tag:blogger.com,1999:blog-19235821058750288792024-03-27T16:53:21.989-07:00Learning with Tape#MTBoS #iteachmath #curriculum #mathcoach #edtech #ncctm #sketchnotesCarolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.comBlogger54125tag:blogger.com,1999:blog-1923582105875028879.post-54909361100907290432019-04-04T09:37:00.001-07:002019-04-04T09:37:06.127-07:00Sketchnoting Resources, Challenges, and Tips<h3 style="text-align: center;">
<i>Sketchnoting: </i><i>visual notes where ideas are conveyed through words, pictures, and visual elements</i></h3>
One of the things I love to do personally and with students is sketchnoting. I realized that while I've been great about sharing my sketchnoting journey, samples, and resources on Twitter, I really hadn't taken the time to make a post here, so it's time to fix that!<br />
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<a href="https://3.bp.blogspot.com/-menOP6p6nx8/XKYaMQmftTI/AAAAAAAAB-I/leGph_lF5-EA3QlF_0jeGX1m2CMe7lpEQCLcBGAs/s1600/The%2Bpath%2Bto%2Bsuccess%2Bis%2Bto%2Btake%2Bmassive%252C%2Bdetermined%2Baction..png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="800" data-original-width="800" height="320" src="https://3.bp.blogspot.com/-menOP6p6nx8/XKYaMQmftTI/AAAAAAAAB-I/leGph_lF5-EA3QlF_0jeGX1m2CMe7lpEQCLcBGAs/s320/The%2Bpath%2Bto%2Bsuccess%2Bis%2Bto%2Btake%2Bmassive%252C%2Bdetermined%2Baction..png" width="320" /></a></div>
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In July 2017, I had the chance to attend a workshop with Silvia Tolisano (<a href="https://twitter.com/langwitches">@langwitches</a>) on sketchnoting. While I'd heard the term, I only had a vague idea of what sketchnoting might look like. Silvia spoke of documenting learning, making thinking visible, and building connections through notetaking, and I was hooked. Here's my very first sketchnote from that workshop:</div>
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<a href="https://pbs.twimg.com/media/DNfbBkUU8AACFRv.jpg:large" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="800" data-original-width="600" height="320" src="https://pbs.twimg.com/media/DNfbBkUU8AACFRv.jpg:large" width="240" /></a></div>
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And let me tell you, I was STRESSED the whole way through making it. I wanted to use all of my pretty supplies, I wanted it to be perfect, and I was TERRIFIED of sharing it on Twitter. Since then, I've sketchnoted nearly every conference session, presentation, PD, and keynote I've attended. I've used sketchnoting with students across so many grade levels, and presented on sketchnoting over and over again. </div>
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<i>This technique that I once believed was so much about artwork and perfection...I've come to love it now that I know it's SOOOO not about those things. </i></h3>
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I love that sketchnoting is personalized, flexible, and fun! It lets you show connections and distinctions between different ideas, or rank things based on importance, or separate common content into small groups of information. </div>
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Along the way, I stopped trying to use all of the markers at once:</div>
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<a href="https://pbs.twimg.com/media/DY5nUovXUAAcdd9.jpg:large" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="800" data-original-width="600" height="320" src="https://pbs.twimg.com/media/DY5nUovXUAAcdd9.jpg:large" width="240" /></a> </div>
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Tried digital sketchnoting...(on an iPad Pro in ProCreate) </div>
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...then promptly went back to paper 😂</div>
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And along with a few friends here in my district (especially the amazing <a href="https://twitter.com/MrsYav">@MrsYav</a>), started up a sketchnoting Twitter account to help teachers use sketchnoting in their classrooms and encourage students along the way. It's <a href="https://twitter.com/SketchnotEDU">@SketchnotEDU</a>, and we also have a website where we store our PD materials (<a href="http://bit.ly/sketchnotEDU">bit.ly/sketchnotEDU</a>). </div>
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<span style="margin-left: 1em; margin-right: 1em;"><a href="https://twitter.com/SketchnotEDU"><img border="0" data-original-height="696" data-original-width="455" height="320" src="https://2.bp.blogspot.com/-uVoctRQrM-Q/XKYoC2vXRuI/AAAAAAAAB-k/g7KY4_SNuggAbReARXUDEjnzwZuPBGgIgCLcBGAs/s320/sketchnotEUD.PNG" width="209" /></a></span></div>
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The Twitter posts aren't as frequent as I'd like, but we do have some prompts and challenges dating back to early 2018. Some of my favorites were the skill challenges, and these remain my #1 tip for teachers trying to support student sketchnoting. </div>
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<i>Each week, pick a skill to work on and to incorporate into your notes. Consider its purpose - what it ADDS to the functionality or organization of the final set of notes, and use that function to guide your decisions of when to use it. </i></h3>
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These skills can be specific to sketchnoting, or can still be used with improving students' ability to take notes more traditionally. There's so much value in thinking about WHY bullet lists are useful, or why we might use arrows to connect topics or demonstrate order. Some of the skills challenges we posted on @SketchnotEDU included:</div>
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Banners and Frames</div>
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And the what-can-you-draw-with-just-lines-circles-triangles-dots-and-rectangles challenge!</div>
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There is so much research to support sketchnoting over outlining or traditional notes. I think my favorite thing though is that sketchnotes end up looking quite different for each student, which allows so many opportunities to share, compare, and discuss. </div>
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One final tip, and I'll save the rest for future posts. This is actually for the same reason that I switched back to paper after trying digital sketchnoting, in addition to the fact that research supports paper notetaking over digital notetaking. </div>
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<b><i>USE PENS. OR MARKERS. DO NOT USE PENCIL. </i></b></h3>
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While sketchnoting, it's best if we all just forget that pencils exist for a little bit. The problem with pencils is that you've got the option to erase, fix, redo, and repeat. Mistakes are a part of math, a part of learning, and a part of sketchnotes. Sometimes you can turn them into a happy little bird, sometimes you just move on. But using pens or markers instead of pencils will make it so much easier to accept what ends up on the paper, and let go of trying to make everything perfect. </div>
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com9tag:blogger.com,1999:blog-1923582105875028879.post-5471947710318442902018-01-10T08:42:00.002-08:002018-01-10T08:42:54.909-08:00Podcasts for PDI've never really been a podcast gal. BUT lately, I've learned that it's about finding the right ones. And I've been thinking about how just listening to something can keep that topic on your mind all day, or sometimes all week.<br />
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There are a couple of AMAZING podcasts that I listen to regularly, and I wanted to share just how amazing they are.<br />
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<li><a href="http://www.cultofpedagogy.com/">Cult of Pedagogy</a>: Just trust me. If you don't add a single other one, add this one. Jennifer Gonzalez is a former MS ELA teacher, and she has a way with words that will encourage you, challenge you, and inspire you in your journey as an educator. SOOO many amazing episodes. Her post was also how I heard about <a href="https://www.cultofpedagogy.com/pineapple-charts/">pineapple charts</a>. We've implemented them digitally in our district in one of our PD groups, and it's so cool to be able to watch someone teach LIVE from across the county! (She also speaks to <a href="https://www.cultofpedagogy.com/open-your-door/">why we need to see each other teach</a>, which I <i><u>highly</u></i> recommend.)<br /></li>
<li><a href="http://novemberlearning.com/teaching-and-learning-news/">November Learning</a>: Our district has been working for the last 2 years with Dr. Alan November and his team. His podcasts are few and far between, but the quality of information you'll get is incredible. I recommend starting with his talk with <a href="http://novemberlearning.com/dr-rob-evans-managing-change/">Dr. Rob Evans on Managing Change</a>. #gamechanger<br /></li>
<li><a href="https://itunes.apple.com/us/podcast/house-of-edtech/id792424937?mt=2">House of #EdTech</a>: So many resources and great interviews! Start with Limited Tech? No Problem, or EdTech & Formative Assessment.<br /></li>
<li><a href="https://thecornerstoneforteachers.com/truth-for-teachers-podcast/">Truth for Teachers</a>: Quick episodes, especially great for short errand runs or loading the dishwasher! ;) #107 on growth mindset is great, and I can't wait to listen to #115: "Goodbye Teacher Tired" that was just released.<br /><br />There are soooo many more. Other lists <a href="https://thecornerstoneforteachers.com/podcastpd-what-youre-missing-if-youre-not-listening/">here</a> and <a href="https://www.edutopia.org/blog/best-education-podcasts-betty-ray">here</a>. <br />Also be sure to check out #PodcastPD on Twitter!<br /></li>
<li>(for BONUS points) My fav podcasts for fun? Thanks for asking!</li>
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<li>Harry Potter and the Sacred Text</li>
<li>Malcolm Gladwell's Revisionist History</li>
<li>Hidden Brain</li>
<li>Love to Sew</li>
<li>Levar Burton Reads</li>
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com3tag:blogger.com,1999:blog-1923582105875028879.post-27686825019224685222017-05-05T08:29:00.001-07:002017-05-08T11:33:51.437-07:00Number Sense Routines for High SchoolHiya!<br />
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Welcome to the blog's new look! (I'm loving the clean, fresh feel...it's like spring cleaning, but for my screen, haha!)<br />
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I just wanted to take a quick moment today to share a Google site I built to house my favorite resources for number routines and building number sense for high school students.<br />
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We've all had students (or at least, I have!) that have been damaged in the past by teachers so concerned with a different recipe/procedure for every type of problem that their students end up uncomfortable thinking about numbers. There are plenty of quick, <i>FUN </i>activities that can build numeracy and just a bit of confidence, all while reinforcing classroom norms for discussion, collaboration, and problem-solving.<br />
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<a href="http://tinyurl.com/HSnumeracy"><img border="0" height="140" src="https://3.bp.blogspot.com/--Yjemi4jGY0/WQyW8f2_jiI/AAAAAAAABeU/wkncSe-0QloG5e2dfw90rxkGu-13mj2OgCLcB/s320/Numeracy%2Bfor%2BHS%2B2017-05-05%2B11-13-59.png" width="320" /></a><span id="goog_2142457593"></span><span id="goog_2142457594"></span><a href="https://www.blogger.com/"></a></div>
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I even made this short link: <a href="http://tinyurl.com/HSnumeracy">tinyurl.com/HSnumeracy</a> to make it easy to access. The site includes routines, links to number talks, & teacher info for implementing these types of activities and routines. There are even a few Global Math Department webinars to get you thinking! Did I mention that I <i>love </i>the new Google Sites? SO easy to use!<br />
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(And in case you're new around here, welcome! I've made a couple other collection websites in the past. One of my favorites is <a href="https://trello.com/b/LOubFTUZ/hs-review-ideas-activities">this Trello collection of review games & activities</a>, from this <a href="http://learningwithtape.blogspot.com/2016/01/my-favorite-trello-mtbos-blogging.html">post</a> on Trello.)Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com6tag:blogger.com,1999:blog-1923582105875028879.post-89414629549168672012016-12-01T08:11:00.002-08:002016-12-01T08:13:28.730-08:00Promoting Productive Struggle & Implementing Formative Assessment Lessons<span style="color: #0c343d; font-family: "verdana" , sans-serif;">We had an amazing meeting yesterday with our district's <a href="http://k12education.gatesfoundation.org/student-success/high-standards/literacy-tools/mathematics-design-collaborative/?gclid=Cj0KEQiAsf_BBRDMpoOHw4aSq4QBEiQAPm7DLyhUefkdIvP1AodJ18MAnDde7Gje93TRY4LCmZUXQxAaAmrY8P8HAQ">Math Design Collaborative</a> yesterday for training on implementing FALs. One of the resources we went through was this article of <a href="http://blog.mindresearch.org/blog/productive-struggle-in-math">8 Teaching Habits that Block Productive Struggle in Math Students</a>. It's kind of a what-not-to-do guide to teaching math. I also like that they paired it with <a href="http://cdn2.hubspot.net/hubfs/237516/Education/Deeper_Learning_2016/Productive_Struggle/Productive_Struggle_Poster.pdf?t=1480547109271">this infographic poster</a> of what to do instead. </span><br />
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<a href="http://2.bp.blogspot.com/-XWjURmHJjnY/WEBBaFlfzlI/AAAAAAAABYY/0F-GscbgFjsfoeKgYnPULVd4uS1cIn2nQCK4B/s1600/Honeycomb.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><img border="0" height="320" src="https://2.bp.blogspot.com/-XWjURmHJjnY/WEBBaFlfzlI/AAAAAAAABYY/0F-GscbgFjsfoeKgYnPULVd4uS1cIn2nQCK4B/s320/Honeycomb.png" width="320" /></span></a></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Our district is involved in a 3-year initiative with SREB, and I really couldn't possibly be more excited about this. Our best teachers have been selected (2 per school) to participate. We have teachers from every grade level 6-12, and from all types of schools. (Even our alternative school is participating!!)</span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">During year 1, we have 8 days together as a group, and yesterday was Day 5. PD focuses on how to implement Formative Assessment Lessons (FALs), which are housed at <a href="http://map.mathshell.org/">map.mathshell.org</a>. </span><br />
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<a href="http://map.mathshell.org/"><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><img border="0" height="34" src="https://2.bp.blogspot.com/-j2fruXqLOL8/WEBCUxkK_-I/AAAAAAAABYc/QcDCXIgZRoUusswBGXXam0m2cI3yuDDiwCLcB/s320/Screenshot%2B%25285%2529.png" width="320" /></span></a></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Now, when I was in the classroom, I was aware of this website, but hadn't implemented any of the lessons in their entirety. (To be REALLY REALLY honest, I had just stolen a few tasks and card sorts, and not used anything else.)</span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">I had NO IDEA that all of the resources on this website are research based and are most effective (by far!) as complete lessons. </span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Here's the basic idea, but you'll really get a better picture by reading through one of the scripted lessons. </span><br />
