tag:blogger.com,1999:blog-80729381884385087212017-02-18T17:45:20.317-06:00The Teacher Studio: Learning, Thinking, CreatingLooking for information about teaching in intermediate grades? Math workshop? Problem solving? Best practice? Quality reading and writing lessons and ideas? Google Classroom and other 1:1 ideas and resources? Teaching tips and educational resources? With rigorous standards and new information about brain research and learning being released all the time, The Teacher Studio is a great place to come to for great teaching ideas, lessons,and products to help you be the best teacher you can be.The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.comBlogger678125tag:blogger.com,1999:blog-8072938188438508721.post-75500235571337500342017-02-18T17:47:00.000-06:002017-02-18T17:45:20.342-06:00Fraction Folding--discovery learning<div style="text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="hands on fraction activities" border="0" height="640" src="https://3.bp.blogspot.com/-wuY79DWAyb0/Vj0Ml4XHCoI/AAAAAAAAO_g/FYGjVd02Gus/s640/pinterest%2Bimage%2Bfraction%2Bpost%2B1.jpg" title="fractions" width="394" /></a></div>Today we kicked off our fraction unit, and I think I am going to really try to do a lot of blogging about it over the next few weeks--because I will be immersed in it AND because it is such a critical component of the Common Core for intermediate grades. I think it is vital that we dialogue about ways to help students <b>build their understanding of fractions</b>, so I invite you to share along with me as I "trace" the path of our unit as it unfolds. I'll try to be clear--but you know how I tend to get wordy! I'll try to include lots of photos and work samples as I go, and I am hopeful that the rest of you will share great ideas and resources that have been successful for you.</div><br />Again, knowing that the CCSS places a great deal of importance on fractional understanding, our district math team made a decision to build in<span style="color: cyan;"> two</span> fraction units into our year--this one and another one later which will work to tie together decimals, fractions, and a more sophisticated level of understanding.<br /><br />Today I started by asking students to reflect on what they already know about fractions and to rate their overall confidence (using our 4 3 2 1 ) scale <a href="http://fourthgradestudio.blogspot.com/2013/01/self-assess-4-3-2-1.html" target="_blank">(Click here to revisit earlier blog post about this!)</a> and the results were quite amazing! In a ten minute writing time, I got to witness a number of misconceptions, poorly explained reasoning, and a bunch of "3's" and "4's" in confidence! Good thing I had planned on starting slowly! Today we started our new math notebooks, and I explained to the students that we are "raising the rigor" one level more (poor things have heard this all year) and we are going to work hard to use our new notebooks to both record our thinking, our practicing, and our new learning. I am going to try a version of interactive notebooks, knowing that I cannot do it in true form as some teachers do . . . I'm just not quite there yet. I'll blog more about this later as it unfolds! For today, we started the section we called "Fraction Concepts" and even talked about what the word "concept" means. Fascinating! I told the students that our job through this unit would be to determine some things we could determine to be "true" about fractions and that we would be working our way through a number of these "truths" during the unit.<br /><br />Today's "truth" involved ensuring that students understand that fractions represent equal parts of something (I didn't really want to use the term "whole" yet--I don't really like to treat fractions of "objects" and "sets" differently until I have to!) and that we would be spending some time creating equal parts.<br /><br />I put the students into pairs (I love popsicle stick picking!) and gave them each 3 minutes to find a classroom object that was either a square, rectangle, or circle and was bigger than a deck of cards and smaller than a book. Each team was then assigned a color of paper and the following task:<br /><br /><span style="color: #351c75; font-size: large;">With your partner, trace and cut out your shape. You will need many of these as the investigation unfolds. Your job is to find ways to divide your shape into equal parts. . . first in two equal parts, then three, and so on. </span><br /><span style="color: #9fc5e8; font-size: large;"><br /></span><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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="fraction unit" border="0" height="480" src="https://1.bp.blogspot.com/-Jm4wOnPw-ss/UQgcwI6zgMI/AAAAAAAABVU/OE3Z9Eng76U/s640/IMAGE_78FEF0C3-6C33-4308-A102-F99FE1C16AC4.JPG" title="teaching fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571">I made sure we had some circles, some rectangles, and some squares...</a></td></tr></tbody></table><span style="color: #9fc5e8; font-size: large;"><br /></span>I then showed the students the following charts--each is labeled "halves", "thirds", "fourths", and so on. As they discovered a way to fold their shape, they were asked to put it on the correct chart. . . and I was on the prowl for work that was not accurate and precise.<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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="teaching fractions" border="0" height="480" src="https://2.bp.blogspot.com/-ZIGgqJjqZcc/UQgctjZoICI/AAAAAAAABVE/c48UkyPOGZg/s640/IMAGE_C1ED33AF-10B1-4CB9-8FB1-CAAD470A1B74.JPG" title="hands on fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Voila! Posters are taped to the ground with deliberate "aisles" so they don't get trampled on!</a></td></tr></tbody></table><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fractions" border="0" height="480" src="https://4.bp.blogspot.com/-YQOkBkLPn7g/UQgcu4IzA0I/AAAAAAAABVM/BTL9A0J8l8o/s640/IMAGE_7039F0C0-42C7-421D-86E3-FC0E14CB2E59.JPG" title="fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Each poster is labeled with the word for the fractional part--I will use the words and different symbols interchangeably throughout the unit. NOTE: The chart does NOT say "1/3" because we were not identifying 1 out of 3 parts.</a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div>Students dug into their work and did need some frequent reminders about using straight edges, working carefully, and so on (I know--shocking!), but the were very engaged and thoughtful. I heard some pretty nifty stuff like:<br /><div style="text-align: center;"><span style="font-size: large;"><br /></span></div><div style="text-align: center;"><span style="color: magenta; font-size: large;">"Hey--as you try to get more pieces, the pieces get smaller!"</span></div><div style="text-align: center;"><span style="font-size: large;"><br /></span></div><div style="text-align: center;"><span style="font-size: large;">and </span></div><div style="text-align: center;"><span style="font-size: large;"><br /></span></div><div style="text-align: center;"><span style="color: #0b5394; font-size: large;">"Man--it's a lot harder to fold the odd numbered pieces!"</span></div><div style="text-align: center;"><span style="font-size: large;"><br /></span></div><div style="text-align: center;"><span style="font-size: large;">and</span></div><div style="text-align: center;"><span style="font-size: large;"><br /></span></div><div style="text-align: center;"><span style="color: magenta; font-size: large;">"If you fold it in half and then in half again, each half gets cut in half!"</span></div><div style="text-align: center;"><span style="color: cyan; font-size: large;"><br /></span></div><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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.blogger.com/goog_311145528"><img alt="fraction unit" border="0" height="480" src="https://3.bp.blogspot.com/-XNs8200vPmg/UQgcxyrA0VI/AAAAAAAABVc/MgMP94FVmFM/s640/IMAGE_DE39FD3F-C2DF-4B3D-B464-7A74C1AEF7E5.JPG" title="teaching fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Tracing...</a></td></tr></tbody></table><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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fraction activities" border="0" height="480" src="https://4.bp.blogspot.com/-9_thfzSmoaY/UQgc3b84jsI/AAAAAAAABV0/8sNpAwG-LB8/s640/IMAGE_2DB9AA2B-1FDD-4CA5-9B3C-76A9CCDA3EC2.JPG" title="teaching fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Using a straightedge for precision...</a></td></tr></tbody></table><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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fraction lessons" border="0" height="480" src="https://3.bp.blogspot.com/-gTomHc6iyx0/UQgc1BQ21JI/AAAAAAAABVs/Dybbbb1kiR4/s640/IMAGE_EFF50082-BFEB-4010-BDFB-F3BE0E18AA47.JPG" title="folding fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Circles are the toughest as this team found!</a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">As the period unfolded (and it became clear that this was going to be a TWO DAY investigation!), our charts began to fill up and things moved a little faster.</div><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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fraction lessons" border="0" height="480" src="https://2.bp.blogspot.com/-SSKGqo8mQnw/VjGIYfQVgiI/AAAAAAAAO8E/mGg-rnvK-xw/s640/fraction%2Bday%2B1%2Bpinterest%2Bimage.jpg" title="fraction activities" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: 12.8px;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">The charts started to fill...first halves and thirds, then fourths and eighths...we'll see how it "unfolds" tomorrow! Got to love a little math humor, right?</a></span></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;">Tomorrow we will finish up our investigation and then ask ourselves if we have discovered any new "truths" to record in our notebooks. Although I am pretty confident that my students would have been able to answer correctly if given a sheet of "shaded fractions" to identify, today's activity showed me that many students are missing some very critical understandings about equal parts and about patterns that arise when dividing shapes. I'm pretty sure that the work we will do over the next few days is going to be very important to build a foundation for the more advanced skills coming. If you aren't familiar with what the CCSS requires from students regarding fractions, I would encourage you to dig in and follow along with us as we try to construct meaning over the next few weeks!</span></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;">***UPDATE***</div><div class="separator" style="clear: both; text-align: center;">This blog post is now a part of my comprehensive fraction unit available by clicking the image below. Hundreds of teachers have now used it to change the way they teach fractions! </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img border="0" height="320" src="https://3.bp.blogspot.com/-2HwOoDzAH_4/VjGFvrklnCI/AAAAAAAAO74/RHKpd66BMSA/s320/fraction%2Bunit%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: left;"><br /></div><br />The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com4tag:blogger.com,1999:blog-8072938188438508721.post-53463456303827359882017-02-15T06:02:00.000-06:002017-02-15T06:02:09.216-06:00Studying Dialogue to Improve Reading AND Writing<div class="separator" style="clear: both; text-align: center;"><a href="http://www.upperelementarysnapshots.com/2017/02/studying-dialogue-to-deepen.html"><img alt="teaching dialogue" border="0" height="332" src="https://3.bp.blogspot.com/--1yUQwl3aWQ/WKPOya1rn6I/AAAAAAAAY9c/sXnYLpF1zaYgtNZNPtNuN_SRyauG_HQIgCLcB/s640/close%2Breading%2Bstudying%2Bdialogue%2BUES%2Bpost.jpg" title="close reading" width="640" /></a></div>Today is my day to post over at Upper Elementary Snapshots, and I hope you'll head over to read about a lesson I did last week to help slow down my readers and get them thinking more deeply about the books they read. I am excited to see if our dialogue studies transfer to their writing next week--so stay tuned! Want to learn more about what we did? Just click the image above and check it out!<br /><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-41126639554257481812017-01-30T06:00:00.000-06:002017-01-30T06:00:17.096-06:00How To Keep The Class Learning While You Pull Small Groups<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Valentines-Day-Product-Bundle-Grades-3-5-1077961"><img alt="teaching math" border="0" height="332" src="https://4.bp.blogspot.com/-lxGKcOgZJ1U/WI55-hgktGI/AAAAAAAAY4o/JCIayVTQezMelTwfLlKt7VsnqYeweIUXgCLcB/s640/keep%2Bthem%2Blearning%2Bwhile%2Byou%2Bpull%2Bsmall%2Bgroup%2Bpost%2BFB%2Bimage.jpg" title="small group math" width="640" /></a></div>This week we are starting our "big multiplying" unit. Not facts--but "big" multiplying. Our standards state that our students must be able to multiply up to 1 x 4 and 2 x 2 digit multiplication, and for some of my students--I know this is going to be a biggie.<br /><br />Because of that, in my planning this week I am planning ahead to be ready to free myself up to pull small groups as much as possible. I know that some students already know the standard algorithm--and others are still not really even confident with arrays. This is going to take some navigating and planning! If you are interested in any of the resources pictured in this post, simply click the image to learn more about it.<br /><br />Here are a few of my "rules to live by" when faced with this type of situation. After all, if I'm going to be working with a small group--I want to do way more than just keep the other students "busy". Right?<br /><br />1. Know where your students are and where they need to be. Make sure you are clear on your content--and have a plan for assessing students formally and informally throughout your teaching so you can really target your instruction to exactly what they need. I'm not a huge fan of pretesting (I think it's tough to make decisions about concepts based on one or two problems) but I am a HUGE fan of formative assessment along the way. If a student can demonstrate mastery, they may need SOME work to build fluency--but their time is better spent doing other things. I use my <a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Multiplication-and-Division-Grades-3-5-1231073">formative assessment resources</a> all the time to take quick snapshots of progress. <br /><br />2. So what if they need that "something else"? I love to immerse my students in challenging, open-ended tasks. For this unit, I am presenting my <a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Valentine-Celebration-Math-Project-Grades-3-5-1629653">Thinker Task Valentine Challenge</a> to the class as one of these options. Notice that I said TO THE CLASS. I make sure ALL students have access to these quality problems. Some students may not get as far into the challenge as others--but we so often "dumb down" our instruction for our struggling students and don't give them access to rigorous and meaningful tasks. I might encourage them to use a calculator...to work in teams...or to use the easier version (I love that these have 2 levels for just this reason!). Again--if I am pulling small groups, there will be time for students to do other work--and this is a great way for students to ALL have a common task. <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Valentine-Celebration-Math-Project-Grades-3-5-1629653"><img alt="Valentine problem solving" border="0" height="480" src="https://2.bp.blogspot.com/-lruOTx2Y_GU/WI5jilFNX1I/AAAAAAAAY4U/VWEJhC-dhDAw7su2cG4phgqBx-KX6uuuwCLcB/s640/Photo%2BJan%2B29%252C%2B3%2B46%2B41%2BPM.jpg" title="Valentine math project" width="640" /></a></div>3. Building fluency is another great thing to do when not in teacher-led groups. Playing games can be a great thing--as long as the students are working on games that are "just right" for them. If students are already fluent with facts, their games should involve some strategy. If they AREN'T fluent, make sure they actually are ready for the skill on the test. There is nothing worse than asking a child to play a game to build fluency and for them to not have the strategies to do it--instead, they spend time practicing wrong! I certainly don't want students who don't know their multiplication facts to practice them incorrectly because I need them to be independent. I'll have to find another skill for them to do independently. For the next two weeks, I am making these multiplication fact fluency games available--each at two levels of challenge. They aren't right for ALL of my students, but they are for MOST.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Valentimes-Math-Games-Set-of-3-Differentiated-Multiplication-Games-1077903"><img alt="multiplication game" border="0" height="480" src="https://4.bp.blogspot.com/-J1XxUPu4sU4/WI5hrXLAnvI/AAAAAAAAY38/NCdeRONQhGUXPidDc-HoZ4PjKsa5hVsZQCLcB/s640/Photo%2BJan%2B29%252C%2B3%2B39%2B06%2BPM.jpg" title="Valentine math game" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">4. Another great thing for students to work on when they aren't with you is word problems. Whether you have them try them alone or work in partners--problem solving is NEVER a bad use of time! Try to find problems that will be engaging (these all have a February or Valentine's Day theme) and are at a variety of levels. I keep mine cut apart and in a pocket chart on my wall and try to put the easier ones toward the top. Many of these also have an "extra" component so students can tackle that piece if it is a good fit for them. As I transition between groups, I'll do some laps around the classroom checking student choices and doing some coaching along the way--but they really do a nice job of coaching each other!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Seasonal-Word-Problem-Collection-Valentines-Day-Grade-3-5-1047616"><img alt="Valentine problem solving" border="0" height="480" src="https://1.bp.blogspot.com/-_h2wXt27xVk/WI5hxZSl8cI/AAAAAAAAY4E/LW03cYV479MA_zuEEXJhfh4gP0BQmDCWQCLcB/s640/Photo%2BJan%2B29%252C%2B3%2B08%2B01%2BPM.jpg" title="Valentine word problems" width="640" /></a></div>5. One more option is to provide the class with a meaningful "warm up" problem or set of problems. By starting off a class like this, you can make sure students understand the task and that they can be productive while you work to pull other groups. <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Valentines-Day-Fun-Learning-Activities-for-Grades-3-5-1050286"><img alt="Valentine printables" border="0" height="480" src="https://2.bp.blogspot.com/-PANtiCRJMXU/WI5h3INzYcI/AAAAAAAAY4I/4MxoJALJEY4t7P7HI48Qlbaf5jnPoCiFACLcB/s640/Photo%2BJan%2B29%252C%2B3%2B07%2B41%2BPM.jpg" title="Valentine word problems" width="640" /></a></div>So...as you are planning for instruction you know might be difficult where you might need to do some focused attention, think about what kind of MEANINGFUL activities you can provide for your students. I can almost guarantee--if you give them engaging things to do, the management concerns all but disappear and you are free to work your magic! <br /><br />Want to pin this for later? Here you go!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Valentines-Day-Product-Bundle-Grades-3-5-1077961"><img border="0" height="640" src="https://4.bp.blogspot.com/-zup-1mKUQdY/WI56DASVxjI/AAAAAAAAY4s/75MpNgeDNdgHXsQuRmhDg1RVuWum4BvKwCLcB/s640/keeping%2Bstudents%2Bworking%2Bwhile%2Byou%2Bpull%2Bsmall%2Bgroups%2Bpin.jpg" width="320" /></a></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-16874980269498660392017-01-28T22:02:00.001-06:002017-01-28T22:02:12.593-06:00More Fraction Number Lines: More Critiquing Reasoning!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction number lines" border="0" height="332" src="https://3.bp.blogspot.com/-_jeylZ4BQhQ/WI1iPlkqpvI/AAAAAAAAY3M/KvMQ3pWNMoI8-J3_swM1tuvbZUwf6x7OwCLcB/s640/fraction%2Bnumber%2Bline%2Bpost%2B2%2BFB%2Bimage.jpg" title="critique the reasoning of others" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">If you missed my post the other day about using number lines to improve fractional reasoning, you might want to take a peek at it before digging into this post! Just <a href="http://www.theteacherstudio.com/2017/01/fraction-number-sense-and-math.html">CLICK HERE</a> if you missed it...because I want you to know that the lesson featured today was not the FIRST time my students had worked with this number lines....and the lesson is one that should come after they have had some other experiences using number lines and having conversations about them.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">So let's dig in! </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Step one--present students with a number line task. As I mentioned the other day, even a number line task can be simplistic and obvious. I am partial to a more "open" number line--where partitions are not already drawn. When you include those partitions, you've done so much of the thinking FOR the students! Remember, I always ask students to THINK before they pick up their pencil so they have a starting point.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="teaching fractions" border="0" height="480" src="https://3.bp.blogspot.com/-wSlggWVBJnU/WIwVecQkEfI/AAAAAAAAY18/EzIrRFJCEgwCXzRO0r8veH9KSLNdRCWAQCLcB/s640/Photo%2BJan%2B27%252C%2B9%2B45%2B34%2BPM.jpg" title="fraction number line" width="640" /></a></div>As students worked, I walked around and checked out their work and hunted for misconceptions. I would make note of how they were organizing their work or strategies they used that I thought might be worth talking about. In my last post, the next step involved pairing up and having discussions together and coming to consensus. Today? Not so much!