tag:blogger.com,1999:blog-47683051909119484982017-10-06T09:13:14.834-07:00The Mindful MathematicianLeandra Clevelandhttps://plus.google.com/101305531040870966092noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-4768305190911948498.post-28819620846402294742015-02-15T19:26:00.001-08:002015-02-19T10:56:16.138-08:00I must ask... Why must you tell?Approximately 2 times a week we have visitors in my 3rd grade classroom. Other teachers come in to watch us do math and after my lesson with 3rd graders, I have the privilege to debrief with my colleagues and share some thoughts about what I'm learning from my 3rd graders. This year has been an amazing journey, and I have learned so much from both my students and my peer observers. <br /><br />Last week, during one of these debriefing sessions, a teacher asked me this string of questions (I'm paraphrasing), "You don't really teach much do you? I mean they teach each other, right? You just guide their discussion by asking questions, right?"<br /><br />Exactly! You got it. That's exactly what happens in my classroom. The students teach. I facilitate. There has not been a single day of direct instruction for my third graders all year long. By direct instruction I mean I have not stood up in front of the classroom and said here is a problem, and here is how you solve it. Nor have I said, we're going to learn about this concept today, here is what it means and this how you do it. (Well there was that one day, when I accidentally modeled, read about it in my post "<a href="http://themindfulmathematician.blogspot.com/2014/08/to-model-or-not-to-model-that-is.html" target="_blank">To model or not to model. That is the question.</a>")<br /><br />Yet my students are learning. On a daily basis. They learn from each other. I pose a problem, or a task, they share their thinking and I ask them questions to refine their thinking. We discuss and argue and discuss until we come to a consensus. I ask questions like:<br /><br />How is your way different from hers?<br />Can you explain to the class what you meant by that?<br />Will you tell us what he helped you understand?<br />Can you repeat what she said?<br />Do you have something you would like to add?<br />Did you use a similar or different strategy?<br />Who can help us understand his thinking?<br />What do you think she meant when she said that?<br />Can you tell your shoulder partner which strategies convince you?<br />Has anyone's thinking changed?<br />Do you agree or disagree and why?<br />Why does that make sense?<br />Would you like to revise your thinking?<br />How can we help this mathematician be more precise?<br />What questions do you have for him?<br /><br />With so much of the focus on my students and their thinking, it could be easy to assume that the discussions in my classroom are random and unpredictable. That's not true though, because I do more than just ask questions. I also listen. I listen with a purpose. Whatever task or problem I posed was posed with certain learning goal in mind and as I listen to my students discuss the task I listen for connections to be made. I listen for key ideas and orient my students toward them. I am the guide that helps the discussion reach its final destination. <br /><br />If you're thinking you don't have time for discussions like this every day, then I have a challenge for you. Just try one. Try one day where you don't tell your students anything. Do nothing but ask questions. Just let go and let them. I think you'll be amazed. <br /><br />If you need some motivation to keep you going during this challenge, just listen to my new favorite song before you get started...<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img border="0" src="http://3.bp.blogspot.com/-BwB_EsqGQEw/VOFhEn0KXrI/AAAAAAAAAPI/NmrIOhU0-nM/s1600/Let%2Bit%2BGo.JPG" height="197" style="margin-left: auto; margin-right: auto;" width="400" /></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.youtube.com/watch?v=moSFlvxnbgk" target="_blank"><span style="font-size: large;">Let it go...</span></a></td></tr></tbody></table><br />Leandra Clevelandhttps://plus.google.com/101305531040870966092noreply@blogger.com2tag:blogger.com,1999:blog-4768305190911948498.post-41520955857913913292015-01-05T22:08:00.000-08:002015-01-06T10:04:46.669-08:00Oh, it's a number line!<i>I have a confession. This post has been written and unwritten and rewritten many times. It is the reason I have not written a blog post for an entire quarter. This project was adapted from a combination of ideas from training sessions, math coaches and friends input. It was fabulous, but nothing I have written about it has turned out to be as fabulous as it actually was when I did it in class. I'm sharing anyway. Hopefully, someone will glean something from it. Here goes...</i><br /><br />In my classroom I have a number line. It's not any old number line. It's different. The first day my students saw my number line it looked like this:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-wMa-jqQFR3M/VKtRwBOY-iI/AAAAAAAAANw/ncpqByIiJuA/s1600/image1.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-wMa-jqQFR3M/VKtRwBOY-iI/AAAAAAAAANw/ncpqByIiJuA/s1600/image1.jpeg" height="176" width="640" /></a></div><br />On this day our number talk went something like this:<br /><br /><b>Do you notice anything new in our classroom? What do you notice about it?</b><br /><br /><i>There is a whiteboard, there is purple duct tape, there are three strings, there is an orange piece of paper, there are many rectangles. </i><br /><i><br /></i><b>Tell me more about the string and the piece of orange paper.</b><br /><b><br /></b><i>The string is long, the paper is short, there is only one paper, there are three strings, the paper is folded over the string, </i><i>the string is longer.</i><br /><i><br /></i><b>What do you mean the string is longer? How do you know?</b><br /><b><br /></b><i>Because there is only one piece of paper, but there could be more. More papers could fit on the string so that makes the string longer than the paper.</i><br /><i><br /></i><b>How many papers could fit on the string?</b><br /><b><br /></b>End day one. Day 2 picked up with that very question, "How many orange papers of the same size could fit on one of the strings? First I took guesses from the students, there was a wide range, then I allowed them time to try different measurement techniques. Some students tried finding other objects that were the same size to lay across the floor, some tried what I like to call "air measuring" with their fingers and their eyes (that was fun because we got all sorts of different "reasonable" answers), some tried moving the paper and marking the white board. After a discussion about what technique seemed to be the most accurate and precise, I "accidentally" dropped my folder which contained many more orange papers. One of my students immediately had the idea that we could just place more orange papers on the string to find out how many would fit. So we did. It looked like this:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-DmG6zMXAaM4/VKtRweALCnI/AAAAAAAAAN0/HQDoyRVVu94/s1600/image2.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-DmG6zMXAaM4/VKtRweALCnI/AAAAAAAAAN0/HQDoyRVVu94/s1600/image2.jpeg" height="185" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Ten orange papers could fit. I asked the students,</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>How many units wide do you think one of the orange papers is?</b> </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">They looked confused. <i>5? Maybe 10? Could be 1,000,000!</i></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>Oh wait, I forgot something:</b></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-_ib0Is2mUmI/VKtRwZLoeEI/AAAAAAAAAN4/dT7DblpwMbk/s1600/image3.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-_ib0Is2mUmI/VKtRwZLoeEI/AAAAAAAAAN4/dT7DblpwMbk/s1600/image3.jpeg" height="180" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><i>Oh, it's a number line! </i> </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">After some guesses, and some skip counting and some discussion, we finally figured out that each piece of paper must be 100 units. So we labeled them and it looked like this:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-wZvN6ZP12Jc/VKtRx7s15PI/AAAAAAAAAOQ/tXPUc8ciMa0/s1600/image5.