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">FALs are separated into 2 categories:</span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Concept Development (named based on content)</span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Problem Solving (name based on context)</span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Concept Development FALs are meant to be used one-half to two-thirds of the way through a unit. The goal is to figure out what kids know, what they don't know, and then use that to guide instruction (both through the remaining part of the unit, and to change how you teach that content next year). Sometimes these FALs also work at the beginning of a unit to review prerequisite content and guide the transition into new content. </span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Problem Solving FALs can be used any time during a unit, and are structured around really great problems with plenty of arguing potential. ;)</span></li>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;"><br />Here's the basic process to go through a FAL (I'll use a concept development FAL as an example, because so far it's the one I've worked with the most)</span></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">The day before the FAL: </span></div>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Give the pre-assessment as an exit slip.</span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">That afternoon, sort the pre-assessments into 1,2, & 3 point piles (1 - little to no understanding, 2 - demonstrates some understanding, 3 - demonstrates understanding). Then use these piles to create homogeneous pairs of students (so the top 2 kids are paired together, then the next highest 2, etc). This isn't a formal grading process. </span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Once pairs are developed, and while the results on the pre-assessment are fresh in your mind, choose (or create) some feedback questions from the script. They should be based on the major misconceptions, obstacles, or gaps in learning you observed on the pre-assessments. </span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Make sure you have all materials & cards prepped and ready.</span></li>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Day of the FAL:</span></div>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Follow the lesson script through the whole class intro, collaborative activity, sharing & whole class discussion, and then administer the post-assessment. </span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Whole class intro: usually involves white boards and some powerpoint slides. During this portion, you're just reminding kids of the work they did on the pre-assessment, and not "teaching." Just ask them some guiding questions to get them to notice differences in each other's responses. </span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Collaborative activity: when students work on activity (usually a card sort) in the pairs you designed based on their pre-assessment. Just give the time allotted in the script, and let go of the idea of completion. Just let each pair get as far as they can in the time given. During this time, project the feedback questions developed the day before.</span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Sharing/Whole Class Discussion: usually involves some time to combine/change groups and compare answers, then a return to the whiteboards to discuss as a class. </span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Post-assessment is "graded" (but not really) the same way that the pre-assessment was, so that you can measure growth for each class.</span></li>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">My personal favorite FAL? Right now, it's <a href="http://map.mathshell.org/lessons.php?unit=9230&collection=8">Generating Polynomials from Patterns</a>. </span></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Students use dot patterns to develop polynomial expressions for the white, black, and total dot patterns and WOW do they have to do some serious work with this one! It seriously challenges the advanced kiddos without being inaccessible for lower-achieving students.</span></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Second runner up is <a href="http://map.mathshell.org/lessons.php?unit=8110&collection=8">Applying Properties of Exponents</a>. I had a huge "AHA" moment with this one. How many times, when we're teaching laws of exponents, do we pretend like addition and subtraction of terms just cease to exist for a week or two? I'm definitely guilty. Here are the first few cards from this FAL so you can see what I'm talking about:</span></div>
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<a href="https://4.bp.blogspot.com/-eDuxwhcjhbk/WEBJ5MxVlXI/AAAAAAAABY0/jFGEXp8NglATYwwB9pij1TK7uTpCte3cwCLcB/s1600/Applying%2BProperties%2Bof%2BExponents%2B-%2BGamma%2B2016-12-01%2B11-03-10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="115" src="https://4.bp.blogspot.com/-eDuxwhcjhbk/WEBJ5MxVlXI/AAAAAAAABY0/jFGEXp8NglATYwwB9pij1TK7uTpCte3cwCLcB/s400/Applying%2BProperties%2Bof%2BExponents%2B-%2BGamma%2B2016-12-01%2B11-03-10.png" width="400" /></a></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">But if we choose not to shy away from types of problems that aren't immediately simplified using one application of one exponent property, our students are all the better for it. And this FAL does a <b><i>phenomenal</i></b> job of facing those obstacles, misconceptions, and gaps in learning square in the face.</span></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Each of the FALs is designed to promote productive struggle in students. Each one is also designed to promote valuable, serious mathematical discourse. And that's something we should all strive to include more of in our classrooms.</span></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">And don't forget about the <a href="http://blog.mindresearch.org/blog/productive-struggle-in-math">What-Not-To-Do</a> and <a href="http://cdn2.hubspot.net/hubfs/237516/Education/Deeper_Learning_2016/Productive_Struggle/Productive_Struggle_Poster.pdf?t=1480547109271">What-To-Do-Instead</a> for Promoting Productive Struggle that I mentioned in the beginning of the post from the <a href="http://blog.mindresearch.org/blog">MIND Research Institute blog</a>! </span></div>
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com6tag:blogger.com,1999:blog-1923582105875028879.post-14448945287169599932016-09-27T08:13:00.004-07:002016-09-27T08:13:30.253-07:00Paper.li - Keeping up with the internet<span style="color: #0c343d; font-family: Verdana, sans-serif;">There is just so much "out there" in the interwebs. </span><br />
<span style="color: #0c343d; font-family: Verdana, sans-serif;">Articles, tweets, ideas, pins, blog posts...</span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">I use <a href="https://www.bloglovin.com/">Bloglovin</a> to keep up with the blog posts, but I only read through every couple of days. Which means some things fall through the cracks. Not to mention, it's only grabbing content from blogs I've already found. </span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">So I stumbled upon <a href="http://paper.li/">Paper.Li</a>. </span><br />
<span style="color: #0c343d; font-family: Verdana, sans-serif;">I think someone must have tweeted it out with a #MTBoS hashtag, because I can't think of another way that I would have actually paid attention to it. But ever since, I keep finding new public paper.lis to follow! </span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">Basically, paper.li lets you build a newsletter out of tweets, articles, or basically anything out on the internet. It's really just a content collector. But I really like it because other people have built paper.lis that align with my interests. (I could build my own, but I feel like the ones I've found online are already so great that I don't need to.)</span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">I keep the links on my bookmark bar, and when I get a free moment, I browse through a couple. I've found some new blogs to follow, and plenty of great ideas. Here's the list from my bookmarks bar:</span></div>
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<a href="http://paper.li/MathDenisNJ/1441550259"><span style="color: blue; font-family: Verdana, sans-serif;">The Math Education Daily</span></a></div>
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<a href="http://paper.li/metamathan/1464288837"><span style="color: blue; font-family: Verdana, sans-serif;">Math Daily</span></a></div>
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<a href="http://paper.li/tag/mathchat/"><span style="color: blue; font-family: Verdana, sans-serif;">#Mathchat Daily</span></a></div>
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<a href="http://paper.li/drwetzel/teachingscienceandmath/#!headlines"><span style="color: blue; font-family: Verdana, sans-serif;">Teaching Science and Math Daily</span></a></div>
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<a href="http://paper.li/e-1452888826#!headlines"><span style="color: blue; font-family: Verdana, sans-serif;">Desmos Daily</span></a></div>
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<span style="font-family: Verdana, sans-serif;"><span style="color: #3d85c6;"><a href="http://paper.li/bsweet321/1434472846?edition_id=27a922a0-81ad-11e6-9e0d-0cc47a0d15fd">Educational Technology Daily</a> </span><span style="color: #0c343d;">(Fridays only)</span></span></div>
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<span style="color: #3d85c6; font-family: Verdana, sans-serif;"><a href="https://paper.li/MsEESL/1410880420#!headlines">ELL Daily</a> </span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">If you know of a great one I didn't list, please let me know! I really love finding new ideas, and this format just <u>works</u> for me. It kind of reminds me of Flipboard, but I never really found it useful because I didn't take the time to fill in all of my interests/fav blogs/etc. I like that with paper.li, I can just flip through everyone else's pages!</span></div>
Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com1tag:blogger.com,1999:blog-1923582105875028879.post-66321821459474988722016-09-23T07:30:00.000-07:002016-09-23T07:30:22.864-07:00Content Literacy in Secondary Math<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Wow - this blog's gotten a bit dusty. But here I am. Let's just pretend it's been 5 minutes instead of ... too long. </span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">I've been asked to work with a small group of teachers regarding content literacy strategies. </span><span style="color: #0c343d; font-family: "verdana" , sans-serif;">We'll be meeting in groups of around 7 teachers (all math and science) during their planning periods. </span><span style="color: #0c343d; font-family: "verdana" , sans-serif;">The school's improvement goal this year is to improve student performance on the ACT and English 2 state exam. The idea is to support that goal through implementation of some new strategies & some serious changes in expectations for reading and writing across the various content areas. </span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">I'll admit, I haven't done much work on this subject in math, but I'm excited to learn some new techniques and get to researching! Obviously, if we want students to have meaningful discourse and justify their thinking, we need to promote academic language and writing in our math classrooms.</span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Of course, my first thought was to check the <a href="http://www.twittermathcamp.com/">TMC</a> and <a href="https://www.bigmarker.com/communities/GlobalMathDept/conferences">GMD</a> archives, but I didn't find very much. If you know of something I missed, please comment below!!</span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">One of the articles I found listed <a href="http://www.teachthought.com/uncategorized/10-ways-literacy-can-promote-a-deeper-understanding-of-math/">10 ways Literacy Can Promote a Deeper Understanding of Math</a>. I found it interesting that most of the items listed are things we do naturally in math class, but that it's important to formalize verbal explanations on paper. </span><span style="color: #0c343d; font-family: "verdana" , sans-serif;">I thought a great "baby step" was to take discussions and put them online, which encourages students to write, edit, and read other responses. </span><br />
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<a href="https://4.bp.blogspot.com/--41f6ai6IXY/V-U8UuYMqOI/AAAAAAAABU4/fuxBNp1C_bAjwaA08mmOYDHsAPn_L7AuwCLcB/s1600/image001.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="230" src="https://4.bp.blogspot.com/--41f6ai6IXY/V-U8UuYMqOI/AAAAAAAABU4/fuxBNp1C_bAjwaA08mmOYDHsAPn_L7AuwCLcB/s320/image001.jpg" width="320" /></a></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">I also reached out to our county's SIOP & Differentiation coach. She does a training every semester on specific strategies for math to help our EL students. She has some incredible resources - check out her <a href="http://ellmatters.blogspot.com/">blog</a> and <a href="https://sites.google.com/a/gaston.k12.nc.us/esl/home/siop">resource site</a>!</span><br />
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<a href="https://4.bp.blogspot.com/-sv5fD1cJsZo/V-UjsTfCx8I/AAAAAAAABUc/Ggrf37A1HYclu3GcHZ0trWXBt1sVcTRLQCLcB/s1600/siop%2Bheader.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><img border="0" height="48" src="https://4.bp.blogspot.com/-sv5fD1cJsZo/V-UjsTfCx8I/AAAAAAAABUc/Ggrf37A1HYclu3GcHZ0trWXBt1sVcTRLQCLcB/s320/siop%2Bheader.png" width="320" /></span></a></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">A couple of my favorite resources from her site are the <a href="http://www.fresno.k12.ca.us/divdept/sscience/siop/siop_docs/InstructionalStrategiesActivities.pdf">Glossary of Strategies & Activities</a> and the <a href="https://drive.google.com/file/d/0B4AYZ6RXAEa5QVk1eHpQN3dEaDg/view">Bloom's Question Stems for ELs</a>. These resources are meant to support EL students, but the idea is that they're <b>necessary</b> for ELs, and beneficial for all students. I think so many times, it's easy to forget about this population within our schools. However, I'm trying to remember that ELs represent a microcosm of our larger student population when it comes to struggles with literacy and academic vocabulary. </span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Link up any math content literacy resources/articles/etc you've got below! </span><br />
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com3tag:blogger.com,1999:blog-1923582105875028879.post-27169251331119940242016-01-30T07:40:00.000-08:002016-02-01T11:19:48.091-08:00Using Mobiles to Solve Equations<span style="color: #0c343d; font-family: "verdana" , sans-serif;">This is a great idea for students to really show what they know with numbers and solving equations. </span><br />