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="standards for mathematical practice" border="0" height="460" src="https://1.bp.blogspot.com/-ctgzKOHvFN8/WIwVebZrpbI/AAAAAAAAY2A/rc-fEF5Ik1MJeCf53PPJAuB3dp2lBGqjgCLcB/s640/Photo%2BJan%2B27%252C%2B9%2B50%2B56%2BPM.jpg" title="fraction number line" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">My next step was to ask students to come up and place a blue dot on this "class number line" to show where they had marked in in their math journal. I reminded them to NOT change their answer based on what they see--because they need to trust their gut!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction number lines" border="0" height="480" src="https://1.bp.blogspot.com/-hSWjh_2-m4w/WIwVktxgAhI/AAAAAAAAY2E/wJmhXhac36YEYckLz1uvrFjEBkDF7A2uACEw/s640/Photo%2BJan%2B27%252C%2B9%2B45%2B15%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">By the time all the dots were up, it was time to have a discussion where we "critiqued the reasoning" and defended our thinking. We had to use math language and vocabulary with our sharing--so I heard things like...</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">"The dots on the far left can't be accurate because they would really be past 0 and into negative numbers."</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;">and</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">"I think [pointing to a dot] this isn't possible because there is no way that you can keep equal parts."</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">and</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">"It was more clear to me when I put in all the whole numbers so I could find where they 1/3 really should go."</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction lesson " border="0" height="480" src="https://4.bp.blogspot.com/-u7698YC-UbE/WIwVklnksiI/AAAAAAAAY2M/0Qq-ZrILzIcEoMbkAWyQoNy8Dkp8vhaGQCLcB/s640/Photo%2BJan%2B27%252C%2B9%2B44%2B55%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">Some students needed some convincing--and we had frequent "turn and talks" throughout to get EVERYONE involved in discussion the ideas people shared. It was great to see some light bulbs REALLY go off! After our discussion, I sent the students back to their own notebooks to study what they had done and to "revise" their thinking if necessary. SUPER powerful stuff!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">This was a very nice and quick warm up for our lesson--and the process can be used not just with number lines but with ANY problem type! Stay tuned for another post coming soon with more fraction fun!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Want to see the resource that these number line problems are from? Lots of different problems and options...</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img border="0" height="320" src="https://1.bp.blogspot.com/--sAvqVEoPys/WI1H6kkM4XI/AAAAAAAAY24/bMbP_kVl3kgQQA2N1X-Ne82Y8zW74kh3QCLcB/s320/number%2Bsense%2Bwith%2Bnumber%2Blines%2Bfractions%2Bdecimals%2Bcover.jpg" width="320" /></a></div>Also available bundled with whole numbers to 1,000 and whole numbers to 1,000,000.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Grade-3-5-BUNDLE-2957028"><img border="0" height="320" src="https://2.bp.blogspot.com/-Vx1ZvvSwSRk/WI1H7rAMX9I/AAAAAAAAY28/ol5UCwilxe0x2YipEo_1LLrvp7tQQQcxwCLcB/s320/number%2Bline%2Bresource%2Bbundle%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Want to pin this for later? Here you go!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-ScSDXQHPpHg/WI1iXuQcnJI/AAAAAAAAY3Q/cQ8OcsST-9EG_7lg48lLLBrLk01z3wwFwCLcB/s1600/fraction%2Bnumber%2Bline%2Bpost%2Bpart%2B2%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="fraction number lines" border="0" height="640" src="https://1.bp.blogspot.com/-ScSDXQHPpHg/WI1iXuQcnJI/AAAAAAAAY3Q/cQ8OcsST-9EG_7lg48lLLBrLk01z3wwFwCLcB/s640/fraction%2Bnumber%2Bline%2Bpost%2Bpart%2B2%2Bpin.jpg" title="critique the reasoning of others" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-77739064865823649142017-01-26T22:48:00.000-06:002017-01-28T08:58:13.017-06:00Fraction Number Sense and Math Discourse Part 1<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction number lines" border="0" height="332" src="https://1.bp.blogspot.com/-4YVNXr8swM0/WIrOV7RxHeI/AAAAAAAAY1g/eMeYl06hsyAwu1aKw5hceTx2p5fsB2MRQCLcB/s640/fraction%2Bnumber%2Bline%2Bpost%2BFB%2Bimage.jpg" title="teaching fractions" width="640" /></a></div>It seems like I have picked a few topics lately that just don't fit into one blog post! I wanted to share two different "warm ups" I did with fraction number lines--and two different types of "math talk" that resulted from them. Give these two lessons a try and see what you think! I went kind of "photo journalism" style because I thought the pictures helped tell the story! Watch not just for the important fraction understanding--but the immersion in the Standards for Mathematical Process as well!<br /><br />First of all...if you have followed me for long, you know I love number lines--especially number lines that think "outside the box"--even number lines can be rote and low level--so we want to watch for that!<br /><br />The other day I gave my students this one...it had the 0 and the 2 marked--and asked student to identify what number they felt that "dot" was showing. My first step is always to ask them to THINK before they even pick up their pencil. While they think, I remind them to consider what they know and can tell from just looking at it. I really think slowing them down before they start writing can lead to deeper understanding and reduce careless errors. Plus--for those students who ARE slower processors...not having to watch 20 other students get to work feverishly while they sit is SO refreshing and validating for them. After some think time, they were off!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="teaching fractions" border="0" height="480" src="https://4.bp.blogspot.com/-F05qvgCeXdc/WIa5x5gC9lI/AAAAAAAAYzw/7XV__LKTlusi6m9fWSYshMAsH11HA4SFwCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B54%2B07%2BPM.jpg" title="fraction number lines" width="640" /></a></div> Some asked if they could use rulers...I simply said, "If you think it will help..."<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="Standards for Mathematical Practice" border="0" height="480" src="https://1.bp.blogspot.com/-QLS2w5HMGLw/WIa5yD5leZI/AAAAAAAAYz0/QNdFUoCm8B0DFvsEq2lHMJ7TXLGV5sLMACLcB/s640/Photo%2BJan%2B23%252C%2B7%2B54%2B23%2BPM.jpg" title="fractional reasoning" width="640" /></a></div> I noticed that some students seemed to be putting fractions on their number lines WITHOUT adding the whole numbers first. I asked, "Are you sure 1/4 goes there? How do you know?" Their answers told me a ton about their level of understanding. Some had already visualized where the "1" went--others were simply putting it "where it looked right".<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="number lines and number sense" border="0" height="640" src="https://4.bp.blogspot.com/-pVAUmf63ShQ/WIa5yKwVQII/AAAAAAAAYz4/YQ-RrNF-LEob53FcvYguuwNV4gVHFwmWgCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B54%2B41%2BPM.jpg" title="teaching fractions" width="480" /></a></div> As with all my number line work, I want them to be able to explain their reasoning both in writing and orally. As students were working to finish, I had students begin to write their ideas down so they were ready to buddy up.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="critiquing reasoning" border="0" height="640" src="https://1.bp.blogspot.com/-oYiPfLN87Vk/WIa5yk5eNZI/AAAAAAAAYz8/SWF6gXKAxsk4LgbAUyFXU7e-evZREJM3gCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B55%2B17%2BPM.jpg" title="teaching fractions" width="480" /></a></div> When we were all in a good place (in other words, essentially finished), I put students in pairs and trios and gave them the following direction:<br /><b><br /></b><b>You must all come to consensus about what fraction you will assign your dot. When you are all in agreement </b>(and this took SOME debate in some groups!)<b>, you will mark it on the white copy and start explaining your thinking. When you present, I will call on whoever I want so make sure everyone is accountable for the information and explanation.</b><br /><br />(or something to that effect)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="teaching fractions" border="0" height="480" src="https://2.bp.blogspot.com/-vXEnJBCLOHM/WIa5zaAM76I/AAAAAAAAY0A/REPrkjzHE3YJaLNuw_-LsBpNWRQZIN6uACLcB/s640/Photo%2BJan%2B23%252C%2B7%2B55%2B52%2BPM.jpg" title="math discourse" width="640" /></a></div> I circulated and listened and coached and looked for misconceptions and mistakes. I also looked to see the variety of strategies shown so I could have a variety of ideas to share under the projector.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="math talk" border="0" height="480" src="https://1.bp.blogspot.com/-KRGNhVR2gH4/WIa5ziGkhKI/AAAAAAAAY0E/jIpS3aicMcYcuyU3TEwUqg8PyPPsyFfDwCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B56%2B12%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">For this particular problem, we had some debate. About half the groups believed the dot to be at 3/4 while the other groups had a variety of answers. One by one, they presented their solution and defended their logic. Along the way, there were a few "a-ha's"...and a few stubborn souls who stood their ground despite very good arguments from others!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="math discourse" border="0" height="484" src="https://2.bp.blogspot.com/-uRaijxm5H8U/WIa50H_LL9I/AAAAAAAAY0M/-IzL0WtyQ9c-A3h9WwsEH-MBQUt93rGGQCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B58%2B53%2BPM.jpg" title="teaching fractions" width="640" /></a></div> At one point, we put two different solutions up and had students try to determine which one they felt was "more right"...and which explanations seemed most plausible.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction number line" border="0" height="460" src="https://1.bp.blogspot.com/-TLYr4Q_msK0/WIa5z7V7_eI/AAAAAAAAY0I/k4qb7i_T8X0wJiTwfAqgDvtxw08KVrTkwCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B58%2B31%2BPM.jpg" title="critiquing math reasoning" width="640" /></a></div> We also showcased different strategies that seemed to help some groups. This group used different colors for each step along the way--and other groups agreed that this seemed to make their explanation easier to follow.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="standards for mathematical practice" border="0" height="482" src="https://4.bp.blogspot.com/-aQ2sPtcZAK0/WIa50s9-y6I/AAAAAAAAY0Q/Ku1IFMboVh4MEAuL6it0Cp1L24r-PMMeACLcB/s640/Photo%2BJan%2B23%252C%2B8%2B04%2B04%2BPM.jpg" title="teaching fractions" width="640" /></a></div> Finally, we ended up grabbing a spare number line and doing some folding to find those midway points and really "prove" what the 3/4 teams were proposing. We had a great discussion...and SO much learning happened--and the students did it ALL! Consider trying the strategy:<br /><br />1. Think time<br />2. Independent time<br />3. Partner/consensus time<br />4. Whole group sharing and debating time<br /><br />Watch how engaged your students will be...and let me know how it goes!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction lesson ideas" border="0" height="480" src="https://3.bp.blogspot.com/-gGl4c4We6ik/WIa51PCO3AI/AAAAAAAAY0U/JHxPsGHyaTMkIP_EeSfEMujste9ZQD5uACLcB/s640/Photo%2BJan%2B23%252C%2B8%2B04%2B31%2BPM.jpg" title="teaching fractions" width="640" /></a></div>Looking for the fraction number line resource pictured?<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img border="0" height="320" src="https://3.bp.blogspot.com/-UBw4RDayXe4/WIrK7EY36uI/AAAAAAAAY1Q/PYXlJXarJCUqZhbHU0cyCSg46p7fXk67ACLcB/s320/number%2Bsense%2Bwith%2Bnumber%2Blines%2Bfractions%2Bdecimals%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;">I also have two other number line resources and a bundle of all three...see what you think! I use them ALL year long.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Grade-3-5-BUNDLE-2957028"><img border="0" height="320" src="https://4.bp.blogspot.com/-ZLgjYUaNn2c/WIrK_weQBLI/AAAAAAAAY1U/lZKpnZIRcTET7PprCwW0En-Dvm2CPrZdgCLcB/s320/number%2Bline%2Bresource%2Bbundle%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;">Want to pin this post for later? Here you go! And watch for several more fraction posts coming soon!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img border="0" height="640" src="https://1.bp.blogspot.com/--NCWSTNFfH0/WIrPlubl0bI/AAAAAAAAY1o/i_mh74Tl9JQZRdtZn7U3iUa-dCjewmeHgCLcB/s640/fraction%2Bnumber%2Bline%2Bpost%2Bpin.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Looking for an entire fraction UNIT to get students thinking and talking? Check this one out! </div><div class="separator" style="clear: both; text-align: center;">(the number lines are not a part of this resource)</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img border="0" height="320" src="https://3.bp.blogspot.com/-dfBRzNE0z2g/WIyxT7dCntI/AAAAAAAAY2k/f80T2OP5bMUzhyFZAN4P1jWLR0Gif3XAgCLcB/s320/fraction%2Bunit%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-74769021682304230182017-01-19T20:36:00.003-06:002017-01-19T20:36:57.519-06:005 Tips for Helping Students Make Sense of Word Problems<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="teaching word problems" border="0" height="332" src="https://4.bp.blogspot.com/-2ps40JOSuMo/WIFzPXjG3xI/AAAAAAAAYyo/CNX6e26S_ssSZoHBN1aD-uE9Mffx3sRcgCLcB/s640/making%2Bsense%2Bof%2Bproblems%2Bdigging%2Bin%2Bpost%2Bimage.jpg" title="problem solving" width="640" /></a></div>How many of you have ever given your students a challenging problem and within SECONDS heard something like...<br /><br /><div style="text-align: center;"><b>"I don't get it." </b></div><div style="text-align: center;"><b><br /></b></div><div style="text-align: center;">or</div><div style="text-align: center;"><b><br /></b></div><div style="text-align: center;"><b>"What are we supposed to do?</b></div><br />This is the point where every teacher sighs and wonders where they went wrong as teachers--or where the students have been during the last months of teaching! I think part of the problem comes from the fact that we too often make assumptions about what our students know about "tackling" problems. Whether they struggle with reading--or maybe with motivation--looking at a problem can often lead to shut down from some students. I have a few tips that I have found to be successful. See what you think!<br /><br />1. Sometimes it's ok to read the problem to the class (or to a small group or individual). Yes, part of math is being able to make sense of a problem independently, but we also need to remember that separating the reading from the math provides equal access for all students. Let's not make all our struggling readers math deficient as well! Reading problems aloud can get students' brains working, focused and ready. Think about your goal--if your goal is "Students will independently be able to read and make sense of a problem", then this tip is not useful. If your goal is more math oriented--like "Students will work to solve multi-step problems." or "Students will use estimation strategies to check their work.", reading certainly can be taken out of the equation (pun totally intended).<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="problem solving" border="0" height="480" src="https://2.bp.blogspot.com/-fKAF2qAheeM/WIAKHtbp1xI/AAAAAAAAYx8/frBRo-DRagUL_C73NDr7bfYjo6ZLjjPigCLcB/s640/Photo%2BJan%2B18%252C%2B6%2B33%2B36%2BPM.jpg" title="helping students with word problems" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">2. Encourage students to take "Think Time" before putting pencil to paper or before working in groups. Ask them to reread the problem. Ask them to imagine or "visualize" what is happening. This could be a great time to ask students to find the question or think about what they need to do or what operations they might need to use. After some think time, ask them to work a bit independently--even if you DO plan on having them work together. By each getting started on their own, they bring something to the table for their group to discuss. This really helps minimize having one partner or team member completely take over--because everyone has SOME sort of start to talk about.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="cooperative problem solving" border="0" height="480" src="https://2.bp.blogspot.com/-h0WdOYo_Li0/WIAKGlUverI/AAAAAAAAYx0/Lob-i9aPa2slvCa9CmiWRc1vYPwc4P1EwCEw/s640/Photo%2BJan%2B18%252C%2B6%2B33%2B21%2BPM.jpg" title="problem solving" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">3. Remind students that sketches, drawings, and charts can help them get key ideas or details down on their paper so they can start making sense of them. Simply rewriting key information or labels can help too--it can help students get started processing the information. ALL students can do this--they can all start looking for key information to record.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="problem solving" border="0" height="480" src="https://1.bp.blogspot.com/-cQ2_gmhlc14/WIAKGjxC1tI/AAAAAAAAYx4/n1yfI2kj5_0-1l2xTw3_uA5xgBjqSa-8wCEw/s640/Photo%2BJan%2B18%252C%2B6%2B33%2B03%2BPM.jpg" title="word problems" width="640" /></a></div> 4. Two heads are better than one! Cooperative problem solving can be SUCH a game changer for students who tend to sit back passively. That being said, it does take some work up front with students to learn the art of partnering. I have a blog post from this fall about it if you are interested. Just <a href="http://www.upperelementarysnapshots.com/2016/09/making-partner-work-perfect.html">CLICK HERE</a> to read it! Some students navigate this seamlessly with minimal coaching and others need help. Put your observation "lens" on and watch to see how students work together--and giving reminders about what is expected in partnerships is a great idea. Creating an anchor chart together about how partnerships work gives you a visual to refer to all year long.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="problem solving" border="0" height="480" src="https://4.bp.blogspot.com/-L-iIlqWqmVE/WIAKGkx4uHI/AAAAAAAAYxw/iuXIKNq3qVQ7L53CdhAzJI-NndvMp0rFwCEw/s640/Photo%2BJan%2B18%252C%2B6%2B31%2B36%2BPM.jpg" title="perseverance in math" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">5. Finally, sharing ideas and talking about problems AFTER students finish can give new insight as to ways to organize work, alternative strategies, and more. If students are already in pair, match two pairs together to share out their strategies and solutions. Hear something interesting as you circulate? Bring it back to the entire class so everyone can benefit.</div><div class="separator" style="clear: both; text-align: center;"><br /></div>So...we really need to put our students in positions where they can take some ownership and dig in without us "'spoonfeeding" them and coaching too much! Coming soon--a blog post about how to do just that! Want to see another blog post about helping students makes sense of problems? Just click the image below to take you there!<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://www.theteacherstudio.com/2016/10/helping-students-make-sense-of-problems.html"><img alt="" border="0" height="640" src="https://2.bp.blogspot.com/-N5P1qSGqMdg/WIFvktkxuhI/AAAAAAAAYyY/Nd-2YAXfsbIz5yw3sxCGdZqBMUPctJVqgCLcB/s640/making%2Bsense%2Bof%2Bproblems%2Bpost.jpg" title="problem solving" width="320" /></a></div><div style="text-align: center;">The problem pictured in this post is from the following resource if you are interested in checking it out!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img border="0" height="320" src="https://1.bp.blogspot.com/-u8MDXiGPdpw/WIFvS6Ev3EI/AAAAAAAAYyU/8do1Mmmj6bwzNMh4KY4dNfZWEKM3sa21ACLcB/s320/perseverance%2Bproblem%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;">Would you like to pin this post for later? Here you go!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="math strategies for word problems" border="0" height="640" src="https://3.bp.blogspot.com/-A5VNoczYpts/WIF129Q_2AI/AAAAAAAAYy0/_5cpeBW_bcQGL-Gkx7LwPYaXd-Wf-SdbACLcB/s640/making%2Bsense%2Bof%2Bproblems%2Bpost%2B2%2Bperseverance%2Bpin.jpg" title="problem solving" width="320" /></a></div><br /><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com1tag:blogger.com,1999:blog-8072938188438508721.post-10940935963176472322017-01-08T07:00:00.000-06:002017-01-08T07:00:08.262-06:00Angle Studies Part 2<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Geometry ideas" border="0" height="332" src="https://3.bp.blogspot.com/-EhiTYCI2Dq8/WHFyNGLRqzI/AAAAAAAAYwE/JqH1J2a8t0weuWnp4mReoR3Z5AVxR2HeACLcB/s640/angle%2Bpost%2B2%2Bimage.jpg" title="Angle lesson ideas" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">So, yesterday I showed you how I got my angle studies kicked off with my students--how I solidified understanding of "right angle". We had lots left to accomplish--so I'll try to share some of the different lessons and activities we did over the next days!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Tip 1: If you can get your hands on thin drinking straws....like the kind you might get in a school cafeteria...taking 2 of them and threading a twist tie between them. (I forgot to snap a picture at school so I did a mock up at home--but these are big straws. The skinny ones are WAY better.) These "magic angle makers" are great for showing students different angles, how they can "get smaller" and bigger. Students often don't realize that a "big" angle means it is open more--not that they rays are longer. These little buggers are great for helping show that.