guess I’m struggling with students seeing 1/2 of something as a group<br /><br />Tina C: I agree-I don’t see half of anything as a group. But we could translate into group language via an orange<br /><br /><br />Bridget Dunbar: I picture a number line and marking off the number of halves in 10 wholes.<br /><br /><br />Justin Lanier: "How many halves are there in 10?" There’s also the other interpretation: “If 10 make a half of a pile, how big is a pile’?”<br /><br />Tina C: I like this question because I find it easier to answer. No one has used that interpretation yet.<br /><br />Justin Lanier: People tend to avoid this interpretation with fractions. I have shed this prejudice :)<br /><br /><br />Math Minds: or you could start with 10 divided by 2 ask for multiplication prob u could use to solve?<br /><br /></blockquote>And then there were the people who offered a context to explain the abstract question:<br /><blockquote class="tr_bq">Paul F: You’re making bread, and your only clean measuring scoop is a half cup. How many scoops do you need to make 10 cups?<br /><br />Zach Schultz: how many "half Oreos" go into 10 Oreos. ( if we had more half dollar coins laying around I'd say how many of these go into $10)<br /><br />Jen Silverman: I need to serve each GI 1/2 pound of home-style potatoes How many servings can I get from a 10-pound bag?<br /><br />Jen Silverman: I had a 10 c. bowl of popcorn. When I split it evenly btwn the Ss in my class, each S got 1/2 c How many Ss?</blockquote><br /> There were a few people who agreed that "How many halves are there in 10?" would be their go to question. What question comes to your mind first? Which approaches best help students understand the computation?http://drawingonmath.blogspot.com/2014/01/ten-divided-by-half.htmlnoreply@blogger.com (Tina C)10tag:blogger.com,1999:blog-812794395259173668.post-7947501614234527629Mon, 20 Jan 2014 22:28:00 +00002014-01-20T17:28:50.787-05:00Folding PolygonsThis weekend I painted my stairs. Most people think the math involved in painting is calculating the volume of paint required. I will grant you that the area of the walls in my stairwell is more interesting than your average wall and includes some cool composite shapes, but really, I only buy paint by the gallon. So knowing the exact area of the walls I needed to paint was not necessary.<br /><br />Instead, I found an interesting math puzzle after I was done painting. I had taped all of the woodwork (quite a lot including trim and railings) and needed to take it all down. I could have just made a huge messy ball, but, boring! So instead, I made up a game:<br /><br /><div style="text-align: center;"></div><blockquote class="tr_bq"><ul><li style="text-align: left;">Start with a piece of tape or long strip of paper</li></ul><ul><li style="text-align: left;">Make a few folds at whatever angle you'd like</li></ul><ul><li style="text-align: left;">Continue wrapping by making a fold to align with the edge (<a href="http://www.origami-instructions.com/origami-lucky-star.html">like this</a>)</li></ul><ul><li style="text-align: left;">You lose if your strip ends up with a vertex in the middle (i.e. no edge to fold along)</li></ul></blockquote><br /><div style="text-align: left;">I started with a 45-45-90 triangle. Of course, it wasn't exactly 45-45-90. All three sides of the triangle ended up much wider than the strip, but the pattern continued nicely. I quit when I got bored, I never lost.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">Then I tried to make an equilateral triangle. This was quite satisfying. It lasted as long as I wanted to play and didn't get too much wider than the tape.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">I tried to make triangles with other angles. Those resulted with the messy shapes on the far left of both the middle and bottom rows:</div><div style="text-align: left;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-7lcRjjO_8YI/Ut2czB5G5VI/AAAAAAAAEkw/UEFDsDwJ-YU/s1600/2014-01-19+13.35.12-1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-7lcRjjO_8YI/Ut2czB5G5VI/AAAAAAAAEkw/UEFDsDwJ-YU/s1600/2014-01-19+13.35.12-1.jpg" height="234" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">My rectangle is completely uninspired. I tried to make a different rectangle by changing the rules - I folded so an edge would line up next to a previous edge. It started making diagonals across a quadrilateral of sorts. But I got distracted when the tape got stuck to the wall and messed this one up. (not pictured, big mess)</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I'm most proud of the pentagon! I continued wrapping for a long time and yet two sides stayed exactly the width of the tape. I know that a regular pentagon is possible too because I've made those <a href="http://www.origami-instructions.com/origami-lucky-star.html">paper strip stars</a>.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Questions: </div><div class="separator" style="clear: both; text-align: left;">What polygons work perfectly? (I'm defining perfect as: the side length stays the same as you wrap once the original polygon is formed)</div>How quickly does a small error magnify? Is this chaos theory or slow and steady? Does a 59-61-60 degree triangle react very differently from at 60-60-60 triangle?<br />Are there any shapes that start out working and then you eventually lose?http://drawingonmath.blogspot.com/2014/01/folding-polygons.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-5797520092213286875Tue, 14 Jan 2014 02:26:00 +00002014-01-13T21:26:32.125-05:00Pre-CalculusModeling Periodic Data<div>Midterms are coming. You need students to practice but don't want to hand them a review sheet and say "do that." Oh, and you only graded one project this quarter, somehow? Note to self: collect things occasionally and give kids feedback. So what do you do? Assign a project that encourages review! The goal is not just practice but the synthesis kind of review and I think this project does that! The task is to collect data that is approximately sinusoidal, write an equation to fit the data and then interpret.<br /><br />Last year I had students write a model for the hours of daylight where each pair got to choose a location, I printed off a ton of data and had them graph by hand. I failed the "use appropriate tools strategically" standard. Graph paper + graphing calculator is not a good way for students to efficiently graph or to easily check their graph. This year I improved, we used <a href="http://desmos.com/calculator">Desmos</a>.<br /><br />When students arrived to class this year there was a laptop cart in the room. Students signed out a laptop and grabbed this <a href="http://www.scribd.com/doc/199493586/Modeling-Periodic-Data">instruction sheet</a>:<br /><br /><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/199493586/Modeling-Periodic-Data" style="text-decoration: underline;" title="View Modeling Periodic Data on Scribd">Modeling Periodic Data</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_3351" scrolling="no" src="//www.scribd.com/embeds/199493586/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br /></div>They all sat quietly and worked the entire period. Some talked to partners. Some asked questions. They were content when I sent them back to the instructions or their notes to answer their own questions. Desmos worked. The Internet worked. Groups who weren’t happy with the options did their own research. It’s nice to have an easy, self sufficient class sometimes!<br /><br />Students have used Desmos on one other occasion and the table feature was new to them. The only person who got stuck making a table didn't read the instructions. We definitely "used appropriate tool strategically" this time - the technology allowed students to quickly compare their model to the data. A few people tried to guess and check but found that their curve wasn't hitting the points, it was much more efficient to use what they knew about period, amplitude and shifts to get an accurate model.<br /><br />Grading these projects was fun! I opened up my email, read about many different sets of data and different interpretations of the data. It's great to have assignments where students have different topics because it makes things more interesting for the students and for me, but usually it's a lot more work to grade projects that are all different since I have to check each set of calculations. In this case, I looked at the graph and if it matched well and their analysis made sense that was all I had to do! Then I sent an email back with feedback. So easy. And I got to read things like this:<br /><br /><blockquote class="tr_bq">I chose to graph the minutes of daylight in Antarctica. My X axis is the Months and my Y axis is the amount of daylight (in minutes). My model does not display perfect accuracy but that is because Antarctica runs out of sun light at some points and it can't have a negative amount of daylight. Also that I did every 21st of the month so it's not the same amount of days in between each selected time.