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-wZvN6ZP12Jc/VKtRx7s15PI/AAAAAAAAAOQ/tXPUc8ciMa0/s1600/image5.jpeg" height="184" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div>The next day our discussion started with this question:<br /><br /><b>If there are 10 hundreds in 1,000, then how many tens are in 1,000?</b><br /><br />Our discussion ended with this:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-Y7gHWqaanqk/VKtRyjLAO0I/AAAAAAAAAOU/D2E1lSBYtJw/s1600/image7.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-Y7gHWqaanqk/VKtRyjLAO0I/AAAAAAAAAOU/D2E1lSBYtJw/s1600/image7.jpeg" height="172" width="640" /></a></div><br />On day four I asked the students if they could write a number sentence to represent the orange pieces of paper. We had a fabulous number talk revolving around equivalent number sentences and equality. Ultimately, one of my students very excitedly suggested 10 x 10 x 10 and we modified our number line to look like this:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-DCWXvraJIVA/VKtRz6jPgPI/AAAAAAAAAOk/97-n7hA_uhc/s1600/image8.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-DCWXvraJIVA/VKtRz6jPgPI/AAAAAAAAAOk/97-n7hA_uhc/s1600/image8.jpeg" height="180" width="640" /></a></div><br />The number line still lives in my classroom and we have referenced it several times. We've used it for rounding, grouping, division and much more. Soon I will remove the original papers and the number line will be used for fractions. I can't wait!<br /><br /><i>One more confession: It took me three tries to build a number line that could survive in a classroom of 3rd graders. On my first attempt I used string. It sagged the top row of papers overlapped the middle row. It was ugly, I took it down and tried again. My second attempt was using 20 gauge wire. Extremely pliable. It also sagged, and broke easily. The kids bumped it with their knees and the wire fell many times. This third attempt was built with 16 gauge wire. Not as easy to work with but much sturdier. I also used flat head nails hammered into the shelving unit through the shower board to hold the wire in place. I think this number line will last through the remainder of the school year. </i>Leandra Clevelandhttps://plus.google.com/101305531040870966092noreply@blogger.com4tag:blogger.com,1999:blog-4768305190911948498.post-70151173996134669652014-11-08T22:41:00.001-08:002014-11-08T22:45:06.692-08:00Everything is Awesome Arithmetic ActivitiesFor the last several weeks I have wrestled with putting in place a system that will allow me to pull small groups in my classroom. I have a need for pulling small groups because I have a few students who just need some up close and personal time on a few skills. They're typically engaged in classroom discussions, but that time with them just isn't moving them forward like I need it to. I feel like this is because my discussions move past their level of thinking way too fast and they're getting left behind. So if I could just have some intense purposeful questioning sessions with these kiddos, on their level, I think I could move them in leaps and bounds. Maybe.<br /><br />Here's what's holding me back. I'm addicted to watching my students work. No matter what I come up with for independent work time, I can't keep myself from stopping to watch them work. Therefore, I can never get to my table to call a small group over to work with me. Nevertheless, I decided to give it a go. <br /><br /><br /><a href="http://1.bp.blogspot.com/-F6P_KLk4m0w/VF787YM9eEI/AAAAAAAAAKE/kNMdj76BA1U/s1600/Student%2BGroups.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-F6P_KLk4m0w/VF787YM9eEI/AAAAAAAAAKE/kNMdj76BA1U/s1600/Student%2BGroups.jpg" height="320" width="216" /></a>I put together eight "Awesome Arithmetic Activities" that my students can work on independently. <br /><br />1.) Math Boggle (3-digit addition practice)<br />2.) Fact Practice (multiplication)<br />3.) <a href="http://gregtangmath.com/materials" target="_blank">Kakooma</a><br />4.) Close to Zero (3-digit subtraction practice)<br />5.) Problem solving<br />6.) Technology (I have four iPads)<br />7.) <a href="http://www.teacherspayteachers.com/Store/Mr-Peterson" target="_blank">Math Mystery</a><br />8.) <a href="http://www.amazon.com/Number-Sense-Routines-Building-Numerical/dp/1571107908" target="_blank">Ways to make a number</a> (Number composition)<br /><br /><a href="http://3.bp.blogspot.com/-60hIPptDDBc/VF784rjIUII/AAAAAAAAAJ8/TiHlA58QQbA/s1600/Rotation%2BWheel.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-60hIPptDDBc/VF784rjIUII/AAAAAAAAAJ8/TiHlA58QQbA/s1600/Rotation%2BWheel.png" height="296" width="320" /></a><br /><br /><br /><br /><br /><br />I created a wheel, and each day they rotate to a new activity. They work for 15 to 20 minutes on these activities four times a week. We've been doing this for four weeks now. I've pulled a small group every day and my students have shown great gains! Oh wait... that was a dream I was sharing there for a second. We have been rotating through these stations for 4 weeks now. But I have only pulled one small group. That's right. ONE.<br /><br />I just can't do it. Each day, I play the song "Everything is Awesome" and my students rush off to get their activity sheets and materials and I... follow them. Stopping by one student at a time, I often have a chance to visit 2 to 3 students during rotation time. That's a small group right? It seems to be working. Or at least helping. I am seeing growth one student at a time. Which brings me to my next challenge. Keeping track. <br /><br />After four weeks and several one on one (sometimes one on two) conversations, I am feeling a bit disorganized. I know I've seen some aha's but I've also worked with some students who still aren't getting it. Somehow I need to keep track of progress and number of visits (for RTI purposes if nothing else.) Also, it would be helpful for me to make sure I'm visiting with all students that need my extra support. Perhaps some sort of organizational tool would help me be more efficient in who I'm visiting with and encourage me to pull small groups with similar needs. So, after a "brief" discussion with a good friend of mine, I decided to utilize Google Drive and created a spreadsheet. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-Geyp5fKhybg/VF8Hi8xuGAI/AAAAAAAAAKU/wdzF3R_HmN0/s1600/photo.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-Geyp5fKhybg/VF8Hi8xuGAI/AAAAAAAAAKU/wdzF3R_HmN0/s1600/photo.PNG" height="480" width="640" /></a></div><br />I love Google Drive because it's free and I can access it on my computer, my iPad, and my iPhone, and did I mention it's free? The colors I chose are in the same order as the behavior clip chart in my classroom. Kiddos will start on green when I notice they need me to work with them on a specific skill and then based on whether or not they seem to make progress they would go to either yellow or blue. Black means they've got it and don't need me anymore and red means I've attempted to help them three times and they're still not getting it. I need to refer those kiddos on to my PLC to see what they recommend. <br /><br />I cannot wait to give it a go this week. I've already filled in some colors based on evidence I've previously collected and I can already tell that it will help me organize groups of students with similar needs. This idea is still in its beginning stages. I would love your input! What do you do?Leandra Clevelandhttps://plus.google.com/101305531040870966092noreply@blogger.com0tag:blogger.com,1999:blog-4768305190911948498.post-70758580120019274452014-10-02T22:02:00.000-07:002015-01-06T10:15:18.973-08:00Lights Camera Action: 3-Act Tasks<blockquote class="tr_bq">"Ask yourself, what problem have you solved ever, that was worth solving, where you knew all of the needed information in advance? Where you didn't have a surplus of information and you had to filter it out, or you didn't have insufficient information and you had to go find some." ~<a href="http://blog.mrmeyer.com/2011/the-three-acts-of-a-mathematical-story/" target="_blank">Dan Meyer</a></blockquote><br />This week, in my classroom, I implemented some training I recently received on an idea known as 3-Act Tasks. I was extremely excited about this idea when I first heard it last April, and even more excited when I recently discovered that <a href="https://www.georgiastandards.org/common-core/pages/math-k-5.aspx" target="_blank">Georgia's Department of Education</a> has updated their curriculum to include many 3-Act Tasks throughout their units in every grade level K-5. Thank you Georgia, I'll be borrowing your tasks this year!