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="teaching geometry" border="0" height="640" src="https://3.bp.blogspot.com/-dCni1CI49Wg/WHF_DPgmcDI/AAAAAAAAYwk/d7U2dkOdynIRfUhnA62YZN0jS0lgQm_ywCLcB/s640/Photo%2BJan%2B07%252C%2B5%2B50%2B41%2BPM.jpg" title="Angle lesson ideas" width="578" /></a></div><div class="separator" style="clear: both; text-align: center;">So we worked on building acute, right, and obtuse angles...went hunting around the room for them...sketched them...made our bodies into them...you get the picture. We also worked to develop our mathematical rules for them--that acute angles are less than 90 degrees, and so on.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Because we had done our folded circles earlier (Missed it? <a href="http://www.theteacherstudio.com/2017/01/teaching-angles-part-1.html">CLICK HERE</a> for that post), my students were ready to do a little more estimation practice. We had done the right angle concept sort yesterday, but today I wanted them to use their "reasoning" to estimate the relative size of different angles. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Angle-Activities-3-Activities-to-Deepen-Understanding-1611117"><img alt="Angle lesson ideas" border="0" height="480" src="https://3.bp.blogspot.com/-2rjMll7Z4G4/WHFPnyUlceI/AAAAAAAAYuc/B_j-4bYOYtkytM-kOFP4uMiBk1KP3ac9QCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B17%2B17%2BPM.jpg" title="Fourth grade geometry lessons" width="640" /></a></div> I loved walking around and hearing the math talk! I did quite a bit of prompting and cuing to help them use their prior knowledge to explain their thinking--but overall it was GREAT to see that they were able to handle this task!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Angle-Activities-3-Activities-to-Deepen-Understanding-1611117"><img alt="Angle lesson ideas" border="0" height="480" src="https://1.bp.blogspot.com/-r4V_cCmziGs/WHFkhMCl2aI/AAAAAAAAYvM/IEFX9jUNxxE2lmDv3BKFkn-UPMTzSE_SwCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B13%2B39%2BPM.jpg" title="Teaching fourth grade geometry" width="640" /></a></div> I wanted to give my students something concrete to continue their work with acute, right, obtuse, and straight angles, so it was time for some angle art! (Both of these activities are a part of my Amazing Angle Activities resource available <a href="https://www.teacherspayteachers.com/Product/Angle-Activities-3-Activities-to-Deepen-Understanding-1611117">HERE</a>.)<br /><br />I wanted students to show their understanding by folding paper strips into the different angle types. They spent some time arranging them on their page, had to "prove" to a classmate that they had all four angle times, then glued them down and made a key.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Angle-Activities-3-Activities-to-Deepen-Understanding-1611117"><img alt="Fourth grade geometry lessons" border="0" height="640" src="https://2.bp.blogspot.com/-66q3Mp_Za6I/WHFwE3H83lI/AAAAAAAAYvs/Op_nELgHDtAhLV1foqVebbDZyqkwpMiKQCLcB/s640/Photo%2BJan%2B07%252C%2B4%2B43%2B58%2BPM.jpg" title="Angle lesson ideas" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Fourth grade angle lessons" border="0" height="482" src="https://2.bp.blogspot.com/-da3tBNnCS0M/WHFwE7oU-OI/AAAAAAAAYvw/S_VAhop_-l0OH5Pr1vGgBOI1i8LWrTFEgCLcB/s640/Photo%2BJan%2B07%252C%2B4%2B45%2B26%2BPM.jpg" title="Angle lesson ideas" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">We think they look pretty cool!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Geometry projects" border="0" height="480" src="https://1.bp.blogspot.com/-xrZk7ZA74aw/WHFkhOzEveI/AAAAAAAAYvI/tf6rGUK5igUX-sm6iXEvjku-SDXBXHV7QCEw/s640/Photo%2BJan%2B06%252C%2B7%2B13%2B12%2BPM.jpg" title="Angle lesson ideas" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">The next step in our journey was to actually break out the protractors and learn how to use them. If you have ever taught this skill, you know it can be really tricky for some students. Here are a few of my tips in case this is on your agenda for this year!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">1. Work with students in small groups. I worked with 4 at a time and it makes such a difference. In 15 minutes, a group of 4 can master it pretty quickly...and if they can't, you sure can tell who is struggling to work with more later!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">2. Stress the importance of estimating. With most protractors, the two sets of numbers can be very confusing. If students always ask themselves, "Is it smaller or larger than 90?", it can be really helpful.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">3. I try to keep my directions very simple--a phrase you here in my classroom a lot is "Dot on the dot, line on the line" which means, "Line up the vertex on the center dot and make sure the ray is on the protractor line pointing to 0.". </div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">4. Make sure you explicitly teach students how to measure angles facing in different directions, angles that are part of shapes like triangles and quadrilaterals (MUCH harder than just two rays), and that you have students DRAW and correctly label angles as well. Some students struggle with the drawing part--so spending some time on that is certainly valuable.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">5. Working in partners is SUCH a meaningful way to work with angles. Having students draw angles for each other, measure them, and try to get within 2 degrees is a great way to tackle precision and get tons of practice in! If they don't get within 2 degrees, have them work together to figure out why. I love to hear the coaching they do with each other!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Angle lesson ideas" border="0" height="480" src="https://4.bp.blogspot.com/-Rw7_4TVLpME/WHFkhYtuSOI/AAAAAAAAYvQ/ktE1MGNfh6MLwxDyiueoL7sHMIzLJDPxgCEw/s640/Photo%2BJan%2B06%252C%2B7%2B13%2B56%2BPM.jpg" title="Teaching protractor skills" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Teaching protractor skills" border="0" height="480" src="https://3.bp.blogspot.com/-u0OQS0ib8YQ/WHFkiXAAGwI/AAAAAAAAYvY/iCqHsDCuc2I9zkOxM6JRqzdwFhZa7Xg4wCEw/s640/Photo%2BJan%2B06%252C%2B7%2B14%2B12%2BPM.jpg" title="Angle lesson ideas" width="640" /></a></div> 6. Provide lots of different opportunities for practice. I love these big cards printed on bright cardstock. They are easy for students to use and can also be used as an assessment tool. I use the sheet that is included to help practice estimation as well (This is also a part of my angle resource mentioned above).<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Using a protractor" border="0" height="540" src="https://2.bp.blogspot.com/-lFQUWRSGg0s/WHFkgN_pLrI/AAAAAAAAYvE/Dv6cx_JBQK0pP3b2KRxcePqEPSsRzRAAACEw/s640/Photo%2BJan%2B06%252C%2B7%2B09%2B20%2BPM.jpg" title="Angle lesson ideas" width="640" /></a></div> Along the way, I did some formative assessment to check on student progress. (I made this into a freebie in my store if you want to grab it--just click the picture below!)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Angle-Studies-Using-a-Protractor-Formative-Assessment-Freebie-2950274"><img alt="Angle lesson ideas" border="0" height="480" src="https://3.bp.blogspot.com/-FXHUCmxT_4I/WHFkfmwJ2rI/AAAAAAAAYvA/-I8egikLFtsXA6VIcRm4Ui_8sX0hGxDaACEw/s640/Photo%2BJan%2B06%252C%2B7%2B08%2B58%2BPM.jpg" title="Protractor skills" width="640" /></a></div> The next steps of our angle studies involved composing and decomposing angles. We started to tackle this that first day when we divided our circle...students started to see from the beginning that angles can be divided into other angles. Each day, we "played" with this idea a little bit more. <br /><br />"If I divide a right angle into two angles and one angle is 34 degrees, how much is the other one?"<br /><br />"If I divide a 180 degree angle into three equal angles, how big will each be?"<br /><br />"What are three different ways to divide a 360 degree circle into 4 different angles?"<br /><br />My students were loving these problems so I decided to come up with something more for our Angle Art wall...I simply told the students one fact. I told them that the small angle on a tan pattern block is exactly 30 degrees. From that point, I asked them to spend some time playing with pattern blocks and making discoveries. Students quickly began to make connections....the green pattern block had 3 equal angles of 60 degrees. The blue pattern block had two 60 degree angles and two 120 degree angles. Light bulbs were going off like crazy!<br /><br />So I decided to push them a little bit. We have an Ellison machine with the die cuts for pattern blocks so I went and cut a bunch. I told the students to take 10-15 shapes and build a design of their choosing. When they finished, we went on a "hunt" for angles--by combining angles and looking for ways to "compose" 360 degree circles! They had so much fun--and now our hallway has even more math art for our friends to check out!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Angle lesson ideas" border="0" height="480" src="https://2.bp.blogspot.com/-nuoxgajeA40/WHFkfIH9B3I/AAAAAAAAYu4/O1PfOM0afFUbUG5ubSavBhA6frwVDWdbwCEw/s640/Photo%2BJan%2B06%252C%2B7%2B08%2B31%2BPM.jpg" title="Geometry problem solving" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Geometry problem solving" border="0" height="640" src="https://1.bp.blogspot.com/-OUHB9PnXiRA/WHFkfXH9iYI/AAAAAAAAYu8/fhdMgKNxs_oXHePKnoH19qJox1XL_x9UgCEw/s640/Photo%2BJan%2B06%252C%2B7%2B08%2B00%2BPM.jpg" title="Angle lesson ideas" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">After our in depth work, I think they are ready for our summative assesssment next week! We will revisit these concepts again later this year when we work more with 2D shapes, but I think for now we are in great shape! Want to see more angle ideas? Just click below.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img border="0" height="320" src="https://4.bp.blogspot.com/-OjfWb0XKxQ0/WHF2yHAtNtI/AAAAAAAAYwU/1aaMiud8p7Icgja-Iik_i0zyu2JUQgG8gCLcB/s320/Slide1.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img border="0" height="640" src="https://1.bp.blogspot.com/-ewQf2rMWfAo/WHFxjxWaeRI/AAAAAAAAYv8/qJQIYQuSooAqyI2BbgcnCpHMyc1L67GrACLcB/s640/angle%2Bstudies%2Bpart%2B2%2Bpin.jpg" width="320" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-9236442999860277022017-01-07T11:28:00.000-06:002017-01-07T11:28:19.817-06:00Teaching Angles: Part 1<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="geometry angles" border="0" height="332" src="https://4.bp.blogspot.com/-u_99e6Z1mV8/WHEh7PSSelI/AAAAAAAAYt8/mWBGxhEfeoATcvwFtOOCPb5nchtACZSfACLcB/s640/angle%2Bpost%2B1%2Bimage.jpg" title="teaching angles" width="640" /></a></div>This week was "Angle Week" in my classroom...a week of intense work with angles to help us prepare for later work with geometry! I love this unit for a bunch of reasons--one, many students who struggle with computation-based concepts shine with more "spatial" concepts. I love it!<br /><br />Another reason I find angle studies to be so much fun is that I LOVE watching students start to make connections between all the other work we have done and a brand new topic. Composing and decomposing? CHECK! Estimating? CHECK! Connecting to fractions? CHECK!<br /><br />So the first thing I did to kick of this unit is to make sure that students understood the third grade concept of "right angles". You see, in the past, I have found a number of misconceptions related to this and this year was no exception. Many textbooks and worksheets present right angles looking the same way...something like this:<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle misconceptions" border="0" height="332" src="https://3.bp.blogspot.com/-6nHHeHrsv9c/WHEGYkebGCI/AAAAAAAAYtU/Is4In2_Ujv84clwMdwVIX9GivlC208UAgCLcB/s640/right%2Bangle%2Bimage%2B1.jpg" title="teaching angles" width="640" /></a></div>Which is fine--it certainly is a right angle. But what I have found is that students don't always generalize....so when they see THESE images, I get some of the following comments!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle lesson plans" border="0" height="332" src="https://3.bp.blogspot.com/-sfPPomUY8XU/WHEGsykEqVI/AAAAAAAAYtY/-U1B5LIVxggFNV937NROXjjpQnWx1nmzgCLcB/s640/right%2Bangle%2Bimage%2B2.jpg" title="teaching angles" width="640" /></a></div>So you can see--there is a huge danger in creating misconceptions if we don't dig in. Here was our first activity. I gave each student a circle of paper and, under the document camera, modeled the following. I'm giving you the abbreviated version...hopefully you can visualize how this unfolded (literally AND figuratively!)<br /><br />We first wrote "360 degrees" on the back to remind us of our "whole" circle.<br /><br />Then we folded in half, traced that fold line, colored one half, and labeled it with "180 degrees". We talked about the concept of "straight angles" and noted that a full circle is comprised of two 180 semicircles. I had them fold again, trace the fold line on half of it, color a new color, and asked how many degrees it must be (they easily knew 90). Again, we tied it back to the full circle...being 1/4...1/2 of a 1/2...and so on. We then folded the circle into it's fourths so only the right angle was exposed and we went on a "hunt" around the room to find examples of right angles. We found them everywhere--the corner of the whiteboard, the lights, the door, their name tags...students were turning their "right angle finder" at all sorts of angles to find them! We then came back and folded our circle in half AGAIN to find a 45 degree angle and went back on a hunt!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="teaching angles" border="0" height="640" src="https://2.bp.blogspot.com/-jcyOxcg0CeY/WHBRKysQToI/AAAAAAAAYso/-OdqnkdaY5oaBJkyL-svybEP6s_nA-b1QCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B16%2B38%2BPM.jpg" title="geometry lessons" width="640" /></a></div> Students found angles in letters, in the angle our easel was set at, and in dozens of other places! I loved watching them really start to "see" how big these different angles are--a huge help in our ability to estimate relative sizes and to check for reasonableness.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle lesson plans" border="0" height="480" src="https://3.bp.blogspot.com/-IYlNapmkEiM/WHBRKljE5iI/AAAAAAAAYss/EotKuGjzSQ4shcHAZSQTr0WNajyUbOdtgCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B14%2B39%2BPM.jpg" title="teaching geometry" width="640" /></a></div> So after I was pretty sure we were in good shape with right angles, I knew I wanted to test it with a concept sort. If you aren't familiar with concept sorts, I have a bunch of blog posts about them so I won't bore you here with the details. Just search in the right side bar for "concept sorts" if you want to find more posts.<br /><br />This one was simply geared toward getting students talking about right angles and defending their thinking based on the foundation we had gotten with our folding activity.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="geometry lessons fourth grade" border="0" height="640" src="https://2.bp.blogspot.com/-sOKMHOXPp1k/WHBRNPWCU1I/AAAAAAAAYtA/yFds62VzQgY4yUKC58akANIamd3qPHV3QCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B19%2B31%2BPM.jpg" title="teaching right angles" width="480" /></a></div> One of my rules for concept sorts is that nobody can place a card in a category without the team agreeing...it is super easy for students to grab cards and start sorting quickly--meaning that the assertive, confident students get the work! <br />No thank you!<br /><br />Groups are required to go one card at a time and take turns leading the discussion. I circulate and ask probing questions, ask them to "prove" it to me, and so on.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="teaching angles" border="0" height="480" src="https://2.bp.blogspot.com/-IyL52252eY8/WHBRL7PtO6I/AAAAAAAAYs0/KLv7Lm5r_FoBa62ke1EAivbcIvfgkfd0QCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B18%2B02%2BPM.jpg" title="fourth grade geometry" width="640" /></a></div> For this sort, some students asked if they could use "tools". I shrugged and told them that I didn't care how they did it--as long as they all agreed!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle lesson plans" border="0" height="480" src="https://1.bp.blogspot.com/-jj7xFG1qweM/WHBRNZEw4rI/AAAAAAAAYtE/PhvCz8SYGng2jzfitWvBk2SRoz35qiVfACLcB/s640/Photo%2BJan%2B06%252C%2B7%2B19%2B55%2BPM.jpg" title="fourth grade geometry" width="640" /></a></div> After about 10 minutes of sorting, I passed out a different colored crayon to each group. I gave them about 5 minutes to do a gallery walk to see what others did--and then mark an "x" on any cards that they disagreed with. Those were the ones that we then projected under the document camera and discussed.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle lesson ideas" border="0" height="480" src="https://1.bp.blogspot.com/-TpNSqY0YrRw/WHBRMbLiX2I/AAAAAAAAYs8/1JVLnfkYDZwW7f0WqmBKtCcge16kaLk8QCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B18%2B41%2BPM.jpg" title="fourth grade geometry" width="640" /></a></div> As we talked about the tricky ones, students had to work on using their specific math language (a big part of "precision") until we could all come to an agreement about whether or not the angle was truly a 90 degree angle.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle lesson ideas" border="0" height="480" src="https://2.bp.blogspot.com/-L9yrNb8WOsQ/WHBRMdguoYI/AAAAAAAAYs4/KwNjeO0bgpktXWZPOlLFCieig2lXmizwQCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B19%2B10%2BPM.jpg" title="fourth grade geometry" width="640" /></a></div>Next steps? Acute, obtuse, and reflex angles....protractor use...and composing/decomposing angles. Stay tuned for that post coming soon!<br /><br />Looking for angle help in your classroom? Check out this teaching tandem and see what you think!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img border="0" height="320" src="https://4.bp.blogspot.com/-EgAaQv3vGjc/WHEQPpFr8lI/AAAAAAAAYts/8v3ixseimqEX6oGdmWjh7uTIu3fLOs1PgCLcB/s320/Slide1.JPG" width="320" /></a></div><div style="text-align: center;">Want to pin it later? Here's a pin for you!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-N6odlf7Fo6Q/WHElA10AzNI/AAAAAAAAYuI/As1NvHFK_es47WQcdxPxVkKIs5tc6OufgCLcB/s1600/angle%2Bstudies%2Bpart%2B1%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://3.bp.blogspot.com/-N6odlf7Fo6Q/WHElA10AzNI/AAAAAAAAYuI/As1NvHFK_es47WQcdxPxVkKIs5tc6OufgCLcB/s640/angle%2Bstudies%2Bpart%2B1%2Bpin.jpg" width="320" /></a></div><br /><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-37796126524433531432016-12-31T06:00:00.000-06:002016-12-31T06:00:21.569-06:00Chilling With a Good Book <div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="snowman bulletin board" border="0" height="332" src="https://2.bp.blogspot.com/-Wi1Ji3X0jS8/WGb2QOE24gI/AAAAAAAAYqs/YHafQ9MfqKASjFWIThhhH0G4y4sRSKKsgCLcB/s640/chilling%2Bwith%2Ba%2Bgood%2Bbook%2Bpost%2Bcover%2Bimage%2B2016.jpg" title="book report" width="640" /></a></div>Teaching minutes are precious, so being able to teach real content while still engaging our students' creativity is key! Check out this book review project that reinforces opinion writing, reading, revising and editing--and creates a beautiful bulletin board as well! I asked my students to think hard about one of the BEST books they have ever read (or heard)--because I wanted them to be ready to write about it. I gave them a few days to think and talk about it so they all had an idea ready.<br /><br />As a class, we talked about what we remembered about OPINION writing--and how good opinion has a clearly stated thesis statement, so students worked to craft quality first sentences that would state their opinion about their book. We did our drafting in our writer's notebooks and then did some peer revising and teacher editing. I had asked students to only write 3-5 sentences which kept them on topic AND made it easy for me to get to everyone for editing!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="winter bulletin board" border="0" height="480" src="https://2.bp.blogspot.com/-sYBvfb0WJ1Q/WGbqki4gj7I/AAAAAAAAYqA/h-wZb5dijpEiYVVQ99ZY6B58uYjLu5VxQCLcB/s640/Photo%2BDec%2B30%252C%2B5%2B09%2B58%2BPM.jpg" title="winter book report" width="640" /></a></div> After they finished writing, self-revising, and peer revision, they put their names on the "teacher time" list on the white board and got ready to "build" their snowman! I had a variety of circle tracers set out as well as colored paper. I explained that they could create their snowman while they waited for their edits--and then they could do their final copy to add to their project. It was fun to see so many students design their snowman to "match" the book they chose!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="winter bulletin board" border="0" height="480" src="https://3.bp.blogspot.com/-dbvh56EkOms/WGbqlVF7eLI/AAAAAAAAYqI/lQEh0Y4IgAEHFpThS_b45kENKe0PAQelgCLcB/s640/Photo%2BDec%2B30%252C%2B5%2B10%2B51%2BPM.jpg" title="snowman book report" width="640" /></a></div> When their snowman was built and their final copy done, it was time to finish the project!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="book report project" border="0" height="640" src="https://1.bp.blogspot.com/-6C9CznpqBNs/WGbqmUA7ZGI/AAAAAAAAYqM/VXCua1LBnJ87Whs_bqAOC4j6rUtrKhXNQCLcB/s640/Photo%2BDec%2B30%252C%2B5%2B11%2B13%2BPM.jpg" title="winter bulletin board" width="480" /></a></div> How stinkin' cute is this one? She worked SO hard and was so proud of it!