<span style="color: #0c343d; font-family: "verdana" , sans-serif;"><br />I found the link on one of <a href="http://www.resourceaholic.com/p/maths-gem.html">Resourceaholic's Gem lists</a>. The post led me to <a href="http://donsteward.blogspot.co.uk/">Don Steward's Median blog</a>. This is his activity. There are 3 posts: '<a href="http://donsteward.blogspot.co.uk/2014/11/mobiles.html">mobiles</a>,' then '<a href="http://donsteward.blogspot.co.uk/2014/11/mobile-inequalities.html">mobile inequalities</a>,' and finally '<a href="http://donsteward.blogspot.co.uk/2014/11/mobile-moments.html">mobile moments</a>'.</span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;"><br /> I really like these activities! They are so adaptable to just about anything. Elementary students through high school students could work with adapted versions of these. Students do so much halving, doubling, sequencing, comparing, etc. <br /><br /><br /> </span><br />
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</span><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><br /><br />I can also see adapting this for fractions or decimals. <br /><br />Maybe radians? Definitely integers...<br /><br />This could even become an activity framework. It could be used for something like basic function notation, students evaluate to a number, then use that number to balance. (Almost as a self-check method)<br /><br />Have a great weekend everyone!</span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">UPDATE: There's also a website called SolveMe, which has these same types of problems, without numbers or expressions. It uses the same logic and reasoning skills, but with a bit friendlier interface. <a href="http://solveme.edc.org/Mobiles.html">Here's the link</a>. </span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;"><br /></span>Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com5tag:blogger.com,1999:blog-1923582105875028879.post-46144157523578388102016-01-29T06:47:00.000-08:002016-01-29T06:47:18.646-08:00Do you know where 2/11 is on a blank circle?<span style="color: #0c343d; font-family: Verdana, sans-serif;">I've been going through the <a href="http://www.resourceaholic.com/p/maths-gem.html">gem list from resourceaholic</a>. I found it about a month ago, bookmarked it, created a checklist in <a href="http://learningwithtape.blogspot.com/2016/01/my-favorite-trello-mtbos-blogging.html">Trello </a>to keep track of my progress, and have been slowly working my way through all 40-something lists. There are so many great ideas, links, and other people to follow embedded in these short, 5-item posts. When I finish up a big project or need a brain break or just need to be inspired, I open up the next one and explore a little. </span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">Today, I got to <a href="http://www.resourceaholic.com/2014/11/gems15.html">Gem #15</a>. </span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">The first item is this cute little fraction applet, called <a href="http://mathmagi.com/slice-the-pie.html">Slice the Pie</a>. </span><br />
<span style="color: #0c343d; font-family: Verdana, sans-serif;">To play the game, you hover over a circle, and click where you want the shaded part of the circle to stop. (So you could shade a tiny slice, or a giant slice)</span><br />
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<a href="http://1.bp.blogspot.com/-tZcpgQG2Klg/Vqt6aoCEaNI/AAAAAAAABN0/mnU3SsLX1Ro/s1600/pie.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://1.bp.blogspot.com/-tZcpgQG2Klg/Vqt6aoCEaNI/AAAAAAAABN0/mnU3SsLX1Ro/s320/pie.png" width="293" /></a></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">The object of the game is to shade the amount of the pie indicated by the fraction shown. However, there aren't any partitions shown (just a blank circle). You have to use your own number sense to get as close as you can. Do you know where 2/11 is on a blank circle? 1/12? 23/30?</span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">I love the estimation skills, the number sense, & how relative number sizes are all a part of this easy, quick, little game. I can even see using something like this when starting the unit circle. (Can you shade for pi radians? pi/4 radians?)</span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">My first try, I scored a 49. Can you beat that?</span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;"><br /></span>Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com5tag:blogger.com,1999:blog-1923582105875028879.post-1557844794809022222016-01-26T18:00:00.000-08:002016-01-27T05:25:21.600-08:00My Favorite: Trello #MTBoS Blogging Initiative<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Warning: This post is LONG. If you hate reading & just want my favorite thing, <a href="https://trello.com/inspiration/education">go here</a> and explore. Or scroll ALL the way down. Have fun. </span><br />
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;">Time to circle back to prompt #2 from the <a href="https://exploremtbos.wordpress.com/posts/">MTBoS Blogging Initiative</a>. </span><br />
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<span style="font-family: "trebuchet ms" , sans-serif;"><u>Here's the prompt: </u><span style="line-height: 28.432px;">Our week two blogging challenge is to simply blog about one of your favorite things. Called a “My Favorite,” it can be something that makes teaching a specific math topic work really well. It does not have to be a lesson, but can be anything in teaching that you love! It can also be something that you have blogged or tweeted about before. Some ideas of favorites that have been shared are:</span></span></div>
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<li style="border: 0px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="font-family: "trebuchet ms" , sans-serif;">A lesson (or part of one) that went great</span></li>
<li style="border: 0px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="font-family: "trebuchet ms" , sans-serif;">A game your students love to play</span></li>
<li style="border: 0px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="font-family: "trebuchet ms" , sans-serif;">A fun and/or effective way to practice facts</span></li>
<li style="border: 0px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="font-family: "trebuchet ms" , sans-serif;">A website or app you love to use in class</span></li>
<li style="border: 0px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="font-family: "trebuchet ms" , sans-serif;">An organizational trick or tip that has been life changing</span></li>
<li style="border: 0px; font-style: inherit; font-weight: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="font-family: "trebuchet ms" , sans-serif;">A product that you use in your classroom that you can’t live without!</span></li>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.432px;">My favorite thing lately is <a href="https://trello.com/">Trello</a>, and it fits #2, 3, 4, & 5 on the list above!</span></span></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.432px;">Trello will change your life if you let it, I promise. ;)</span></span></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.432px;">I'll walk you through what it is, & the amazing education potential, and then I'll share the ways I like to use it. </span></span></div>
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<a href="http://2.bp.blogspot.com/-Dopmum0IQC4/VqZQC649FaI/AAAAAAAABMo/8HOt969Etrg/s1600/Screenshot%2B%25283%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><img border="0" src="http://2.bp.blogspot.com/-Dopmum0IQC4/VqZQC649FaI/AAAAAAAABMo/8HOt969Etrg/s1600/Screenshot%2B%25283%2529.png" /></span></a></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.432px;"><b><u>What is it?</u></b></span></span></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.432px;">From the Trello site:</span></span></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 1.2em; text-align: center;"><b>Trello is the free, flexible, and visual way to organize anything with anyone. </b></span><span style="line-height: 28.8px;">Drop the lengthy email threads, out-of-date spreadsheets, no-longer-so-sticky notes, and clunky software for managing your projects. Trello lets you see everything about your project in a single glance.</span></span></div>
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<span style="line-height: 28.8px;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Trello is really the ultimate organization tool. You can very visually organize projects, lesson plans, ideas, or even use it like Pinterest. It's easy to collect and organize and reorder ideas, attachments, and links. It's incredibly easy to use on any device. Sharing is easy. Updating your progress on items is easy. And it connects with <a href="https://ifttt.com/">IFTTT</a>. (Can you tell I love it yet?!? haha)</span></span></div>
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<span style="line-height: 28.8px;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Trello has 3 parts: </span></span></div>
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<li><span style="line-height: 28.8px;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Boards (think like a Pinterest board - these are general topics, like Unit 1) </span></span></li>
<li><span style="line-height: 28.8px;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Lists (columns, or sub-boards, such as topics within a unit)</span></span></li>
<li><span style="line-height: 28.8px;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Cards (individual pieces of information, like activities for a specific topic)</span></span></li>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">I should mention that cards can include labels, color coding, due dates, attachments, links, comments, pictures, and can be assigned to certain people. </span></span></div>
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Trello is free as long as you're ok with solid colors for backgrounds instead of custom pictures. Here's the link to the <a href="https://trello.com/b/bKbdmCKB/welcome-board">welcome board</a> shown so the hands on peeps can understand what I'm saying. </span></span></div>
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<span style="line-height: 28.8px;"><b><u><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Ok, so what? Why should I care?</span></u></b></span></div>
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<span style="line-height: 28.8px;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Trello has infinite potential! </span></span></div>
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<span style="line-height: 28.8px;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;">In my personal life, I have boards for grocery lists, organizing quilt projects in different stages, keeping track of what's in the freezer (we do OAMC in my house), keeping track of chores & other good habits, gift ideas for family, and so much more. My husband is shared on several of these, so he can add/edit as needed. I'm a list girl, and Trello helps me keep all my lists electronically.</span></span></div>
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<span style="line-height: 28.8px;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Professionally, I find new ways almost every week to use Trello. </span></span></div>
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<span style="line-height: 28.8px;"><span style="color: #0c343d; font-family: "verdana" , sans-serif;">Here's the rundown. </span></span></div>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">Professional Development Approval & Progress</span></span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">My dept shares a board to discuss PD opportunities we will offer. We attach handouts, make to-do checklists, and communicate approval of funding all in one place. As each PD session moves through various levels of approval, its card progresses into new lists on the board, until it's finally sent to True North Logic, our county PD software.</span></span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">Brainstorming, & To-Do Lists</span></span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">categorized, with attachments or links as needed </span></span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">I use this board as my "thoughtbox." </span></span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">Future blog post ideas, activities or foldable ideas, etc. stay here until I get to them. </span></span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">I have "Resource" Boards for various math topics</span></span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">the lists are things like "quadratics" and each card is a link or idea</span></span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">I also have a list of places I like to look for questions, activities, etc.</span></span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">Sorting, ordering, etc activities. </span></span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">Example: <a href="https://trello.com/b/lvaNk5xC/exponential-functions-sort">Exponential Equations Warmup</a></span></span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">Students drag & drop matching cards together into a new list.</span></span></li>
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<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">I use Trello the same way I like to use the Post It Plus app (<a href="http://teachinghighschoolmath.blogspot.com/2015/03/using-post-it-plus-app-in-math-class.html">blog post for that is here</a>). Trello has the advantage of being possible on ANY device, including Chromebooks. Post It Plus is iPad/iPhone only.</span></span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">I want to make some ordering activities too - FDP, integer ops, etc. </span></span></li>
<li><span style="color: #0c343d; font-family: "verdana" , sans-serif;"><span style="line-height: 28.8px;">This is totally graph/picture/equation compatible - you just need a screenshot for the card image. </span></span></li>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif; line-height: 28.8px;">I also use Trello to collect my favorite things - very much like Pinterest. Here's the <a href="https://trello.com/b/LOubFTUZ/review-ideas-activities">link to my Review Games board</a>. Most ideas are from other MTBoS blogs. </span></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif; line-height: 28.8px;">Trello even has </span><a href="https://trello.com/inspiration/education" style="font-family: Verdana, sans-serif; line-height: 28.8px;">inspiration boards</a><span style="color: #0c343d; font-family: "verdana" , sans-serif; line-height: 28.8px;"> for you to look at, to get an idea of what it's capable of, in specifically education-related ways. There are some really cool ones - I especially like the project board & classroom newsletter. </span></div>
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<span style="color: #0c343d; font-family: "verdana" , sans-serif; line-height: 28.8px;">Have fun exploring!</span></div>
Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com2tag:blogger.com,1999:blog-1923582105875028879.post-50128255747469951842016-01-25T07:36:00.001-08:002016-01-25T07:36:54.476-08:00Better Questions #MTBoS Blogging Initiative<span style="color: #0c343d;">I may have skipped <a href="https://exploremtbos.wordpress.com/2016/01/17/week-2-of-the-2016-blogging-initative/">prompt #2</a> - I'll get back to it. :)</span><br />
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<span style="color: #0c343d;">In the meantime, I have this great resource to share that fits perfectly with the <a href="https://exploremtbos.wordpress.com/2016/01/24/week-3-of-the-2016-blogging-initiative/">prompt for this week</a>. </span><br />