</blockquote><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/--JTdF2WRZ5U/UtSX8MZBsEI/AAAAAAAAEjw/n9MetBO5brk/s1600/Screen+Shot+2014-01-13+at+8.50.07+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="278" src="http://1.bp.blogspot.com/--JTdF2WRZ5U/UtSX8MZBsEI/AAAAAAAAEjw/n9MetBO5brk/s320/Screen+Shot+2014-01-13+at+8.50.07+PM.png" width="320" /></a></div><br /><br /><blockquote class="tr_bq">As my real world periodic function, I chose to analyze the stages of the moon during its period in the month of January. The "synodic period" of the moon is exactly 29.5305882 days, however in this graph, the period is simply 30. The rough equation derived from this data (what percentage of the moon is seen illuminated in Salem Massachusetts throughout the month of January) is y=50sin(.2094x-1.68)+50, where y is the percentage and x is the day of the month. We can determine that this equation makes sense in context because in the equation, the period (30 days) is the rough length of one synodic period and the amplitude is in fact half of the total percentage possible in regard to the moon being illuminated by the sun (100%, Full Moon). The accuracy of this equation is not perfect, my assumption is that this inaccuracy is due to both the gravitational forces acting upon and between the earth, moon, and sun as well as the angles created by these 3 celestial bodies as they revolve around one another in space and their speeds change.</blockquote><br /><blockquote class="tr_bq">The topic we chose is the average temperature each month in Salem MA. One period represents the 12 months within a year. Year after year the temperatures are the same on average and it is shown with this periodic equation. In context this equation shows what each coefficient and constant represent. The coefficient before sine is a. A equals 22 because a is amplitude and amplitude is found by subtracting the lowest average temperature from the highest average temperature in this set of data then dividing that answer by 2. In this equation b is 12. 12 represents the number of months represented per period showing that 1 period is equal to 1 year. The model of the data versus the actual data fit more accurately than one would have expected. It is not perfect however. Since temperature is an always changing factor and periodic graphs are repetitive and stay the same the periodic graph does not match exactly. </blockquote>http://drawingonmath.blogspot.com/2014/01/modeling-periodic-data.htmlnoreply@blogger.com (Tina C)1tag:blogger.com,1999:blog-812794395259173668.post-6925695963080423695Wed, 18 Dec 2013 00:29:00 +00002013-12-17T19:29:13.139-05:00Teaching_PracticesGradesToday I gave out progress reports in my classes. The school sends out progress reports with comments selected from a list, those went out last week, that's not what I gave out today. I printed the list of all the assignments I have graded this quarter and the student's current score for each one. Our quarter doesn't close until the end of January, I handed these sheets to students as a check-in, so they would take some time now to get caught up on missing work. There were plenty of students who took their list, immediately pulled out a pen or highlighter and started checking off things they had completed and marking assignments they wanted to improve. But there were far too many students who refused to look at the sheet, gave a panicked response "I can't have that grade!" or who immediately tossed it in the recycling bin. They know, because I tell them frequently, (including today as I handed out the reports) that none of those grades are set in stone. They can retake, resubmit, hand in late or otherwise make up every assignment we've done this quarter. The grades in the computer and on that printout are a snapshot of what students have demonstrated up to this point. I don't think students think of grades like this. I dare say I don't think many teachers think of grades like this. All of these thoughts, plus the recent discussions we have had on growth mindset, left me with this:<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-P2B-ir5yVok/UrDroNZ8x-I/AAAAAAAAEaw/M_L3wwiDUVk/s1600/Screen+Shot+2013-12-17+at+7.13.09+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="http://2.bp.blogspot.com/-P2B-ir5yVok/UrDroNZ8x-I/AAAAAAAAEaw/M_L3wwiDUVk/s400/Screen+Shot+2013-12-17+at+7.13.09+PM.png" width="308" /></a></div><br />What do you think? What does a grade mean to you?http://drawingonmath.blogspot.com/2013/12/grades.htmlnoreply@blogger.com (Tina C)5tag:blogger.com,1999:blog-812794395259173668.post-477392172423731518Sun, 08 Dec 2013 23:51:00 +00002013-12-08T18:51:52.671-05:00GeometryTransformationsMind Dump!<br /><br />My next unit in geometry is on transformations. I'm going to lay out all my options and then organize them via blog post, just for fun.<br /><br />As a geometry team at school we got together and decided these were the important ideas:<br /><br /><ul><li>translate</li><li>rotate about the origin multiples of 90 degrees</li><li>reflect over a variety of horizontal and vertical lines, not just the axes</li><li>wait to dilate until we get to similarity, for now rigid transformations only</li><li>use the phrase rigid transformations</li><li>use the prime notation P -> P'</li><li>incorporate language about congruence, including corresponding parts</li><li>one of our textbooks emphasizes coordinate rules, we will not emphasize them, in fact we will encourage students to physically rotate the paper rather than memorize a rule</li></ul><div>Last year I had kids draw block letters on the coordinate plane and then perform two transformations in different orders (first translate then reflect vs. first reflect then translate) and compare. The worksheet is not getting along with scribd or I'd share.</div><div><br /></div><div>This year I think I will have students do one example of each type (translate, rotate, reflect) individually or in pairs and then take notes on the basic definitions as a whole class activity (most kids are familiar with the terms but I have a crew of English Language Learners, definitions are important). From there we will break into stations.</div><div><ol><li><a href="http://mathforum.org/mathtools/tool/51057/">transformation mini golf</a> (the game link isn't working at the moment, I hope it's back soon!)</li><li>draw your own image and then transform it all three ways</li><li>basic practice problems </li><li>more advanced practice problems (last year's sheet? MCAS problems?)</li><li>something with transparencies, because we have them and they're cool</li></ol><div>And that's my outline. We are going to spend about a week on this. What have you done in the past? I know other people have different mini golf options - I think I have some links saved at school but I am currently at home.</div></div>http://drawingonmath.blogspot.com/2013/12/transformations.htmlnoreply@blogger.com (Tina C)6tag:blogger.com,1999:blog-812794395259173668.post-4845528012889685167Fri, 06 Dec 2013 11:00:00 +00002013-12-06T06:00:10.813-05:00Teaching_PracticesClassroom EnvironmentsI teach three sections of fundamentals of geometry. It should be easy, prep once, teach three times, repeat. But you know it never works out like that. All three classes are substantially different.<br /><div><br /></div><div>The first is small, 9 students, all with more substantial learning disabilities. Most of them were in the same math class last year but even though they know each other, they don't work together. My desks are arranged in pairs, but only two students sit together, and they never talk to each other. When we do stations, the problems rotate rather than the students and we don't bother putting the desks into groups. They all sit quietly and are pleasant to work with. A couple are resistant to working, but in non disruptive ways. When my co-teacher and I tell the students to use their resources, we mean their binders not their neighbors. We frequently get to sit with a student or alternate between two rather than running around the room. These students struggle with math, so even with three adults (one student has a medical para) they don't get through as much math as the other groups, but they are generally aware that math is hard for them. They recognize it takes extra effort, but that we won't ask anything impossible of them. I wait for volunteers during class discussion or ask every student to answer (some have issues focusing and repetition is necessary for them to commit some definitions to memory). </div><div><br /></div><div>The next class is down to 14 students (we lost several and gained one as the year progressed) but I don't think I've had a single class with every student present; we usually start class with only a handful. Many of them are beyond their second year of high school. They either repeated algebra last year or are repeating geometry this year. There are clashing personalities and a whole lot of obstinant defiance. It's the end of the day and they're done. On some days a couple decide to be role models and get groups working together, but they can just as easily turn the class against me. The ones who are consistently ready to learn at the beginning of class are easily frustrated and shut down regularly. This group can't handle stations, I tried them in a variety of ways and determined this crew needs much more structure. This class revolves around timers, a lot more whole class work and brain pop. A student requested it once and so I've used every relevant video they have (can you tell I'm a bit desperate?). Usually a student is excited to push the button during the quiz and most of the class will give some thought to the questions when cold called. They do a few practice problems at a time and then we switch to get the practice in without running the risk of anyone getting sidetracked. They make use of the white boards. Students stand, sit on desks, wander the room, jump between groups and generally look like chaos, but somehow we always end up ahead of the other classes. These students don't struggle with math, they struggle