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="snowman project" border="0" height="640" src="https://1.bp.blogspot.com/-Oo0GTfGEXdQ/WGbqm90mOvI/AAAAAAAAYqQ/c2vosY8eMi0HaQj-1V2p15T450nOkNQ6ACLcB/s640/Photo%2BDec%2B30%252C%2B5%2B12%2B24%2BPM.jpg" title="winter bulletin board" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">After they were all finished, I tore a paper snowhill out of bulletin board paper and hung our new friends above our lockers. The students had a blast...got some great writing practice...and I have a beautiful new display that can be up for a VERY long time! </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="snowman book report" border="0" height="348" src="https://1.bp.blogspot.com/-I_O8q3nWP0I/WGbqkjL8ngI/AAAAAAAAYp8/I4J-nbBfmr8NnsM7Oe8mvNO_RQar26XDwCEw/s640/Photo%2BDec%2B29%252C%2B5%2B28%2B27%2BPM.jpg" title="winter bulletin board" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Interested in the letters and the template? Here you go!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img border="0" height="240" src="https://3.bp.blogspot.com/-F2nSOk_vDII/WGbq1ThhGVI/AAAAAAAAYqU/xGnx16Y63vsWF643szYoScqSPlzyJggcgCLcB/s320/Slide1.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Want to pin it for later?</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img border="0" height="640" src="https://4.bp.blogspot.com/-dzCLOs3LslQ/WGb3xVqI22I/AAAAAAAAYq4/J62vqTGTiXwFMfbTmz4HwKkPLlG0uFrfACLcB/s640/chilling%2Bwith%2Ba%2Bgood%2Bbook%2Bpin%2B2016.jpg" width="320" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com2tag:blogger.com,1999:blog-8072938188438508721.post-67177532536603749222016-12-30T13:09:00.000-06:002016-12-30T13:21:29.634-06:00Pioneer Research! Learning Collaboratively <div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img alt="fourth grade social studies" border="0" height="332" src="https://1.bp.blogspot.com/-YPuv1JrRucw/WGWs_puHIRI/AAAAAAAAYos/GKMrFnHPGg4jOTbCWYF5YU_DPwXFfNk4gCLcB/s640/pioneer%2Bresearch%2Bpost%2Bimage.jpg" title="pioneer westward expansion activities" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">One thing that I love to do is immerse my students in resources on a topic we have in our curriculum--with a specific task to accomplish. If your school is like mine, social studies and science time are getting reduced more and more, so we need to be constantly searching for meaningful ways for students to incorporate this real world learning into our language arts curriculum. Informational research "mini projects" are a great way to combine the two!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">This book by Christopher Lehman is a really great way to think about research in a little different way...it's FULL of strategies that are super helpful in getting students to master key elements of research. For this little project, I focused on a strategy he calls, "Slow and Steady Wins the Race" where he stresses the importance of helping students pause before writing notes to make sure they read, stop, cover the information, and then jot notes. This really helps reduce the direct copying. I add one more layer to the process by having students read, cover, then explain to a partner where the two together decide if the information is important enough to write down. If you are interested in more of his strategies, I put an affiliate link to his book at the bottom of this post. It's short and easy to read--and I have it FULL of sticky notes with ideas!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">So here is what we are doing...I went to our library and got all the books possible on pioneer life and westward expansion--the next step in our social studies curriculum. The textbook is another option, and I will be using it as well--but I really want my students to understand that true research uses multiple sources. True research also involves students generating their research questions--and this project is too small for that. What I really want is for students to practice their paraphrasing skills and to refine their ability to find facts that are most important. To keep the project small in nature, I gave the students categories to "collect" facts about...and to record in this research guide. We used the textbook, the library books, and even some ebooks that our library has (if you haven't looked at TrueFlix, check it out!). I gave the students two work times to work together to gather facts, practice paraphrasing orally and then in writing, and then we prepared to select the most important information to display.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img alt="pioneers" border="0" height="426" src="https://2.bp.blogspot.com/-sN-nIGiH8Oc/WGWwth4NN1I/AAAAAAAAYpA/SCNJ6YIoy_sf4kDSb_luAf7gqtvTDGSvACLcB/s640/Slide11.JPG" title="fourth grade research" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">I then show my students a sample of how the lap book can be arranged--and tell them that it is their job (with the input of their partners) as to what is the most important information to include on each flap. Students take their notes, explain in their own words, and then get creative!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img alt="fourth grade history" border="0" height="426" src="https://2.bp.blogspot.com/-DbWBJUUz_-c/WGWwtr6lRRI/AAAAAAAAYpE/bmy7Q5xkRoghNyskqq2STwJFMZIO-UEEgCEw/s640/Slide9.JPG" title="pioneers" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img alt="interactive notebook lapbook" border="0" height="426" src="https://4.bp.blogspot.com/-2toXOei92nE/WGWwthGWmkI/AAAAAAAAYo4/ZmBSv--4MeUo1LaqdPxdVZ3jvPwOVNpPQCEw/s640/Slide12.JPG" title="pioneers" width="640" /></a></div>It's fun to watch students take on this project and get creative...and the best part is I know that they are learning the content, working together, and learning more about informational reading and writing. I love watching them share their "lap books" in small groups and compliment each other on how they did things!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img alt="interactive notebook lap book" border="0" height="426" src="https://1.bp.blogspot.com/-zGxHkCE3bqM/WGWwtvE-bzI/AAAAAAAAYo8/2Tc7vFELHR0wkyrCrfJcb9_oAH0Q8s0pgCEw/s640/Slide10.JPG" title="pioneers" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Interested in the lap book (or you can use as a part of an interactive notebook) resource? Here it is!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img border="0" height="320" src="https://3.bp.blogspot.com/-Bc3JtI29GOM/WGZ_IdL7X2I/AAAAAAAAYpc/wYunqPSBEZ4x8SvZ4gL7BPZ1Z_mnfGCxgCLcB/s320/Slide1.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Here is the Christopher Lehman book that I love!</div><div style="text-align: center;"><iframe frameborder="0" marginheight="0" marginwidth="0" scrolling="no" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ac&ref=qf_sp_asin_til&ad_type=product_link&tracking_id=theteastu0e-20&marketplace=amazon&region=US&placement=0325043574&asins=0325043574&linkId=d936b171f8f12c4983500993bff86758&show_border=false&link_opens_in_new_window=false&price_color=333333&title_color=0066c0&bg_color=ffffff" style="height: 240px; width: 120px;"> </iframe></div><div style="text-align: center;">Thanks for stopping by!</div><div style="text-align: center;"><br /></div><div style="text-align: center;">Want to pin this for later?</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img border="0" height="640" src="https://3.bp.blogspot.com/-4cxB_wlHKfY/WGau5lKoluI/AAAAAAAAYps/BZU_NTXFBbUIwI5maJXb8UDlaMWkSsZDwCLcB/s640/pioneer%2Bresearch%2Bpost%2Bpin.jpg" width="320" /></a></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-19091204821151044452016-12-27T14:36:00.000-06:002016-12-27T14:36:00.395-06:005 Teaching Resolutions for the New Year!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Store/The-Teacher-Studio"><img border="0" height="332" src="https://4.bp.blogspot.com/-pp8lkj9MAbI/WGLMBENWrGI/AAAAAAAAYnw/0CVYlWuINpgWN2lcg0XfVPAWNlbjZqxeQCLcB/s640/resolution%2Bpost%2Bimage.jpg" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">As 2016 wraps up, I--like many others--start to think about things I want to do better in 2017. I have tons of personal goals (get healthy, get more organized, etc), but today's post has a few musings about some classroom goals I have to better meet the needs of my students in the new year. </div><div class="separator" style="clear: both; text-align: center;"><b>Ready for five of them?</b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-33XaWN3hgok/WGKi22lTGdI/AAAAAAAAYlo/d6sahbzFgNc-xyZuDsbQMpuFfOf8qUCswCLcB/s1600/Slide1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://4.bp.blogspot.com/-33XaWN3hgok/WGKi22lTGdI/AAAAAAAAYlo/d6sahbzFgNc-xyZuDsbQMpuFfOf8qUCswCLcB/s200/Slide1.JPG" width="200" /></a></div> My first "resolution" is to incorporate more deliberate instruction on how to write about math. My students have really struggled with this...they seem to be conditioned to "write the algorithm" and instead of explaining their THINKING, they simply tell me what they did. They might write:<br /><br />I put the 483 under the 820. I crossed out the 8 to get more ones... (you get my drift)<br /><br />What I WANT them to do is explain WHY they did what they did...and to look for patterns...and to make connections. I made this anchor charts a few weeks ago but haven't done nearly enough with it. <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-bxzE7MrlEKo/WGKxEhQPzVI/AAAAAAAAYmM/we_DwfrVlyoYDmmGBHEhsU0Ads4a_kbfgCLcB/s1600/Photo%2BDec%2B27%252C%2B11%2B33%2B49%2BAM.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://4.bp.blogspot.com/-bxzE7MrlEKo/WGKxEhQPzVI/AAAAAAAAYmM/we_DwfrVlyoYDmmGBHEhsU0Ads4a_kbfgCLcB/s640/Photo%2BDec%2B27%252C%2B11%2B33%2B49%2BAM.jpg" width="592" /></a></div>I am going to use the problems in this resource to help--because each problem is available in three formats--one of which requires students to explain their thinking!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-hY7-qyUzu18/WGKyZe2crgI/AAAAAAAAYmg/2qY6Jj6YY_odx50DsibY0vUNq-c3KYo1ACLcB/s1600/grade%2B4-5%2Bword%2Bproblem%2Bcover.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-hY7-qyUzu18/WGKyZe2crgI/AAAAAAAAYmg/2qY6Jj6YY_odx50DsibY0vUNq-c3KYo1ACLcB/s400/grade%2B4-5%2Bword%2Bproblem%2Bcover.jpg" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-NNHjTKXpr7Q/WGKi3FLPWQI/AAAAAAAAYlw/fc_3THteg90U1KQUwEQtXtRV8C6t03zvACLcB/s1600/Slide2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://2.bp.blogspot.com/-NNHjTKXpr7Q/WGKi3FLPWQI/AAAAAAAAYlw/fc_3THteg90U1KQUwEQtXtRV8C6t03zvACLcB/s200/Slide2.JPG" width="200" /></a></div> Another big goal for me is to spend more time conferring with students about their reading. I have so many strugglers--and I find myself scrambling to pull together intervention groups and lessons. I need to make sure to not ignore my top readers, so I am really going to make a concerted effort to keep up with my status of the class and anecdotal records. It's such a nice time with students--even a few minutes a week helps keep me really connected to what they are reading and how they are doing. Here is a blog post with more details about what I do...just <a href="http://www.theteacherstudio.com/2015/12/refocusing-on-reading-behaviors.html">CLICK HERE</a>!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Reading-Status-and-Anecdotal-Records-Calendars-2016-2017-for-Readers-Workshop-444716"><img border="0" height="480" src="https://2.bp.blogspot.com/-UfamdwZAhwU/WGK7jbu8hKI/AAAAAAAAYnA/Xmsbi8nCBWMPCO0iNVzu85t9gCF2X8iCACLcB/s640/Slide3.JPG" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Reading-Status-and-Anecdotal-Records-Calendars-2016-2017-for-Readers-Workshop-444716"><img border="0" height="300" src="https://3.bp.blogspot.com/-qUaSE9leKvg/WGKxUg5OiVI/AAAAAAAAYmQ/mv1g60a6LIQs9P9qWxpNkNBGcUsOPUrmgCLcB/s400/Reading%2BStatus%2BCalendar%2B2016%2B-%2B2017%2Bcover.jpg" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-bR8D3yStzwU/WGKi3MnSwNI/AAAAAAAAYls/b8fTwFISDcQJcStWOnjUcS5IGavwAClUwCLcB/s1600/Slide3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://4.bp.blogspot.com/-bR8D3yStzwU/WGKi3MnSwNI/AAAAAAAAYls/b8fTwFISDcQJcStWOnjUcS5IGavwAClUwCLcB/s200/Slide3.JPG" width="200" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Another goal I have is to do a better job giving students feedback on their writing. I feel I do a pretty decent job TEACHING writing...but I know I have a long way to go in giving them timely feedback on what they do. Each student is, of course, at an entirely different place with their writing, so simply doing great whole-class lessons isn't enough. I need to do more quick collections of work with a fast turnaround time. Even ONE piece of specific feedback can make such a difference. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Writing-Demand-Prompt-Assessments-Bundled-Set-1669124"><img border="0" height="640" src="https://3.bp.blogspot.com/-Zeia7A6IZyA/WGLBFStochI/AAAAAAAAYng/nIR3UKmwlAcKL-3C-dZOxlOFzu3NDGVmgCLcB/s640/Photo%2BDec%2B27%252C%2B1%2B27%2B16%2BPM.jpg" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Writing-Demand-Prompt-Assessments-Bundled-Set-1669124"><img border="0" height="400" src="https://1.bp.blogspot.com/-kU2sr1Nmcwg/WGKxePeQHiI/AAAAAAAAYmU/GO1DF7MP1cE_ml6q_D-5NXFkme24-gIuQCLcB/s400/Great%2BEight%2BBundle%2BInformation%2BCOVER.jpg" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-NDrRkrWTr5w/WGKi3Efl5OI/AAAAAAAAYl0/Kczu2Ko2GIcblGRySeG1yQzR3OoVO4CfQCLcB/s1600/Slide4.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://2.bp.blogspot.com/-NDrRkrWTr5w/WGKi3Efl5OI/AAAAAAAAYl0/Kczu2Ko2GIcblGRySeG1yQzR3OoVO4CfQCLcB/s200/Slide4.JPG" width="200" /></a></div> A fourth resolution for me is to build in more time for creative thinking activities. Before break, we did a few different things in class and my students were SO engaged and had some AMAZING discussions. It doesn't take long--and the benefit of thinking outside the box carries forward into other learning. I also love these exercises because it allows some students who are less confident with our academic content to really shine and be actively engaged in what we are doing. It was great for community building AND to get those neurons firing in new ways!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinking-Outside-the-Box-Exercising-Creative-Minds-Bundled-Set-1217847"><img border="0" height="640" src="https://4.bp.blogspot.com/-E8g-KBElFtE/WGK9uuaJ3DI/AAAAAAAAYnU/SJBySHOvtuE9l0QqUBxyazxJAzWqDr4xQCLcB/s640/Photo%2BDec%2B23%252C%2B5%2B45%2B42%2BAM.jpg" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinking-Outside-the-Box-Exercising-Creative-Minds-Bundled-Set-1217847"><img border="0" height="320" src="https://2.bp.blogspot.com/-U96YCOKX2Q8/WGKy0aDlhpI/AAAAAAAAYmo/UN4DxEXghHkNp2rlzqr_1Qzmw9FFcp-VACLcB/s320/creativity%2Bbundle%2Bcover.jpg" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-C6rTJWQvreQ/WGKi3PhoSII/AAAAAAAAYl4/lpOjb8jFlOAODs34t51VAs8_hWfnF_EfQCLcB/s1600/Slide5.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://3.bp.blogspot.com/-C6rTJWQvreQ/WGKi3PhoSII/AAAAAAAAYl4/lpOjb8jFlOAODs34t51VAs8_hWfnF_EfQCLcB/s200/Slide5.JPG" width="200" /></a></div><div style="text-align: center;">Finally, I am going to rework my math workshop time to find more minutes for EXPLICIT fact strategy instruction for my students who need it--and it's QUITE a few of them. I started off in the fall pretty strong working with those students who needed review on doubles, tens, and fives but then things kind of fell apart. I NEED them to be more fluent with their facts before we get into big multiplying, so I am really going to be diligent about working with them. They love the activities...it's matter of ME doing a better job scheduling my time!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Multiplication-Facts-Instruction-and-Intervention-Resource-Kit-2623243"><img border="0" height="480" src="https://1.bp.blogspot.com/-CYTHSc19vfs/WGK73nfnilI/AAAAAAAAYnE/6Loe3xazHmck_ZzFpy-JiRxk6Urq49SWgCLcB/s640/Photo%2BOct%2B28%252C%2B8%2B14%2B37%2BPM%2B%25281%2529.jpg" width="640" /></a></div><div style="text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Multiplication-Facts-Instruction-and-Intervention-Resource-Kit-2623243"><img border="0" height="320" src="https://4.bp.blogspot.com/-xn1YKsnQdTw/WGKy5V1fpZI/AAAAAAAAYms/WbHC5m1rnBUdPiU30650LO7Si7Csq-FCACLcB/s320/math%2Bfact%2Bintervention%2Bresource%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;">So...in case YOU want to set any of the same resolutions as me, I am marking these five products on sale until January 1! Grab them and make a difference in your teaching for 2017!</div><div style="text-align: center;"><br /></div><div style="text-align: center;">Want to pin it for later?</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Store/The-Teacher-Studio"><img border="0" height="640" src="https://1.bp.blogspot.com/-uhCW1IShoNc/WGLQP_NkyXI/AAAAAAAAYn8/LAcohklsZrQSpWaqNU2qctHidbXvTwCvwCLcB/s640/resolution%2Bpost%2B2016.jpg" width="320" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com3tag:blogger.com,1999:blog-8072938188438508721.post-8013939535558944192016-12-18T08:29:00.003-06:002016-12-18T08:55:05.840-06:00More work with fractional reasoning!<div class="separator" style="clear: both; text-align: center;"><a href="http://www.upperelementarysnapshots.com/2016/12/critiquing-fractional-reasoning.html"><img alt="fraction lessons" border="0" height="640" src="https://2.bp.blogspot.com/-xVRnQ1G-Iyo/WFaal8xsrgI/AAAAAAAAYkw/P2o8ikBctpcIAZBrqhkEtCuIjl6JxK2lwCLcB/s640/UES%2Bfraction%2Breasoning%2Bpost.jpg" title="teaching fractions" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Today is my day to blog over at Upper Elementary Snapshots--so I hope you will stop by and check out this fun lesson we did last week...and REALLY showed me where my students were with their math thinking! Just click the image above to check out the details.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Missed any of my other fraction posts last week? Click <a href="http://www.theteacherstudio.com/2016/12/examples-counterexamples-and-more-with.html">HERE</a> and <a href="http://www.theteacherstudio.com/2016/12/using-our-fractional-reasoning.html">HERE</a> to check out a few more!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Also...don't forget that I have a few holiday resources on sale for the next week for those of you who are still teaching--like me!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-IIxf02E9jp0/WFabVidfBII/AAAAAAAAYk4/yZXYXAwSBg82HCIWIC1k1xEttu9nx8ZnwCLcB/s1600/christmas%2Bsale%2Bitems.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://3.bp.blogspot.com/-IIxf02E9jp0/WFabVidfBII/AAAAAAAAYk4/yZXYXAwSBg82HCIWIC1k1xEttu9nx8ZnwCLcB/s320/christmas%2Bsale%2Bitems.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Feast-Math-Project-Grades-3-4-1531237">Holiday Cookie Task</a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Seasonal-Word-Problem-Collection-Christmas-Grade-3-5-1012901">Christmas Word Problems</a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Winter-Word-Problems-Algebra-Thinking-454583">Winter Algebra Thinking Task Cards</a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>If you are still teaching....hang in there! It's all we can do...keep joy in your heart as best you can!<br /><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-13784714101858354592016-12-14T19:26:00.001-06:002016-12-14T19:26:17.314-06:00Examples, Counterexamples, and More with Equivalent Fractions<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="equivalent fractions" border="0" height="640" src="https://1.bp.blogspot.com/-BX8rAFnvtQQ/WFHvYqCTu5I/AAAAAAAAYi8/llhj-CXe630G4kRiu8cjQLh3n3M3D2qjACLcB/s640/fraction%2Bpost%2Bequivalent%2Bexample%2Bcounterexample.jpg" title="teaching fractions" width="320" /></a></div>As I have been working to build my students' understanding of key fraction concepts, I wanted students to really work to deepen their understanding that fractions can have more than one name--and can be represented in more than one way.<br /><br />Today's "warm up" was geared toward reminding students that they can represent fractions in many ways...so I gave them 5 minutes to make a "mini poster" (literally 4 inches by 4 inches!) to show as many ways to show 1/2 as possible. After they worked, we did a little gallery walk. We came back together and had a discussion about what we saw...different shapes...number lines...fractions of sets...equivalent fractions...<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="equivalent fractions" border="0" height="480" src="https://1.bp.blogspot.com/-pihoUK_n1Pc/WFHYy_p6O7I/AAAAAAAAYiY/XVPu4WH50vA4CNXekXuUN74HfyhH6iQBgCLcB/s640/Photo%2BDec%2B14%252C%2B5%2B32%2B11%2BPM.jpg" title="teaching fractions" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="equivalent fractions" border="0" height="640" src="https://3.bp.blogspot.com/-O7l-WBVmqQk/WFHYz1gNtOI/AAAAAAAAYik/bzV6uTrEZ74nqm-m0vCZvDXI-LtNbzgrQCLcB/s640/Photo%2BDec%2B14%252C%2B5%2B34%2B08%2BPM.jpg" title="teaching fractions" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;">It was a good warm up to our main lesson which worked to help students derive the "computation" method for finding equivalent fractions. (If you missed my post yesterday about building that understanding, </span><a href="http://www.theteacherstudio.com/2016/12/using-our-fractional-reasoning.html" style="text-align: start;">CLICK HERE</a><span style="text-align: start;"> to read that one!). After our explorations, it wasn't that big of a stretch for students to recognize that multiplying or dividing the numerator and denominator by the same number generated new fractions that are equivalent. We proved it with some drawings, some manipulatives, and then moved to bare numbers.