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<span id="docs-internal-guid-fa1a95ba-7969-1d4a-860b-9e96214d5436"><span style="color: #0c343d;"><br />This resource was shared with me by one of our county's elem math curriculum facilitators. I've had a shortened version of this taped to my classroom document camera for several years, but never knew where it came from (I got it at a conference as a handout once upon a time, and didn't realize its value until I got home and looked at it). I am SO HAPPY to have the entire list, and to be able to give credit to Dr. Gladis Kersaint. This is a GREAT list!</span></span><div>
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<span style="font-family: Arial; font-size: 16px; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">100 Questions That Promote Mathematical Discourse </span></div>
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<span style="background-color: white; font-family: Arial; font-size: 22.6667px; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Help students work together to make sense of mathematics</span></span></h2>
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<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What strategy did you use?</span></span></div>
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<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Do you agree?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Do you disagree?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Would you ask the rest of the class that question?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Could you share your method with the class?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What part of what he said do you understand?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Would someone like to share ___?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Can you convince the rest of us that that makes sense?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What do others think about what [student] said?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Can someone retell or restate [student]’s explanation?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Did you work together? In what way?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Would anyone like to add to this?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Have you discussed this with your group? With others?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Did anyone get a different answer?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Where would you go for help?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Did everybody get a fair chance to talk, to use the manipulatives, or to be recorded?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How could you help another student without telling the answer?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How would you explain ___ to someone who missed class today?</span></span></div>
</li>
</ol>
<div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Refer questions raised by students back to the class.</span></span></div>
<h2 dir="ltr" style="line-height: 1.44; margin-bottom: 4pt; margin-top: 18pt;">
<span style="background-color: white; font-family: Arial; font-size: 22.6667px; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Help students rely more on themselves to determine whether something is mathematically correct</span></span></h2>
<ol start="19" style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Is this a reasonable answer?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Does that make sense?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Why do you think that? Why is that true?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Can you draw a picture or make a model to show that?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How did you reach that conclusion?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Does anyone want to revise his or her answer?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How were you sure your answer was right?</span></span></div>
</li>
</ol>
<h2 dir="ltr" style="line-height: 1.44; margin-bottom: 4pt; margin-top: 18pt;">
<span style="background-color: white; font-family: Arial; font-size: 22.6667px; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Help students learn to reason mathematically</span></span></h2>
<ol start="26" style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How did you begin to think about this problem?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What is another way you could solve this problem?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How could you prove that?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Can you explain how your answer is different from or the same as [student]’s?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Let’s see if we can break it down. What would the parts be?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Can you explain this part more specifically?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Does that always work?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Is that true for all cases?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How did you organize your information? Your thinking?</span></span></div>
</li>
</ol>
<h2 dir="ltr" style="line-height: 1.44; margin-bottom: 4pt; margin-top: 18pt;">
<span style="background-color: white; font-family: Arial; font-size: 22.6667px; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Help students evaluate their own processes and engage in productive peer interaction</span></span></h2>
<ol start="35" style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What do you need to do next?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What have you accomplished?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What are your strengths and weaknesses?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Was your group participation appropriate and helpful?</span></span></div>
</li>
</ol>
<h2 dir="ltr" style="line-height: 1.44; margin-bottom: 4pt; margin-top: 18pt;">
<span style="background-color: white; font-family: Arial; font-size: 22.6667px; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Help students with problem comprehension</span></span></h2>
<ol start="39" style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What is this problem about? What can you tell me about it?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Do you need to define or set limits for the problem?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How would you interpret that?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Would you please reword that in simpler terms?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Is there something that can be eliminated or that is missing?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Would you please explain that in your own words?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What assumptions do you have to make?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What do you know about this part?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Which words were most important? Why?</span></span></div>
</li>
</ol>
<h2 dir="ltr" style="line-height: 1.44; margin-bottom: 4pt; margin-top: 18pt;">
<span style="background-color: white; font-family: Arial; font-size: 22.6667px; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Help students learn to conjecture, invent and solve problems</span></span></h2>
<ol start="48" style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What would happen if ___? What if not?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Do you see a pattern?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What are some possibilities here?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Where could you find the information you need?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How would you check your steps or your answer?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What did not work?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How is your solution method the same as or different from [student]’s?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Other than retracing your steps, how can you determine if your answers are appropriate?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What decision do you think he or she should make?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How did you organize the information? Do you have a record?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How could you solve this using (tables, trees, lists, diagrams, etc.)?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What have you tried? What steps did you take?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How would it look if you used these materials?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How would you draw a diagram or make a sketch to solve the problem?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Is there another possible answer? If so, explain.</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How would you research that?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Is there anything you’ve overlooked?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How did you think about the problem?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What was your estimate or prediction?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How confident are you in your answer?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What else would you like to know?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What do you think comes next?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Is the solution reasonable, considering the context?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Did you have a system? Explain it.</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Did you have a strategy? Explain it.</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Did you have a design? Explain it.</span></span></div>
</li>
</ol>
<h2 dir="ltr" style="line-height: 1.44; margin-bottom: 4pt; margin-top: 18pt;">
<span style="background-color: white; font-family: Arial; font-size: 22.6667px; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Help students learn to connect mathematics, its ideas and its application</span></span></h2>
<ol start="74" style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What is the relationship of this to that?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Have we ever solved a problem like this before?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What uses of mathematics did you find in the newspaper last night?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What is the same?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What is different?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Did you use skills or build on concepts that were not necessarily mathematical?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Which skills or concepts did you use?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What ideas have we explored before that were useful in solving this problem?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Is there a pattern?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Where else would this strategy be useful?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How does this relate to ___?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Is there a general rule?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Is there a real-life situation where this could be used?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How would your method work with other problems?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What other problem does this seem to lead to?</span></span></div>
</li>
</ol>
<h2 dir="ltr" style="line-height: 1.44; margin-bottom: 4pt; margin-top: 18pt;">
<span style="background-color: white; font-family: Arial; font-size: 22.6667px; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Help students persevere</span></span></h2>
<ol start="89" style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Have you tried making a guess?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What else have you tried?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Would another recording method work as well or better?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Is there another way to (draw, explain, say) that?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Give me another related problem. Is there an easier problem?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How would you explain what you know right now?</span></span></div>
</li>
</ol>
<h2 dir="ltr" style="line-height: 1.44; margin-bottom: 4pt; margin-top: 18pt;">
<span style="background-color: white; font-family: Arial; font-size: 22.6667px; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Help students focus on the mathematics from activities</span></span></h2>
<ol start="95" style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What was one thing you learned (or two, or more)?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">Where would this problem fit on our mathematics chart?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">How many kinds of mathematics were used in this investigation?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What were the mathematical ideas in this problem?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What is the mathematically different about these two situations?</span></span></div>
</li>
<li dir="ltr" style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.92; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; font-family: Arial; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #0c343d;">What are the variables in this problem? What stays constant?</span></span></div>
</li>
</ol>
<div>
<span style="color: #0c343d; font-family: Arial;"><span style="font-size: 14px; line-height: 26.88px; white-space: pre-wrap;"><br /></span></span></div>
<div>
<span style="color: #0c343d; font-family: Arial;"><span style="font-size: 14px; line-height: 26.88px; white-space: pre-wrap;">Google Doc version <a href="https://docs.google.com/document/d/1374nQAj9-aI7LIEcFaaIp0sOCfnAo9nPptxqc-_8AVA/edit?usp=sharing">here</a>. </span></span></div>
<div>
<span style="color: #0c343d; font-family: Arial;"><span style="font-size: 14px; line-height: 26.88px; white-space: pre-wrap;">Stay warm, friends! (And enjoy your snow/ice day GCS friends!)</span></span></div>
</div>
Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com3tag:blogger.com,1999:blog-1923582105875028879.post-24547185294799823612016-01-11T07:28:00.000-08:002016-01-11T07:28:12.581-08:00One Good Thing (or perhaps a few)Aaaahhh...Monday!<br />
The <a href="https://exploremtbos.wordpress.com/2016/01/10/week-1-of-the-2016-blogging-initiative/">latest blogging prompt from the MTBoS</a> was just released. I've got to say, prompts work for me. So do premade whatchamacallits. :)<br />
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<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-RwhkAZs4aGg/VpO_eu9oM7I/AAAAAAAABLw/T9aTu6s4LAI/s1600/unnamed.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-RwhkAZs4aGg/VpO_eu9oM7I/AAAAAAAABLw/T9aTu6s4LAI/s1600/unnamed.png" /></a></div>
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Ok, well here are my good things for today.<br />
<br />
<ul>