with school. </div><div><br /></div><div>The third class is 21 students. One third have a math disability, one third are English language learners and the remaining third have a variety of emotional issues. This group is also at the end of the day (we have an alternating day schedule) and they, too, are worn out by the time they arrive. They're boisterous but good natured. They get back to work when told, but then are giggling about something else a few minutes later. When they work in stations they happily talk to each other, sometimes even about math. When we tell this group to use their resources we mean - don't sit there not doing anything waiting for a teacher when your neighbor knows how to help you! They move around the room but mostly with purpose, they use the tools available, many like to solve problems on their desk and getting their paper stamped for completing a station is a good reward. They monitor each other. It's a needy class that has my co-teacher and I on the move the entire 90 minutes but we are slowly training them to be independent learners. A variety of students participate in class discussions and we leave the others alone since we checked in with them during the activity. </div><div><br /></div><div>While I prep one lesson for all three classes, the implementation is substantially different. One class does problems from the board while the others get printed problems cut up into individual assignments. They all do the activities, but some on paper, others on the big white boards and still others on the dry erase desks. Some classes discuss, others report out answers having already discussed nearly every question with us individually. In all cases each student gets practice solving problems and everyone both uses and hears geometry vocabulary. But each class is a different environment and I strive to maximize the potential of each unique grouping. It's exhausting, but it's more exhausting to battle with a class to fit some ideal they aren't ready for!</div>http://drawingonmath.blogspot.com/2013/12/classroom-environments.htmlnoreply@blogger.com (Tina C)5tag:blogger.com,1999:blog-812794395259173668.post-9201632724677138111Thu, 05 Dec 2013 23:08:00 +00002013-12-08T18:24:48.726-05:00Sharing a Lesson<strike>I haven't shared a lesson on this blog all year!</strike> I have only shared one post on a lesson so far this year! Part of that is that neither of my preps are new this year, but that doesn't mean I've written about everything already. Not to mention I'm tweaking everything I do this year. But since no lesson is jumping out at me that I want to share, I'm asking you. A few requests should get me back in the momentum of sharing.<br /><div><br /></div><div>I teach fundamentals of geometry, a course for students with learning disabilities and a significant contingent of English language learners. We started with patterns. Then lines and angles. Most recently triangle inequalities and properties of special triangles. Up next are transformations and congruence. </div><div><br /></div><div>My other course is honors PreCalculus. They had a summer assignment on functions. Then we jumped right into trig. Unit circle, graphing, identities and currently law of sines and law of cosine. </div><div><br /></div><div>So, what topic do you want to read about? If you want to read about something other than a lesson feel free to ask about that too!<br /><br />Edit 12/8/13: Turns out I lied. When I saw the comment about compass and straightedge I remembered posting about using <a href="http://drawingonmath.blogspot.com/2013/11/properties-of-triangles.html">graph paper rulers</a> as fake compasses. But still, only the one post!</div>http://drawingonmath.blogspot.com/2013/12/sharing-lesson.htmlnoreply@blogger.com (Tina C)7tag:blogger.com,1999:blog-812794395259173668.post-4608461532452411179Mon, 02 Dec 2013 00:10:00 +00002013-12-01T19:10:51.372-05:00Talking Math With Your ParentsI spent Thanksgiving break at my parents house. This involves a lot of time spent playing games. The conversations during the games Saturday evening stuck out to me the most. Now, my brother is in medical school and I'm a math teacher, so when my parents talk math with us it isn't to teach us reasoning, but because it is so engrained in all of us that these are the conversations we have while playing games, no matter how old we are.<br /><div><br /></div><div><b>Cosmic Wimpout: </b></div><div>My mom rolls 3 fours and a ten. She is way behind. Should she roll the one remaining die and keep all four scoring dice or only keep the ten and hope for better scoring dice? We discussed some contributing factors (if she only rolls one die she will need to get a five or ten out of the six options, that's a 1/3 chance, if she rolls all four there are lots of good options but also lots of bad ones) but didn't solve the probability problem. It's still on my mind though and I'm tempted to solve it now.</div><div><br /></div><div><b>Dealing Cards: </b></div><div>As I deal the cards, my dad counts aloud the number of cards he has. 1...2...3...4...5...6... ... He doesn't count the seventh card. He leaves us hanging. Finally someone breaks and says seven! This repeats a few rounds, then he doesn't count at all during the following deal. My mom and I take turns counting (she says the odds and I say the evens) without announcing that's the plan. </div><div><br /></div><div><b>Tallying Points: </b></div><div>At the end of a round of 500 Rummy you compute your score. Any cards you have on the table are positive points, any cards still in your hand are negative points. My mom was recording other people's scores so my dad started helping her tally the number of points she had on the table, he got 48. However, she wanted to use a strategy of making zeros - match a negative six in her hand with a positive six on the table. Since he had already added up the positives, my mom decided to be flexible and go with his method. She found two cards in her hand that made ten, put them down and said "ten." My dad responded "38." Which got strange looks from the rest of us until I realized he was finding the total. My mom made another ten, my dad did more subtracting and eventually we found her score. At the end my mom and I shared that first, we make zeroes. If that's not an option, we add all the positives, then add all the negatives, and finally subtract. We laughed and decided my dad was weird, although his method was also valid. </div><div><br /></div><div><b>Discard Pile:</b></div><div>We play the all or nothing rule. If you want some cards in the discard pile you can have the top card or the whole stack. The pile was getting more and more tempting so finally my mom picked up the whole thing. She only put down 30 points so I asked if it was worth it. She thought she only added 28 points to her hand so it was, barely. But she created lots of future opportunities. I went out the very next turn. I turned to her and asked again, was it worth it? She said maybe not. I offered, what if you'd had one more turn? And she responded it probably would have been worth it then. </div><div><br /></div><div><b>Negative Scores:</b></div><div>One round my dad lost seven points, his score the previous round had been 403. My mom, as scorekeeper, said "I have to go back into the 300's!" I commented that this is difficult because you have to think about all three digits at once. </div><div><br /></div><div>This post was inspired by <a href="http://talkingmathwithkids.com/">Talking Math With Your Kids</a> (the <a href="http://talkingmathwithkids.com/2013/">blog</a> and <a href="http://www.amazon.com/Talking-Math-Your-Kids-ebook/dp/B00EYSZH8E/ref=sr_1_2?ie=UTF8&qid=1378483262&sr=8-2&keywords=talking+math+with+your+kids">book</a>). Christopher Danielson, how did we do?</div>http://drawingonmath.blogspot.com/2013/12/talking-math-with-your-parents.htmlnoreply@blogger.com (Tina C)1tag:blogger.com,1999:blog-812794395259173668.post-7095006812393722588Sun, 01 Dec 2013 13:00:00 +00002013-12-01T08:00:04.026-05:00TMCTMC14: Speaker ProposalsWe are starting our gear up for TMC14, which will be at Jenks High School in Jenks, OK (outside of Tulsa – map is <a href="https://maps.google.com/maps?q=jenks+high+school+jenks,+ok&hl=en&ll=36.015782,-95.865326&spn=0.986379,2.113495&sll=37.0625,-95.677068&sspn=60.764775,135.263672&hq=jenks+high+school&hnear=Jenks,+Tulsa,+Oklahoma&t=m&z=10" style="color: #1155cc;" target="_blank">here</a>) from Thursday, July 24 through Sunday, July 27, 2014. We are looking forward to a great event. Part of what makes TMC special is the wonderful presentations we have from math teachers who are facing the same challenges that we all are.<br /><br />To get an idea of what the community is interested in hearing about and/or learning about we set up a Google Doc (<a href="http://bit.ly/TMC14-1" style="color: #1155cc;" target="_blank">http://bit.ly/TMC14-1</a>). It’s an open GDoc for people to list their interests and someone who might be good to present that topic. If multiple people were interested in a session idea, they added a “+1” after it. The doc is still open for editing, so if you have an idea of what you’d like to see someone else present as you’re writing <a href="https://docs.google.com/forms/d/1Kryo0tX6qkZNThp5vlBa1WXM6VRQA76oYN_npsNwsR4/viewform" style="color: #1155cc;" target="_blank">your own proposal</a>, feel free to add it!