<br /><br />What is a 3-Act Task you ask?<br /><blockquote class="tr_bq"><em>A Three-Act Task is a whole-group mathematics task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.</em> </blockquote>Got it? Clear as mud? Maybe I can help. I'll take you through the one I did this week in my class. <em>(Keep in mind, this is not the only thing I did in my class this week. I spent about 20-30 minutes a day on it. I still had number talks, fluency practice, and fact strategy reinforcement activities taking place each day as well.)</em><em></em><br /><strong>Day 1 Act 1:</strong><br /><br />It all began with this 30-second video of someone dumping coins out of a very full piggy bank.<br /><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowFullScreen='true' webkitallowfullscreen='true' mozallowfullscreen='true' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dw7YQ9PQsZiiszgdi-0wLhqDySL5gmMfx-l7bgFLXuLhNS_hZ7PkeS20bI_QctLZbcGNm-5Y16P_vyilvbb2w' class='b-hbp-video b-uploaded' FRAMEBORDER='0' /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://vimeo.com/91754671">http://vimeo.com/91754671</a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">After showing this video, my script went something like this, "What are you thinking? What questions do you have? Write the first question you think of in your journal. Meet with your partner and share your question. Did you have the same question as your partner? Let's share some of your questions."</div><div class="separator" style="clear: both; text-align: left;"> </div><div class="separator" style="clear: both; text-align: left;">This is what they came up with...</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-COa3bWjSLcE/VC4Zu2ln80I/AAAAAAAAAIQ/XSspmFGzCBo/s1600/Questions.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-COa3bWjSLcE/VC4Zu2ln80I/AAAAAAAAAIQ/XSspmFGzCBo/s1600/Questions.png" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">After a quick discussion about the answers to their questions (which included much inferring I might add) we landed on the idea that the mystery person probably didn't have that many coins to start with. Instead, my students decided that they must have saved and saved and saved until the piggy bank was crammed full. At that point I asked the question, "I wonder how many coins it took to fill the piggy bank like that?" This of course was the "main" question. The one that I wanted them to answer all along. One of my students offered a guess, and I asked all of them to pull out their journals again and record their own personal guess in their journal. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><strong>Day 2 Act 2:</strong></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">To re-engage my students in the task on day 2, I had them get out their journals, watch the video again, and update their guess for how many coins there were if they needed to. Then we shared out their estimates and wondered who's was the closest to the actual number of coins. Then I said, "Well how many is it?" A few tried to share their guesses again. I said, "No, I want to know exactly, how many is it?" Protests. We don't know. We can't figure that out! "You can't?" I asked. "Well, we could count," one student offered. So we tried. Unsuccessful. Too many hidden coins in that pile. After about five minutes of conversation we weren't getting anywhere, so I let them in on a little secret. "I know more about this video than you do. I'd be happy to share my information with you, as soon as you figure out what you need to know and ask me for it." I sent them off to work with their partners and come up with a question for me that they thought would help them solve our problem. Once again, here's what they came up with...</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-KLJzVEfJIeY/VC4iHIyfjRI/AAAAAAAAAIg/Xh_qiq6cvQs/s1600/Questions2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-KLJzVEfJIeY/VC4iHIyfjRI/AAAAAAAAAIg/Xh_qiq6cvQs/s1600/Questions2.png" height="236" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">You can see that these questions are marked through with a red highlighter. This is because as we discussed each question, and I answered them, we determined that none of these questions would actually help them solve the "main" question. We ended day two with them completely frustrated and dying for me to tell them something. Anything. It was awesome!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><strong>Day 3 Act 2 Continued:</strong></div><div class="separator" style="clear: both; text-align: left;"></div><div class="separator" style="clear: both; text-align: left;">Today was day 3. I started this part of my lesson by having them get out their journals once again. I told them I wanted them to watch the video again. This time, I had them write in their journals a list of details. Specific things that they noticed about the video. A few of their details included: </div><ul><li><div class="separator" style="clear: both; text-align: left;">There are pennies, nickels, dimes and quarters</div></li><li><div class="separator" style="clear: both; text-align: left;">There are more pennies than quarters and dimes</div></li><li><div class="separator" style="clear: both; text-align: left;">It was daylight when this video was recorded (yes I entertained even the random details)</div></li></ul><div class="separator" style="clear: both; text-align: left;">Next I asked them to join their partners and think of a detailed question that would help them solve the problem. Finally, the questions I had been waiting for... </div><div class="separator" style="clear: both; text-align: left;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-W07_eS47ew8/VC4n4Oz6IpI/AAAAAAAAAI4/VdLEjg3tzBw/s1600/Questions3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-W07_eS47ew8/VC4n4Oz6IpI/AAAAAAAAAI4/VdLEjg3tzBw/s1600/Questions3.png" height="251" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">As I began to answer these questions I noticed two things. </div><ol><li><div class="separator" style="clear: both; text-align: left;">Light bulbs were going off. Students were realizing what information they needed to solve the problem.</div></li><li><div class="separator" style="clear: both; text-align: left;">Every single one of my students was engaged. 100% engaged. </div></li></ol><div class="separator" style="clear: both; text-align: left;">They were so upset that time was up and they didn't have time to take their new found information and apply it to the problem. I had to force them to put pencils down and put journals away. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><strong>Day 4 Act 3:</strong></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Tomorrow will be Act 3. I cannot wait. They cannot wait. They will solve the problem using whatever strategy they see fit, and we will discuss their strategies, as well as their estimates. Who got the closest? I cannot wait to find out. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">For more information on 3-Act Tasks, visit <a href="http://blog.mrmeyer.com/2013/teaching-with-three-act-tasks-act-one/" target="_blank">the blog of Dan Meyer</a>, the creator of 3-Act Math. Also, you can find a library of these tasks <a href="http://gfletchy.com/3-act-lessons/" target="_blank">here at gfletchy's blog</a>. Last but not least, as I mentioned before, Georgia has these tasks scattered through their <a href="https://www.georgiastandards.org/common-core/pages/math-k-5.aspx" target="_blank">Common Core Math Units</a>. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Happy acting!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div>Leandra Clevelandhttps://plus.google.com/101305531040870966092noreply@blogger.com4tag:blogger.com,1999:blog-4768305190911948498.post-47601234813886902402014-09-14T19:43:00.000-07:002014-09-14T19:48:47.830-07:00Rounding in a Round About WayHave you ever seen an assessment item like this one?<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-3Ca2osde7R0/VBZRc8EaEPI/AAAAAAAAAIA/xmQzS2oyGDg/s1600/Rounding.