<li>I finished creating editable copies of ALL of the NC Final released exams. Now I can copy & paste into other worksheets, packets, notes, activities, & games to my heart's content. I also made a smart notebook file for each one with one slide per question, with a hint & answer key "hidden" on the bottom of the page. If you're in NC and want the files, <a href="mailto:cbspencer@gaston.k12.nc.us">email me</a> with what subjects you'd like. (Math 1, 2, 3, AFM, & Precal, or everything!)<br /></li>
<li>I found <a href="http://ecfmath.weebly.com/">Lauren Russell's weebly</a>. If you're in NC and a Math 1 teacher, this is a BIG DEAL. She's created a mini-NC-based-MTBoS inside of Google Drive. And you can join. She has prep packets, practice tests, and tons of other awesome activities. Seriously, her page is a WEALTH of resources, and I'm super grateful she shares with everyone.<br /></li>
<li>I also found <a href="http://www.resourceaholic.com/">www.resourceaholic.com/</a> and I'm super excited to start digging through these resources. It's going to take me a LONG time to just get through the gems sections (a collection of 5 amazing math ideas per week. There's an archive! #bliss)<br /></li>
<li>The <a href="http://www.fishing4tech.com/mtbos.html">MTBoS search engine</a> is something I didn't know existed. I know now. I'm definitely on resource overload these days, trying to gear up for the start of second semester! This is now a permanent tab in my browser.<br /></li>
<li>I found out that my grandfather taught my boss's dad in high school in Madison County years ago! They both left Mars Hill in the 70s/80s, but have been back there for several years now, and live within 5 minutes of each other. My boss & I have been spending Christmases about a mile apart without knowing it (even though we live about 3 hours from there)! Small world!</li>
</ul>
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com1tag:blogger.com,1999:blog-1923582105875028879.post-67177595844630839442016-01-06T10:13:00.000-08:002016-01-06T10:13:29.711-08:00Cool Thing of the DayI promise this post isn't spam...I just really like this tech tool!!<br />
I got a gift for Christmas that I have been using like CRAZY ever since I got it.<br />
<br />
It's an eWriter called <a href="https://www.amazon.com/Boogie-Board-9-7-Inch-eWriter-ST1020001/dp/B00E8CIGCA/ref=sr_1_2?s=electronics&ie=UTF8&qid=1452103033&sr=1-2&keywords=boogie+board+sync">Boogie Board Sync</a>. Super cool!<br />
<br />
There are $20 versions that act just like scratch paper, but don't use paper. It's basically a magna-doodle for adults. I have one of those (and have for a while) but I mostly just use it to replace a billion post it notes & to do lists on my desk.<br />
<br />
The one I got for Christmas is a bit more (around $70-80), but you can save your drawings/writings/etc. using bluetooth. Which means I can hand-write solutions, and save them to post for students! We all know there are times that creating a geometric drawing or some math mumbo-jumbo that just isn't convenient to create electronically.<br />
<br />
This thing lets me sketch out what I want, & save it as an image. I can edit it later, highlight, etc. once it's saved on my iPad. Then I can use the images in tests, worksheets, or just to project when going over answers.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-wtxwg95q2Sg/Vo1YeG8XQ7I/AAAAAAAABLc/hsEdsczw49g/s1600/BB_00014.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-wtxwg95q2Sg/Vo1YeG8XQ7I/AAAAAAAABLc/hsEdsczw49g/s320/BB_00014.png" width="220" /></a></div>
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Just thought I'd share! :)<br />
<br />
Thoughts for other uses:<br />
<br />
<ul>
<li>Differentiation during small group time. It would be so easy to write out 1-2 problems, click save, and export to classroom, or drive, for students to work on. </li>
<li>Use live mode with students & smartboard - this can function just like an airliner</li>
<li>Student observation notes. Maybe connected to evernote, and saved in some sort of classroom file? I'm always writing myself notes about what I need to work with a student a bit more on, or misconceptions I'm seeing. </li>
</ul>
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<br />
<br />Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com2tag:blogger.com,1999:blog-1923582105875028879.post-51899733079056697422016-01-04T06:50:00.001-08:002016-01-04T06:56:52.866-08:00Dusting off my blog for the #MTBoS Blogging Initiative<span style="color: #0c343d; font-family: Verdana, sans-serif;"><br /><br />I, Carolyn Spencer, resolve to blog in 2016 in order to open my classroom up and share my thoughts with other teachers. I hope to accomplish this goal by participating in the <a href="https://exploremtbos.wordpress.com/2016/01/03/kicking-off-the-2016-blogging-initiative/">January Blogging Initiative</a> hosted by<a href="https://exploremtbos.wordpress.com/"> Explore MTBoS</a>.<br /><br />You, too, could join in on this exciting adventure. All you have to do is dust off your blog and get ready for the first prompt to arrive January 10th!</span>Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com0tag:blogger.com,1999:blog-1923582105875028879.post-43724174317496180842015-09-16T11:13:00.001-07:002015-09-16T11:13:28.014-07:00A new year, a new job, & a fresh perspective<span style="color: #0c343d; font-family: Verdana, sans-serif;">By now, most teachers in my county have found out - I've left the classroom, and started a brand new job as the high school math curriculum facilitator for Gaston County Schools. As such, and being that this blog is personal, not professional, I feel the need to insert a disclaimer here: the ideas here are mine, and don't represent GCS's views, opinions, goals, etc. </span><br />
<span style="color: #0c343d; font-family: Verdana, sans-serif;"><br /></span>
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<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-VhdK24nzR88/VfmxNltcTrI/AAAAAAAABJE/8JMgLLB_wR8/s1600/Learning%2Bwith%2BTape.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://2.bp.blogspot.com/-VhdK24nzR88/VfmxNltcTrI/AAAAAAAABJE/8JMgLLB_wR8/s320/Learning%2Bwith%2BTape.jpg" width="320" /></a></div>
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<br />
<span style="color: #0c343d; font-family: Verdana, sans-serif;">It was a big leap of faith for me to even apply, but I'm so glad I did. The past three and a half weeks, I've learned more about myself, my own teaching style, and the profession as a whole than I ever would have locked up in my own little classroom. </span><br />
<span style="color: #0c343d; font-family: Verdana, sans-serif;"><br /></span>
<span style="color: #0c343d; font-family: Verdana, sans-serif;">It's really made me think about how often teachers get an opportunity to watch each other. Those of us familiar with the MTBoS tend to feel more connected, because we read and watch what each others do with their students. I've learned though, that so many teachers DON'T spend time online connecting with peers. We're the rarity. MOST teachers instead learn of new ideas from their school based peers. </span><br />
<span style="color: #0c343d; font-family: Verdana, sans-serif;"><br /></span>
<span style="color: #0c343d; font-family: Verdana, sans-serif;">When I was in the classroom, I was constantly sharing ideas I had found. In fact, it was a completely normal thing for me to burst into a coworker's room during our common planning period, and to say something like, "Check out this amazing (fill in activity/idea/resource here)" on a near daily basis. I'm an idea gatherer. </span><br />
<span style="color: #0c343d; font-family: Verdana, sans-serif;"><br /></span>
<span style="color: #0c343d; font-family: Verdana, sans-serif;">I want other teachers to be able to experience that rush of inspiration that happens when you can see a new way to connect students with content. That's the feeling that keeps <b><i>good </i></b>teachers from feeling burned out (or at least, it does most of the time). </span><br />
<span style="color: #0c343d; font-family: Verdana, sans-serif;"><br /></span>
<span style="color: #0c343d; font-family: Verdana, sans-serif;">So I'll end with a few questions I'm pondering today:</span><br />
<br />
<ul>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">How can we, as teachers, show each other our classrooms in more tangible ways? How can we give each other a better picture of how a lesson went, how our students interacted with the material, or how our energy/style gave the lesson a certain flair that increased engagement and retention?</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">As I've done hundreds of walkthroughs over the past (almost) month, I've noticed the <i style="font-weight: bold;">significant impact </i>that a teacher's questioning style has during a lesson (especially during direct instruction). How can we share this very subtle art with each other in order to improve?</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">How can we, as the online-engaged, blog-reading, globally-connected teachers encourage others to reach out, and engage? </span></li>
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com1tag:blogger.com,1999:blog-1923582105875028879.post-37889363370238792072015-07-23T12:19:00.001-07:002015-07-23T12:19:37.441-07:00Playing SPOONS in Math Class: Ideas, Template, & a Download <div class="separator" style="clear: both; text-align: center;">
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<span style="color: #0c343d; font-family: Verdana, sans-serif;"><a href="https://twitter.com/treverreeh/status/624258670080212996">I saw a tweet today</a> that really got me thinking. It leads you to <a href="http://www.games4gains.com/teaching-ideas/2015/4/23/equivalent-fractions-game">a game of SPOONS with equivalent fractions</a> and the directions to play the game, in case you've never played the card deck version. #TMC15 is happening, and I'm at GCS Pinnacle feeling a bit left out of the fun. So when I saw this, I knew I had to whip up a batch of cards. </span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">Pinnacle's topic of the day is Gamification/Gamed-Based Learning (turns out, those are 2 different things). This morning, we played Minecraft, learned about the SERIOUS educational potential there. I'm still pondering if there's something I can use for upper level Secondary Math. Comment below if you think of something. In the meantime, I'm content to see its value for other content areas, particularly in MS Social Studies/History. We ran through WWI and colonization simulations this morning, and it was powerful, even for adults. VERY COOL STUFF. </span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">This afternoon, our assignment was to create a game. I'm always on the lookout for new games, but I haven't created very many. So it seemed more productive for me to take this new (to me) idea, and make it useful for my grade level. </span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">Step 1: Create cards. <a href="https://sites.google.com/site/spenceralgebra/home/teacher-files/Go%20Fish-Old%20Maid-Memory-War%20Template.docx?attredirects=0&d=1">Click here for my 9-card template</a>, which creates 9 playing cards from every sheet of cardstock. Most of the time, I copy this onto cardstock, cut apart, then write on the cards. Occasionally, I'll type up a batch. You need 4 cards per player (I'm planning on groups of 4-6) with a few (4-8) extra. </span><br />
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">Step 2: Decide on a topic. Spoons is fast paced. It's perfect for skill-and-drill type questions, or at least topics that can be identified/classified/etc. quickly. </span><br />
<span style="color: #0c343d; font-family: Verdana, sans-serif;">Here's the list I can think of off of the top of my head (feel free to add more in the comments!) You will need 4 components/equivalent forms to match up. </span><br />
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<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">Linear equations (matching slope/y-int/table/equation)</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">Linear equations (multiple forms - words/table/equation/graph)</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">Exponent Rules</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">Quadratic equations (matching vertex form, vertex, graph, & ??? )</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">Simplifying radicals (perhaps matching like radicands)</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">Circles (matching equation, radius, graph, and center)</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">Transformations (1 equation w mult. transf., other 3 cards have transf. )</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">Factored form of polynomial & roots, maybe with # of real roots/# complex</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">Exp. Growth & Decay (situation, equation, % rate, growth or decay)</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">Parallel Lines & Transversals (match up 4 examples of alt int, etc.)</span></li>
<li><span style="color: #0c343d; font-family: Verdana, sans-serif;">Triangle Congruence (match up 4 examples of SSS, etc.)</span></li>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">I'm sure there are lots more. Typing this list, it occurred to me that ALL of these would be great post-it activities as well. (Need a reminder about that? <a href="http://teachinghighschoolmath.blogspot.com/2015/03/using-post-it-plus-app-in-math-class.html">Check out this post.</a>) I need to do a better job this year of allowing students to get some practice in a non-worksheet way. </span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">My friend @sgibson and I wrote up this set for linear equations pretty quickly. </span></div>
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<a href="http://4.bp.blogspot.com/-IMGDbnY8qOI/VbE07hfacqI/AAAAAAAABHo/SMIpwHj1S1Y/s1600/IMG_0403.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="239" src="http://4.bp.blogspot.com/-IMGDbnY8qOI/VbE07hfacqI/AAAAAAAABHo/SMIpwHj1S1Y/s320/IMG_0403.JPG" width="320" /></a></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">I typed out a batch of simplifying square roots - students would simplify mentally, then match up based on the simplified radicand. An answer key/master list is included! It took me about 20 mins. from start to finish - not too bad for a new activity! <a href="https://sites.google.com/site/spenceralgebra/home/teacher-files/simplifying%20radicals.docx?attredirects=0&d=1">Click here to download it. </a></span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;"><u>To wrap up, here's my Top 10 take-aways from #GCSPinnacle this week:</u></span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">1. CANVA is amazing. I've used it 10+ times in 2 days. LOVE. </span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">2. Badges work. If adults love it, so can high school kids. </span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">3. It's hard to find teaching techniques that work for all content areas. Some just won't. And that's ok. </span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">4. Sitting in a desk every day is NOT any easier than teaching. It takes serious personal motivation to stay focused. </span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">5. There's not a gazebo in McAdenville anymore. There IS one 5 seconds from the Rader Center. </span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">6. People get goofy after sitting in the same room for 4 days straight. </span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">7. I need to be on Twitter more. #ILiketoHashtag</span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">8. I need to share more, and worry about having "finished products" less. </span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">9. You can accomplish a LOT of planning when you're not focused on 1 topic (like what's happening next week, or tomorrow) but rather on an entire course.</span></div>