<br /><br />This conference is by teachers, for teachers. That means we need you to present. Yes, you! What can you share that you do in your classroom that others can learn from? Presentations can be anything from a strategy you use to how you organize your entire curriculum. Anything someone has ever asked you about is something worth sharing. And that thing that no one has asked about but you wish they would? That’s worth sharing too. Once you’ve decided on a topic, come up with a title and description and submit <a href="https://docs.google.com/forms/d/1Kryo0tX6qkZNThp5vlBa1WXM6VRQA76oYN_npsNwsR4/viewform" style="color: #1155cc;" target="_blank">the form</a><br /><br />If you have an idea for something short (between 5 and 15 minutes) to share, plan on doing a My Favorite. Those will be submitted at a later date.<br /><br />The deadline for submitting your <a href="https://docs.google.com/forms/d/1Kryo0tX6qkZNThp5vlBa1WXM6VRQA76oYN_npsNwsR4/viewform" style="color: #1155cc;" target="_blank">TMC Speaker Proposal</a> is January 20, 2014. This is a firm deadline since we will reserve spots for all presenters before we begin to open registration on February 1, 2014<br /><br />Thank you for your interest!<br /><br />Team TMC – <a href="mailto:lmhenry9@gmail.com" style="color: #1155cc;" target="_blank">Lisa Henry</a>, Lead Organizer, Shelli Temple, Justin Aion, Mary Bourassa, Tina Cardone, James Cleveland, Cortni Kemlage, Jami Packer, Anthony Rossetti, and Glenn Waddellhttp://drawingonmath.blogspot.com/2013/12/tmc14-speaker-proposals.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-1389487862394799750Sat, 30 Nov 2013 14:32:00 +00002013-12-03T18:53:07.095-05:00nixNix the Tricks: The BookIt is the last day of November. My self-imposed deadline for typesetting <a href="http://nixthetricks.com/">Nix the Tricks</a>. And I've done it!<br /><br />In the beginning, there was a calculus teacher complaining about students' lack of a good definition for slope. Then there was a conversation among my department members on tricks we hate seeing kids show up to our classes with. I expanded the conversation to members of my online math community. We brainstormed and debated what constituted a trick and which were the worst offenders. I organized. More people joined in on the conversation and shared better methods to emphasize understanding over memorization. I organized some more. Contributions started to slow down. The end result was 17 pages. I had grand dreams of a beautifully formatted resource that we could share with teachers everywhere. A few people shared my dream. We discussed formatting and organization and themes. Then the end of the school year craze happened, and suddenly it was August! School started, life got busy, and then I started hearing about NaNoWriMo. I decided that in November I would typeset the whole thing. If someone could write 50,000 words in a month, I could code something that was already mostly written. It was difficult, I had never paid attention to all the types of pages in a book, but the internet was there for me, and today, the last day of the month, I can say:<br /><br />Hey, I just wrote it,<br />And this is crazy,<br />But here's the <a href="http://www.nixthetricks.com/Download.html">download</a>,<br />So read it, maybe!<br /><br />Check out the website: <a href="http://nixthetricks.com/">NixTheTricks.com</a><br /><br />And now that I've gotten that song stuck in your head, listen to <a href="http://www.youtube.com/watch?v=GwpNgGyQYt8">Tweet Me Maybe</a> from <a href="http://www.twittermathcamp.com/">TMC12</a> while you browse.<br /><br />Thank you so much to everyone that helped, not just this month, but since the beginning of this project. I am so thankful for this community and all that we offer to each other.<br /><br />I do ask one more thing of you. As anyone who has coded anything knows, you eventually go cross-eyed and as many times as you re-read something, you are bound to miss an error that is glaring to anyone with fresh eyes. I've been typesetting the document and editing the website all weekend. I tried to check the links, to look for typos and to test several devices. I got an error on my phone once, but I can't replicate it to know how to fix it. So, if you see any issues at all, no matter how small they seem, please let me know. Leave a comment here, send a note via twitter or use the submission form.<br /><br />Enjoy, share widely and know that I'm rooting for all the teachers who explain and all the students who still ask why.<br /><br />[Edited 12/3/2013 to add background for newcomers to the blog, like those who are here via the Math Forum Newsletter. Welcome!]<br /><a href="http://mathforum.org/electronic.newsletter/"><img src="http://mathforum.org/electronic.newsletter/images/mf.drexel.new.gif" /></a>http://drawingonmath.blogspot.com/2013/11/nix-tricks-book.htmlnoreply@blogger.com (Tina C)8tag:blogger.com,1999:blog-812794395259173668.post-511587755345026706Mon, 25 Nov 2013 02:29:00 +00002013-11-24T21:29:24.505-05:00Mission #8: Sharing is Caring in the MTBoSReblogged from Explore MTBoS:<br /><br /><hr /><br />It's amazing. You're amazing. You joined in the <em>Explore the MathTwitterBlogosphere</em> set of missions, and you've made it to the eighth week. It's Sam Shah here, and whether you only did one or two missions, or you were able to carve out the time and energy to do all seven so far, I am proud of you.<br /><br />I've seen so many of you find things you didn't know were out there, and you tried them out. Not all of them worked for you. Maybe the twitter chats fell flat, or maybe the whole twitter thing wasn't your <em>thang</em>. But I think I can be pretty confident in saying that you very likely found at least one thing that you found useful, interesting, and usable.<br /><br />With that in mind, we have our last mission, and it is (in my opinion) the <em>best</em> mission. Why? Because you get to do something to help someone else. A random act of kindness.<br /><div style="text-align: center;"><a href="http://exploremtbos.files.wordpress.com/2013/11/sharingiscaring.jpg"><img alt="sharingiscaring" class="aligncenter wp-image-281" height="189" src="http://exploremtbos.files.wordpress.com/2013/11/sharingiscaring.jpg" width="403" /></a></div>We want you think about something you saw in the MathTwitterBlogosphere that you think might be useful to a colleague, a department head, an administrator, a student, whatever. And then let them know about it.<br /><br />Some ideas:<br /><ul><li>You have a colleague teaching Precalculus, and you saw a blog author that has posted a lot of good resources and thinking about Precalculus. You email this resource and why they might find it useful.</li><li>You have a math coach who may be interested in the <a href="http://mathmistakes.org/"><em>Math Mistakes</em></a> blog. You share it with this math coach!</li><li>You saw an issue of <a href="http://mathmunch.org/" target="_blank">Math Munch</a> that might spark some interest to one of your particular students (or maybe all of them).</li><li>You saw an activity on fractions that your middle school colleagues would <em>looooove</em>. You share the wealth!</li><li>You think a fellow teacher might benefit from joining twitter. You help them take the leap.</li><li>You attended a <a href="https://www.bigmarker.com/communities/GlobalMathDept/conferences" target="_blank">Global Math Department meeting</a> and you thought of someone who should have been there! You send the recording to that person.</li><li>You belong to an AP Statistics list-serv, and there is a great activity you saw on a blog. You email the list-serv.</li><li>You did an activity inspired by something in the MTBoS. You share that activity with another teacher in your school who teaches the same subject.</li><li>You ask for 5 minutes in a department meeting to share what you have learned about the online math teacher community.</li><li>ANYTHING ELSE! Just share, my little Care Bears, share!</li></ul>In other words, spread the word about something in the MTBoS that you found. You should let someone else who doesn't know about the stuff we're doing (yes, <strong>we</strong>: if you weren't before, you're one of us now! mwahahahaha!) see it, and know that it's out there for them too!<br /><br /><strong>This is the coda to the work you've done over the past two months. We wanted to show you what was out there because all that good stuff out there helped us and inspired us as teachers. Now we want you to be in our shoes. We want you to show others what is out there in the MTBoS that helped you and inspired you as a teacher!</strong><br /><br /><a href="http://exploremtbos.files.wordpress.com/2013/11/pay-it-forward.jpg"><img alt="pay it forward" class="aligncenter wp-image-282" height="409" src="http://exploremtbos.files.wordpress.com/2013/11/pay-it-forward.jpg" width="409" /></a><strong>Your Final Mission</strong><br /><ol><li>Share!</li><li>Write a blog post talking about what you shared, who you shared it with, and why you shared it!</li><li>Tweet out your blog post. Include the #MTBoS hashtag.</li><li>Include your blogpost in the comments <strong>here</strong> and then read and comment on the blog posts of the three commenters directly above you. <strong>Be sure that you are commenting on their blog and not here.</strong></li><li><a href="https://docs.google.com/forms/d/14iPYN03iRASddG2rurlUgZcXSLCNGfpjztC3PpE4udE/viewform" target="_blank">Please fill out our survey</a> to help guide us in future missions. We promise, it's very short. Don't skip the survey as we are planning on compiling all of your fabulous blogs and virtual filing cabinets so we can share them with the world! :)</li></ol>If the survey below is not viewable, please <a href="https://docs.google.com/forms/d/14iPYN03iRASddG2rurlUgZcXSLCNGfpjztC3PpE4udE/viewform">click here.