</span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;">So after working with equivalent fractions for a while, I wanted to put my students to the test to see how WELL they understood the concept! So often we give students a quick exit slip or something like that--a "fill in the blank" worksheet that follows whatever computation rule we have taught. If they fill in the blanks correctly, we assume understanding. It just isn't that simple.</span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;"><br /></span></div><div class="separator" style="clear: both; text-align: start;">To really get students talking, I asked them to do an activity in my big fraction unit....an activity where they need to first generate equivalent fractions (sometimes I do this activity where they can write fractions, draw fractions, etc like the warm up) but today I simply wanted them to use their new algorithm to make a set of 5-7 equivalent fractions for the "unit fraction" I assigned them. The group below was working to generate a list of fractions equivalent to 1/8.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="equivalent fractions" border="0" height="480" src="https://2.bp.blogspot.com/-KrnwWIod_Ls/WFHYzNrZlUI/AAAAAAAAYic/tarpB4GyymwkM5zX4SP5UKbfAE4g5ssUQCEw/s640/Photo%2BDec%2B14%252C%2B5%2B32%2B59%2BPM.jpg" title="teaching fractions" width="640" /></a></div> Here's where the fun (and really deep understanding) kicks in. The next task is to create ONE more fraction for their poster--that does NOT fit their "team"...in other words, that is NOT equivalent. I explained that they would be then traveling from team to team to try to find the "mystery" fraction. I had them write their "counterexample" on the back so students could check their work...and encouraged them to try to be as sneaky as possible when making their "outsider" so other students would really have to work! Some groups did an AMAZING job...and I heard some great math talk! This really immersed them in this idea of equivalent fractions and having to think hard about number patterns and the true meaning of equivalence. We came back together after their gallery walk and discussed their findings--and talked about some of the trickier ones. It was a ton of fun and a great use of time. The paper and pencil practice work we did after this was done in a snap--almost all students were really getting it, and those who weren't met with me for a little extra practice.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="equivalent fractions" border="0" height="480" src="https://2.bp.blogspot.com/--afEnDzAXzY/WFHYzHnvYeI/AAAAAAAAYig/YESl29a37UAA4dtvM3w_AffGrDxJ6hCBgCEw/s640/Photo%2BDec%2B14%252C%2B5%2B33%2B27%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>I wrote about this a few years back with a slightly different twist if you want another idea. Just <a href="http://www.theteacherstudio.com/2013/02/fractions-day-4-example-counterexample.html">CLICK HERE</a> for that post! These ideas are a part of my full fraction unit which you can check out by clicking the image below. If you are looking for ways to deepen your students' understanding--plus have fun teaching, you might want to check it out!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img border="0" height="320" src="https://2.bp.blogspot.com/-zpCzn_fLOE8/WFHsc3FQLNI/AAAAAAAAYi0/S2Kq3OydfNA772EZ4nSEQ02N0v9_YWoMACLcB/s320/fraction%2Bunit%2Bcover.jpg" width="320" /></a></div><br /><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-83735084447906267622016-12-13T22:50:00.000-06:002016-12-14T06:13:38.892-06:00Using Our Fractional Reasoning!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="fractions" border="0" height="640" src="https://1.bp.blogspot.com/-E6G-MMQq4Ho/WFDLgrICdsI/AAAAAAAAYh0/IOVkUZx1JpEGlFtcqfdHrL_A3XC5d71ggCLcB/s640/fractional%2Breasoning%2Bpost%2Bconcept%2Bsort.jpg" title="concept sort" width="320" /></a></div>We had a great concept sort today...and I just wanted to share a little about what we did!<br /><br />We are working on the concept of equivalent fractions...we have drawn pictures, told stories (If I had half a pizza but cut the half into two pieces, what fraction would I have?), and generated lists of equivalent fractions. What we DIDN'T do is what most math programs do right away--teach students to multiply the numerator and denominator by the same number. We'll get there-but first I really want students to use their reasoning to really show their understanding of some key fraction concepts.<br /><br />One of the Standards for Mathematical Practice involves the ability to "reason"--to create strong understanding of key concepts without merely computing. It states:<br /><br /><span style="color: #202020; font-family: "lato light"; font-size: 16.8px;"><b>"Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects."</b></span><br /><span style="font-family: inherit;"><span style="color: #202020; font-size: 16.8px;"><br /></span><span style="color: #202020; font-size: 16.8px;">By helping students learn to reason about fractions, they become better at understanding without relying on tricks and computation--which helps them with estimating and checking for reasonableness as the math gets more challenging. I love trying to help students VISUALIZE math and make sense of it before teaching them--so that's what today was all about!</span></span><br /><span style="font-family: inherit;"><span style="color: #202020; font-size: 16.8px;"><br /></span><span style="color: #202020; font-size: 16.8px;">Most students have a pretty decent understanding of the concept of "one half", so I wanted to experiment with a sort and see what my students could do. We've already talked about the concept of "unit fractions"--and how they can by used to "count" fractions...1/4, 2/4, 3/4 and so on. We also have used our reasoning to picture the relative size of these unit fractions...that even though "seven" is a bigger number than "three", sevenths are smaller than thirds because more parts must mean smaller parts!</span></span><br /><span style="font-family: inherit;"><span style="color: #202020; font-size: 16.8px;"><br /></span><span style="color: #202020; font-size: 16.8px;">This was really enough information for us to begin this sort--where students used what they know about fractions to sort them into three categories--greater than 1/2, exactly 1/2, and less than 1/2.</span></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="480" src="https://3.bp.blogspot.com/-UXbOl7xSd7Q/WFC4wsgNnMI/AAAAAAAAYhU/kATthHZFj00TYljJz_p_qSzdY71knN7NQCLcB/s640/Photo%2BDec%2B13%252C%2B9%2B09%2B06%2BPM.jpg" title="teaching fractions" width="640" /></a></div> One of our rules about concept sorts is that students work in small groups (usually trios) and must go one card at a time where they discuss together and make a decision about which category the cards fall in. If they have any debate, they set it aside for later.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="480" src="https://3.bp.blogspot.com/-Ue8TLcxtV4g/WFC40HY5H9I/AAAAAAAAYhk/JP-kJP53spgkJwzpLrTjVR6IiDfgQP1XACLcB/s640/Photo%2BDec%2B13%252C%2B9%2B09%2B55%2BPM.jpg" title="teaching fractions" width="640" /></a></div> While students are working, I'm circulating, asking questions, listening--and looking for misconceptions. Anything "interesting" gets thrown under the document camera at the end!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="640" src="https://4.bp.blogspot.com/-hN6KFP4qzpg/WFC4wQsP5kI/AAAAAAAAYhQ/nhW0KL6YA1grMuQREiVvdQ8YCbxj2OLewCLcB/s640/Photo%2BDec%2B13%252C%2B9%2B10%2B18%2BPM.jpg" title="teaching fractions" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">For groups finishing early, I ask them to write their OWN examples for each category...</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="480" src="https://2.bp.blogspot.com/--tMXb5Tk_ao/WFC4zoC5EBI/AAAAAAAAYhg/CVg7mL1xuoksK4kXXiNnNwKL_p-boW4kgCEw/s640/Photo%2BDec%2B13%252C%2B9%2B08%2B18%2BPM.jpg" title="teaching fractions" width="640" /></a></div> I LOVED hearing the discussion this group had--they write the example and then couldn't come to an agreement about which category! One of the students was trying SO hard to explain that HALF of 310 would be 155...so 149/310 HAD to be less than one half. The other two were NOT understanding her reasoning!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="640" src="https://2.bp.blogspot.com/-8fqX5lcrxAU/WFC4zgCTPpI/AAAAAAAAYhc/jZsL8nCxCAgmdfLUc77fH0kIwjGZGNLLwCEw/s640/Photo%2BDec%2B13%252C%2B9%2B07%2B55%2BPM.jpg" title="teaching fractions" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">After we worked for a while, I picked THIS fraction to discuss...and with NO computation about finding fractions equivalent to 1/2, we had two very justifiable explanations for why 7/15 is less than one half. One student came up and explained how it HAD to be less than one half because 7/14 would be one half...and fifteens are smaller than fourteenths--so 7/15 had to be smaller than 7/14. Pretty slick!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">The other argument explained that the "halfway" point of fifteenths would have to be "seven and a half" of them...so 7 of them ha to be less than one half. Such GREAT math discussions...with no computation. This is a perfect example of why I love concept sorts...so much discourse. So much math. So much engagement. Tomorrow--we learn the algorithm for generating equivalent fractions...and I think they are more than ready for it!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="480" src="https://2.bp.blogspot.com/-3lnQL3XqS1A/WFC4zbfjJkI/AAAAAAAAYhY/-QmQve0gVZkSZanFvTmiUGghpD3fA3SSwCEw/s640/Photo%2BDec%2B13%252C%2B9%2B07%2B29%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">This sort is one of the five sorts in this resource. Check it out if you are curious!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img border="0" height="320" src="https://2.bp.blogspot.com/-6FDdle-Krhw/WFDODy4QOpI/AAAAAAAAYiA/WhcOP8NHVZocstVSmpv7XqTmXqcc6J8EQCLcB/s320/concept%2Bsort%2Bfraction%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;"> <span style="text-align: center;">Looking for just a single sort to address equivalent fractions? Check out this one!</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Single-Sort-Resource-for-Equivalent-Fractions-1601711"><img border="0" height="320" src="https://1.bp.blogspot.com/-VIocu33MMKU/WFDOHCGZ-qI/AAAAAAAAYiE/Chfs1t6ivL8MggSI_o5UeYd4VPrs5KsXgCLcB/s320/Slide1.JPG" width="240" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-54223363885980454242016-12-10T15:39:00.000-06:002016-12-10T15:39:11.048-06:00Coming Up with a Math Plan, Teamwork, and Perseverance!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img alt="standards for mathematical practice" border="0" height="640" src="https://3.bp.blogspot.com/-wobDYJoenTI/WExwUo8cD6I/AAAAAAAAYgw/O8ARTKZGF-4E-NsGptVwcuHUvNRWi5megCLcB/s640/thinker%2Btask%2Bcookie%2Bpost.jpg" title="problem solving" width="320" /></a></div>I just wanted to share a quick blog post about what I am doing in math workshop over the next two weeks because my students are SO excited! We are digging into the next series of fraction lessons, and I know that some of my fourth graders are going to handle the material easily. To make sure they have plenty of meaningful work to do when they finish their learning, I introduced the holiday cookie task to them! They were thrilled! One even said, "Is this one going to challenge us even more than the Thanksgiving feast one?" and I just smiled and reminded him that different tasks provide different challenges for different people because we all bring different background to it. I was going to introduce it Friday and get started on Monday, but we had extra time and they begged and I was tired. So I caved.<br /><br />I told them that the main part of this project that I wanted them to focus on (always good to keep a simple focus on complicated tasks, I have found) was that with their partner(s), they needed to come up with a plan. This task has many solutions...but the key direction is to "make as many cookies as possible"...so I wanted my students to really be thinking about what they could do to "test" if they could possibly make more cookies than their first attempt showed them. I also told them that they would really have to remember all they know about basic fractions AND solving problems with more than one step--and they were ready.<br /><br />So they looked...<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img alt="problem solving" border="0" height="480" src="https://4.bp.blogspot.com/-h5pLqhHsC6Q/WEtFOp5gJcI/AAAAAAAAYgE/spbdDLBwt5MydbJZHCn0BW-U_kJiZ4oRgCLcB/s640/Photo%2BDec%2B09%252C%2B5%2B13%2B08%2BPM.jpg" title="word problems" width="640" /></a></div> And they read...<br /><br />I really like my students to read these complicated tasks on their own to try to "make sense" of problems without me spoon-feeding. Depending on the student, I may restate the task, ask THEM to restate the task, or let them proceed and then adjust along the way with questions like, "Hmmm...does it SAY that you can do that?" Great opportunities for teaching mathematical thinking sometimes require students to make mistakes and adjust--and they learn quickly to dig in deeply to find information. It's too easy when the teacher tells them everything they need to know! This is also a great way to push students toward better perseverance; when everything is "coached", they don't learn those critical skills needed to push themselves, ask good questions, and have great "math talk" with each other. I heard some of the GREATEST "arguments" as they were working to make sense of this problem--and THAT is exciting math!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img alt="preseverance" border="0" height="480" src="https://4.bp.blogspot.com/-BxBzLWcYDtI/WEtFOsDJ6lI/AAAAAAAAYgI/7uHNt38SJDoIZYtLvaE6GUbYHlOPj_RYgCLcB/s640/Photo%2BDec%2B09%252C%2B5%2B13%2B29%2BPM.jpg" title="standards for mathematical practice" width="640" /></a></div> And they started to record their ideas<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img alt="fraction problem solving" border="0" height="480" src="https://1.bp.blogspot.com/-yWBvNtcCaWc/WEtFOU-8exI/AAAAAAAAYgA/tVb3ODNVpgElfYYqOrm_l4iZ0sjJfj5jwCLcB/s640/Photo%2BDec%2B09%252C%2B5%2B13%2B47%2BPM.jpg" title="math problem solving" width="640" /></a></div> I love that some immediately went to abbreviations ("SC" for sugar cookie, etc), others drew pictures, some made tables...and they were off and running. As I circulated, I kept asking students to remember to have a plan to see if they are REALLY maximizing how many cookies they could make. I love the hum of collaborative math work...seriously. I sometimes just stand back for a few minutes and watch them ENJOYING math.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img alt="holiday word problems" border="0" height="640" src="https://2.bp.blogspot.com/-lJDMFOXV3n4/WEtFO1LFEZI/AAAAAAAAYgM/yYKIdtownk8V6OEu0S_TGZotBJZwjJC2QCLcB/s640/Photo%2BDec%2B09%252C%2B5%2B14%2B21%2BPM.jpg" title="fraction problem solving" width="480" /></a></div>As they worked to get going, I got some of the BEST questions...so I am super excited to see how the next few days unfold! "Can we cut recipes in half? What about fourths?" and "Is this a problem where we can work backwards?" Love it! I think when we finish, students who are interested will report back to the class how their strategies and plans changed and evolved throughout the process. Like my other Thinker Tasks, I know some students will get a lot farther into the project than others--but those discussions about planning and modifying and adapting are so important as students begin to realize that problem solving is about FAR more than the answer! Stay tuned!<br /><br />Interested in seeing more about this project?<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img border="0" height="320" src="https://4.bp.blogspot.com/-_oCgdSN5Z-A/WExtfNA_RUI/AAAAAAAAYgc/JG-w0CIQkvAntJ614b69jBXbTBldP95xgCLcB/s320/holiday%2Bcookie%2Bthinker%2Btask%2Bcover.jpg" width="320" /></a></div><br />Here is the discounted bundle of all my Thinker Tasks!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Task-Bundle-Differentiated-Open-Ended-Math-Tasks-1843282"><img border="0" height="240" src="https://4.bp.blogspot.com/-mPxt6ZXn7Cg/WExtkdKcDwI/AAAAAAAAYgg/gfi7cWtBmRU9_OMlXF9PaPnf11UZIfvUACLcB/s320/Slide1.JPG" width="320" /></a></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-38796670389884606532016-12-02T22:58:00.001-06:002016-12-02T22:58:19.213-06:00Getting students ready to divide and tackle remainders!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Division-Concepts-Grades-3-and-4-1214093"><img alt="division fact games" border="0" height="640" src="https://1.bp.blogspot.com/-ksWZ3XTkOt0/WEJLyZBVHZI/AAAAAAAAYe8/fwe2lsHB4Vwzt_6mUBwpk0soyGksu6M-ACLcB/s640/division%2Bherding%2Bgame%2Bpost%2Bpin.jpg" title="Teaching division" width="320" /></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 21.3333px;">It's division time--and I am always shocked at how students freak out about division...and how much "harder" it is than multiplication. I always promise them that I can make it easier for them! I posted a picture on Instagram the other day and I had a bunch of requests for more details on the "Herding Game"!</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">To begin, I wanted students to really understand the idea that multiplication and division are so linked that we can almost use them interchangeably in our minds—but that our math language needed to reflect what we are doing. What do I mean? We often teach students what many call “turn around” facts. We tell them that 4 x 3 is the same as 3 x 4. But is it? Is four boxes of 3 pies the same as 3 boxes of 4 pies? No it isn’t. They both represent 12 pies—but the situation is totally different. To help students see this, I made up a game a few years ago...and it has proven to be super effective--and FUN!</span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">I told the students that they were going to be a “herd” of animals today and that I had researched a whole bunch of animals that traveled in herds. I also let them know that when animals who travel in herds are threatened, they sometimes break into smaller groups to protect each other. I told them that I was going to break them into smaller groups today and then we would write the mathematical equations that we discovered in the process. We counted our “herd” and found that we had 22 animals this day.</span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">I taped off an area of one of our empty classrooms (this would have been fun to do outside as well with a chalked off area) to have as our “holding pen” for extra animals that couldn’t find a group. I also put some animal “tokens” in the pen so that each child who ended up there took a token—and the token was a “get out of the pen free” card so the same students didn’t always up there. For some reason, some students WANT to land in the holding pen so they don't actively participate in the herding...so once is enough!</span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">Here's how we play.</span></span></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Division-Concepts-Grades-3-and-4-1214093"><img alt="teaching remainders" border="0" height="640" src="https://1.bp.blogspot.com/-xrtqiujiQsE/WEJIoiaSUwI/AAAAAAAAYec/lCuen5LKN7o6qpFC7l1r6_8Ry_GERe94QCLcB/s640/Photo%2BDec%2B02%252C%2B6%2B24%2B48%2BAM.jpg" title="teaching division" width="640" /></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">First of all, I called out a type of animal (buffalo, giraffes, zebras, wild boars, cows, bison, elephants…) and the size of the group I wanted them to form. For example…</span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">“Elephants—form groups of 5!”</span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">The students scampered to make their groups, and I asked for help writing the equation on the board. I had to help a bit, but with coaching, we got it. I asked,</span></span><span style="font-family: inherit; font-size: 16pt;">“So I just formed four groups of 5?"</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">I wrote 4 x 5 = 20. "What about the leftovers?" I wrote (4 x 5) + 2 = 22</span></span></div><div class="separator" style="clear: both; text-align: center;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">We tried again. “Giraffes—form </span></span><span style="font-family: inherit; font-size: 16pt;">groups of 2!” </span><span style="font-family: inherit; font-size: 16pt;">Students quickly paired up and we wrote the equations.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: center; unicode-bidi: embed; word-break: normal;"><span style="font-family: inherit;"><span style="font-size: 16pt;">22 </span><span style="font-size: 16pt;">÷ </span><span style="font-size: 16pt;">2 </span><span style="font-size: 16pt;">= </span><span style="font-size: 16pt;">11</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: center; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">11 x 2 = 22</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: center; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: center; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">No remainders this time!</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: center; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">The students were getting the hang of the game so I decided to move to the next steps. “Buffalo—form groups of 7.”