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-3Ca2osde7R0/VBZRc8EaEPI/AAAAAAAAAIA/xmQzS2oyGDg/s1600/Rounding.png" height="82" width="400" /></a></div><br />I have. As a matter of fact there is a similar question on my district's third grade unit 1 assessment. The expectation is that the student's would read the word "about" (which has been bolded, italicized, and underlined for emphasis) and they would then know that they should not perform exact arithmetic on this problem, but instead round first, then add. Why?! Because it's easier? I think not. Not to mention the conundrum of the teacher who gets two answers to this problem: $70 if they rounded before adding, and $60 if they rounded after adding. Which is correct? Who cares? I have been fighting this battle in my head throughout the last week as I attempt to get my third graders to see a purpose for rounding. <br /><br />They don't, by the way. See the purpose I mean. The majority of my students came to me fluently adding 2-digit numbers (as the Common Core Standards say they should have). Most of them can look at those two numbers and add them in their head using mental math. Most of them do just that when presented with a problem such as this. So the question remains, how do I get them to solve this type of a problem correctly? I don't. Hear me out...<br /><br />I spent some time this weekend searching for a purpose that my students could connect with. In the process I read my standards again, and I happened to notice some key words that flipped the switch in my head. So here we have it... 3.NBT.1 says students should be able to "Use place value understanding to round to the nearest 10 or 100." and 3.OA.8 says "Assess the reasonableness of answers using mental computation and estimation strategies including rounding." There's the purpose statement. At this level, students should be using rounding as an approximation strategy, after they've solved the problem, to make sure their answer makes sense. <br /><br />I'm not saying it's never appropriate to round before you add. I'm just saying, with the size of numbers that we're working with right now, why would you. So from now on, in my classroom, we'll be focusing on Standard for Mathematical Practice 1, which says (among other things), "Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, 'Does this make sense?' " Rounding will be one of our strategies for making sure our answers make sense. <br /><br />I feel good about this decision. I feel like this approach really matches with the intent of the standards. Just to make sure, though, I looked up the topic of rounding in the <a href="http://ime.math.arizona.edu/progressions/" target="_blank">Progressions for the Common Core State Standards in Mathematics</a> (written by the Common Core Standards Writing Team). After some explanation about how rounding to the nearest 10 in a three digit number can be more difficult for students, they ended their section on rounding with this statement, "Rounding two numbers before computing can take as long as just computing their sum or difference." No wonder my students couldn't see the purpose. Leandra Clevelandhttps://plus.google.com/101305531040870966092noreply@blogger.com2tag:blogger.com,1999:blog-4768305190911948498.post-24229061684522678552014-08-31T13:36:00.001-07:002014-08-31T13:36:12.318-07:00To model or not to model. That is the question.<span style="font-family: Verdana, sans-serif;"><span style="color: black;"></span>This is the problem I started with on the second Monday of 3rd grade:</span><br /><blockquote class="tr_bq"><span style="font-family: Verdana, sans-serif;">Mrs. Cleveland found a bunch of pencils in her garage. She organized them into bags and boxes. Each bag could hold 10 pencils and each box could hold 10 bags. If she had 3 full boxes and 7 full bags how many pencils did she have? </span></blockquote><br /><a href="http://4.bp.blogspot.com/-vDgIC_MssKI/VAK8RjQPmII/AAAAAAAAAGc/X8lWqOP9-Uw/s1600/photo%2B4.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://4.bp.blogspot.com/-vDgIC_MssKI/VAK8RjQPmII/AAAAAAAAAGc/X8lWqOP9-Uw/s1600/photo%2B4.JPG" height="184" width="320" /></a><br /><a href="http://3.bp.blogspot.com/-55sLV_CQLN8/VAK8X0yaUBI/AAAAAAAAAGk/KIZbaq4Djb8/s1600/photo%2B5.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://3.bp.blogspot.com/-55sLV_CQLN8/VAK8X0yaUBI/AAAAAAAAAGk/KIZbaq4Djb8/s1600/photo%2B5.JPG" height="153" width="320" /></a><span style="color: black; font-family: Verdana, sans-serif;">Multiplication you say? Place value I say. I needed to assess their place value knowledge. What did I find? Nearly half my students showed evidence that they knew 10 tens is 100. Many of the other students had good counting strategies to figure it out. I did have a few students who were unsuccessful but only three who didn't have a place to start. I counted it as a success. The next day's discussion revealed that even some of the students who didn't show evidence of place value understanding when solving the problem actually did have some understanding, they just got lost in the steps of solving this particular problem. </span><br /><br /><span style="color: black; font-family: Verdana, sans-serif;"><br /></span><span style="color: black; font-family: Verdana, sans-serif;"><br /></span><span style="color: black; font-family: Verdana, sans-serif;">The next problem I posed was a measurement division problem using groups of ten. There were 270 pieces of candy being put into goodie bags. Each bag was to hold 10 pieces of candy. The students were asked to find out how many goodie bags could be made. With this problem, the same group of kids that were unsuccessful the day before were unsuccessful again plus a few. The difference was that this time, most of them didn't even have a valid strategy. Perhaps they weren't ready for this type of problem, or perhaps I didn't support them enough in making sense of the problem. The day before we had done a little skit and acted out putting pencils in bags and bags in boxes (though we didn't do any solving together.) On the other end of the spectrum I had 6 students who wrote some sort of multiplication number sentence such as 27 x 10 = 270 or a string of multiplication sentences to arrive at the total. </span><br /><span style="color: black; font-family: AGaramondPro-Regular;"></span><br /><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="https://lh6.googleusercontent.com/-Gio4ucnl3BM/VANW4IoGEoI/AAAAAAAAAHw/bbtiPNmwVFQ/s640/blogger-image--2134125544.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="232" src="https://lh6.googleusercontent.com/-Gio4ucnl3BM/VANW4IoGEoI/AAAAAAAAAHw/bbtiPNmwVFQ/s320/blogger-image--2134125544.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">After Classroom Discussion</td></tr></tbody></table><span style="color: black; font-family: Verdana, sans-serif;">With the variety of strategies my students used, I felt like I had the perfect papers to introduce multiplication in our next discussion, but I didn't. Mostly because I was worried about those students who weren't making sense of groups yet and weren't using grouping strategies on these problems. Instead I shared a valid strategy and represented all 27 bags but displayed an answer of 26 bags. We focused on the standard for mathematical practice 6: attend to precision as well as grouping. We circled groups within the strategy to double check the answer and realized it was written incorrectly. </span><br /><span style="font-family: Verdana, sans-serif;">As a side note, I was careful not to have the students go back and count one by one to check the work, because that encourages the most inefficient strategy... counting by ones.</span><br /><div class="separator" style="clear: both; text-align: center;"></div><span style="color: black; font-family: Verdana, sans-serif;"><br /></span><span style="color: black; font-family: Verdana, sans-serif;"><br /></span><span style="color: black; font-family: Verdana, sans-serif;">After our discussion about grouping, I decided to return to a multiplication problem but this time with predetermined groups of 100. I was hoping the students wouldn't get caught up on the multiple steps aspect of the problem solving. The problem I posed was this:</span><br /><span style="color: black; font-family: Verdana, sans-serif;"><br /></span><div><blockquote class="tr_bq"><span style="font-family: Verdana, sans-serif;">All of MMJ students are going on a field trip to the Zoo. The buses will hold 100 students and the vans will hold 10 students. If there are 6 full buses and 4 full vans then how many students will go on the field trip?