</a><br /><br /><iframe frameborder="0" height="500" marginheight="0" marginwidth="0" src="https://docs.google.com/forms/d/14iPYN03iRASddG2rurlUgZcXSLCNGfpjztC3PpE4udE/viewform?embedded=true" width="760">Loading...</iframe>http://drawingonmath.blogspot.com/2013/11/mission-8-sharing-is-caring-in-mtbos.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-9121330252282184698Fri, 22 Nov 2013 23:26:00 +00002013-11-22T18:26:36.881-05:00A Day In My LifeMy day yesterday:<br /><b><br /></b><b>6:20 am</b> Alarm goes off. Normally I snooze or check twitter/email/reader on my phone before getting up, but this week I am dog sitting while Ashli attends a conference so I have to get up and attend to his needs as well as mine.<br /><b>7:00 am</b> Leave the house. In my mind I leave at 7 am every morning, in reality it's always a few minutes after.<br /><b>7:04 am</b> Arrive at school. Yup, it's a 4 minute drive to get to school, all right turns and only one light on the way in. Contractually we need to be here at 7:12. Class starts at 7:24, but I have a 90 minute prep first block every day so the motivation to arrive early is lacking. I stop in one coworker's room to say hi, then head to my room to deal with my email. My co-teacher arrives to chat, then another coworker has a question, then another coworker with another question. We all have first block prep which is great for collaborating, but rough because kids are more focused on learning at the beginning of the day than the end, ah well.<br /><b>8:20 am</b> Finally manage to finish responding to all my email. Realize how late it is and wonder if I'll ever have time to grade. Realize I'm still wearing my winter coat and scarf, remove coat and take a bathroom break while I have the opportunity. Prep for tomorrow's classes. Stop by coworker's room and we head to the copier together. I complain about being cold and she mocks me for not wearing a jacket. I have a fleece on the back of my chair that I usually wear but I thought just maybe it would be warm enough today to be comfortable in a sweater.<br /><b>8:55 am</b> "bell rings" Well, the bell would ring if we had functioning bells. I think they broke in September, maybe early October, and they're so old it's taking this long to order the part.<br /><b>9:00 am</b> PreCalculus starts. We have a do now and discuss homework, then I project some problems and have a seat. I've found that if I sit down rather than immediately circulate to see who needs help the students are more likely to use their resources and make an attempt. I clean off my desk then start moving through the room to see who's stuck.<br /><b>10:00 am</b> Three students have completed the problem set but the rest of the class is making good progress I don't want to interrupt. Two of the students who are done are trying to sneakily do their English homework, I tell them to feel free. I get the third student to help me hang some student work in the hallway (geometry class did the triangle quilt project a few weeks ago and they were still sitting on my desk). Before the end of the class more students are done and so we discuss. As the students leave one asks me if I have a plan for pep rally week. I raise my eyebrow and he explains that he'd like to do something with Fibonacci numbers and the golden ratio because they're really cool. Another student asks what Fibonacci numbers are. I remember that on Wednesday we have a weird schedule - regular first block, shortened second block and then the pep rally. Fibonacci numbers sounds like a great idea for the shortened second block, especially if there's a student in Honors PreCalc who doesn't know what they are!<br /><b>10:26 am</b> PreCalc is dismissed and it's lunch time for half the school. I call this second breakfast and heat up some oatmeal. I eat with mostly math teachers, so I tell them about the student requesting Fibonacci and ask what ideas they have. By the end of lunch I have a list of potential projects and a promised email forward.<br /><b>10:56 am</b> Lunch ends, time for the geometry meeting. I'm in the sophomore house, which means that all teachers with 3 or more sophomore classes have the same block off. On Monday/Tuesday (depending on how our alternating day schedule works out) we meet as a full team. On the remaining days we meet in curriculum groups; today was a day for the four geometry teachers to meet. We discussed plans to continue reinforcing concepts students struggle with during upcoming units. Including an outline of a midsegment lesson I'm excited for (and hope to share soon - hold me to that?). The curriculum director stopped by the meeting for a while. At one point he says something about how I use "that Dan Meyer stuff" which got a confused look from me. Turns out he was talking about discovery style teaching as opposed to "I do - We do - You do." The reference was amusing. At the end of the meeting we get caught up talking about how to engage one of the new teacher's classes - it's filled with repeaters so there isn't much buy-in.<br /><b>12:15 pm</b> Finally make it upstairs, I'm a bit late for hall duty. My exciting job is to stand at the end of the hall to the cafeteria during lunch so that kids don't go any further than the bathroom without a pass. Luckily my mentee's classroom is right there and he has a prep so we get to chat every other day for half an hour. Today we worked together on a PreCalc project we'll assign next week.<br /><b>12:28 pm</b> Lunch duty ends, I race across the school and down two flights of stairs to get to my class before the students do.<br /><b>12:33 pm</b> Geometry class starts. Most of them have a productive class working through stations.<br /><b>2:02 pm</b> School ends. I immediately open the tray of brownies and my co-teacher and I each eat one. I made them last night for the club I run after school. Only a couple students show up since powderpuff practice is at the same time and my seniors are there instead. We still manage to redecorate our bulletin board.<br /><b>2:55 pm</b> Students head out. I clean up a bit and type some random letters in a word document. Leaving an unsaved document prevents the computer from shutting down at automatic shutdown time. It's not energy efficient but it saves me from extreme frustration on the days that the network is down so I can't sign in, plus it takes so long to quit all the programs I don't want running it's much better to let it sleep during the week and only shut down on weekends.<br /><b>3:15 pm</b> Coworker and I arrive at my house. The dog is very excited to see us and we all head out for a walk around my neighborhood. Nice chance to chat and unwind for the day. Coworker suggests doing this regularly, whether I'm dog sitting or not, which is a great idea.<br /><b>4:00 pm</b> Arrive at class (also close by, it's at the middle school which is just up the street from the high school). The state recently added an ELL training requirement for licensure so last year I had to do 10 hours of PD and this year I'm taking a full course. It's run by the state so it's not well organized but the instructor is great and it's a chance to work with my co-teacher as well as a few other math teachers from the district, which has been nice.<br /><b>4:30 pm</b> Break out the last of the brownies. Class still going.<br /><b>5:00 pm </b>Realize I never ate my sandwich, I usually have lunch at 2 when students leave but I got distracted by brownies. Have a very late lunch. Class still going.<br /><b>6:40 pm</b> Class ends, 20 minutes earlier than scheduled - thanks instructor!<br /><b>6:50 pm</b> Arrive home, try to get caught up with the internet.<br /><b>8:00 pm</b> Realize it's late and I haven't had dinner yet. I had plans to work on Nix the Tricks this evening too. Food takes priority.<br /><b>8:15 pm</b> My mom calls, I'm finishing dinner as I answer.<br /><b>8:30 pm</b> Finished with phone call and decide to play on my phone. Too late to do any writing.<br /><b>9:00 pm</b> I'm exhausted and start heading toward bed. Thank goodness tomorrow is Friday!http://drawingonmath.blogspot.com/2013/11/a-day-in-my-life.htmlnoreply@blogger.com (Tina C)0tag:blogger.com,1999:blog-812794395259173668.post-1356054880252911262Sat, 16 Nov 2013 04:39:00 +00002013-11-15T23:41:11.590-05:00nixNix the Tricks: More ChaptersThis week I decided that front matter was more fun than writing regular chapters. So now I have a cover, title page, colophon, epigraph and preface. Then an introduction. Finally, a new chapter of tricks. It's up to 26 pages! Of course, by NaNoWriMo standards I've accomplished very little, that dotted line is where I'm supposed to be to hit the 50,000 word goal.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-VHbXtIuhxpg/Uob0QvyX7ZI/AAAAAAAAEYE/xf4lK3ld5Ss/s1600/Screen+Shot+2013-11-15+at+11.25.10+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="235" src="http://2.bp.blogspot.com/-VHbXtIuhxpg/Uob0QvyX7ZI/AAAAAAAAEYE/xf4lK3ld5Ss/s320/Screen+Shot+2013-11-15+at+11.25.10+PM.png" width="320" /></a></div><br />They don't know that this isn't a novel and 50,000 words was never a goal. I remind myself I have at least an extra thousand 'words' when you include the code. Whatever that means. But I appreciate the email reminders to write, so I stay connected with that organization. The time I spend formatting and making images and researching the parts of a book aren't represented in this graph though, I have been working a lot! The only remaining productive procrastination option would be to figure out how an index works in LaTeX, but mostly all I have left is the regular writing so I'm hoping things move quicker the second half of the month.