</span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">The students struggled a bit to make their groups—but eventually the leftover buffalo found its way to the holding pen. </span></span><span style="font-family: inherit; font-size: 16pt;"> </span><span style="font-family: inherit; font-size: 16pt;">We worked</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">to write the equations this time. </span></span><span style="font-family: inherit; font-size: 16pt;">22 </span><span style="font-family: inherit; font-size: 16pt;">÷ </span><span style="font-family: inherit; font-size: 16pt;">7 </span><span style="font-family: inherit; font-size: 16pt;">= </span><span style="font-family: inherit; font-size: 16pt;">3 groups with 1 remaining</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"> </div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: inherit;"><span style="font-size: 16pt;">(3 </span><span style="font-size: 16pt;">x </span><span style="font-size: 16pt;">7) + 1 </span><span style="font-size: 16pt;">= 22. We tried again..."Make 3 herds of antelope!" (Different than herds of 3, right?)</span></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Division-Concepts-Grades-3-and-4-1214093"><img alt="teaching about remainders" border="0" height="480" src="https://2.bp.blogspot.com/-8Y6Vj-lC3wc/WEJI2DwOhaI/AAAAAAAAYek/X7g2mFLeFvYkWd8QMRqYm1qgT2afOgZYQCLcB/s640/Photo%2BDec%2B02%252C%2B10%2B20%2B40%2BPM.jpg" title="teaching division" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Division-Concepts-Grades-3-and-4-1214093"><img alt="teaching remainders" border="0" height="480" src="https://1.bp.blogspot.com/-80LuQ2RIb40/WEJI1HlOxfI/AAAAAAAAYeg/sLygXgfvpckLQ-hClEimvPU5DshMJBhFgCLcB/s640/Photo%2BDec%2B02%252C%2B10%2B21%2B43%2BPM.jpg" title="teaching division" width="640" /></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: inherit;"><span style="font-size: 16pt;">Everything was going beautifully--until one of our specialist teachers showed up...so we had to redo the game a few times with 23 animals!</span></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Division-Concepts-Grades-3-and-4-1214093"><img alt="division and multiplication" border="0" height="480" src="https://1.bp.blogspot.com/-fvV6BueuTYY/WEJF1zHqXlI/AAAAAAAAYeI/PU9kUbwxOWwZbOvXLTTgMLOtRCCcL0SEwCLcB/s640/Photo%2BDec%2B02%252C%2B10%2B09%2B12%2BPM.jpg" title="teaching division" width="640" /></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">We continued with several more rounds until I could see that the students were getting the hang of it! We wrote down some of our rounds on the board (when I remembered!) and then I asked them to try to do some mental math to determine what would happen if I asked them to make groups of 9…then groups of 6. They did a great job! I knew that I had given my entire class enough to go on—and </span></span><span style="font-family: inherit; font-size: 16pt;">I was ready to continue the </span><span style="font-family: inherit; font-size: 16pt;">work with my more struggling </span><span style="font-family: inherit; font-size: 16pt;">students back in the classroom.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">While my other students were working on some multi-step problem solving, I pulled some of my struggling students to try our “herding” activities in a smaller group. I made some cute little animal tokens to use as counters and we started working to tell herding stories. I</span></span><span style="font-family: inherit; font-size: 16pt;"> wanted to see if they could apply the skills of the game a little more independently and could make the shift to recording their math equations on their own.</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Division-Concepts-Grades-3-and-4-1214093"><img alt="teaching remainders" border="0" height="480" src="https://4.bp.blogspot.com/-yV8WabKCML4/WEJOFYct8CI/AAAAAAAAYfI/3TNFnGLP4RUYI66Vpf1o7qzAFnrMJz_bgCLcB/s640/Photo%2BDec%2B02%252C%2B10%2B45%2B03%2BPM.jpg" title="teaching multiplication and division" width="640" /></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: inherit; font-size: 16pt;">Much like the game, I told herding stories but this time gave each student a baggies of animals—and I was able to change the number of animals in the herd at will.</span><span style="font-family: inherit; font-size: 16pt;"> </span><span style="font-family: inherit; font-size: 16pt;">So the questions began…</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="color: #0070c0; font-size: 12pt;"><span style="font-family: inherit;">“You have a herd of 12 animals. Divide them into 3 groups—what do you get?” </span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="color: #0070c0; font-size: 12pt;"><span style="font-family: inherit;">“You have a herd of 16 animals. Divide them into 8 groups—what do you get?”</span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="color: #0070c0; font-size: 12pt;"><span style="font-family: inherit;">“You have a herd of 20 elephants. Divide them into 5 groups—what do you get?”</span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 16pt;"><span style="font-family: inherit;">We did several rounds where </span></span><span style="font-family: inherit; font-size: 16pt;">the groups worked out with </span><span style="font-family: inherit; font-size: 16pt;">no remainders, but after a few minutes, I moved to working with remainders.</span><span style="font-family: inherit; font-size: 16pt;"> Students </span><span style="font-family: inherit; font-size: 16pt;">started really seeing the </span><span style="font-family: inherit; font-size: 16pt;">connection between their </span><span style="font-family: inherit; font-size: 16pt;">multiplication facts and the division </span><span style="font-family: inherit; font-size: 16pt;">problems! We kept track on the </span><span style="font-family: inherit; font-size: 16pt;">recording sheet to make sure </span><span style="font-family: inherit; font-size: 16pt;">that we were getting the </span><span style="font-size: 16pt;"><span style="font-family: inherit;">practice with the math </span></span><span style="font-family: inherit; font-size: 16pt;">language and grouping </span><span style="font-family: inherit; font-size: 16pt;">concepts. I really started seeing light bulbs go off!</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: inherit; font-size: 16pt;"><br /></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: inherit; font-size: 16pt;">As a follow up, I introduced "The Pretzel Game"...perfect for practicing these division with remainders situations. See what you think and give it a try! I probably should make more copies of this...I only have two right now and my students are clamoring for it!</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Dollar-Deals-The-Pretzel-Game-A-Game-for-Basic-Division-and-Remainders-1596260"><img alt="math game remainders" border="0" height="480" src="https://2.bp.blogspot.com/-Tn1dfsyEEZU/WEJI_vbgdMI/AAAAAAAAYeo/pBRZ3rdzMnMEbva_qesHMl9YyQt1cyzRACLcB/s640/Photo%2BDec%2B02%252C%2B10%2B07%2B16%2BPM.jpg" title="division game" width="640" /></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: inherit; font-size: 16pt;">If you want to see more, here are the two resources I used to get this division unit going!</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Dollar-Deals-The-Pretzel-Game-A-Game-for-Basic-Division-and-Remainders-1596260"><img border="0" height="320" src="https://2.bp.blogspot.com/-8_hKnkoip3Y/WEJJOSTT0DI/AAAAAAAAYes/aeUIZovJ2PkRQlKbMyuXPrN1DqV1G72GgCLcB/s320/Slide1.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Division-Concepts-Grades-3-and-4-1214093"><img border="0" height="320" src="https://3.bp.blogspot.com/-a97T7P03Gk8/WEJJT-WRU9I/AAAAAAAAYew/U53ueSCb9SYqE7vHNqP_jgjTzGHpVD5LwCLcB/s320/Slide1.JPG" width="240" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com3tag:blogger.com,1999:blog-8072938188438508721.post-19693150252902767242016-11-21T21:46:00.001-06:002016-11-21T21:48:44.044-06:00Team Challenge: Subtraction with Regrouping...and FUN!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Precision-Practice-Addition-and-Subtraction-Activities-to-Build-Understanding-1477782"><img alt="computation practice" border="0" height="640" src="https://1.bp.blogspot.com/-6Xeyce9BiLQ/WDO6Q0jNdBI/AAAAAAAAYck/FkEajOJgA0gNXyNgO6-RG_042KsCc9PNwCLcB/s640/subtraction%2Bchallenge%2Bpost%2Bpin.jpg" title="subtraction with regrouping" width="320" /></a></div>Just a quick "photojournalistic" post today to show you what fun we had with a class warm up today! Our goals? To continue working on our subtraction with regrouping fluency and accuracy--and to be able to look for errors and fix them.<br /><br />Here's what we did. You could easily do this with a set of cards you make...but I used the cards from my Precision Practice resource (this activity is listed at the beginning as one of the extra activities) because we had just used the cards a few weeks ago and, in typical fashion, they were not yet put away! I have probably used them 8-10 times since the start of the school year in different ways--but this was a new one for us!<br /><br />The directions were simple: Students worked in pairs to draw two cards (I used 3 different levels of cards and students picked their own level of challenge--3 digit, 4 digit, or 5 digit). Each child found the difference between the two cards, and then compared answers.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Precision-Practice-Addition-and-Subtraction-Activities-to-Build-Understanding-1477782"><img alt="collaborative work" border="0" height="480" src="https://3.bp.blogspot.com/-nBCsM8ILCyE/WDOevLt4chI/AAAAAAAAYcQ/yDdwfaDg-okt3vaD9d795d0yg0WFVXSogCLcB/s640/Photo%2BNov%2B21%252C%2B5%2B48%2B30%2BPM.jpg" title="subtraction with regrouping" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Precision-Practice-Addition-and-Subtraction-Activities-to-Build-Understanding-1477782"><img alt="accountable math talk" border="0" height="480" src="https://4.bp.blogspot.com/-_tSJLRNiDe4/WDOeuAC6A_I/AAAAAAAAYcI/vC5rkB6o10gMtVyZ_41e4E-l856MWqfpACLcB/s640/Photo%2BNov%2B21%252C%2B5%2B48%2B06%2BPM.jpg" title="subtraction with regrouping" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">If they both got the problem right, one teammate went to the smartboard and added two tallies to our "class challenge". If they did NOT both get it right but were able to work together to figure out where the error was, they got to put up ONE tally. I really stress how important it is to be able to make mistakes--and to be willing to hunt out how to fix them so this activity was PERFECT for that!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Precision-Practice-Addition-and-Subtraction-Activities-to-Build-Understanding-1477782"><img alt="cooperative learning" border="0" height="532" src="https://4.bp.blogspot.com/-VX4nlciGw80/WDOet9jEL1I/AAAAAAAAYcE/xFtKs9ZYQkMDH9b3U3No-8bWSuGjvWcPwCLcB/s640/Photo%2BNov%2B21%252C%2B5%2B47%2B25%2BPM.jpg" title="subtraction with regrouping" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">I set the timer for 15 minutes and the teams worked to earn as many tallies as they could in 15 minutes. When they finished we looked at the tallies, estimated how many there were, and then made groups of 10 to get the grand total.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Precision-Practice-Addition-and-Subtraction-Activities-to-Build-Understanding-1477782"><img alt="cooperative learning" border="0" height="480" src="https://2.bp.blogspot.com/-V6b0k3j7vjI/WDOeua68_3I/AAAAAAAAYcM/uuLUAzPkFF8DIa3BH9mNnr4COg80P758wCLcB/s640/Photo%2BNov%2B21%252C%2B5%2B47%2B42%2BPM.jpg" title="subtraction with regrouping" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">We could have done a subtraction practice sheet--but WHY? Students got a ton of practice...and the added benefit of troubleshooting mistakes. It was a great kick off to get our brains ready for our lesson today--subtracting across multiple zeroes. Give it a try and see what you think! My students asked when we could do it again!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;">Looking for the Precision Practice resource that I used? It includes this and many other activities to practice addition and subtraction in challenging and unusual ways. Just click the image below to see more. (Also available in multiplication)</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Precision-Practice-Addition-and-Subtraction-Activities-to-Build-Understanding-1477782"><img border="0" height="320" src="https://3.bp.blogspot.com/-wMfOp8hgVcI/WDO9J2maYaI/AAAAAAAAYcs/tly8KgcKoYEfJ4sPwWXhqqw0e8RHxxlcwCLcB/s320/precision%2Bpractice%2Baddition%2Bsubtraction%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-10955946963671167702016-11-19T19:44:00.000-06:002016-11-19T19:44:10.091-06:00Subtraction Observations...the power of working one-on-one with students<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Addition-and-Subtraction-Grades-2-4-1446312"><img alt="math assessment" border="0" height="640" src="https://4.bp.blogspot.com/-xZfpyXQbXCw/WDD4RjjrD1I/AAAAAAAAYbg/KAMuZHscm2sSWkZyWWAUSRfQ-4V3aaRHgCLcB/s640/math%2Bobservation%2Bsubtraction%2Bpost.jpg" title="teaching subtraction with regrouping" width="320" /></a></div>As you know, formative assessment is a critical part of the teaching/learning cycle. Without knowing what our students know and can do, it is very hard to make sound instructional decisions. I use exit slips (and entrance slips) ALL the time to try to keep a clear vision of what my students can do--and what more we need to work on.<br /><br />There are, however, times that I believe a paper and pencil assessment can only give us part of the information we need. Giving students a few subtraction problems to do can tell us if they CAN get the right answer...but it doesn't always show us HOW they do it or where they may be getting off track.<br /><br />For something important like the standard subtraction algorithm, it is critical to see where students who are struggling are going wrong. This is what I wanted to do on Friday before we move into bigger numbers and lots of 0's! Although you can do this with only students you are worried about, I truly wanted to watch each of my students solve two problems so I could look for the following things:<br /><b><br /></b><b>1. Accuracy </b><br /><b>2. Fluency</b><br /><b>3. Efficiency</b><br /><b>4. Confidence</b><br /><br />I kept a recording sheet right next to me and as they worked, I watched every step they took, asked questions if I couldn't tell what they were doing, and then jotted down what I noticed. Did they get it right? Could they do the algorithm AND use correct subtraction facts to get the right answer? After all, we DO want students to get the right answer, don't we?<br /><br />But getting the right answer is only part of the deal--if this was all I was concerned about, I would just give them a paper and pencil assessment (which I will be doing often over the next week or so!). I really want to get a sense for students' fluency (speed at which they work) and efficiency (are they using notation and strategies that make sense and contribute to fluency?). I also wanted to know if they could EXPLAIN what they were doing...not just do it. All of these things work together to show me their overall CONFIDENCE with the skill. I have to say--it was time well spent!<br /><br />Throughout the day, I pulled students one or two at a time (two if I was 100% confident in their skill level) and watched them work the two problems. I watched them like a hawk to see if they were REALLY having to think through the steps or whether it was smooth and natural. I jotted down my observations, used the time as a coaching session for any mistakes that were made, and noticed something really important in about 1/3 of my students--how one sentence I had said during a lesson might have gotten them confused! <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Addition-and-Subtraction-Grades-2-4-1446312"><img alt="math assessment" border="0" height="640" src="https://2.bp.blogspot.com/--dyT3CMyuSY/WDC9fi5n_CI/AAAAAAAAYbI/Q6hUSpOUOMwOyQ4ZuE5Xe86eeoTEzNQPwCLcB/s640/Photo%2BNov%2B19%252C%2B2%2B58%2B38%2BPM.jpg" title="teaching subtraction with regrouping" width="468" /></a></div><div class="separator" style="clear: both; text-align: center;">So here's what I learned about how important MY language is with students! The other day during my mini lesson, I mentioned to students that it "can be a good idea to look at ALL the numbers you are subtracting from to see if trading will be needed." Harmless, right?</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Well...something I discovered in my assessment interviews was that I had a number of students who started this problem by doing just THIS--looking at EVERY place and crossing off everything needing a trade right off the bat! I was confused...in all of the modeling I had done, I carefully and methodically went place by place--if we needed "ones", we traded for a ten. If we needed "tens", we traded for a hundred--one step at a time.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Because seeing this "crazy crossing out" got me curious, I started asking questions...and students all came back to that line--that I had mentioned to look at ALL the numbers to see if they would need to"regroup"--and if they did, they got them ready to trade! Although some could do this "cross off" and keep their brains organized--most of them went WAY over to the thousands and started working from there--with obviously unsuccessful results! So, despite my careful (and repeated!) modeling (even with manipulatives), they took hold of that one sentence and went down a dangerous path.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Addition-and-Subtraction-Grades-2-4-1446312"><img alt="assessment" border="0" height="640" src="https://1.bp.blogspot.com/-6GKg-lUOQrg/WDC9fvDllTI/AAAAAAAAYbE/1Mbnj0BbTHAEgKOyzLKhHof8hLT3IZ4OwCLcB/s640/Photo%2BNov%2B19%252C%2B2%2B58%2B06%2BPM.jpg" title="subtraction misconceptions" width="500" /></a></div><div class="separator" style="clear: both; text-align: center;">When I saw what these students were doing, I realized how they misinterpreted my suggestion--and I NEVER would have seen it if I wouldn't have been working with them one-on-one and making those careful observations. I also would not have seen it on an exit slip--I would have seen the wrong answer but would not have seen the order of steps they took.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">So what were MY next steps? I went back to those other students who had been doing the multiple cross outs and we worked together to correct the misconception. By the end of the day, I knew which students were extremely fluent and confident and ready to move at a faster speed, which students understood the concept and just needed fluency work, and which students needed a variety of different misconceptions corrected--whether due to MY miscommunication or other errors they might have been making! I know now exactly where each student is in their learning--and I know how to group them next week. As we continue, I will do more observations with students who are struggling so I can continue to guide them with "just right" instruction. We will also be doing frequent exit slips to check for accuracy and fluency as the problems we do get more and more complicated. Thanks for stopping by!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Addition-and-Subtraction-Grades-2-4-1446312"><img border="0" height="320" src="https://1.bp.blogspot.com/-dl_DhTmswVk/WDC9wkGcg7I/AAAAAAAAYbM/8Me_BmbB5NsarAfB4VLcT4RfqZs6TtZqwCLcB/s320/Slide1.JPG" width="240" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" height="155" width="200" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-35862322065495246982016-11-16T20:12:00.000-06:002016-11-16T20:12:16.503-06:00Math Workshop Thanksgiving Style<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Addition-and-Subtraction-Grades-2-4-1446312"><img border="0" height="640" src="https://1.bp.blogspot.com/-dhlpLgiaQJk/WC0MEKvj6mI/AAAAAAAAYZw/tpz4O6LYD-wLXI3uPWJ2alCZgSfmowcOQCLcB/s640/a%2Bweek%2Bin%2Bmath%2Bworkshop%2Bthanksgiving%2Bpost.jpg" width="320" /></a></div>So often, I get questions like, "What does math workshop look like in your classroom?" and it's always such a tough question to answer--because it changes all the time. So I thought I'd tell you about my plans for the next week or so leading up until Thanksgiving--and see if you can picture what I'll be doing! Maybe in a month or so I'll do another post and show another "twist" on math workshop organization!<br /><br />For the next week or so, our curriculum has me scheduled to work on subtraction with regrouping. As you can imagine, I have students at ALL levels of sophistication with that skill--so there is no real way I can teach for a week or more whole class! My goal is always to maximize the amount of time students spend on "just right" instruction, so here's what the next week will look like.<br /><h2></h2><h2>1. Pretesting and regular formative assessments</h2>Although I don't do them every day, doing quick progress checks are SO important to me. Based o what I find, I can group students in different ways on different days to make sure that everyone gets as much "just right" instruction as possible. Everyone leans at different rates--and waiting until the end of unit is simply not an ok time for students to get feedback on their performance. These quick checks literally take minutes and can help me see who is getting it--and what types of mistakes students are making. This error analysis is so important in helping us streamline instruction.