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<span style="color: #0c343d; font-family: Verdana, sans-serif;">10. Cutesy activities usually make me wince, but they really do build a sense of teams. (Shoutout to People Machines & our toaster!)</span></div>
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com1tag:blogger.com,1999:blog-1923582105875028879.post-19274413583780943272015-07-21T08:33:00.002-07:002015-07-21T08:33:29.526-07:00Review Fun: How to Play the Dice Game<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-CT2UAOPZ2nI/Va5hA6RGPDI/AAAAAAAABGk/4o6FfOnX0mg/s1600/MANHATTAN.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><img alt="" border="0" height="266" src="http://1.bp.blogspot.com/-CT2UAOPZ2nI/Va5hA6RGPDI/AAAAAAAABGk/4o6FfOnX0mg/s320/MANHATTAN.png" title="How to Play the Dice Game" width="320" /></span></a></td></tr>
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<span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br />This great, low-prep, EASY review game was shared with me by my classroom neighbor. He heard about it from a friend at his last school. Who knows where this game has its roots?!</span><div>
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<span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><u>SETUP</u>:</span></div>
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<li><span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Game template file (Download it <a href="https://sites.google.com/site/spenceralgebra/home/teacher-files/Dice%20Game%20Template.notebook?attredirects=0&d=1">here</a>) on SmartBoard</span></li>
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<li><span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Medium Tech: Don't have SmartNotebook software? Go to <a href="http://express.smarttech.com/">express.smarttech.com</a></span></li>
<li><span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">No/Low Tech: Use real dice and display the 1-6 choices & score on the board. </span></li>
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<li><span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Change #1-4 to be 4 topic "groups" that you want to review. Have questions to read aloud or display (task cards are great for this).</span></li>
<li><span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Students need to be in teams and have scrap paper/dry erase boards for their work.</span></li>
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<span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><u>GAMEPLAY</u>:</span></div>
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<span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">One student from the 1st team comes up to the board and hits the dice to roll them. Their team may CHOOSE which number they want. (So if they roll a 1 and a 3, they can choose which category to answer a question from. The only time 6 is chosen is if they roll a double 6.) Teams continue to roll until they answer a question. I also make a double 5 the "special roll" where they can erase 2 points. </span></div>
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<span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">I don't allow negative points, so there's no use for them to choose a 5 until another team has points.</span></div>
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<span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Each correct answer earns their team 1 point. They work together to answer, and may only answer one time. If they are incorrect, I allow any other team to "steal" the point. </span></div>
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<span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><u>WINNER</u>:</span></div>
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<span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">The team with the most points wins. I keep score in the boxes at the bottom of the page. We usually play until a pre-determined time, so that the game doesn't take over an entire class period. </span><span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><br /></span>
<u><span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">WHAT I LOVE: </span></u><br />
<span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Basically no prep. Works with any content.</span><br />
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<u><span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">ISSUES/THINGS TO CHANGE:</span></u><br />
<span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">Sometimes they'll avoid a certain category. If that happens, I replace an "overused" topic with the topic they're avoiding (for example, #1 might start out as absolute value, and end up half way through the game as direct/inverse variation). I've also been known to have a "random" category on one of the numbers to fill in what I think they need. </span><br />
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<span style="color: #0c343d; font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">I also want to make students individually accountable for their answers - in the future, I can see myself using Nearpod for them to send in their responses with work, <a href="http://learningwithtape.blogspot.com/2015/02/bingo-20-nearpod-app-smash.html">like I do with BINGO</a>. Sometimes the tech isn't always available on the fly, so I'd love any ideas for a low-tech way to collect their work without having to grade a bunch of messy papers. </span><br />
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com2tag:blogger.com,1999:blog-1923582105875028879.post-217754646090975252015-07-20T13:27:00.002-07:002015-07-20T13:27:54.623-07:00Summer PD, and WBWO<div class="separator" style="clear: both; text-align: center;">
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Happy Summer!<br />
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This week, the Pinnacle team is meeting for our Summer PD sessions. On today's agenda: Google Classroom, personalized learning, and so much more. My brain is full.<br />
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Our summary assignment for today: 3-2-1. So here we go!<br />
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3 Things I Found Out:<br />
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<li>Canva.com (or the Canva app) is free, and pretty amazing. The graphics on this post came from Canva, and it only took about 5 minutes to create both. I can see this in my classroom for our presentations, and maybe to create some classroom displays. Most of the fonts I love are already added. </li>
<li>Our neighboring school district has committed to having every school use personalized learning for their students by 2018. We talked a lot about what that means for us, and if we could start implementing some of these techniques in our classrooms (perhaps one unit at a time)</li>
<li>(This one was by accident, but still awesome) IFTTT connects with the Amazon Echo! I was one of the lucky people that snagged one of these on Prime Day (they sold out in seconds). If This Then That is a great website for streaming your life, but I might also find a couple of ways to use this in planning. We'll see. </li>
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2 Interesting Things:<br />
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<li>Kagan Talking Chips actually works - we used paperclips today, and I was surprised to see that after a few minutes, it really helped keep the conversation going. There was a slight pressure to use all of your chips, and it forced me to speak up. </li>
<li>CopyDown as an add-on is also pretty useful. It lets you use formulas for Google Form responses, even before all of the responses have been completed. </li>
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1 Question I Have:<br />
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<li>Can personalized learning be implemented in a HS Math classroom without SBG? There wasn't ANY talk of SBG this morning (mostly because we're a K-12 group focused on technology). My concern is students that move at their own pace/on their own pathway won't all "end up" at standard proficiency. Is that ok? I don't know. Does a kid that "meets" his goal of a below-grade achievement get a 70, AND a kid that "meets" her goal of a above-grade achievement also get a 70? Does SAME GROWTH=SAME GRADE? </li>
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Since I don't have the answer, let's move on. I promised before to explain some of my review games, and this one's an easy one that I use A LOT. </div>
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<a href="http://3.bp.blogspot.com/-97_2cjhMEzY/Va1UPcAoIoI/AAAAAAAABGI/OlCkmHhDDbk/s1600/QUINOA.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="http://3.bp.blogspot.com/-97_2cjhMEzY/Va1UPcAoIoI/AAAAAAAABGI/OlCkmHhDDbk/s320/QUINOA.png" width="320" /></a></div>
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<u>SETUP</u>: </div>
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Students need dry erase boards and markers, or a device with a doodling app. </div>
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Teacher needs questions, answer key, and a space on the board. </div>
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Each kid needs to write their name on the board with 3 X's underneath their name. (I used to make a template for each class with this done, but it takes only 2-3 mins. to have them write their name, and it lets them get their supplies as well.)</div>
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<u>GAME PLAY:</u></div>
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The game works just like Grudgeball - but students compete as individuals. I got the idea from <a href="http://nathankraft.blogspot.com/2013/05/i-shall-never-play-review-game-again.html">this blog post about exponents</a> from Nathan Kraft. </div>
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I read/show/display a question, and EVERY student works it out on their own board. I walk around, and when they get it right, I tell them to line up at the board. Each right answer means they get to erase someone's X. I pause every few minutes to "supervise" the erasing, so that we don't have a division of people standing/sitting that got the question right/wrong. </div>
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<u>WINNER</u>: </div>
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It's an easy way to do a skill drill that doesn't make them want to whine. Winner is the kid with the last X! (It's always a quiet kid that doesn't do anything to draw attention to themselves.)</div>
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My favorite thing about this game: the smart kid doesn't win. The kid(s) that gets the most right has the most CONTROL over who wins, but can't usually win (Since typically, the other kids will erase the X's from the "smart" group right away). </div>
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com1tag:blogger.com,1999:blog-1923582105875028879.post-52743688826057465862015-06-08T12:51:00.000-07:002015-07-21T08:34:44.740-07:00Exam Review, An Awesome Quadratic Question, & Problem-AtticWell, it's finally exam week.<br />
NC has standardized tests for each subject for final exams. My kids (and I!) are just worn out.<br />
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<a href="http://3.bp.blogspot.com/-NcvbiVvlzdo/VXXxvdDPgLI/AAAAAAAABEo/dut7ZUk4tbA/s1600/download.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="227" src="http://3.bp.blogspot.com/-NcvbiVvlzdo/VXXxvdDPgLI/AAAAAAAABEo/dut7ZUk4tbA/s320/download.png" width="320" /></a></div>
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I've yet to find a really effective method for final review. We usually play a game a day.<br />
A couple of my favorites include:<br />
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<li><a href="http://mathequalslove.blogspot.com/2012/10/review-auction-game-for-solving.html">Auction game</a></li>
<li><a href="http://mathequalslove.blogspot.com/2014/04/place-your-bets.html">ABCD Gambling</a></li>
<li><a href="http://learningwithtape.blogspot.com/2015/07/summer-pd-and-wbwo.html">White-Board Wipe-Out</a></li>
<li><a href="http://learningwithtape.blogspot.com/2015/07/review-fun-how-to-play-dice-game.html">Dice Game</a></li>
<li><a href="http://mathtalesfromthespring.blogspot.com/2009/10/ghosts-in-graveyard.html">Ghosts in the Graveyard</a></li>
<li>And of course lots of dry-erase board practice</li>
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We also create 1 study page for each unit, with practice problems for key topics. We typically have about 7-8 school days for review, and we do 2 units per day. The last day before exams, we play life-size Monopoly (I use the basic set up from <a href="http://mrpiedrasclassroom.blogspot.com/2013/10/monopoly-multi-unit-review-game.html">this blog post</a>). I typically use the released forms of the tests to practice with along the way, as well as lots of questions from problem-attic.</div>
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<a href="http://www.problem-attic.com/">Problem-attic</a> (which, by the way, if you've never heard of it, is completely AWESOME) has lots of released tests from many states, and you can search by test or topic. </div>
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Every once in a while, I find a question I really like. Here's the one I found this year that I LOVE. (From NY Regents Alg2 Exam Jan. 2014) It's short, but it packs in quite a bit of math into one teeny little sentence. </div>
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<a href="http://4.bp.blogspot.com/-6XrbX11j5jI/VXXupfGIhJI/AAAAAAAABEg/Am9sABLcfpg/s1600/Capture2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="55" src="http://4.bp.blogspot.com/-6XrbX11j5jI/VXXupfGIhJI/AAAAAAAABEg/Am9sABLcfpg/s320/Capture2.PNG" width="320" /></a></div>
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Using this site, you can create tests, quizzes, worksheets, etc. I typically print a couple of "flashcards" to project using my document camera, and we use them for games or dry-erase board practice. </div>
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<a href="http://3.bp.blogspot.com/-Aji-AhXnLdU/VXXupRfWS8I/AAAAAAAABEc/M4CGXivgLww/s1600/Capture.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="242" src="http://3.bp.blogspot.com/-Aji-AhXnLdU/VXXupRfWS8I/AAAAAAAABEc/M4CGXivgLww/s320/Capture.PNG" width="320" /></a></div>
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You can also use the flashcards function to create task cards using their questions! I use this feature all the time! I really love not having to make or pay for task cards, and you can color code sets by printing them out on colorful cardstock. There are also plenty of questions without answer choices. </div>
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We'll be testing until Wednesday, the last day of school. I've already got my summer to-do list for school started, and I'm sure it's only going to grow over the next few days. </div>