<br /><br />I think this week I convinced the linked text to stay active. It definitely works on scribd, maybe while embedded as well. [Update: the links to sections of the document work, but not the ones to the world wide web. Intriguing.]<br /><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/184605902/Nix-the-Tricks" style="text-decoration: underline;" title="View Nix the Tricks on Scribd">Nix the Tricks</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_31102" scrolling="no" src="//www.scribd.com/embeds/184605902/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />Two things:<br /><br />Michael did an amazing job of matching up <a href="http://mathmistakes.org/">math mistakes</a> with tricks, but he didn't have one to match every trick. For the new chapter I'm seeking: 1) messing up order of operations by multiplying before dividing 2) cancelling a square and a square root<br /><br />Editors. Doesn't appear that I'm going to get much feedback by posting here. You want to be an editor? I'll put your name on the verso! (Check out that lingo I learned.)http://drawingonmath.blogspot.com/2013/11/nix-tricks-more-chapters.htmlnoreply@blogger.com (Tina C)8tag:blogger.com,1999:blog-812794395259173668.post-7965385756702445387Sun, 10 Nov 2013 19:25:00 +00002013-11-10T14:25:10.345-05:00GeometryProperties of TrianglesLast year when we started talking about triangles one of my colleagues did the relationship between angles and sides first (the largest angle is opposite the longest side etc.) and found great success. The angle properties of isosceles and equilateral triangles easily follow the definition, the hypotenuse is obviously the longest side of a right triangle, the impossibility of an obtuse equilateral triangle is quickly apparent. So I wrote down that I would do that first this year. But then I forgot the definition of first, I had students define types of triangles and try to draw obtuse equilateral triangles before discovering this relationship. I know now, first means first. At the very beginning. As soon as we say the word triangle, we should be doing the exploration relating sides to angles.<br /><br />A fun way to transition from lines to triangles is this <a href="http://mr-stadel.blogspot.com/2012/10/transversals-tape-and-stickies.html">activity from Mr. Stadel</a>. I retyped it to get the instructions and diagram on one page, it's exactly the same as his though.<br /><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/183060934/Matching-Angles-doc" style="text-decoration: underline;" title="View Matching Angles.doc on Scribd">Matching Angles.doc</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_16978" scrolling="no" src="//www.scribd.com/embeds/183060934/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />With just a single extra line, you can prove that the angles of a triangle add up to 180:<br /><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="http://1.bp.blogspot.com/-95kuKAa9iSQ/Un_bXYxyfSI/AAAAAAAAEWs/J-SNQ5yxZxU/s1600/500px-Triangle_angle_sum.svg.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="167" src="http://1.bp.blogspot.com/-95kuKAa9iSQ/Un_bXYxyfSI/AAAAAAAAEWs/J-SNQ5yxZxU/s320/500px-Triangle_angle_sum.svg.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">http://en.wikibooks.org/wiki/Trigonometry/Proof:_Angles_sum_to_180</td></tr></tbody></table><br />Now we've mentioned the word triangle, time to explore sides and angles! This sheet is adapted from one in my textbook. I edited it with my colleagues. It was awesome. Kids sat quietly cutting out their side lengths, trying triangles and figuring out what worked. They weren't just quiet because they were cutting and tracing, there was thinking involved in the process. They were noticing and wondering, because, as one student declared, "You <b>always</b> ask us that!" She was complaining that I asked her to write something down when she finished, but what a great complaint 'You always want to know what we think!' I smiled, I have no idea what thoughts ran through her head, but then she commenced recording her ideas.<br /><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/183061610/Triangle-Inequalities-pdf" style="text-decoration: underline;" title="View Triangle Inequalities.pdf on Scribd">Triangle Inequalities.pdf</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_90457" scrolling="no" src="//www.scribd.com/embeds/183061610/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br />I'd have a picture of graph paper rulers, but I forgot to take one. Might remember tomorrow. Idea: cut out rectangles 1 box wide in the length needed. Compasses, wooden rulers and plastic rulers all work as well, but compasses are tough to hold steady and most rulers are long and thus unwieldy. We used graph paper just a bit larger than the standard size. Give kids one full sheet to draw on and a quarter sheet to cut from and they're good to go.<br /><br />Goals of this activity: figure out what side lengths make a triangle (triangle inequality) and discover the angle-side relationship. Having the side lengths in decreasing order would make the second discovery more obvious. I chose to have kids work for it a bit, but am open to change. This page was typeset in LaTeX, if you want the original file so you can edit it please let me know.<br /><br />My next step would have been to define all the words that we use to classify triangles, but since I already did that it will be to have kids work through stations practicing and applying the rules they discovered. I'm unreasonably excited about the coupon holder I got at Staples for keeping all of my station activities in order. Organizers are such fun!http://drawingonmath.blogspot.com/2013/11/properties-of-triangles.htmlnoreply@blogger.com (Tina C)3tag:blogger.com,1999:blog-812794395259173668.post-9100484649696823261Fri, 08 Nov 2013 02:06:00 +00002013-11-07T21:06:16.700-05:00nixNix: Ratios and Proportional Reasoning ChapterI've realized that while I'm pretending to do NaNoWriMo, it's a week in and I have 2,426 "words" typeset (let's not talk about how many of those are numbers or symbols). Anyone who manages to write 50,000 words in a month is seriously impressive! Still, I have made progress that I want to share. I started with Chapter 2, because I can (and I have a soft spot for proportional reasoning). It has taken a lot of tinkering to figure out how I want to format this thing, but I have something I think I like. Right now I'm working in full page mode, which is good for printing but not a whole lot else. The back of my mind is swirling with eBook and tablet friendly formats, but I'm trying to focus on getting the whole thing typed first. So, without further ado, Chapter 2:<br /><br /><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/182487023/Ratio-Chapter-pdf" style="text-decoration: underline;" title="View Ratio Chapter.pdf on Scribd">Ratio Chapter.pdf</a></div><iframe class="scribd_iframe_embed" data-aspect-ratio="undefined" data-auto-height="false" frameborder="0" height="600" id="doc_90205" scrolling="no" src="//www.scribd.com/embeds/182487023/content?start_page=1&view_mode=scroll&show_recommendations=true" width="100%"></iframe><br /><br /><b>Things I'm excited about: </b><br />Clickable links! (referring back to previous sections, the table of contents - not pictured - and linking to math mistakes)<br />Words wrapping around images (magic!)<br /><br /><b>Things I'm wondering about: </b><br />Does it read smoothly?<br />Are the reasons convincing and the alternatives do-able?<br />I accidentally made an image set for multiplying fractions when I meant to do addition, so I added in the rectangular array method even though there isn't a trick for that (that I know of). Worth including?<br /><br /><b>Things I changed:</b><br />I didn't feel that Least Common Denominator qualified as a trick, I still included a passage about it which uses all the language we had previously, but it doesn't get a title anymore.<br />I created illustrations for each trick (with colors! yay keynote!) because there are so many names for tricks that I wanted it to be completely clear what we were talking about.<br /><br /><b>Up next: </b><br /><a href="https://twitter.com/mjfenton">Michael Fenton</a> is the awesomest! He typed Chapter 1: Operations and Algebraic Thinking into LaTeX so I will be elaborating on and formatting that one next.<br /><br />I thought you would be able to leave comments on a pdf in google drive like you can any other google doc, but apparently not. Feel free to comment here or <a href="https://twitter.com/crstn85">tweet me</a> with thoughts. I really want this to be as peer edited as possible. So grammar to content, I'd love your feedback on all of it.http://drawingonmath.blogspot.com/2013/11/nix-ratios-and-proportional-reasoning.htmlnoreply@blogger.com (Tina C)1tag:blogger.com,1999:blog-812794395259173668.post-1720016566699085783Sun, 03 Nov 2013 20:14:00 +00002013-11-03T15:17:55.936-05:00Teaching_PracticesQuarter 1 SuccessesI haven't changed much about my classroom layout this year, but the one new addition, Mathy McMatherson's <a href="http://mathymcmatherson.wordpress.com/2013/06/06/sbg-the-wall-of-champions/">Wall of Champions</a>, is awesome!!<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-E6uK2p0BOtQ/UnalxUJCk5I/AAAAAAAAEU4/3ceYh2xrla4/s1600/perfect+score.