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Addition-and-Subtraction-Grades-2-4-1446312"><img alt="addition and subtraction exit slips" border="0" height="477" src="https://1.bp.blogspot.com/-rb5xl_ADlPM/WCz_gr6abbI/AAAAAAAAYY4/lLOK9UHywxA32TY9mza8IaA6dbaiHYlDgCLcB/s640/Photo%2BNov%2B16%252C%2B6%2B52%2B11%2BPM.jpg" title="addition and subtraction formative assessment" width="640" /></a></div><h2></h2><h2>2. Full class and partner warm ups</h2>To warm up our brains each day, I make a choice of a warm up activity. Some days it might be a number talk, other days it may be a review problem or two--but one of my favorite warm ups is a challenging word problem! I LOVE using word problems to warm up because it sets the stage for thinking all day! I often have them try a problem alone first where they try to implement all the strategies I have taught to "dig in". After a bit of work time, I offer up the option to pair up to continue. Some choose to keep working on their own, others like the collaborative part. I circulate and check for understanding, encourage organization and precision, and hunt for interesting work to share under the document camera. What problems am I using? Thanksgiving problems, of course! I love these because they are filled with cool facts--and each has two levels of challenge. I use several as warm ups, and then the rest of them get put on the wall in a pocket chart for students to do when they have time--or as a rotation in math workshop. I try to have other problems available that might be more "accessible" as well--so that those "wall problems" are not seen as something for only my top students. ALL students can easily access word problems to do during their math choice times.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Seasonal-Word-Problem-Collection-Thanksgiving-Grade-3-5-956001" style="margin-left: auto; margin-right: auto;"><img alt="Thanksgiving problem solving" border="0" height="477" src="https://2.bp.blogspot.com/-hjJGct0gOOE/WCz89nrvpVI/AAAAAAAAYYs/uIQtdCr6nj0LNy_c-Ooz8sjxsrVsEjy0gCLcB/s640/Photo%2BNov%2B16%252C%2B6%2B36%2B21%2BPM.jpg" title="Thanksgiving word problems" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">These Thanksgiving problems are fun because students LOVE some of the cool facts they include--and each has an "extra" part to allow those students who are ready to add a level more challenge!</td></tr></tbody></table><h2>3. Small group, targeted instruction</h2> For these weeks, the lessons focus on subtraction...starting small (even with base 10 blocks for some) and then eventually moving through subtraction across zeros with increasingly large numbers and money problems. I definitely will need to be grouping over the next week or so--and I am planning on two different approaches to this. Some days I will be splitting my class in half and teaching the concept at two levels. This allows me to spend more time with my struggling students and to use more hands on teaching methods to help build their conceptual understanding. When I do this, I do NOT meet with my two groups for equal amounts of time...my mini lesson for my "on track" students might be 10-12 minutes followed by some supported practice while my strugglers might get my full attention for 25-30 minutes.<br /><br />Other days I might teach the lesson to the entire class (I did this today) and then I either assess or have students self-assess and I follow up the lesson with a second "reinforcing" lesson. I often call this "coaching time" where I invite (or mandate!) students who might have struggled during the minilesson to come do some additional work with me. Students who are ready to roll can do some independent practice, make sure they are on track, and then move to some differentiated activities that are a good match for them.<br /><br /><h2>4. Differentiated activities during workshop time</h2><div>So...if I am only working with a part of my class at a time, I need some quality independent or cooperative work for them to do. I have a HUGE problem with doing math "fillers", so I am always looking to find engaging work that my students love and ask them to really apply math skills--or to practice fluency on skills they need. Here are some of the options we will be using during that workshop time. Some things may be required (like my top students are required to work on this Thanksgiving Feast Thinker Task and some of my students needing fact fluency are required to do some of the fluency games), and other activities are offered as choices. Here they are!</div><div><br /></div><div>First, this is an differentiated problem solving task that has many parts--so students who solve the first part can continue on. Almost all students choose to work together and I just LOVE the conversations they have. They truly "teach" and coach each other as well as any adult can...and they really are pretty independent so I can focus my attention on specific students or groups.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Feast-Math-Project-Grades-3-4-1531237"><img alt="problem based learning" border="0" height="477" src="https://2.bp.blogspot.com/-Q0z8SMyAwl0/WCz_y2SXLEI/AAAAAAAAYZA/qYPwSsJQHQoIcYgwJxSypqKeYYrN0OS6ACLcB/s640/Photo%2BNov%2B16%252C%2B6%2B36%2B42%2BPM.jpg" title="Thanksgiving problem solving" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Feast-Math-Project-Grades-3-4-1531237"><img alt="Thanksgiving math problems" border="0" height="477" src="https://1.bp.blogspot.com/-MdAKg3fH3fE/WCz_y_UNpkI/AAAAAAAAYY8/rX4IF_6XksMBUOuZDKpV-SEOMetGlARjwCLcB/s640/Photo%2BNov%2B16%252C%2B6%2B37%2B45%2BPM.jpg" title="Thanksgiving problem based learning" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">The next option that I have ready for my students is a set of Thanksgiving games...it comes in both addition and multiplication--and each of THOSE has two levels of challenge. My students LOVE this game (We started it last week) and they get tons of fact fluency practice. It's also a super easy one to copy and send home...just a few dice and markers (even pennies or paper scraps) and they are ready to roll! I have had students begging to stay in for recess to play!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Dollar-Deals-Thanksgiving-Addition-Challenge-A-Game-to-Build-Fluency-1573567"><img alt="Thanksgiving addition game" border="0" height="480" src="https://1.bp.blogspot.com/-xbX3uGiNlRE/WC0H12lBsMI/AAAAAAAAYZY/9Vzt6vgthbMMKVyETkxht6DJsw57NUQSgCLcB/s640/Photo%2BNov%2B16%252C%2B7%2B23%2B18%2BPM.jpg" title="addition fact game" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Dollar-Deals-Thanksgiving-Multiplication-Challenge-A-Game-to-Build-Fluency-1573584"><img alt="Thanksgiving math game" border="0" height="640" src="https://2.bp.blogspot.com/-R83hLVzAP0E/WC0H12S76aI/AAAAAAAAYZc/oHrzERI1J2MoV1WF9iVVQccEJcX66TTCgCLcB/s640/Photo%2BNov%2B16%252C%2B7%2B24%2B41%2BPM.jpg" title="multiplication math game" width="520" /></a></div>One third choice is another fluency practice activity I call "Toss and Solve". Students have laminated cards that look like this--from two digit on up to 4 digit. They roll dice to make the bottom number and then work to solve. They can either check their work on a calculator or two students can each solve it, compare answers, and then work to solve any discrepancies. I LOVE having students hunt for errors...and brain research says this is a great way to build those brain connections!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Toss-and-Solve-Addition-and-Subtraction-Task-Cards-1113487"><img border="0" height="480" src="https://4.bp.blogspot.com/-ja7MhGrz5c0/WC0Hv6y5I4I/AAAAAAAAYZU/laiLMAcRfJ8pr4gRwhtahlPjWiGiwbjmwCLcB/s640/Slide117.JPG" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;">I have a recording sheet that students use--or they can simply do their work on the cards or in a math spiral. Although this is a more traditional computation practice activity, it's far more fun than a worksheet--and when you involve partners and error analysis, it's WAY more than a worksheet!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Toss-and-Solve-Addition-and-Subtraction-Task-Cards-1113487"><img alt="addition and subtraction activities" border="0" height="640" src="https://3.bp.blogspot.com/-ndW6W7yykFk/WC0I13NDEiI/AAAAAAAAYZk/bg25ZtHq2qAJB6AIdI2PZz3udgclOk2rgCLcB/s640/toss%2Band%2Bsolve%2B2.jpg" title="subtraction practice" width="480" /></a></div>Remember, too, that there are always word problems available as well, so students really have several choices during this short unit. I work hard to help my students make just right choices, but there are times when gentle reminders are needed!<br /><br />When I am not teaching my small groups, I am circulating and coaching as students do these different activities--and my goal is also to pull a few intervention groups along the way as well. I still have a number of students FAR below grade level who need work on basic number sense and fact strategy work, so while students are busy during math workshop, I have time to pull them and work on their varying needs.<br /><br />Thanks for stopping by and taking a peek at my next week and a half or so of math workshop as we dig into our subtraction with regrouping review. If today was a sign, I know I am going to have a pretty sizable group needing enrichment during this time--not a bad problem to have, right?<br /><br />Interested in any of the resources mentioned above? Just click the photos above or these images below. Thanks for stopping by!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Addition-and-Subtraction-Grades-2-4-1446312"><img border="0" height="320" src="https://2.bp.blogspot.com/--HkVga-h2qI/WC0PQ9T2qQI/AAAAAAAAYaY/BBcffIZmccsj8Q4TkHbR5EMfWMICct8EwCLcB/s320/Slide1.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Feast-Math-Project-Grades-3-4-1531237"><img border="0" height="320" src="https://4.bp.blogspot.com/-IMcVwrWJQ-Q/WC0NqV9VIbI/AAAAAAAAYZ8/m28StoHTnDo4YJ-Utk_KjdwJP99HD3b9wCLcB/s320/thinker%2Btask%2Bholiday%2Bfeast%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Seasonal-Word-Problem-Collection-Thanksgiving-Grade-3-5-956001"><img border="0" height="320" src="https://1.bp.blogspot.com/-TQnCJpVqTq4/WC0N2BCqFhI/AAAAAAAAYaI/txKmE3-Fjr87MnP8-umn6kFBuJBuPMpqwCLcB/s320/Slide1.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-56XZS0cNWHs/WC0NtcSDpuI/AAAAAAAAYaA/LGbBEIwUrOkDuxFaiLiK6CMaC_VUJbHDQCLcB/s1600/Slide1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://2.bp.blogspot.com/-56XZS0cNWHs/WC0NtcSDpuI/AAAAAAAAYaA/LGbBEIwUrOkDuxFaiLiK6CMaC_VUJbHDQCLcB/s320/Slide1.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Dollar-Deals-Thanksgiving-Multiplication-Challenge-A-Game-to-Build-Fluency-1573584"><img border="0" height="240" src="https://1.bp.blogspot.com/-WFQyz3hTMYY/WC0Nvt1oGnI/AAAAAAAAYaE/QZ8YaK1CUMEUUODY3Ugp0vXlLNoGs5ZYACLcB/s320/Slide1.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Toss-and-Solve-Addition-and-Subtraction-Task-Cards-1113487"><img border="0" height="320" src="https://4.bp.blogspot.com/-nxCuhsK3LsI/WC0N6JjldPI/AAAAAAAAYaM/jTL-DZbIcg4rCB_WWuSw3lJj5VHfUFJRgCLcB/s320/toss%2Band%2Bsolve%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-29516908932953115742016-11-10T19:45:00.001-06:002016-11-10T19:45:50.406-06:00Google Drawing Tools and Scientific Drawings!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Electricity-Unit-and-Interactive-Notebook-Resource-Grades-3-5-1291700"><img alt="Google drawing tools" border="0" height="640" src="https://3.bp.blogspot.com/-2ZES9bDIpXA/WCUhM3zDT2I/AAAAAAAAYXs/4B8x1sHvrt4VR_yGBQBrHZzlws2xzAcQQCLcB/s640/electricity%2Bscientific%2Bdrawing%2Bpost.jpg" title="teaching electricity" width="321" /></a></div>One thing I like to do every year when I study electricity with my class is to take the time to teach them how to use drawing tools on a Google slide. Most have had very limited experience with this--but take to it quickly and use it often throughout the year.<br /><br />As we have worked our way through our lessons on safety, how light bulbs work, conductors and insulators, and different types of circuits, we have been reading books and articles, taking notes in our interactive notebook, building circuits and testing out hypotheses--and I wanted to give them a technology connection to let them show some of what they have learned.<br /><br />We reviewed the different types of circuits--and the point of "scientific drawings"--to convey information graphically with pictures, symbols, and labels. I showed students the following Google tools:<br /><br /><ul><li><b>Drawing shapes, changing color, changing line color and thickness</b></li><li><b>Drawing different types of lines</b></li><li><b>Creating and resizing and moving text boxes</b></li><li><b>Selecting shapes and changing their size and rotating them</b></li></ul><div>For a few students, I showed them about "ordering" their shapes as well--so they could "hide" their wires and so on. I showed them these skills on the projector and then sent them off to get creative! I encouraged them to coach each other and to think of different ways to use the shapes and lines to create a drawing that would clearly show either a series or a parallel circuit--and off they went!</div><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Electricity-Unit-and-Interactive-Notebook-Resource-Grades-3-5-1291700"><img alt="electric circuits" border="0" height="477" src="https://3.bp.blogspot.com/-mErDXruADHo/WCUZm8Z002I/AAAAAAAAYXM/9MuN9qfomBUobvQzcemrqUmrkqfqM71bQCLcB/s640/Photo%2BNov%2B10%252C%2B6%2B21%2B55%2BPM.jpg" title="Google drawing tools" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Electricity-Unit-and-Interactive-Notebook-Resource-Grades-3-5-1291700"><img alt="Google slide lesson" border="0" height="505" src="https://3.bp.blogspot.com/-0fNb3k47H9c/WCUZm_NhQ4I/AAAAAAAAYXI/_JmFJFuRMGQMkzvpWjEJeCSBPUUm_jZKgCLcB/s640/Photo%2BNov%2B10%252C%2B6%2B23%2B46%2BPM.jpg" title="teaching electricity" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">I loved watching the students dig in and help each other! I walked around coaching, asking questions, and trouble shooting but overall I was SO pleased to see how much initiative students took to "try" on their own and to ask desk group neighbors before asking me. Each student found their own way to show their circuits--some very simple, some more complicated--and not all 100% accurate...but they learned a ton, talked about science and technology, and were VERY proud of their work!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Electricity-Unit-and-Interactive-Notebook-Resource-Grades-3-5-1291700"><img alt="scientific drawing" border="0" height="511" src="https://3.bp.blogspot.com/-cHDw9karvaU/WCUZm7bwvfI/AAAAAAAAYXE/QVa4gTHD3EojlR0xofxw4A0ie5wnrRbSQCLcB/s640/Photo%2BNov%2B10%252C%2B6%2B25%2B17%2BPM.jpg" title="teaching electric circuits" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">We think they turned out pretty cool!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Electricity-Unit-and-Interactive-Notebook-Resource-Grades-3-5-1291700"><img alt="electricity project" border="0" height="640" src="https://2.bp.blogspot.com/-Dn5KdkeGGPY/WCUZo6dCdeI/AAAAAAAAYXQ/Q0JaaXiaMS8XXVUP-pX-ODk_v8oeY6BFgCLcB/s640/Photo%2BNov%2B10%252C%2B6%2B21%2B36%2BPM.jpg" title="teaching electricity unit" width="477" /></a></div><div class="separator" style="clear: both; text-align: center;">You could certainly do this lesson with pretty much any science content...drawings of plants...simple machines...the water cycle. Get creative! If you are teaching electricity and want to see more of what I do with my class, just check out my resource that can supplement a textbook or a hands-on kit. See what you think!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Electricity-Unit-and-Interactive-Notebook-Resource-Grades-3-5-1291700"><img border="0" height="400" src="https://1.bp.blogspot.com/-cIe5VDsSeUc/WCUe9ibHOcI/AAAAAAAAYXg/hI8q183pEIwjkuVtS_YckSQF5oIkmZ1PQCLcB/s400/electricity%2Bunit%2Binteractive%2Bnotebook%2Bcover.jpg" width="398" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-85321500840139151902016-11-08T19:56:00.001-06:002016-11-08T19:58:59.175-06:00Getting Students Thinking about Fractions<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="fraction unit" border="0" height="640" src="https://1.bp.blogspot.com/-PABYzf6qvUQ/WCJ9oNXuwII/AAAAAAAAYWg/5PBbSw-fSp0XJVENj0mQzuTB_JfLg5z3QCLcB/s640/deep%2Bfraction%2Bthinking%2Bpost%2BNEW%2Bposts.jpg" title="teaching fractions" width="321" /></a></div><br />Just wanted to share some fraction fun from our first day of fraction review! I like to dig in by really getting students thinking--no fill in the blanks for THIS review! Check out what we did today to kick off our fraction studies.<br /><br />One thing I love to do is to start off lessons with discussions... we start in discussion pairs and then share out key ideas with the entire class. These "Discussion Starters" are simply true statements that might be interpreted in different ways and can get students talking about what they might mean and to think of examples. We practice our math talk too--adding on to what others say, asking or clarification, and so on. We had some GREAT ideas shared!<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="teaching fractions" border="0" height="477" src="https://4.bp.blogspot.com/-eROyskdO0J4/WCJxw09JgpI/AAAAAAAAYWM/ibUb9Y0-IvIP_s4FftLwrMELZNlcdi_kQCLcB/s640/Photo%2BNov%2B08%252C%2B6%2B36%2B05%2BPM.jpg" title="critique reasoning" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">After we got our brains warmed up with key ideas--like that fractions have equal parts, can be shown in different ways (on a number line, with shapes, with collections of objects, etc), I sent my students off with small groups to find different ways to "make" representations of different fractions--halves through eights. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="fourth grade fractions" border="0" height="477" src="https://3.bp.blogspot.com/-ueSdXHRtWuc/WCJxv5kfx7I/AAAAAAAAYWA/gAWTHQwpr9czgyA5khnF7bhqrfHi0ebzwCEw/s640/Photo%2BNov%2B08%252C%2B6%2B35%2B33%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">As students were working, I put out a stack of post it "flags" for students to use to mark contributions they want to talk about...for whatever reason. LOTS of discussions going on at this time! Love it! </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="fraction activities" border="0" height="640" src="https://2.bp.blogspot.com/-uEMaD7uOqR8/WCJxwZnBCKI/AAAAAAAAYWI/BNHM8166HqM6ugiNa4oA7pSfVcWpMrdIACEw/s640/Photo%2BNov%2B08%252C%2B6%2B35%2B16%2BPM.jpg" title="fractional thinking" width="477" /></a></div><div class="separator" style="clear: both; text-align: left;">So...as students marked certain "samples", I picked a few to redraw and share under the projector--and the debates began!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="fraction unit" border="0" height="640" src="https://3.bp.blogspot.com/-rCH4US-MLGY/WCJxxM_oecI/AAAAAAAAYWQ/DzXoCCBGD2MV3qDaPRNHybiw3ErTuc7cwCEw/s640/Photo%2BNov%2B08%252C%2B6%2B36%2B58%2BPM.jpg" title="fraction misconceptions" width="477" /></a></div><div class="separator" style="clear: both; text-align: left;">I just love inviting students to come up and try to use their reasoning and math language to explain their ideas in front of the class...and have their classmates agree, add on, ask for clarity, or respectfully disagree. The fun part? We didn't come to any FINAL conclusions...math class doesn't have to end when the bell rings! Let them think and stew on things overnight. Seriously.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="fraction reasoning and thinking" border="0" height="477" src="https://4.bp.blogspot.com/-aN5iwlZS6cI/WCJxwN34UlI/AAAAAAAAYWE/zEdIbpNAj1sHQDnAOOmFwGL0KoBiGMx_ACEw/s640/Photo%2BNov%2B08%252C%2B6%2B34%2B56%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">If you like this lesson, you might enjoy my fraction unit--16 lessons that promote deep thinking. It includes tons of activities, assessments, discussion topics, and more! Check it out and see what you think--teaching fractions can be fun!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="constructivist fractions" border="0" height="320" src="https://4.bp.blogspot.com/-GXFBCe4ej0E/WCJ-PYLninI/AAAAAAAAYWk/qFNSPmkm3TAfb6Vprd34QcwyTcl__E2KACLcB/s320/fraction%2Bunit%2Bcover.jpg" title="fourth grade fraction unit" width="319" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-92023796514479077832016-10-30T07:00:00.000-05:002016-10-30T07:00:11.964-05:00Interacting Deeply With Texts<div style="text-align: center;">Today is my day to post over at Upper Elementary Snapshots, so I hope you'll click over and read today's post--with THREE ways to interact with texts that you might not have tried!</div><div class="separator" style="clear: both; text-align: center;"><a href="http://www.upperelementarysnapshots.com/2016/10/interacting-with-text-3-ideas-to-help.html"><img alt="close reading strategies" border="0" height="640" src="https://3.bp.blogspot.com/-NOL5WE0W-9M/WBVK_BArBKI/AAAAAAAAYVU/BIq3FqG1v8A39FBvYo6Ctbuvl7GikDTlQCLcB/s640/interacting%2Bwith%2Btexts%2Bmy%2Bblog%2Bteaser%2Bpost%2Bfor%2BUES.jpg" title="teaching reading comprehension" width="321" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;">I hope everyone is doing well...hoping to get a few more blog posts done this week--so much fun going on in our classroom these days! </div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-40562502132350998072016-10-26T20:43:00.000-05:002016-10-26T20:43:45.033-05:00The importance of concrete models: Multiplication Arrays<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Arrays-Factors-and-Prime-Numbers-932226"><img alt="concrete models multiplication" border="0" height="640" src="https://1.bp.blogspot.com/-QnDAzbyUbVs/WBFaE1Lny-I/AAAAAAAAYSI/y_3bZYymZAs4zSVTjBppHdKWOkg1OwsoACLcB/s640/concrete%2Bmodels%2Bmultiplication%2Barrays%2Bpost%2Bpin.png" title="teaching math" width="320" /></a></div>We are moving into our mini-unit on factors, multiples, prime numbers, and factoring--SO much vocabulary and such complicated ideas for students who may or may not be secure with their multiplication facts. To really try to help students "SEE" the concepts, I believe super strongly in using concrete models.