</span></blockquote><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="https://lh4.googleusercontent.com/-_m9Kh46g5wY/VANSNIfoPsI/AAAAAAAAAHU/UAyZJBO4fvs/s640/blogger-image--1693954494.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="208" src="https://lh4.googleusercontent.com/-_m9Kh46g5wY/VANSNIfoPsI/AAAAAAAAAHU/UAyZJBO4fvs/s320/blogger-image--1693954494.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Direct Place Value</td></tr></tbody></table><span style="font-family: Verdana, sans-serif;">Success! 19 of my 23 students were completely successful. Many of the kids were still using a counting strategy, but most of them were writing repeated addition sentences. Almost all of the students grouped their hundreds together and then the tens when writing these sentences. This is likely due to the structure of the problem, but it gave me a great platform to introduce the multiplication symbol. Again I had several students who relied on direct place value understanding to solve the problem. I even had 3 students who had not yet used place value understanding move to using place value strategies in this problem. I was excited about the progress. </span></div><div><span style="font-family: Verdana, sans-serif;"><br /></span></div><div><span style="font-family: Verdana, sans-serif;"><br /></span><span style="font-family: Verdana, sans-serif;">On Thursday, I decided that I would pose one more problem before jumping into introducing the multiplication symbol. Because of the success on the most recent problem, I decided to take problem solving one step further and introduce multiple number sets. This, I feel, is essential to differentiation. I have a rather large group of students who have direct place value understanding and I needed to push their thinking. So I chose to make my third number set 18 groups of 5 and wondered if any of them would make the connection back to the groups of 10 that we had been working with. </span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><br /><a href="https://lh4.googleusercontent.com/-4U5wKA_ZpXU/VANW2vsCd9I/AAAAAAAAAHo/i9VYUqqYkRw/s640/blogger-image--259575758.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="151" src="https://lh4.googleusercontent.com/-4U5wKA_ZpXU/VANW2vsCd9I/AAAAAAAAAHo/i9VYUqqYkRw/s400/blogger-image--259575758.jpg" width="400" /></a><span style="font-family: Verdana, sans-serif;">With the implementation of multiple number sets, I felt like I needed to model for my students. They needed to be shown how to plug in the numbers and keep their papers organized. So I used a basic problem with blanks and number sets and we worked together as a class to go through the process. First we entered the numbers from the first set and solved the problem. We discussed how they should show what they did with either a picture or a number sentence or both. I also pointed out the need for labels and showed them how to draw a line to separate the work for each number set. Then we moved on the next set of numbers and went through the process again. After solving the problem 3 times, we did a brain break (<a href="http://www.gonoodle.com/">www.gonoodle.com</a>). They needed it!</span></div><div><br /></div><div><br /><span style="font-family: Verdana, sans-serif;">I then posed a multiplication problem with 3 number sets: 8 groups of 10, 18 groups of 10 and 18 groups of 5. After a quick story telling session and visualization of the problem I sent my students off to their quiet spots to solve. You will not guess what happened next. They ADDED! I looked at the first completed problem and said, "Would you please go draw me a picture that matches the story." Then another student showed me the same strategy. Student after student brought their paper to me with three addition sentences and exclaimed, "I'm done." Nearly half my class. These were students that had been using grouping strategies and place value understanding just the day before. What happened?</span></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://lh6.googleusercontent.com/-8Mr7RVwXHjY/VANSJ4jj2CI/AAAAAAAAAG0/7qrMOpkn0OE/s640/blogger-image-2052100702.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://lh6.googleusercontent.com/-8Mr7RVwXHjY/VANSJ4jj2CI/AAAAAAAAAG0/7qrMOpkn0OE/s320/blogger-image-2052100702.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://lh4.googleusercontent.com/-Cl2hfWtvlv0/VANSNng2DYI/AAAAAAAAAHc/KGnr8Q5UOLk/s640/blogger-image-1278003882.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="184" src="https://lh4.googleusercontent.com/-Cl2hfWtvlv0/VANSNng2DYI/AAAAAAAAAHc/KGnr8Q5UOLk/s320/blogger-image-1278003882.jpg" width="320" /></a></div><div><br /><br /><span style="font-family: Verdana, sans-serif;">I modeled. I showed them how to solve the problem. Well not really, but really. Unintentionally, while modeling for them how to solve with multiple number sets, I showed them how to solve a part part whole problem with addition and they took what I showed them and applied it to the new problem. I was in shock. All week these students had been problem solving and progressing. Several went from not having a strategy to having a viable strategy to being successful. The minute I provided them with direct teaching, no matter what my intent, they latched on and all sense making went out the window. </span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><span style="font-family: Verdana, sans-serif;">Granted, not <em>every</em> student regressed. As a matter of fact, even many of the students who added revised their strategy when asked to draw a picture to match the problem and support their number sentence. Still though, initially they adopted my strategy and thought nothing of it. So hear me out, I believe that students have an inate problem solving ability. When given the opportunity to think through a problem on their own and make sense, they can do it. Some will make sense faster than others, but still they can. They do not need us to show them how to solve the problem, they need us to facilitate their thinking and question them so that they make connections. At least for a certain population of our students, modeling and mini-lessons impair their own problem solving abilities. If you want multiple strategies, don't show them yours. </span><br /><blockquote class="tr_bq"></blockquote><blockquote class="tr_bq"></blockquote></div><span style="color: black; font-family: AGaramondPro-Regular;"></span>Leandra Clevelandhttps://plus.google.com/101305531040870966092noreply@blogger.com0tag:blogger.com,1999:blog-4768305190911948498.post-89852337654766685792014-08-24T22:10:00.000-07:002014-08-24T22:10:22.372-07:0090 Minutes of MathRecently I've received several requests to share the schedule I plan to use in my math block. I must first say that the schedule I am about to share has not yet been put to the test and I will likely tweak it throughout the year. Also, keep in mind that I have a straight 90 minute block with no interruptions. I know many don't have that luxury, so as you read this, you can think of it in parts, that could be scattered throughout your day. Here's what I'm thinking:<br /><div><br /></div><div><strong><span style="font-size: large;">15 minutes - Number Talks</span></strong></div><div><br /></div><div><em>A <a href="http://www.mathsolutions.com/documents/numbertalks_sparrish.pdf" target="_blank">Number Talk</a> is a short, daily routine that provides students with meaningful ongoing mental math practice. During Number Talks students are expected to use number relationships and the properties of operations to add, subtract, multiply and divide. Often a number talk is comprised of a string of related expressions that are intended to elicit a specific strategy or operational property. For instance, in my classroom this past week one of my number talks featured the following string:</em> </div><div><br /></div><div>100 - 89</div><div>100 - 49</div><div>250 - 24</div><div><br /></div><div><em>This string was intended to elicit the "add-on" strategy and while a few of my students counted back by tens and then ones, I did have many that added up, and we were able to discuss those strategies and make comparisons between the two. </em></div><div><em></em><br /></div><div><em>It is important to keep Number Talks short, as they are not intended to replace current curriculum or take up the majority of your math time. Number Talks are most effective when they are kept short and done every day.