tag:blogger.com,1999:blog-80729381884385087212017-03-28T15:59:20.544-05:00The Teacher Studio: Learning, Thinking, CreatingLooking for information about teaching in intermediate grades? Math workshop? Problem solving? Best practice? Quality reading and writing lessons and ideas? Google Classroom and other 1:1 ideas and resources? Teaching tips and educational resources? With rigorous standards and new information about brain research and learning being released all the time, The Teacher Studio is a great place to come to for great teaching ideas, lessons,and products to help you be the best teacher you can be.The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.comBlogger687125tag:blogger.com,1999:blog-8072938188438508721.post-15857995748187709062017-03-28T15:59:00.000-05:002017-03-28T15:59:20.576-05:00Area and Perimeter Studies: Part 2--Math Talk, Guided Practice, and More!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Task-Cards-2441353?utm_source=http%3A%2F%2Fwww.theteacherstudio.com&utm_campaign=Perimeter%20Post%202%20Area%20and%20Perimeter%20Task%20Cards"><img alt="teaching area and perimeter" border="0" height="332" src="https://3.bp.blogspot.com/-Wqyg_r6wRuA/WNrN3nntQDI/AAAAAAAAZVA/LIVkElEdZTgY5qvbg7hZJ9P6-TkbiOMKgCLcB/s640/area%2Band%2Bperimeter%2Bpost%2B2%2Bmarch%2B28%2B2017.jpg" title="area and perimeter activities" width="640" /></a></div>I blogged a few days ago about some of the fun area and perimeter activities we had done in class (If you missed it, just <a href="http://www.theteacherstudio.com/2017/03/perimeter-and-area-constructivist.html">CLICK HERE</a>.) and I promised you a follow-up post!<br /><br />With "big" concepts, I tend to have a sequence of teaching that doesn't really follow a formula but does have a certain sequence. First of all, I want the students to explore and build their understanding. That's what that first post was all about--immersing students in meaningful activities to develop their foundations.<br /><br />Once that happens, we do need some guided practice and formative assessment to see where students are with their depth of understanding. Sometimes this means I use some of the lessons that area a part of our math series, sometimes it involves other practice activities. After I taught a few mini-lessons from our math series, I wanted to give students the opportunity to practice finding area and perimeter--and time for me to observe and look for any misconceptions and problems.<br /><br />Here's what I did. I used a set of task cards that were differentiated by level and put them in a giant circle around the room (I couldn't 'get a good picture that showed this! Just picture 20 cards scattered around the perimeter!). I explained to the students that the cards asked them to find area and perimeter--and were arranged in order from most simple--rectangles and shapes with the grid built in--to more complex shapes. I partnered students up with partners of similar math abilities and asked them to start at a location that they thought matched their confidence level.<br /><br /> I asked them to take a wipe off marker, their math spiral, and something to erase with (most of my students have a sock or washcloth in their desk). Their job was to solve a card as a team, make sure they used math talk to "prove" that their solutions were correct. I encouraged them to write directly on the cards to help with that "proof". As they solved a card, they then moved to another one.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Task-Cards-2441353?utm_source=http%3A%2F%2Fwww.theteacherstudio.com&utm_campaign=Perimeter%20Post%202%20Area%20and%20Perimeter%20Task%20Cards"><img alt="teaching area and perimeter" border="0" height="640" src="https://4.bp.blogspot.com/-5szusbTPn3M/WNq9lEjjXLI/AAAAAAAAZUU/vrP1odlTze09JC7FSkiMm90ZUyOska9YQCLcB/s640/Photo%2BMar%2B25%252C%2B10%2B39%2B43%2BPM.jpg" title="area and perimeter lessons" width="480" /></a><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Task-Cards-2441353?utm_source=http%3A%2F%2Fwww.theteacherstudio.com&utm_campaign=Perimeter%20Post%202%20Area%20and%20Perimeter%20Task%20Cards"><img alt="teaching area and perimeter" border="0" height="480" src="https://2.bp.blogspot.com/-BrwDSedRSB8/WNq9dTsU09I/AAAAAAAAZUE/QiWZSUaj3R8rWmxan327lxDkjYVPwjT6wCLcB/s640/Photo%2BMar%2B25%252C%2B10%2B39%2B17%2BPM.jpg" title="area and perimeter lessons" width="640" /></a></div> I had a blast walking around and listening to their thinking...this card was being tackled by some of my struggling students. The strategy? One of them suggested "moving" the bottom two squares over to the end to make it a rectangle which would be easier to count. It took some convincing to get her partner to believe it (we actually broke out some tiles and built it) but the light bulb went ON after that!