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com0tag:blogger.com,1999:blog-1923582105875028879.post-17768292129424547862015-05-01T11:47:00.000-07:002015-05-01T11:47:13.899-07:00Skitch Connect Four/Tic Tac Toe with Circle TermsHi everyone!<br />
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I thought it'd be best to start the first of May off with a blog post left over from April.<br />
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We've been starting some geometry lately, and my Math 3 kids really needed a few days to get their brains wrapped around the vocabulary.<br />
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I found a neat <a href="http://www.education.com/pdf/tic-tac-circles/">Circles Tic Tac Toe activity</a> and <a href="http://journalwizard.blogspot.com/2013/07/unit-7-properties-of-two-dimensional_29.html">this blog post</a> including paper folding notes, which helped me plan my instruction for my kiddos.<br />
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I've really been trying to put my 10 class iPads to use with partner activities, and this fit the bill perfectly. My class is one of the pilot BYOD rooms in the school, but there's still many of my students that don't have a device to bring. Often, lessons where they can work in pairs instead 1:1 with the tech are much more doable. Here's what we did.<br />
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Setting up an ISN page that's got several pieces can seriously EAT class time. So I replaced their usual warmup activity with some simple instructions. I had the first 3 people in the room pass out the strips of paper, which were 1/3 each of a colorful letter sized paper.<br />
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<a href="http://1.bp.blogspot.com/-cFnx66plIS0/VUPG-DN0fOI/AAAAAAAABCo/uZhlCe-RYdQ/s1600/IMG_0370.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-cFnx66plIS0/VUPG-DN0fOI/AAAAAAAABCo/uZhlCe-RYdQ/s1600/IMG_0370.JPG" height="239" width="320" /></a></div>
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We worked together to fill out the index cards, talking about what they knew, and the importance of certain distinctions (line vs. line segment, etc).<br />
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<a href="http://1.bp.blogspot.com/-ujK-49IJy8A/VUPG-MR48II/AAAAAAAABCk/OK3s1QaqayU/s1600/IMG_0369.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-ujK-49IJy8A/VUPG-MR48II/AAAAAAAABCk/OK3s1QaqayU/s1600/IMG_0369.JPG" height="320" width="239" /></a></div>
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We also separated their cards into three groups (the idea I got from the post linked above). </div>
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<a href="http://1.bp.blogspot.com/-m2zcsRS5UQY/VUPG9doikaI/AAAAAAAABCU/4d3XrPtFkFQ/s1600/IMG_0368.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-m2zcsRS5UQY/VUPG9doikaI/AAAAAAAABCU/4d3XrPtFkFQ/s1600/IMG_0368.JPG" height="239" width="320" /></a></div>
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We practiced using some task cards and a game of Scoot. </div>
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Then students were sorted into pairs, and each pair needed 1 device. </div>
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I posted the picture file in Google Classroom, and they opened it using Skitch. </div>
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(If you don't have devices, you can also print & copy one per pair, or laminate and reuse with dry erase markers.) The Slides file with the instructions and complete list of vocab is <a href="https://docs.google.com/presentation/d/1qVUZzWjZsr7mPdnhX8GyAFmR3Jzm7iFj5neEA6ZkEcI/edit?usp=sharing">here</a>. </div>
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The <a href="https://drive.google.com/file/d/0BxRGncihqgqgTnFRVEtlb0JiV1k/view?usp=sharing">picture file </a>that my students used looked like this:</div>
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<a href="http://3.bp.blogspot.com/-f6C-XH-MshI/VUPG9fHFuoI/AAAAAAAABCQ/ZrA0QryzecE/s1600/Circle%2BBlank%2BConnect%2BFive%2BBoard.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-f6C-XH-MshI/VUPG9fHFuoI/AAAAAAAABCQ/ZrA0QryzecE/s1600/Circle%2BBlank%2BConnect%2BFive%2BBoard.png" height="176" width="320" /></a></div>
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They used the Skitch app to draw their X's and O's on the board. </div>
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Below is what the board looked like after one pair finished a game. </div>
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<a href="http://4.bp.blogspot.com/-KJRg6ntx82w/VUPG9axCaeI/AAAAAAAABCY/_wuuCtwp0T4/s1600/Completed%2BGame.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-KJRg6ntx82w/VUPG9axCaeI/AAAAAAAABCY/_wuuCtwp0T4/s1600/Completed%2BGame.png" height="179" width="320" /></a></div>
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The tech allowed us to save some paper, play multiple times, save the results, and have a bit of fun!</div>
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My students enjoyed the activity, and I appreciated the 5 minutes that it took to create this activity. I'll definitely be using Skitch for ed games again soon!</div>
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<span id="goog_301197525"></span><span id="goog_301197526"></span><br />Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com60tag:blogger.com,1999:blog-1923582105875028879.post-75216237245536503372015-03-31T10:43:00.000-07:002015-03-31T10:45:05.933-07:00MTBoS Directory & Post-it Plus AppHi everyone!<br />
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I just want to give a quick list of 3 awesome things:<br />
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1. MTBoS Directory!<br />
Wow this is going to be amazing - one comprehensive list for our little math world!<br />
Go to <a href="http://sites.google.com/site/mtbosdirectory">http://sites.google.com/site/mtbosdirectory</a> to sign up! Click add entry, and let us know who you are. I've been having some fun today looking up teachers in my area, and finding some amazing new blogs to follow.<br />
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2. Post-it Plus App<br />
This is random, but I read a blog post today that just ROCKED MY WORLD. I do so many sorting, matching, and ordering activities, and I've finally found a way to digitize this process. Check out the idea from Teaching High School Math <a href="http://teachinghighschoolmath.blogspot.com/2015/03/using-post-it-plus-app-in-math-class.html">here</a>. I tried it out very briefly while my students were working on the warmup, and I'm already planning to use it tomorrow for students to practice switching between log and exponential form.<br />
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3. ScoodleJam and Nearpod App-Smash<br />
Is it still called an App Smash if it's only smashed by the teacher? Hmm....I'll have to think about that.<br />
ScoodleJam is a great doodling app - I downloaded it last week when it was free, and have been using it to create some cool activities. It's easy to save an image created in ScoodleJam, and I imported them into Nearpod to create some introduction puzzles based on <a href="http://squarerootofnegativeoneteachmath.blogspot.com/2015/03/solving-exponential-equations-no-logs.html">this blog post</a>. I used it at the beginning of my lesson for solving exponential equations without logs. You can check out the Nearpod presentation I used <a href="https://app.nearpod.com/#/?pin=313BAB04244D8C858AD2A226D46BE4A6-0">here</a>. It's not too fancy, but it really made this lesson so much easier on my students, and it only took me about 10 minutes to create!Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com0United States35.173808317999587 -79.80468759.6517738179995867 -121.1132815 60.695842817999591 -38.4960935tag:blogger.com,1999:blog-1923582105875028879.post-86688353690166172012015-02-28T08:32:00.000-08:002015-02-28T08:32:53.379-08:00BINGO 2.0 (Nearpod App-Smash)I had a moment during 1st period today, where I realized how different my classroom is from when I started teaching. (Yes, we were at school for a half day on a Saturday, for a snow make-up day)<br />
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My plan was to play bingo with my Math 2 students, who are working on simplifying radicals today. We also had the Ipad cart checked out, which I had intended to use for a quick Google Classroom update. Instead, the Ipads ended up being exactly the thing that took this activity to the next level. </div>
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Whenever we play bingo in my classroom, I print out a Kuta (or similar test bank) worksheet with questions and an answer page. Usually, I print out 1 copy with 40-50 questions. I put the answer sheet under the document camera, and students copy random answers into squares on a blank bingo card. </div>
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Quick ideas/suggestions for a last minute bingo game:</div>
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<li>Any worksheet with an answer key works - just copy the answers onto the board for the students to choose from. </li>
<li>Quick, repetitive type questions work best, such as complex number operations, simplifying expressions of any kind, or switching forms of linear or quadratic equations. (I'll be repeating this activity Monday with Math 3 for completing the square)</li>
<li>Students can use a <a href="http://www.creativeforecasting.net/PDFImage/BlankBingoCard.pdf">blank template</a> if you have time/resources to copy one for each student. I usually have 1 class set, which we put inside sleeve protectors and use as dry erase boards. Students write on the cards with either pencils/dry erase markers. </li>
<li>Bingo chip ideas: I use foam sheets from the dollar store that I cut into 1-inch pieces several years ago. I've also used the small glass vase-fillers from the dollar store, although they make much more noise. On the few occasions that students have their own copy of the bingo template to write on, they've used markers to mark their squares. </li>
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But here's how it changed today. We used the <a href="http://www.nearpod.com/">Nearpod </a>app's "Draw It" feature. That meant that each time I called out a question, they showed their work and sent it to me! Each question, I had a student sample that I could scroll through, so that we could talk about any mistakes or misconceptions along the way. Below is a screen shot of the teacher's view from the app.<br />
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Nearpod has this great "share" feature after using the Draw It slides. It allows you to send the picture of any student's work, without their name, to <i>every other student. </i>This is such a game changer. They can see their peers' work, and discuss it without the pressure of going to the board. This is a view of what the teacher sees from the app, with the blue "Share" button in the top corner of each response. </div>
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<a href="http://1.bp.blogspot.com/-h6T8PkX2IUY/VPHrvgroHZI/AAAAAAAABA8/DDImxq2b2Mw/s1600/photo.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-h6T8PkX2IUY/VPHrvgroHZI/AAAAAAAABA8/DDImxq2b2Mw/s1600/photo.PNG" height="240" width="320" /></a></div>
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My students also figured out that they could take a picture of the projected question, import it into Nearpod, and then complete the work over the image. Some choose to write the question out, as shown above.<br />
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When we review homework, this feature means they're able to snap a pic of their work from their homework page, then send it to me, without having to rewrite anything. Then we look over several responses together, and sort out any confusion. This is a great time saver, and it's definitely an app I hope to find more uses for in the future. </div>
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com2Mount Holly, NC, USA35.2981943 -81.0159080999999935.1945328 -81.177269599999988 35.4018558 -80.854546599999992tag:blogger.com,1999:blog-1923582105875028879.post-68852728724575525642015-02-03T11:53:00.001-08:002015-02-03T11:53:33.215-08:00One week into the new semester update!Hello!<br />
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This semester is off to a great start - with Math 2, Math 3, and Math 3 Honors classes. Here's a glimpse at what's changed for this semester, a few things that haven't, and what we've done so far.<br />
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What's changed:<br />
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<li>Notebook setup (again!) </li>
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<li>Last semester, I had them use 2 notebooks, with the extra used for warmups and formulas/reference. This extra notebook was not as useful as I had hoped. I switched back to one notebook per 6 weeks grading period. </li>
<li>Each unit now starts with the Unit TOC, then 2 pages for warmups. The unit TOC page also now includes a column for their <a href="http://learningwithtape.blogspot.com/2014/10/daily-quizzes-easy-way-to-start-kind-of.html">daily quiz grades</a>, homework grade, and averages for each. You can see more setup pictures in Evernote <a href="https://www.evernote.com/shard/s385/sh/c8bfb7fc-a38b-456e-b754-eb72f04d2526/5d676467a2c80a29aff88a63990182dc">here</a>.<br /><br /><div style="text-align: center;">
<a href="http://2.bp.blogspot.com/-OH98ppuHdec/VNEiII7EXuI/AAAAAAAABAU/xqyvkSsqS-s/s1600/Evernote%2BSnapshot%2B20150126%2B142551.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-OH98ppuHdec/VNEiII7EXuI/AAAAAAAABAU/xqyvkSsqS-s/s1600/Evernote%2BSnapshot%2B20150126%2B142551.jpg" height="239" width="320" /></a></div>
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<li>I changed the <a href="http://learningwithtape.blogspot.com/2013/07/classroom-incentives.html">punch passes</a> to only 3 points for my honors classes - it made their grades a bit too high last semester. </li>
<li>I'm trying to do much more difficult iterations of problems than in previous semesters. I really want my students to think, and to not have such a tendency to skip over word problems. I want them to be more confident! I'm also trying to make sure we discuss multiple ways to approach the same problem, so we can have conversations about efficiency, and multiple representations of the same situation. </li>
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Things that haven't changed:<ul>
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<li>Still working a second job on Thursday nights and Saturdays - it's why I've been a bit absent as far as blogging. </li>
<li>Still using a LOT of foldables and trying to increase gradually to infuse more tech into my lessons</li>
<li>Using <a href="http://evernote.com/">Evernote </a>to keep my interactive notebooks online. You can see Math 2 <a href="https://www.evernote.com/pub/cb666/math2">here </a>and Math 3 <a href="https://www.evernote.com/pub/cb666/math3">here</a>. </li>
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Some cool tech stuff we've done so far:</div>
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<li><a href="http://piktochart.com/"><span id="goog_633341225"></span>Piktochart <span id="goog_633341226"></span></a>introductions</li>