<br /><br /><div style="text-align: center;"><b>OK.</b></div><div style="text-align: center;"><b><br /></b></div><div style="text-align: center;"><b>Chocolate models--let's be honest. </b></div><div style="text-align: center;"><br /></div>Seriously though...I really want my students to deeply understand the concept of arrays and how they relate to multiplication, factors, products--and eventually prime and composite numbers.<br /><br />So the other day I asked my students to tell me what they knew about arrays--and they shared out their ideas. They DID have a bit of a hard time using precise mathematical language so I flipped on the projector and document camera, whipped this Dove monster out of my school bag, dramatically wafted the smell toward them, and threw it under the camera asking, "Will THIS help you describe what an array is?" After a few moments of whining about how it wasn't fair that I had one and they didn't, we got to work using clear math language to describe this array. We used the words factor and product and array. We talked about directionality (Is 6 rows of 3 the same as 3 rows of 6? Is 6 bags of 3 apples the same as 6 bags of 3 apples?)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Arrays-Factors-and-Prime-Numbers-932226"><img alt="multiplication arrays" border="0" height="480" src="https://3.bp.blogspot.com/-gB5RCg0mgSM/WA_2bI9vlBI/AAAAAAAAYRE/cRQPZ8TPx0g62BVLHc5ZrOuwYYXdMQiEACLcB/s640/Photo%2BOct%2B25%252C%2B6%2B50%2B18%2BPM.jpg" title="teaching arrays" width="640" /></a></div> I then pulled out a bag of these to a roar of delight from the crowd and asked to practice that mathematical language to describe THIS array. The results were much more clear!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Arrays-Factors-and-Prime-Numbers-932226"><img alt="teaching multiplication" border="0" height="436" src="https://2.bp.blogspot.com/-Q6FDlvEieKo/WBFIuE8qOPI/AAAAAAAAYRo/8W5uiSV8AMYZ_m3wyTBKYJvQuba6_lQ0ACLcB/s640/Photo%2BOct%2B26%252C%2B7%2B07%2B43%2BPM.jpg" title="multiplication arrays" width="640" /></a><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Arrays-Factors-and-Prime-Numbers-932226"><img alt="multiplication" border="0" height="480" src="https://3.bp.blogspot.com/-aZWODxWppB4/WA_2bA2okqI/AAAAAAAAYRA/_FRPHUx3Bj8vgV0zI_bx28bpYDj5YS_7wCLcB/s640/Photo%2BOct%2B25%252C%2B6%2B51%2B02%2BPM.jpg" title="teaching arrays" width="640" /></a></div> After consuming a little "Brain Food", we got to work on one of my favorite hands-on lessons of the year--the Candy Factory! In this project, we arrange candy "tiles" in all the possible arrays trying to look for patterns...we uncover the "double/half" strategy, started to notice some thing about arrays with odd numbers, and more!<br /><br />As students moved forward from making "boxes" of one candy...then two candies...then three, you could feel their confidence growing--and their willingness to model with the tiles diminishing. I continued to encourage them to use them...but some were insistent that they could do it in their head. I was noticing everyone getting the "one by..." arrays (1 x 12... 1 x 13...and so on) but were starting to miss some of the "short, chubby" rectangles. Some students had even made a claim that "All odd products only have 2 factors." Hmmmmmm<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Arrays-Factors-and-Prime-Numbers-932226"><img alt="multiplication arrays" border="0" height="640" src="https://2.bp.blogspot.com/-FYvM-qFixa8/WA_2bnATw4I/AAAAAAAAYRM/WaNxDSv67rMIG9sNEw0VVVmq71G9-N3nACLcB/s640/Photo%2BOct%2B25%252C%2B6%2B51%2B26%2BPM.jpg" title="factors products multiples" width="480" /></a></div> But it was when I came upon this example that I knew we had problems. <br /><br />Big. Problems.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Arrays-Factors-and-Prime-Numbers-932226"><img alt="multiplication arrays" border="0" height="640" src="https://4.bp.blogspot.com/-kyki2GIpRrM/WA_2c5Qpw9I/AAAAAAAAYRc/atV4nWrxcfguLbsBeIEknZLR-9UWR-JJwCEw/s640/Photo%2BOct%2B25%252C%2B6%2B53%2B30%2BPM.jpg" title="math misconceptions" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div> So at this point, I INSISTED that he break out the tiles and SHOW me the array he had drawn. As you can imagine, he wasn't able to do so and a little light bulb went off. I asked him how he thought he COULD arrange the 9 tiles and, after some experimenting, figured out that, in addition to the 1 x 9 array, he could also build a 3 x 3. He could NOT do it in his head...he needed that tangible tool--FOR NOW. I asked him if I could share his story with the class so we could all learn from it and he agreed.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Arrays-Factors-and-Prime-Numbers-932226"><img alt="multiplication arrays" border="0" height="480" src="https://4.bp.blogspot.com/-73ddLSDzvnk/WA_2cjp98yI/AAAAAAAAYRU/MfrF7DIhPOINj9FWWkkmODK-9IpvMS0qACLcB/s640/Photo%2BOct%2B25%252C%2B6%2B52%2B15%2BPM.jpg" title="factors and arrays" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;">All in all, we have been really building some solid conceptual understanding of factors, products, and arrays--and we are ready to dig into the second part of the activity--determining the difference between prime and composite numbers! We are on our way! If you are interested in seeing more, just click the image below to see more about this resource. </div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Double-Scoop-Lesson-Introducing-Arrays-Factors-and-Prime-Numbers-932226"><img alt="teaching factors" border="0" height="320" src="https://4.bp.blogspot.com/-oWqy4wdnsMo/WBFK86fCd6I/AAAAAAAAYR4/eoZqN92nc8s6Vi3N1H2IEqIdhtD7CP6pwCLcB/s320/double%2Bscoop%2Bprime%2Bnumber%2Bcover.jpg" title="prime and composite numbers" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;">Thanks for stopping by!</div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-82728393743928596892016-10-23T20:04:00.000-05:002016-10-23T20:04:31.168-05:00Helping Students "Make Sense" of Problems<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Open-Ended-Math-Challenges-Problem-Solving-BUNDLE-2222043"><img alt="math practice standards" border="0" height="640" src="https://2.bp.blogspot.com/-pryUmMos-RI/WA1dKpCuR7I/AAAAAAAAYQc/7S4nx9GLZAY7ACcZMOrXkWsEAcqKoJxHgCLcB/s640/making%2Bsense%2Bof%2Bproblems%2Bpost.jpg" title="problem solving" width="320" /></a></div>Teaching math is a complicated venture--to say the least. Between figuring out how to meet the needs of all our students, balance a jam-packed curriculum, worry about interventions and enrichment--and then throw in fire drills, strep throat epidemics, students gone on vacations, meetings...it's a wonder we get anything done!<br /><br />The one thing I always use to "center" myself is the Standards for Mathematical Practice--or "Math Behaviors", if you prefer. These "ways of being" in math class are the glue that holds my math class together...whether my students are above or below grade level--and no matter if we are doing addition or fractions or measurement. <br /><br />One of these standards is often called the "perseverance" standard...and people do a GREAT job of teaching students that word and stressing that "I can" spirit in their classrooms. That being said--"perseverance" is only a small part of that standard and we cannot forget the rest. This standard talks about sticking with problems--but perhaps more importantly talks about MAKING SENSE of problems...using a thoughtful, logical, and organize process to dig in to the information presented and to tackle it. It's hard to persevere on a problem until you have "decoded" it!<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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Kid-Friendly-Math-Practice-Standards-Posters-Classic-Black-2004662"><img alt="perseverance" border="0" height="480" src="https://2.bp.blogspot.com/-hq3RqCr68Yc/WA1U3bv6jQI/AAAAAAAAYPs/Go4zSciyGNYOw2a5oe-AND48j2WGgQgIACLcB/s640/Slide4.JPG" title="standards for mathematical practice" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Kid-Friendly-Math-Practice-Standards-Posters-Classic-Black-2004662">This is one of the posters in my "kid friendly" math standards posters resources.</a></td></tr></tbody></table>So the other day I decided to give my students one of my open ended challenges--with NO preliminary work. I didn't read it to them. I didn't give them any hints or talk them through it. I told them--your goal today is to figure out WHAT this problem is asking, think about how to get started, and how you will organize your work. I told them I would read them any word they struggled on (not reading class!) but it would be up to them to try to "decode" the problem. I built up the energy...told them I KNEW they could do it and explained we would start tackling it alone but then would move into partnerships to compare notes and to get started.<br /><br />So off they went! I walked around and circulated...asked a few questions here and there--mostly things like, "What have you figured out so far?" and "Tell me what you notice." to try to get a sense for what they were gleaning from the problem.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Open-Ended-Math-Challenges-Set-1-Problem-Solving-Grades-3-5-467242"><img alt="math challenges" border="0" height="640" src="https://4.bp.blogspot.com/-OSVXmZsxNvQ/WA1Y0pw1LpI/AAAAAAAAYP8/cMA41-v3xq0TPTQmx0ecClS3IEEHMEPQQCLcB/s640/Photo%2BOct%2B23%252C%2B7%2B41%2B13%2BPM.jpg" title="problem solving" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">After five minutes or so, I then partnered students up to compare notes. I started to see some great stuff...highlighters came out. Students were pointing out information and underlining it. I heard things like "OHHHH...now I get it!" and "I totally missed that part!". After a while longer, we came back as a class and talked about our findings--and also talked about the power of partners! It was pretty evident to students that two heads were definitely better than one in this case!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Open-Ended-Math-Challenges-Set-1-Problem-Solving-Grades-3-5-467242"><img alt="math workshop" border="0" height="480" src="https://1.bp.blogspot.com/-QXxz9cVBzIM/WA1Y8mvOQjI/AAAAAAAAYQA/fYnJbVbLnFYJ1IuSX0pZPBdy_CqS9QMtgCLcB/s640/Photo%2BOct%2B23%252C%2B5%2B57%2B41%2BPM.jpg" title="problem solving" width="640" /></a></div>At that point, I put a copy of the problem under the document camera and we shared out our findings. I used highlighters and my pen to showcase what students told me they had found in the problem and what they were noticing about getting it started. After a few more minutes of processing, I was pretty sure that partnerships were ready to go tackle it! They were chomping at the bit to get going, and I am pretty sure that taking the time to process on this problem was just as valuable as actually working the problem itself! I quickly reminded them about working precisely and in an organized fashion (our recent goal) and sent them off on their way.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Open-Ended-Math-Challenges-Set-1-Problem-Solving-Grades-3-5-467242"><img alt="math practices" border="0" height="640" src="https://4.bp.blogspot.com/-NBN_-pM0VKg/WA1BaziT4wI/AAAAAAAAYPY/8NxqsMus3EgP2p_Mn7MJHYKzy1arhguTgCEw/s640/Photo%2BOct%2B23%252C%2B5%2B57%2B22%2BPM.jpg" title="teaching problem solving" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">From beginning to end, my students worked for 45 minutes on this problem this day--and could have done another 15. We finished up the next day and had a ton of fun sharing our different solutions. I love hearing the students' logic about which solution made the most sense for them. I think I have some entrepreneurs in training in my class!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Open-Ended-Math-Challenges-Set-1-Problem-Solving-Grades-3-5-467242"><img alt="math challenges" border="0" height="640" src="https://2.bp.blogspot.com/-js5tml0UTq8/WA1BZpY6b-I/AAAAAAAAYPQ/dauX-gXTwtwHB5l9FuxmfaS6_waCD62EgCEw/s640/Photo%2BOct%2B20%252C%2B9%2B53%2B16%2BAM.jpg" title="math problem solving" width="554" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">So today's food for thought? Think about how much work YOU are doing for your students by helping them get started...and consider how many opportunities you are giving them to try to learn how to make sense of tricky problems on their own. Want to try </div><div class="separator" style="clear: both; text-align: center;">the Marco Problem with YOUR class? It's one of the three challenges in Set 1 of my "Open Ended Challenges" resource.. Click the image below if you want to see more!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Open-Ended-Math-Challenges-Set-1-Problem-Solving-Grades-3-5-467242"><img alt="math word problems" border="0" height="320" src="https://1.bp.blogspot.com/-nu5kzf5L8vQ/WA1bc24rDTI/AAAAAAAAYQM/UahNPsBzkBAigTRXHp7-JhhzPRPS1e2wQCLcB/s320/open%2Bended%2Bchallenges%2Bset%2B1%2Bcover.jpg" title="problem solving" width="320" /></a></div><div style="text-align: center;"> Also available in this bundled set of 9 challenges!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Open-Ended-Math-Challenges-Problem-Solving-BUNDLE-2222043"><img alt="open ended problems" border="0" height="320" src="https://4.bp.blogspot.com/-OTI395pcNiw/WA1bfn_ljfI/AAAAAAAAYQQ/XErZ968MJz8t6gjMxVd5AIeeYZCq_2qlwCLcB/s320/open%2Bended%2Bmath%2Bchallenge%2Bbundle%2Bcover.jpg" title="math problem solving" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Thanks for stopping by!</div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-29393443271686011362016-10-13T19:55:00.000-05:002016-10-13T19:55:06.910-05:00The importance of watching students work...helping with place value misconceptions<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Expanded-and-Standard-Form-Task-Cards-Grades-3-5-2826314"><img alt="expanded and standard form" border="0" height="640" src="https://4.bp.blogspot.com/-iaoxQ1_GT8o/WAAma492f2I/AAAAAAAAYOQ/9mhYOJ9-9V8cEbeBZvA7M1YyqSXC8eC1QCLcB/s640/expanded%2Bform%2Bblog%2Bpost%2Bpin.jpg" title="teaching place value" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>We recently finished our unit on place value and I KNEW that not all students were solid. As I usually do, I continued to give occasional entrance slips to try to keep my finger on the pulse of the class. When I do this, I try to work in time to meet with strugglers--and I try to do it in groups of no more than 3 so I can WATCH them.<br /><br />Here's what I mean...I gave my students an entrance slip on Wednesday as class started. As they turned them in, I did a quick check of them and sorted them into two piles--"no problem" and "better check it out".<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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Place-Value-Grades-3-5-2771134"><img alt="formative assessment" border="0" height="480" src="https://2.bp.blogspot.com/-qCtgtB8A_5s/WAAbaiPn5jI/AAAAAAAAYNY/n_3AMbLQ218fZEW_i7l9G5vLQVPYCJ9QwCLcB/s640/Photo%2BOct%2B13%252C%2B5%2B43%2B05%2BPM.jpg" title="place value assessment" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Place-Value-Grades-3-5-2771134">These assessments are from my "Formative Assessment Toolbox: Place Value Edition" resource. CLICK HERE to see it!</a></td></tr></tbody></table>Looking at student work can tell you certain things...but I firmly believe we need to take things a step further and WATCH students to see HOW they are making their mistakes. For example, I was looking at some addition with regrouping work a student had done--and time after time there was an error in the "regrouping". I could NOT for the life of me figure out what she was doing so I called her over and asked her to do a problem. Within ten seconds I figured it out--she was starting on the left and regrouping to the right--showing a HUGE misunderstanding. Turns out she had been pretty solid with partial sums (which can be done left to right or right to left) and was overgeneralizing that algorithm. Without sitting right next to her and watching, I wouldn't have figured it out and I wouldn't have known to pull out the base ten blocks and model with her.<br /><br />The same was true with a few of my kiddos who were making some mistakes with expanded and standard form. I need to sit right with them and watch them work--and ask their thinking. <br />I worked with a few students at a time with my expanded form task cards (actually, to make it more fun, I put the cards in piles and the students took turns picking cards--it's AMAZING how something as simple as letting students flip a card can keep them more engaged!)--and I watched them work on their white boards, asked them questions, and asked them to explain their thinking.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Expanded-and-Standard-Form-Task-Cards-Grades-3-5-2826314"><img alt="place value" border="0" height="480" src="https://4.bp.blogspot.com/-2y-xPVusPAo/WAAdUE1o8_I/AAAAAAAAYNk/caHHwgo3SaEbXbBBnFm8D3QfCVw7ymLVACLcB/s640/Photo%2BOct%2B10%252C%2B7%2B01%2B03%2BPM.jpg" title="task cards" width="640" /></a></div>As I was reassured that misconceptions were being fixed, I would send students away and fill their spot with new ones. Other students were busy working on their math workshop options and I had a glorious 40 minutes to work up close and personal with these students. The light bulbs kept going off-and I know the WATCHING was a huge part of it...putting myself in their shoes and trying to be a scientist figuring out where their thinking was going wrong. It is SO validating for a child to hear, "I can TOTALLY see what you did it that way! Let me show you something..." instead of only seeing problems marked wrong or sitting back in a large group discussion feeling confused and lost.<br /><br />Watching students can help you see exactly what misconceptions students have--and for these place value concepts, several things come to the forefront and need coaching:<br /><br /><ul><li>A lack of understanding of our base 10 system (especially once students get past 1,000 numbers get much harder to visualize)</li><li>A misunderstanding of "0" and how having "no" thousands gets represented</li><li>An inability to understand the organization of our number system...that we need three "places" before a comma, then three more and a comma, and so on--and that each of those "groups" or "periods" has a name and follows the pattern of one, ten, hundred.</li><li>The inability to recognize expanded form terms out of order (they might write 50 + 3 + 600 as 536)</li><li>Difficulties reading and writing big numbers and "hearing" the parts. For example, if I say "four hundred thirty-two thousand", students should hear that "432" and know it will come in front of the thousand comma. If I say, "four hundred thirty-two thousand, seven", they should know that they need to write a 0 in the hundreds and tens spots because there are no hundreds or tens. Asking students to read and write big numbers is a great way to check for understanding.</li></ul><div>So much of this is tricky whole class--you can present information this way, but when you see how many different ways place value understanding can break down, it becomes more and more clear how our interventions need to be much more personalized.</div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Expanded-and-Standard-Form-Task-Cards-Grades-3-5-2826314"><img alt="standard form expanded form" border="0" height="480" src="https://1.bp.blogspot.com/-4B5MpnKiWrA/WAAeGRnsFBI/AAAAAAAAYNo/ORmuU_oujkodHDRBafB8lMRu6znH3sJHgCLcB/s640/Photo%2BOct%2B10%252C%2B7%2B01%2B49%2BPM.jpg" title="math intervention" width="640" /></a></div>An added bonus of working next to small groups is the ability to "coach" them through some partner work. After solving a card, I would ask students to compare work and try to reconcile any differences. Learning how to check over their work, look for errors, and explain thinking is such a key part of the standards for mathematical practice. As they got better at catching each other's errors, my role became much more of an observer than a teacher--and the power got turned over to them. Hearing things like, "Wait--you wrote 50,000 but that 5 is in the one thousands place" or "Remember that if there aren't any tens you need to write a 0." is enough to make THIS math teacher melt. Seriously.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Expanded-and-Standard-Form-Task-Cards-Grades-3-5-2826314"><img alt="teaching place value and expanded form" border="0" height="480" src="https://4.bp.blogspot.com/-QBc2ELKzKMk/WAAffTCnREI/AAAAAAAAYN0/jhRCQmoNObA5zxJaTObJdiuHoB5m0yDGgCLcB/s640/Photo%2BOct%2B10%252C%2B7%2B01%2B25%2BPM.jpg" title="math misconceptions" width="640" /></a></div>Interested in checking out the task cards I used with my groups? Just check them out below! There are 36 cards with three different types of questions. Each one has a "bonus" question too--so I used them with my entire class and then pulled my intervention kiddos and used them again. See what you think!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Expanded-and-Standard-Form-Task-Cards-Grades-3-5-2826314"><img alt="expanded standard form task cards" border="0" height="320" src="https://1.bp.blogspot.com/-pEeKm5I8C4I/WAApucfFx8I/AAAAAAAAYOc/dYTG0iNMT4Y-YbOVsu176v7v14Uu82VyQCLcB/s320/expanded%2Bform%2Btask%2Bcard%2Bcover.jpg" title="place value task cards" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">I have a ton of place value activities in my store so check them out if you are looking for games, lessons, and more. Just type "place value" into the search bar of <a href="https://www.teacherspayteachers.com/Store/The-Teacher-Studio">my store</a>!</div><div style="text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0