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Task-Cards-2441353?utm_source=http%3A%2F%2Fwww.theteacherstudio.com&utm_campaign=Perimeter%20Post%202%20Area%20and%20Perimeter%20Task%20Cards"><img alt="area and perimeter lessons" border="0" height="640" src="https://2.bp.blogspot.com/-n4y4r2zBNvk/WNq9dN_zKTI/AAAAAAAAZUA/cMUaGUeD7k0pREWKJIWbq28VLpuFm0VwACLcB/s640/Photo%2BMar%2B28%252C%2B11%2B49%2B53%2BAM.jpg" title="area and perimeter activities" width="480" /></a></div> We had investigated two strategies for finding the area of these irregular shapes--finding the entire rectangle and subtracting the missing "bite", and subdividing the shape into smaller rectangles. If students were working quickly, I asked them to try both methods to confirm if they were getting the same amount. <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Task-Cards-2441353?utm_source=http%3A%2F%2Fwww.theteacherstudio.com&utm_campaign=Perimeter%20Post%202%20Area%20and%20Perimeter%20Task%20Cards"><img alt="area and perimeter task cards" border="0" height="480" src="https://3.bp.blogspot.com/-WG3rx2I1Otk/WNq9eaXMXkI/AAAAAAAAZUI/MkHOUS52bIc77YJHFcNWgZLytkBhejNDwCLcB/s640/Photo%2BMar%2B28%252C%2B11%2B50%2B09%2BAM.jpg" title="area and perimeter lessons" width="640" /></a></div> This partnership was REALLY struggling with their math talk! (See that really dark blue line? She traced over it about 12 times to try to make her point!). The two students had totally different answers and neither were having much success being open to other ideas. I listened to them for a little while and then asked another partnership to join them to try to get them "unstuck". It worked.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Task-Cards-2441353?utm_source=http%3A%2F%2Fwww.theteacherstudio.com&utm_campaign=Perimeter%20Post%202%20Area%20and%20Perimeter%20Task%20Cards"><img alt="area and perimeter lessons" border="0" height="480" src="https://4.bp.blogspot.com/-Nnzs0ntuRk8/WNq9ecYE7vI/AAAAAAAAZUM/Ny2v3YBC1OIEHjHiacO5AnNgT6O7Sl0mACLcB/s640/Photo%2BMar%2B28%252C%2B11%2B50%2B47%2BAM.jpg" title="standards for mathematical practice" width="640" /></a></div> I was able to keep a running list of students who seemed to be struggling--but the best part was that there was some amazing teaching being done from student to student! The next day, I gave an entrance slip to take the temperature of the group, refined my "watch" list, and then planned for some reteaching for those who needed it. Not bad for about 25 minutes of math class!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Task-Cards-2441353?utm_source=http%3A%2F%2Fwww.theteacherstudio.com&utm_campaign=Perimeter%20Post%202%20Area%20and%20Perimeter%20Task%20Cards"><img alt="area and perimeter ideas" border="0" height="480" src="https://4.bp.blogspot.com/-jFlzyRSTgEI/WNq9feSNYRI/AAAAAAAAZUQ/PFtpbH7EA1slj8jiu_av1UUUqXnglYfbwCLcB/s640/Photo%2BMar%2B28%252C%2B11%2B51%2B05%2BAM.jpg" title="area and perimeter lessons" width="640" /></a></div><br />Interested in checking out these task cards?<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Task-Cards-2441353?utm_source=http%3A%2F%2Fwww.theteacherstudio.com&utm_campaign=Perimeter%20Post%202%20Area%20and%20Perimeter%20Task%20Cards"><img border="0" height="320" src="https://4.bp.blogspot.com/-68S2cfMUtFw/WNrF0tNrVPI/AAAAAAAAZUk/0SHFgIf0osk_hRoRIjISUvRrviYDZFNgwCLcB/s320/area%2Band%2Bperimeter%2Btask%2Bcard%2Bcover.jpg" width="320" /></a></div><br />How about some area and perimeter formative assessments?<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Area-and-Perimeter-Grades-4-5-1188310"><img border="0" height="320" src="https://4.bp.blogspot.com/-5G_d1AMEeN0/WNrF79wwByI/AAAAAAAAZUo/QY234pebTIIQZesfYz42ouZokq_GDQSvgCLcB/s320/Slide1.JPG" width="240" /></a></div><br />Want to pin this post for later?<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Task-Cards-2441353"><img border="0" height="640" src="https://1.bp.blogspot.com/-lagpNDJVOZk/WNrGuavjHtI/AAAAAAAAZUs/i27PdY2xZiUdAVnXyEuj9sXkKa3LmisUwCLcB/s640/are%2Band%2Bperimeter%2Bpost%2Bpin%2B%2Bpart%2Btwo%2BMarch%2B28%2B2017.jpg" width="320" /></a></div><br />The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-40300587020843677602017-03-26T08:25:00.001-05:002017-03-26T08:25:57.690-05:00Making Task Cards More Interactive<div class="separator" style="clear: both; text-align: center;"><a href="http://www.upperelementarysnapshots.com/2017/03/making-task-cards-more-interactive.html"><img border="0" height="332" src="https://1.bp.blogspot.com/-9MW7uWh7nbc/WNfBIXhCW_I/AAAAAAAAZS4/g8nqzGgHtIwwwi8lMviQazi1pa1qu-05QCLcB/s640/upper%2Belementary%2Bsnapshots%2Btask%2Bcard%2Bpost%2Bmarch%2B26%2B2017.jpg" width="640" /></a></div>Today's