</em></div><div><br /></div><div><a href="http://4.bp.blogspot.com/-FcIgRGRQH4c/U_rCk-2klzI/AAAAAAAAAGM/KYQZCU26TQg/s1600/gonoodle.PNG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://4.bp.blogspot.com/-FcIgRGRQH4c/U_rCk-2klzI/AAAAAAAAAGM/KYQZCU26TQg/s1600/gonoodle.PNG" height="149" width="200" /></a><strong><span style="font-size: large;">5 minutes - Brain Break</span> </strong></div><div><br /></div><div><em>Because my math block begins at 8:00, the kiddos have already been trying to focus for 45 minutes to an hour at this point in the morning and I've found that they need a brain break early. Depending on when you get started with math, you may choose to move or eliminate this break. As I mentioned in my last post, I'm using <a href="http://www.gonoodle.com/" target="_blank">GoNoodle</a>, and so far the kids love it!</em><br /><em> </em><br /></div><div><br /></div><div><span style="font-size: large;"><strong>20 minutes - Discussion of Previous Day's Problem or Task</strong></span></div><div><br /></div><div><em>In the <a href="https://sites.google.com/a/archford.org/arch-ford-mathematics/purposeful-pedagogy-and-discourse-model" target="_blank">Purposeful Pedagogy and Discourse Instructional Model</a> (PPD Model) a huge part of the students learning and growth happens during the discussion of student strategies that emerged while working the task or problem chosen by the teacher. When I first saw this model in action, the teacher posed a problem and then walked around the room watching the students work, making mental notes of which student strategies she wanted to share during the whole group discussion. As I watched the discussion that took place after problem solving I remember thinking, "Wow she's good to facilitate a discussion like that on the fly... she couldn't possibly have known what the kids were going to do with that problem." I found out later, of course, that she had planned that discussion based on the strategies she had anticipated her students would produce. At that point I thought, "Wow, she's good, she must have lots of experience in order to be able to anticipate what her students will do with every problem." </em></div><div><em></em><br /></div><div><em>What I'm trying to say is, facilitating a discussion on the fly takes practice. Even if you plan in advance, you have to have a really good idea of the students will likely do, and that takes experience and deep understanding of student thinking. So, in the meanwhile, until I get good at that, I plan to have my discussions the following day. This will allow me time to look at my student work, sort it, think about it, and plan a discussion based on what they actually did, not what I think they'll do. Look for more details and examples of this process in future posts. </em></div><div><br /></div><div><strong><span style="font-size: large;">20 minutes - Introduce Today's Problem/Task & Work Independently</span></strong></div><div><br /></div><div><em>I'm not going to lie, choosing the just right problem or task is not easy. Sometimes I might choose a problem from my CGI or ECM book or sometimes I might choose a problem or task from our district resource <a href="http://www.origoeducation.com/steppingstones/?mageloc=US" target="_blank">Stepping Stones</a>, by <a href="http://www.origoeducation.com/" target="_blank">Origo Education</a>. At other times I may use Contexts for Learning or I might even write my own. No matter where it comes from, I try to choose something that has the potential to produce the discussion I need, in order to push at the learning goal I have chosen for my students. </em> <br /><br /><em>This past week I was focused on these two common core standards as my learning goal:</em><br /><br />3.NBT.2 - Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.<br /><br />3.OA.9 - Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.<br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-kvMKcfyv5Vo/U_q-_XM7W3I/AAAAAAAAAF0/h6RLRdPWXIE/s1600/Thinking%2BCap%2B3.06.PNG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-kvMKcfyv5Vo/U_q-_XM7W3I/AAAAAAAAAF0/h6RLRdPWXIE/s1600/Thinking%2BCap%2B3.06.PNG" height="151" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Posted with permission: <a href="http://www.origoeducation.com/" target="_blank">Origo Education</a></td></tr></tbody></table><em>I chose the task you see here from Thinking Caps (an add-on to our district provided resource <a href="http://www.origoeducation.com/steppingstones/?mageloc=US" target="_blank">Stepping Stones</a>). I posed this task to students without a mini-lesson, and without providing them an example. The strategies that students came up with to write multiple subtraction sentences with a difference of 115, generated a fabulous discussion of patterns along with the relationship between addition and subtraction. It was really quite exciting.</em> <br /><br /><strong><span style="font-size: large;">5 minutes - Brain Break</span></strong><br /><br /><em>Have I mentioned </em><a href="http://www.gonoodle.com/"><em>www.gonoodle.com</em></a><em>?</em><br /><br /><span style="font-size: large;"><strong>25 minutes - Number Sense Routines and Fact Fluency</strong></span><br /><br /><a href="http://2.bp.blogspot.com/-5xcANPSGNm4/U_rAqECId4I/AAAAAAAAAGA/v75DgTuXAVI/s1600/Flare.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-5xcANPSGNm4/U_rAqECId4I/AAAAAAAAAGA/v75DgTuXAVI/s1600/Flare.PNG" height="149" width="200" /></a><em>I don't have this time completely worked out in my head yet. This past week I used this amazing number board which is again found in our district provided resource <a href="http://www.origoeducation.com/steppingstones/?mageloc=US" target="_blank">Stepping Stones</a>. We did some count around the circle and identifying patterns/missing numbers on the hundreds board during this time. Then I used a problem solving activity from Stepping Stones that had students using what they knew about patterns on the hundreds chart to identify missing numbers on a given piece of the hundreds chart. </em><br /><br /><em></em><br /><em>In the future I intend to use this time to focus on fact fluency strategies at least a few days a week. The first few minutes will be used to introduce/elicit strategies. After that I will use the rest of the time to reinforce strategies and allow students to practice basic facts. This time will likely be partner work and purposeful game play. I can't wait to get started!</em><br /><br />So there you have it. My 90 minute math block. As it stands right now at least. I can promise you this will not be the last you hear about my schedule. I'm already considering employing some sort of workshop model a couple of days a week. I'm not sure how that will work yet, but I know I need to figure out how to get in some small group time with my kiddos. So I'll be playing around more with that idea soon. I'm so excited!</div>Leandra Clevelandhttps://plus.google.com/101305531040870966092noreply@blogger.com0tag:blogger.com,1999:blog-4768305190911948498.post-5532158582880143412014-08-19T20:53:00.000-07:002014-08-19T20:56:09.636-07:00Can't wait to start math instruction? Me too!<div class="separator" style="clear: both; text-align: center;"><br /></div>As a part of my job as elementary math specialist this year, I am teaching a demonstration classroom full of third graders. I am so excited about what I am going to learn this year! Yes, I that's right, I said it... I am teaching a demonstration classroom and I AM GOING TO LEARN! I have spent 4 years studying theory and preaching to teachers about implementing <a href="http://en.wikipedia.org/wiki/Cognitively_Guided_Instruction" target="_blank">Cognitively Guided Instruction</a>, the <a href="http://www.corestandards.org/" target="_blank">Common Core State Standards for Mathematical Practice</a>, and the <a href="https://sites.google.com/a/archford.org/arch-ford-mathematics/purposeful-pedagogy-and-discourse-model" target="_blank">Purposeful Pedagogy and Discourse Instructional Model</a>. Now it's time to practice what I'm preaching. I plan to demonstrate how to make it all work in a school district that uses standards based reporting. But first, I have to figure it out.