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<li>Super cool website! We spent about 30 minutes in class, then they shared their final product with me. Volunteers were allowed to present. They really turned out great! I had them do an infographic, and they had to include at least 3 images and 5 facts about themselves. </li>
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<li>Lots of <a href="http://create.kahoot.it/">Kahoot</a></li>
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<li>It is SOOO easy to search for a public kahoot on a topic, and just edit 1-2 questions to fit my needs. My students love the competitive nature, and I love the easy data. </li>
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<li><a href="http://thinglink.com/">Thinglink</a></li>
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<li>I decided to try this after reading <a href="http://www.mathycathy.com/blog/2015/01/trading-worksheets-for-desmos/">this post</a> from Mathy Cathy. This activity went very well with my students, and I plan to use Thinglink again in the future - if you have other ideas, please let me know! I'm trying to brainstorm other uses of this tool. </li>
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Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com0tag:blogger.com,1999:blog-1923582105875028879.post-55760052352548417002014-12-08T10:33:00.000-08:002014-12-08T10:33:21.190-08:00App-smashing with DesmosHi everyone!<br />
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So I wanted to share an activity I did for function transformations and piecewise functions (well, maybe more exploring domain restrictions that are used in piecewise functions)<br />
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Since I know this post will be shared with some of my non-math friends from Pinnacle, I'll give you a bit of background (hopefully in language that's as non-mathy as possible.)<br />
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Our Math 2 students are supposed to learn different types or classifications for equations (functions). They also learn to "move" the graphs of those equations by changing different parts of the original function's equation. (For example, they can add to the end of an equation to move it up on the graph).<br />
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Here's what we did:<br />
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1) Students created a drawing of their choosing in Desmos (an online graphing calculator).<br />
They were instructed to include 4 linear, 1 absolute value, 1 exponential, and 1 quadratic equation. They were required to have a minimum of 15 components of their graph, including no more than 4 horizontal or vertical lines. They were encouraged to be creative.<br />
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2) After creating and saving their graph in Drive, they shared it with me, so I could grade the equations.<br />
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3) Then they took a screenshot of their graph, and imported it into skitch. They used the app to label a minimum of 7 of the 15 components. Then they sent the skitch image to me.<br />
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It was a great, quick (2-day) activity that lead to some AWESOME conversations. It was also really interesting to see the shapes they could create from certain functions by changing the scale of their graph, or only using a certain piece of that function. Cool stuff.<br />
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Here are some of the skitch images (I'm not sharing the equations files because I know so many of my secondary friends do similar projects, and I don't want to create opportunities for cheating). There is one file below that included that in the screenshot, so you can see generally what they were creating for the equations.<br />
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<br />Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com0tag:blogger.com,1999:blog-1923582105875028879.post-38985475922215150932014-11-30T18:57:00.001-08:002014-11-30T18:57:21.731-08:00Grading homeworkWell, here we are at the end of Thanksgiving Break. I hope all of you had a safe, relaxing break. I used most of mine to quilt, sew up some Christmas gifts, and I was blessed this year to have family visit as well for a bit. But now it's Sunday night, so of course I'm already in school mode. :)<div><div>We'll start our trig unit tomorrow and I am sooo excited!</div><div><br></div><div>We also have grades due tomorrow, which means I've been reflecting on my students' homework completion grades for the last six weeks. </div><div><br></div><div>Having technology in my classroom on a regular basis has changed the number of graded assignments in the grade book for my class. I've done more formative assessments and informal participation activities than ever before. This means that rather than getting so many classwork grades, their homework grades are now worth more than usual. </div><div><br></div><div>I know we all have problems with some students forgetting/refusing/neglecting to finish their work at home. I've started grading homework only once at the end of the unit, all at once. While I think that it's been good for my athletic students to have the flexibility to finish it around their own schedule, I'm worried that it's encouraged procrastination as well. </div><div><br></div><div>I used to grade homework daily during the warmup. Choosing to grade it all at once (usually around 10-12 assignments at a time) has saved me so much class time. I interact and chat with my students during the warmup more than I used to. I start class calmer and feeling more prepared, since I don't have an immediate to-do list within 30 seconds of the bell besides attendance. It frees me up to help out with more challenging warmup questions, and to get students settled more quickly. </div><div><br></div><div>Despite all of that, I'm not sure I'm convinced it's worth the trade off. I truly believe that math success comes from practice. My problem is that if my not-so-motivated kiddos aren't doing their work, I don't think they realize the impact each individual assignment has on their grade - they only see the impact of their homework average for the unit. </div><div><br></div><div>I don't know how to shift the balance on this - I want to get them to complete the work by a deadline, but with the freedom to distribute the work over that given time as they see fit. I really have been working hard this year to teach them to be reliable and responsible "employees." Does that mean if we're going over work they haven't done yet, that it's ok? I really don't know. </div><div><br></div><div>For the majority of them, they still get it done that night, and for the most part are prepared for when we go over it. I'd love any suggestions for making this system work better for those that put it off. Eventually, I'd like to flip my class, and this same type of issue is my biggest hesitation. </div><div><br></div><div><br></div></div>Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com0tag:blogger.com,1999:blog-1923582105875028879.post-45125447742971646082014-10-17T07:30:00.000-07:002014-10-17T07:30:09.421-07:00Daily Quizzes - An Easy Way to Start a (kind-of) SBG System & Provide Classroom Incentives<div class="separator" style="clear: both; text-align: center;">
I want to share the biggest change I've made to my classroom this year: Daily Quizzes. </div>
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This is the brain child of one of my amazing colleagues. Last year, he did 6 question exit tickets as a homework replacement. YES. A math teacher that assigned NO HOMEWORK. </div>
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Well, I wasn't quite ready to take that leap. However, I did like the idea of having plenty of skill-based data reports, and tying it to an incentive. So we decided as a PLC to compromise. DQs emerged from that compromise. Here's how it works.</div>
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Each day, after notes, students have around 15 minutes to start their homework. (We have 90 minute blocks.) After that initial practice time, I project a 6 question quiz on the board (My PLC creates these together ahead of time). </div>
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Students are allowed to use their notes. Once they're finished, they bring it up to me, and I grade it immediately (It takes less than 15 seconds per quiz. I use open ended questions, and there's no partial credit. Each is right or wrong, and I spend no time at that point looking through work or evaluating mistakes.) I record their score, tell them, and keep the card (which helps keep the answers from traveling around the room). Here's a picture of my recording sheet:</div>
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The topics are along the top, and scores range from 0-6. I do give half credit VERY rarely for students that made arithmetic errors, or for answers not in best form (such as answers with negative exponents). I color code the scores at the end of a unit, on the morning of the review day. This helps me remember where our weaknesses were throughout the unit. </div>
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0-1 are red</div>
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2 is pink</div>
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3 is orange</div>
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4 is yellow</div>
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5-6 are green</div>
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Absent is blue - I don't typically require students to make these up.</div>
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You can see the clear difference in my honors classes (above) and my regular class (below).</div>
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Another difference between honors and regular classes is the number of questions, and incentive attached. Honors classes get 5 question DQs, and students that score a perfect 5 are permitted to complete every other homework problem that's assigned that day. Regular classes get 6 questions, and students that score a 5 or 6 get to only do half the problems. </div>
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This homework incentive has been FANTASTIC. Students take the notes seriously, because they know they're going to want to reference them during the quiz. They work furiously during that initial practice time, and even my withdrawn/shy kiddos will reach out to their group or to me to ask questions to iron out any issues during that time. </div>
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After they get their score, they resume work on the homework assignment. I typically reserve around 20 minutes for the DQ, which means the early finishers have around 15 minutes to work in addition to the 15 they already spent. As much as they hate getting 4s, they get so competitive about the 5s and 6s. We had to start a class vs. class competition - and I think adding an extra question for my regular class puts them on a level playing field. </div>
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<tr><td class="tr-caption" style="text-align: center;">Class DQ Board: 1st Regular, 2nd & 4th Honors</td></tr>
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I go back once everyone's finished and look through work. We clarify common issues, and I give cards back so students can post them on the bragging wall (shown below), or look over their mistakes. </div>
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Let's talk about some details on logistics:</div>
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<b>Grading</b>: I grade these as a single quiz grade per unit. I drop the lowest one from the unit, then average the rest. The percentage for the average out of 5 is their grade. (For the regular class, this means that they could get a quiz score over a 100 for their 6s. I haven't had an average over 102 yet this year, so I'm not concerned about giving them a few extra points for a 6. I make sure that the questions are difficult enough so that 5s and 6s aren't guaranteed.) These have completely replaced normal quizzes for me, and I'm ok with that even though they're all open note quizzes.</div>
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<b>Supplies</b>: I have students bring in index cards to turn in at the beginning of the year. These are in the supply bins for their groups, and most of the time we use them to complete DQs. Occasionally, they prefer using a piece of notebook paper instead, especially for problems that take up a bunch of space. </div>
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<b>Student Data Tracking</b>: Students keep up with their own scores in 2 places. </div>
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They record the score first on a page I created to go beside their Unit TOC page (from Math=Love). </div>
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This score goes right beside their homework assignment page number and homework grade, so I can quickly check their scores as I grade homework. This means I know whether to give a 50% or a 100% for a page that has every other problem completed. They get a stamp on this page and on their punch pass for each 100%. (My blog post on punch passes is <a href="http://learningwithtape.blogspot.com/2013/07/classroom-incentives.html">here</a>.)</div>
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The second place they record these is at the beginning of their Reference & Warmup notebook (post on my new notebook setup is <a href="http://learningwithtape.blogspot.com/2014/09/2014-isn-setup.html">here</a>). They record a daily I Can sentence from the board, with the corresponding page number, their DQ score that matches, and fill in a bar graph beside it. I encourage them to use this right before their test to reflect on what to spend the most time studying.</div>
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<tr><td class="tr-caption" style="text-align: center;">My regular students have 6 boxes, since they can score up to a 6.</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">My honors students have only 5 boxes.</td></tr>
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<tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-oNXhhIIADvA/VEEkHqqwglI/AAAAAAAAA8w/DSXqntFAXz8/s1600/IMG_0161.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-oNXhhIIADvA/VEEkHqqwglI/AAAAAAAAA8w/DSXqntFAXz8/s1600/IMG_0161.JPG" height="239" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">As you can see, some students are a bit more colorful with their records, and there are days we run out of time for a DQ.<br />I have also done "Daily Double Quizzes" where we do a makeup DQ from the day before along with that day's regular DQ.<br />Also - note the frowny faces. They HATE getting 4s. </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">I post the entire week's I Can Statements at once on the front whiteboard.</td></tr>
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I'm painfully aware that this system is missing a couple of things: a method for reassessment, make-up DQs for absent kids, and a way to tie this info with their tests. However, it's also been the easiest transition to something close to SBG that I've ever implemented. I've been able to save time grading too, which is always great. </div>
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Enjoy your weekend!</div>
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<br />Carolyn Spencerhttp://www.blogger.com/profile/16599260326463707273noreply@blogger.com2