my day to blog over at Upper Elementary Snapshots! Just click the image above to take you to today's post...hope you enjoy it.The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-43717891134690181602017-03-24T19:11:00.002-05:002017-03-24T19:11:13.569-05:00Elementary Homework: Some Food for Thought<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Practice-Outside-the-Box-Grades-3-5-1386876"><img alt="math homework" border="0" height="332" src="https://1.bp.blogspot.com/-DDOKNbHDXC0/WNWw5D5vRCI/AAAAAAAAZRA/EgTiR37-1_kb44IYo5tbC81Ajg7eiXY_QCLcB/s640/homework%2Bthoughts%2Bpost%2Bmarch%2B24%2B2017.jpg" title="creative homework" width="640" /></a></div>As I approach my fifth year of blogging (YIKES!), I cannot tell you how touched I have been by the connections I have made with teachers around the world. I have learned so much from them--and I hope I have been able to give a little in return.<br /><br />One topic that ALWAYS gets people a little ramped up is...<br /><br /><div style="text-align: center;"><b><span style="font-size: x-large;">HOMEWORK</span></b></div><div style="text-align: center;"><br /></div>That's right. Just bring THAT topic up to a group of parents--or teachers--and see the mixed reviews you get! You can find all sorts of studies that talk about the benefits (or not) of homework...but I caution you to always take note of the age group studied! Most of the research out that was done with high school students! Check out this statement from an article on <a href="https://www.edutopia.org/blog/research-trends-is-homework-effective-youki-terada">Edutopia</a> that tries to clarify this.<br /><br /><span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 13px;">"Although the debate about homework generally falls in the "it works" vs. "it doesn't work" camps, research shows that grade level makes a difference. High school students generally get the biggest benefits from homework, with middle school students getting about half the benefits, and elementary school students getting little benefit (Cooper et al., 2006). Since young students are still developing study habits like concentration and self-regulation, assigning a lot of homework isn't all that helpful."</span><br /><span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 13px;"><br /></span>So, that being said, I DO give occasional homework. In fact, I do require my students to read a minimum of 20 minutes daily at least 5 times per week. Why? I am wanting them to build a reading habit! There are no rules--it can be the same book they are reading at school, articles online, cartoons, magazines--anything that builds their "readerly life".<br /><br />I also at times will assign homework something like this: "Find someone not in our class to teach about the difference between potential and kinetic energy." By keeping it this open-ended, it can be a parent. A babysitter. A sibling. A friend. Even ME if necessary. This type of homework is fast and easy and is very reinforcing of what is being done at school.<br /><br />Finally, I do assign a little math homework at times...but not what people might typically think. I do not want parents having to teach math. I'm a little possessive of that! I don't want homework to be stressful for anyone--so any math homework I give is either fluency work (skills they are secure with and are just building automaticity) or open-ended in nature. If I don't think a student can handle a task, I replace it with a fluency game. Because I believe this strongly, I will often assign a practice page from a unit earlier in the year. Of course, it's super important to communicate this to parents...that the homework doesn't match the topic OR level of classwork...and that it is meant to build responsibility and fluency not reinforce that day's lesson.<br /><br />When I talk about open-ended homework, I am referring to work that is, by its very nature, differentiated. Check out these pictures from some homework we did within the last week or so--and note that these would be FANTASTIC for classwork as well--but they are wonderful for homework because they are so flexible. I love using these--we had done a multiplication review (it IS testing season) so I gave them one to do--and then space to make up two similar problems. When they finished, they needed to check them on a calculator and find any errors. There are so many problem types that work for this--and once students learn the process, there is no miscommunication on directions.