<br /><br />Today was the second day of school. I have been granted a 90 minute block for math instruction. Today my plan was to focus on procedures... How do we treat our manipulatives? How do we use them as tools? How can we organize them for easy use? That was my plan. What transpired, though, was a different story. I did math... on the second day of school. Am I crazy?<br /><br />Here's how it started. First, I posed a problem to the students: We need to figure out how to move our book boxes off our table and onto the shelves at the same time as taking our math toolkits off the shelves and putting them on our table. We want to make sure and do this <em>without</em> putting anything on the floor and <em>without</em> having all 24 students up at once. Innocent enough right? It was. The kiddos came up with a few possible solutions right away, and we voted on which team's procedure would be the most efficient. Done 25 minutes down. <br /><br />Now that we had the math tools on the tables, I told the kids a story. "This morning I got here really early... at 6:45a.m.! I worked and worked and worked to organize your math tools, but I ran out of time. At 7:15, you all were here and ready to come into the classroom. So I had to hurry to finish what I was doing." At this point, I couldn't help it, I let the first math question sneak into our day, "How long did I work on the math tools before you got here?" Really though, I was working on procedures, the students learned how to give a thumbs up when they had the answer instead of raising their hand. :) Carlton was the first to share his strategy, "6:45 is just a quarter from 7:00 and a quarter is 15 minutes. Then from 7:00 to 7:15 is another 15 minutes, and 15 plus 15 is 30 minutes." Now the kiddos got to learn the <a href="http://www.signingsavvy.com/sign/ME%20TOO/3866/1" target="_blank">"me too" signal</a>. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F3.bp.blogspot.com%2F-iL6NGWo6pvc%2FU_PjkeCPcoI%2FAAAAAAAAAEI%2FnEg4bXx7hY4%2Fs1600%2FMe%252BToo.PNG&container=blogger&gadget=a&rewriteMime=image%2F*" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="www.lifeprint.com" border="0" src="http://3.bp.blogspot.com/-iL6NGWo6pvc/U_PjkeCPcoI/AAAAAAAAAEI/nEg4bXx7hY4/s1600/Me%2BToo.PNG" height="117" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"> </div><div align="left" class="separator" style="clear: both; text-align: center;"></div>So, you see, I really was focused on procedures. :) After we had our short elapsed time discussion, I explained to the students that because I had run out of time, I needed their help to open up our fraction squares and circles and remove the stickers so they could be used more easily. <br /><div class="separator" style="clear: both; text-align: left;"><a href="http://1.bp.blogspot.com/-cJezuk4AekM/U_PlpUy575I/AAAAAAAAAEQ/v0Y1s4F6Cyc/s1600/photo%2B3.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-cJezuk4AekM/U_PlpUy575I/AAAAAAAAAEQ/v0Y1s4F6Cyc/s1600/photo%2B3.JPG" height="200" width="150" /></a>The kids enjoyed this activity and I did too. They got to "play" with the tools, and I got to facilitate a discussion about how we treat our tools. </div><br />After we finished breaking apart the fraction manipulatives, we had to squeeze in a brain break from <a href="http://www.gonoodle.com/" target="_blank">www.gonoodle.com</a>! This was definitely a highlight of the day. But even as I introduced brain breaks, we had to vote on our classroom champ, and I created a tally chart. Which turned into a quick number talk. How many more votes did Flappy Tuckler get than McPufferson? See I really just can't help myself. <br /><br />After a quick "Happy" dance and a calming stretch we moved on to the real problem of the day. I had passed out place value blocks, but after I had counted out all the hundreds of unit cubes, I didn't have enough time or energy to count out the tens rods and make sure each team had the same amount so I just grabbed a pile and put some in each tray. Now, in my classroom there are four table teams, and two math toolkits per table. I could smell a number talk/collection counting activity coming and like a preditor hunting it's prey, I pounced on the opportunity to dig into some student thinking. <br /><div class="separator" style="clear: both; text-align: left;"> </div><div style="clear: both; text-align: left;">The kids were in complete agreement that things must be fair, and therefore we must count the tens rods, and determine how many, if any, needed to be redistributed so that each table team would have the same amount. So it began, they counted and I observed. They added and I listened. Then we "fishbowled" and the class counted together as Marissa moved the rods on her desk. Then again, the class counted as Henry moved the rods on his desk. This is what I observed. </div><div style="clear: both; text-align: left;"> </div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="clear: left; float: right; margin-bottom: 1em;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-dLK5521-N9I/U_Pukx7MPAI/AAAAAAAAAEo/bdS6Opgr_NU/s1600/photo%2B2.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-dLK5521-N9I/U_Pukx7MPAI/AAAAAAAAAEo/bdS6Opgr_NU/s1600/photo%2B2.JPG" height="150" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Henry's blocks</td></tr></tbody></table><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-13ZIoaCv1wE/U_Pwhg7nqAI/AAAAAAAAAFI/PoPgPM6UgWE/s1600/photo%2B1.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-13ZIoaCv1wE/U_Pwhg7nqAI/AAAAAAAAAFI/PoPgPM6UgWE/s1600/photo%2B1.JPG" height="150" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Marissa's blocks</td></tr></tbody></table><div style="clear: both; text-align: left;"></div><div style="clear: both; text-align: left;">As the class counted, Marissa moved the blocks and grouped them into tens. Two groups of ten and 6 more. </div><br /><div style="text-align: left;">Henry, on the other hand, grouped off the first set of ten, and then grouped all the rest together. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">What does it mean? I don't know. Is it significant? I think maybe. Am I overanalyzing? Likely. </div><br />Oh well, moving on. After counting the number of tens rods in each tray I recorded that information on the board, and what do do you think I did next? A number talk of course! <br /><br />A little bit of mental math, some strategy sharing, and some answer defending and in no time at all we had totals per team... 51, 50, 48 and 62 tens rods. <br /><br />I love strategy sharing. I am always amazed at how they think about numbers. <br /><br />So that was it. I ran out of time. I wanted to keep going, but the kiddos were obviously over it. It's the second day of school and I got in as much as I could without going overboard. Crazy? Maybe. But do you blame me? I hope not. <br /><br /><em>*Children's names have been changed.</em><br /><div class="separator" style="clear: both; text-align: center;"></div>Leandra Clevelandhttps://plus.google.com/101305531040870966092noreply@blogger.com1tag:blogger.com,1999:blog-4768305190911948498.post-55690540447108409052014-04-18T17:00:00.003-07:002014-04-18T17:02:14.601-07:00Common Core or Common Sense?<div align="center"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-KV9dsLd2A0U/U1G8GsahtXI/AAAAAAAAAD4/-Rb_fkoJqcA/s1600/Array.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-KV9dsLd2A0U/U1G8GsahtXI/AAAAAAAAAD4/-Rb_fkoJqcA/s1600/Array.jpg" height="320" width="307" /></a></div><br /><span style="font-family: Verdana, sans-serif;">As I was trolling my facebook page one evening this week, I happened upon a post by one of the second grade teachers that I work with in my district. She was expressing her frustrations with all the negativity surrounding the Common Core and gave a fabulous example of something that happened in her classroom which she attributes to the Common Core. I just had to share:</span><br /><br /><blockquote class="tr_bq"><div class="text_exposed_root text_exposed" id="id_53519e1da4e117233381403"><span style="font-family: Times, "Times New Roman", serif;"><span class="userContent" data-ft="{"tn":"K"}"><em>I have read so much negativity about common core lately that it makes me want to invite all the Negative Nancy's to my classroom to see it in action. In my opinion, and it's only my opinion, common core would have gotten a better following if they had named it Common Sense standards...because that's what it really is. Common sense! The following is an example of Common Sense in my classroom.