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-E6uK2p0BOtQ/UnalxUJCk5I/AAAAAAAAEU4/3ceYh2xrla4/s320/perfect+score.jpg" width="238" /></a></div>Last year any time a student got a perfect score I would stamp their paper with a gold star (because a student told me even high schoolers like stickers and I compromised with stamps). Then I read Dan's post, found yellow star sticky notes at Staples and claimed a spot on the wall. I purposely picked a section of wall in the front of the room near my desk - as soon as the first class had gotten their quizzes back other classes, students I had after school who weren't in my class and colleagues started asking about the stars. Since I took the photo above I've run out of yellow stars and started in on the orange ones (they come in a two pack). Students are competing to get their star the highest on the wall, creating a cluster with all their stars and spreading to other parts of the wall. It's great to see kids celebrating successes and aiming for perfection rather than "good enough."<br /><br />I started using a required binder system in geometry last year and have fine tuned it this year. For PreCalc I don't require a binder but offer them all the same resources except the structured notes. The very first thing is a plastic sandwich bag we forced through the rings filled with a pencil, a dry erase marker and a cloth for erasing the dry erase marker (cotton face wipes were destroyed within a day, kids did not interpret them as reusable). There are still kids looking for a pencil or pen sometimes, but less often than in the past I think. Next is a plastic sleeve that contains a graph on one side and a <a href="http://www.scribd.com/doc/181051262/problem-solving-template-docx">problem solving template</a> on the back. Both were essential in our pattern unit. They've gotten less use lately, I need to mix in more word problems and multi-step problems.<br /><br />The first section is the reference section. <a href="http://drawingonmath.blogspot.com/2013/08/geometry-curriculum.html">Flappers</a> are still working well. Last week my co-teacher had an awesome idea - a <a href="http://www.scribd.com/doc/181216626/notation-dictionary-doc">notation dictionary</a>. There are plenty of symbols that don't warrant an entire index card for the flappers but students need to have notes on them. Since we started mid-year we did a matching activity where I put all the symbols on the board and they had to match to the definitions. From now on we'll add symbols and definitions as they come up.<br /><br />The next sections are classwork and homework. Boring. Following those is the assessment section. I made yet another <a href="http://www.scribd.com/doc/181217481/Grade-Record-doc">grade recording chart</a> and finally got this one to stick! It helped that I started at the very beginning of the year so either I remember to tell them to fill in the chart as I pass papers back or I see someone flipping to it and tell everyone to do the same. It turned out to have more space than I needed so I'll be modifying it to record their investigations (graded classwork/projects) as well. I wanted to use it when kids requested to reassess, especially if they reassess on the same topic more than once so I give them a different version, but I haven't been remembering to do that. Maybe this quarter...<br /><br />The final section is the journal. Using "<a href="http://drawingonmath.blogspot.com/2013/10/journaling-in-math-class.html">I notice, I wonder</a>" has been great. I'm going to try <a href="http://musingmathematically.blogspot.com/2013/10/digitizing-exit-slips.html">QR code journaling</a> a la Musing Mathematically, but just with PreCalc to start. Baby steps.<br /><br />So, students are motivated to do well and have the support to do so with their binders. All that's left is great lessons to let them show off! Having two preps that I taught last year is awesome. My filing system + dropbox + memory (functional since it was just last year) = tons of resources. This year has been much more about "I want to do this - I have this thing that needs a bit of modification" than "I want to do this - should I write it or look for one?" Memory is key in that equation though, I need to remember that I have resources all the time, even when it seems easy to make a new version of a quiz off the top of my head, because that means the retakes I wrote last year won't quite match up. I'm hoping to get better at looking at last year's version first to see if I <b>need</b> to change things.<br /><br />How about you? How are you <a href="http://drawingonmath.blogspot.com/p/matheme.html#Year">faring so far</a>? What are your <a href="http://drawingonmath.blogspot.com/p/matheme.html#Goals">goals</a> for the school year? The world wants to know.http://drawingonmath.blogspot.com/2013/11/quarter-1-successes.htmlnoreply@blogger.com (Tina C)2tag:blogger.com,1999:blog-812794395259173668.post-3710625776016494516Sun, 03 Nov 2013 01:25:00 +00002013-11-02T21:52:25.904-04:00Teaching_PracticesIntentionsAs first quarter draws to a close I find myself frustrated with my work flow. I always feel rushed, behind and overwhelmed by my pile of grading. I have ideas but forget to implement them, or do once and then lose them to some other more urgent priority. Some of this can be attributed to the panic the administration is feeling over inadequate progress after a year of being labeled an underperforming school. This panic is passed on to us in the form of more paperwork, requirements and initiatives. However, all of this is out of my control, so I need to find ways to manage the things that are in my control so I'm happy and healthy throughout the school year.<br /><br />My school runs a block schedule and it worked out this year that I have a 90 min prep first thing both days. It's not been good because I put things off until the next day, knowing I have that chunk of time in the morning. I do use the time productively, but we all know that things come up and a couple times I've been scrambling to finish something as the bell rings (well, the imaginary bell, our system has been broken for weeks). So, I'm setting the intention to <b>be a day ahead in my prep</b>, that way if the bell rings I can save and finish after school.<br /><br />It will be easier to stay ahead if I take the time to look at my unit plans more frequently. The district wants all the curriculum online, which has actually been good because it means lots of time for conversations about our units and sharing of ideas. For geometry the website has a list of topics, vocabulary and standards; this year we're adding in a suggested order (but are being clear with administration that we have no intention of being in lockstep). For PreCalc we are putting in all of that information as we go, but I have notes from last year to refer to. In both cases, I've taught the class before and have ideas on what works and what needs altering, but I need to take the time to look at all of that. So, I intend to <b>outline the whole unit before starting day to day prep</b> by looking at the online curriculum and my own resources.<br /><br />Between things I think of, conversations with colleagues and conversations with you (my online math community) I always have new ideas I want to try. I simply don't have time to implement them all, and I need a regular reminder of that. If I try everything then I won't have time to follow through with any of them, and that's not good for anyone. So, I will <b>be really picky about trying new things and follow through </b>on those that make the cut. Note: this is not about lesson ideas - those can happen one day and be gone the next and I always love new lessons, I'm talking about procedures, classroom management methods and other such things that require continuity to work.<br /><br />All that said, I've done tons of cool things this year that I'm really excited about. I will share some things that have been working in the next post. But before I end this post, a final intention:<br /><br /><b>Typeset <a href="http://www.nixthetricks.com/">Nix the Tricks</a></b>. Yes, I just wrote an entire post about how I'm overwhelmed with things to do, but this is an at home project, not a school project (I only do school work at home on Sundays) and this project is one that reminds me why I love teaching. I can give up a couple episodes of Doctor Who a week to work on this. As other people work on their novels for <a href="http://nanowrimo.org/">NaNoWriMo</a> I will work on taking this database and turning it into something readable. There are just about 30 tricks right now, so if I average one per day I'll be golden. I'm working in LaTeX because I hate typing formulas in anything else, and it even has a book template, which makes this feel very official. Plus pdf's are everyone friendly. As I finish each chapter, I'll post it here for feedback - I want a lot of feedback. I've realized that it's my project and no one is going to write it for me, but I still need your help! This community is hugely important to me and I want to spread our communal expertise to a still broader audience.<br /><br />What are your <a href="http://drawingonmath.blogspot.com/p/matheme.html#Goals">goals</a> for the school year? How are you <a href="http://drawingonmath.blogspot.com/p/matheme.html#Year">faring so far</a>? The world wants to know.http://drawingonmath.blogspot.com/2013/11/intentions.htmlnoreply@blogger.com (Tina C)3tag:blogger.com,1999:blog-812794395259173668.post-8721708606057596751Wed, 09 Oct 2013 21:48:00 +00002013-10-09T17:49:04.044-04:00Teaching_PracticesJournaling in Math Class<span style="font-family: inherit;">My first experience with teaching was at a summer camp for high schoolers. One of the routines involved each student writing in a journal at the end of class to record their accomplishments of the day. I've carried this routine into all of my classes, from pre-algebra to AP calculus, and it makes my classroom unique. (This post is part of <a href="http://exploremtbos.wordpress.com/2013/10/06/mission-1-the-power-of-the-blog/">Explore MTBoS</a>, for Mission 1.)