</em> </span> </span></div></blockquote><blockquote class="tr_bq"><div class="text_exposed_root text_exposed" id="id_53519e1da4e117233381403"><span style="font-family: Times, "Times New Roman", serif;"><span class="userContent" data-ft="{"tn":"K"}"><strong>CCSS 2<span class="text_exposed_hide">.OA</span></strong><span class="text_exposed_show"><strong>.4</strong> Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.</span></span> </span></div></blockquote><blockquote class="tr_bq"><div class="text_exposed_root text_exposed" id="id_53519e1da4e117233381403"><span class="userContent" data-ft="{"tn":"K"}"><span class="text_exposed_show"><span style="font-family: Times, "Times New Roman", serif;"> </span><em><span style="font-family: Times, "Times New Roman", serif;">From the beginning of the year, my class sat on the floor in a rectangular array. They had no idea that was what it is called. I say "class, class please go sit four on the floor." The students move to the floor and sit four students across and five students back....20 students. We did this all year with no problems. Recently, we got another student. This happened right about the time we started learning about arrays. The students started complaining that it just didn't work out to sit four on the floor anymore. They always had an odd man out. So, I told them to see if they could come up with a way to fix our problem. And they turned to each other and communicated, they discussed, they planned, and they reported their ideas all while I sat there and watched and listened in amazement. They used the "smart part" of their brains and came up with two solutions 3+3+3+3+3+3+3=21 or 7x3 and 7+7+7=21 or 3x7. They also discussed which array would fit best on our carpet space. See Common Core really is Common Sense! <br /> <br /> I just wish my teachers would have taught Common Core... I mean Common Sense standards, I might have enjoyed school a whole lot more.</span></em></span></span></div></blockquote><br /><span style="font-family: Verdana, sans-serif;">The Common Core State Standards do not mandate HOW this teacher must teach in her classroom. They do not require that her students use specific strategies to solve problems (until the expectation of the standard algorithms which come in the intermediate grades). They do, however, expect that she develops innovative thinkers and problem solvers who don't have to rely on a given procedure to find the solution to a problem. Kudos Amy Barnett for embracing the Common Core and preparing your students for tomorrow!</span>Leandra Clevelandhttps://plus.google.com/101305531040870966092noreply@blogger.com0tag:blogger.com,1999:blog-4768305190911948498.post-31788354948966158392014-03-24T21:22:00.001-07:002014-03-24T22:47:53.132-07:00A Letter to Frustrated Parents of Common Core Math Students<div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><a href="https://lh3.googleusercontent.com/-L6ztkHNo5yA/UzEOFIo1bvI/AAAAAAAAAC8/4Y1GFYLj5fE/s640/blogger-image--2050698035.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh3.googleusercontent.com/-L6ztkHNo5yA/UzEOFIo1bvI/AAAAAAAAAC8/4Y1GFYLj5fE/s640/blogger-image--2050698035.jpg" /></a></div><br />Dear frustrated parents of Common Core math students,</div><div><br /></div><div>Think back to your math education, did you learn the steps required to add numbers? To subtract numbers? Did you learn another set of steps for how to add and subtract fractions? How about a procedure for how to add and subtract negative numbers? Were each one of those procedures different and specific to the "type" of number you were adding or subtracting? What about as you got older? More procedures? Were you successful? If so, you likely had a great capacity for memorization. The ability to memorize multiple steps and multiple procedures and know when to apply each of those procedures. What happened when you forgot just one step? The procedure failed to produce the correct answer. Were you ever frustrated because you couldn't figure out why it didn't work? No? How about your classmates? Any of them ever confused? Don't know? Try this, survey one hundred adults. Ask them, were you good at math in school? Did you love math? Did it make sense? I guarantee the majority will have a negative response. Our generation is full of math haters. Think about it, you would never hear someone say, I'm just not a literacy person, reading was always hard for me. On the contrary, I'm just not a math person, it never made sense... that's common place, socially acceptable. I was never taught to make sense of numbers, I was taught one way to solve every problem, every problem had ONE way, memorize these steps and you will be able to solve this problem. Sorry if you can't remember the steps. This is how we do it. I was robbed. I was not taught to persevere and try to make sense of the problem... who cares what it means, here's how you do it, just do this. </div><div><br /></div><div>Hold on, why am I crossing out this number and changing that one? </div><div>Because you don't have enough to take away. Just do it! </div><div>But wait, I have 453 and I'm just trying to take away 17 I think there is more than enough to take away. </div><div>No you can't take 7 away from 3... Just cross out the 5. Just do it!</div><div>But wouldn't 3 take away 7 be negative...</div><div>NO! You can't take a bigger number from a smaller number, sit down, JUST DO IT MY WAY!</div><div><br /></div><div>Hold on, why do I have to have common denominators? </div><div>Because you can't add apples and oranges! Just do it! </div><div>But... but... If I add 2 apples to 3 oranges I get 5 fruit... </div><div>Stop being sarcastic! Sit down, find common denominators... JUST DO IT! </div><div><br /></div><div>I was wondering... why do I have to flip the fraction upside down if I'm dividing? </div><div>It's not your place to reason why, just invert and multiply! JUST DO IT!</div><div><br /></div><div>Don't get me wrong, like some of you, I had a high capacity for memorization. I just did it, I memorized and memorized and very rarely made mistakes. I graduated in the top 3% of my almost 400 member class and I went on to high levels of math in college and was quite successful. Now, I'm a math specialist. It's what I do. I have spent four years studying and researching math instructional methodologies. Nothing but math every day for 4 years. Do you know what I've discovered? I didn't have any conceptual understanding of math. That made me angry. I have learned more about numbers and how they work in the last four years than I learned in my 19 years in public and post-secondary education. I have also learned how to help young students make sense of numbers, using their own innate understandings, their own built in mathematical ability. I have learned how to start with what they know, and what they understand and refine that into efficient strategies. In addition, I have also learned that it takes time. I must first allow them to be creative with numbers before I push my own ideas of how they "must" solve a problem. If I have patience and let them make sense of it, they will adopt the most efficient method, and they will become successful in math, not only knowing how to do it the way we learned it, but why that way works and when it's the best strategy. </div><div><br /></div><div>The "new" methods you're seeing are not being taught. They are methods that students naturally invent. Just the way that mathematicians invented them before our formal mathematics system existed. Believe it or not, simplicity and efficiency are at the forefront of our classroom discussions EVERY day. We are guiding students through their own sense making methods not only to understand numbers and operations but to find the most efficient methods for each problem. </div><div><br /></div><div>I understand your frustration. I was frustrated at first too. Remember, this is not the way I learned it either. Please be patient. Please reach out to your school's math leaders to help you understand. Please don't rob your child of the opportunity to make sense of math. We are trying to develop math lovers, problem solvers, and creative thinkers. How can that be wrong? </div><div><br /></div><div>Sincerely, </div><div>Lover of math and children</div>Leandra Clevelandhttps://plus.google.com/101305531040870966092noreply@blogger.com267