</span><br /><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">I am ashamed to admit that I have sullied the good intentions of this routine by using it to meet the administration's strange requirements like "students must engage with the written objective" by asking them to journal on "How did you meet today's objective?" before reaching the more interesting second question (<a href="http://drawingonmath.blogspot.com/2011/10/reflection-and-self-assessment.html">wrote about that</a> and had a discussion in the comments). Other years I haven't had the requirement so I struggled to phrase the question in a way that would get the students writing about "least common multiples" instead of "hot dogs and buns" or "p. 132." I've asked "What math did you learn?" but without the results I was really hoping for; it just wasn't reflective enough and that's what a journal is supposed to be, a place to reflect on class. This year I think I've got it: </span></div><div><blockquote class="tr_bq"><span style="font-family: inherit;">What did you notice or wonder during class?</span><br /><span style="font-family: inherit;"></span><span style="font-family: inherit;">(Plus a varying second question, which I <a href="http://drawingonmath.blogspot.com/2012/05/math-journals.html">analyzed and listed once</a>)</span></blockquote></div><div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;">This phrasing finally allows me to say:</span></div><div style="margin: 0px;"><ul><li><span style="font-family: inherit;">I don't want to know what you did, I want to know what you thought. </span></li><li><span style="font-family: inherit;">Its impossible to be awake in my class for 90 minutes and not have a single thought. In the past it was possible to not meet the objective or not learn any new math, but "I didn't notice or wonder anything" is 100% cop out and once I call kids on it they start sharing. </span></li></ul></div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;">Bonus- the answers to this question are 100 times more interesting to read than "I learned about least common multiples" but still has them using the vocabulary that I want them practicing. I've recorded some of the most interesting responses, first to share back with students to model the types of answers I'm looking for, then to share with you because I've been meaning to write this post for a month!</span></div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;"><br /></span></div><div style="margin: 0px;"><span style="font-family: inherit;"><b>Honors PreCalculus:</b></span></div><div style="margin: 0px;"><span style="font-family: inherit;">I wonder how a function is even or odd. </span></div><div style="margin: 0px; min-height: 15px;"><br /></div><div style="margin: 0px;"><span style="font-family: inherit;">I noticed that the graph had symmetry on the y-axis. </span></div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;"><br /></span></div><div style="margin: 0px;"><span style="font-family: inherit;">South America must have the most drastic change in speed of rotation. </span></div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;"><br /></span></div><div style="margin: 0px;"><span style="font-family: inherit;">I realized that different parts of the world spin slower than others depending on how close they are to the north/south pole. </span></div><div style="margin: 0px; min-height: 15px;"><br /></div><div style="margin: 0px;"><span style="font-family: inherit;">I wonder if I can find an easier way to calculate revolutions</span></div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;"><br /></span></div><div style="margin: 0px;"><span style="font-family: inherit;">I wonder about the guy who created pi, if he knew it would be used for this sort of stuff.</span></div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;"><br /></span></div><div style="margin: 0px;"><span style="font-family: inherit;">I noticed how easy it is to see the patterns on a graph</span></div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;"><br /></span></div><div style="margin: 0px;"><span style="font-family: inherit;">Class keeps getting more difficult every class/week, I like the challenge.</span></div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;"><br /></span></div><div style="margin: 0px;"><span style="font-family: inherit;">I noticed that the sin/cos graphs are like parabolas.</span></div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;"><br /></span></div><div style="margin: 0px;"><span style="font-family: inherit;"><b>Fundamentals of Geometry:</b></span></div><div style="margin: 0px;"><span style="font-family: inherit;">I notice that this class teaches math differently than I'm used to learning. </span></div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;"><br /></span></div><div style="margin: 0px;"><span style="font-family: inherit;">I notice that I remember some things from last year. </span></div><div style="margin: 0px; min-height: 15px;"><span style="font-family: inherit;"><br /></span></div><div style="margin: 0px;"><span style="font-family: inherit;">Day 1: I wonder how difficult geometry will be. </span></div><div style="margin: 0px;"><span style="font-family: inherit;">Day 3: I notice that geometry is easier than I thought. </span></div></div>http://drawingonmath.blogspot.com/2013/10/journaling-in-math-class.htmlnoreply@blogger.com (Tina C)3tag:blogger.com,1999:blog-812794395259173668.post-4527970019933479252Wed, 25 Sep 2013 01:29:00 +00002013-09-24T21:45:08.397-04:00Pattern PuzzleI have leftover yarn from another project that I want to use to crochet a blanket. So far I've crocheted two rows and I'm not sure what color to make the next row so I use up as much yarn as possible without needing to buy more yarn of any color. The <a href="http://www.crochetgeek.com/2009/04/larksfoot-crochet-pattern-stitch-baby.html">stitch I'm using</a> looks best if every row is a different color. I took some measurements and found:<br><div><br></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-e6IQXlGVT7U/UkI8c48MozI/AAAAAAAAEPc/3lMCNgJ280w/s1600/2013-09-24+21.25.13-2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-e6IQXlGVT7U/UkI8c48MozI/AAAAAAAAEPc/3lMCNgJ280w/s320/2013-09-24+21.25.13-2.jpg" width="267"></a></div><div><br></div><div><br></div>Yarn:<br>1.8 oz white<br>5.3 oz multi<br>2.3 oz blue<br>11.8 oz brown<br><br>2 rows:<br>1.0 oz<br>1.25 inches x 5'8"<br><br>What order should I use the colors in? I want an easy to remember pattern ideally, so I don't have to look up the next color after every row. How big will the blanket be if I follow your pattern? If you don't think this is big enough for a blanket, what's the least amount of yarn I need to buy to get a full blanket?<br><br>Answers I get before 7 pm Sept. 25 will be taken into consideration. Answers I get after that will be interesting to chat about, but I'll have already committed to a plan.http://drawingonmath.blogspot.com/2013/09/pattern-puzzle.htmlnoreply@blogger.com (Tina C)1tag:blogger.com,1999:blog-812794395259173668.post-3788071401202909469Sat, 21 Sep 2013 19:20:00 +00002013-09-25T19:27:17.473-04:00Teaching_PracticesStrategies DatabaseI took a course on Differentiation in Math, people read Embedded Formative Assessment and Teach Like a Pirate for Twitter Book Club and several of us reached the point where we had too many strategies to hold in our heads - we needed something easy to flip through when classes stagnated.<br /><br />@Druinok made this <a href="http://statteacher.blogspot.com/2013/07/made4math-student-engagement-flipchart.html">awesome flipchart</a>. I wanted to make an online version of index cards that were searchable and sortable. People suggested Evernote. <a href="http://function-of-time.blogspot.com/">Kate</a> graciously offered to set up a public notebook. I added my stuff. I couldn't decide how to format things so I let it fall to the wayside.<br /><br />Whether or not you have evernote, you can <a href="https://www.evernote.com/pub/k8nowak/differentiationstrategies">view the notebook</a>. Check out what I currently have. <strike>Add a note of your own. Leave a comment or edit the note with tags that would be helpful.</strike>[Edited 9/25: apparently you can't edit unless I add you, anyone want to transfer this to google docs?] I copied and pasted from the assignments I wrote for my class so the formats are inconsistent. It's a work in progress, but I'd rather it be a public work in progress than wait until it's nicely formatted! Eventually I'd love to have each note give a brief description of the strategy, link to blog posts with more complete descriptions or specific examples and have labels that would help someone search the database (indroductory vs. review type things).<br /><br />So:<br /><a href="https://www.evernote.com/pub/k8nowak/differentiationstrategies">Read stuff on Evernote</a>.<br /><strike>Add stuff.</strike><br /><strike>Propose tags (grand master Kate has to add them since she owns the note)</strike><br />Use the strategies and share how they work!http://drawingonmath.blogspot.com/2013/09/strategies-database.htmlnoreply@blogger.com (Tina C)2