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Practice-Outside-the-Box-Grades-3-5-1386876"><img alt="creative homework" border="0" height="480" src="https://4.bp.blogspot.com/-WHNQe-D3WRU/WNWsc7CLbeI/AAAAAAAAZQw/Sm_qh5ydJ8MlWtbdFwewGOvHcyDwA2MlwCLcB/s640/Photo%2BMar%2B24%252C%2B6%2B16%2B20%2BPM.jpg" title="math homework" width="640" /></a></div> Another favorite homework "type" for me is the "Make it Your Way" sheet...you can put ANYTHING in that oval and then ask them to generate a list of at least 10 (or 5 or 15 or whatever) ways to "make" that number or amount. You will see students at a most basic of levels able to accomplish this...<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Practice-Outside-the-Box-Grades-3-5-1386876"><img alt="homework ideas" border="0" height="640" src="https://2.bp.blogspot.com/-xUvkCEVvx1Y/WNWsc5d-4KI/AAAAAAAAZQs/gWkekm0WGK4L7fT_m4w-MlNzvmdmUa8VACLcB/s640/Photo%2BMar%2B24%252C%2B6%2B16%2B37%2BPM.jpg" title="creative homework" width="480" /></a></div> ...but also those who have additional skills can really showcase them. This is where I'll see students playing with negative numbers, decomposing, and more--and the more they do, the more creative they get! They just always have to be able to prove that they are right. Again, once they are taught how to do it, there is no worry about directions. These are GREAT for sharing the next day as well! I often have students "star" their favorite 3 and then we do a gallery walk...or I let them write their favorite one on the Smartboard and we try to not get any repeats...lots of options.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Practice-Outside-the-Box-Grades-3-5-1386876"><img alt="creative homework" border="0" height="480" src="https://2.bp.blogspot.com/-XnZGwG_N0W4/WNWsc6msN4I/AAAAAAAAZQ0/zglkgllKfNcaav0OceEKdyovcFAWG70QACLcB/s640/Photo%2BMar%2B24%252C%2B6%2B16%2B53%2BPM.jpg" title="fourth grade homework" width="640" /></a></div>So...if I do assign homework, do I grade it? Nope. Students bring it into class in the morning and quickly buddy check it. I check whether or not it was finished, and then partners work to reconcile any discrepancies! End of story. I am aware that there are people who are required to give and grade homework which just makes me a little sad...but perhaps you can come up with an easy rubric to use--related to effort, completion, and precision or something like that.<br /><br />So anyway...I thought I'd just spark some discussion--either in the comments or in your own mine--about your own thoughts about homework for elementary students. There certainly are MANY points of view--and many, many different situations. I have actually changed my point of view over the last five years or so; I think it's always important to continually refine our beliefs and seek out deeper understanding. Hope I got you thinking!<br /><br />Want to see where I got these homework sheets?<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Practice-Outside-the-Box-Grades-3-5-1386876"><img border="0" height="320" src="https://4.bp.blogspot.com/-TSDHDYJpvJA/WNW0NVxjANI/AAAAAAAAZRQ/hCWjXT-Bb04t4-Rh67uo0okrdbyktkx8ACLcB/s320/Slide1.JPG" width="240" /></a></div>Want to pin this post for later? Here you go!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Practice-Outside-the-Box-Grades-3-5-1386876"><img border="0" height="640" src="https://3.bp.blogspot.com/-TIrH68zXy5E/WNWz0RsU6BI/AAAAAAAAZRM/_Nmv3j5klhoWVoMZ3pLfJjToPsnIba6QQCLcB/s640/homework%2Bthoughts%2Bpost%2Bpin%2Bmarch%2B24%2B2017.jpg" width="320" /></a></div><br />The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com1tag:blogger.com,1999:blog-8072938188438508721.post-64646020789069227092017-03-23T20:18:00.003-05:002017-03-23T20:22:14.369-05:00Perimeter and Area: Constructivist Learning<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img alt="area and perimeter lessons" border="0" height="332" src="https://2.bp.blogspot.com/-YSBaMQP8oMw/WNRpFzXTfMI/AAAAAAAAZPs/XKZDV9D-uxMmOmJAwjvUhOVqOjIwE0B1gCLcB/s640/perimeter%2Band%2Barea%2Bblog%2Bpost%2Bimage%2BMarch%2B23%2B2017.jpg" title="teaching area and perimeter" width="640" /></a></div>Some of my favorite math units/topics are those where I feel I have a handle on how to really get my students to construct their own understanding. This is NOT the way most textbooks operate! Most textbooks have you set a clear learning target:<br /><br /><b>I can find the perimeter of a rectangle by using the perimeter formula.</b><br /><br />Then, the teacher models how to do the problems...talks through them...gives some guided practice...some independent practice--and then assesses student understanding. It works--for some.<br /><br />Instead, I really try to find ways to put students in situations where they are exploring, looking for patterns, and deriving their own rules. I have found that this type of learning is more engaging, more meaningful, and "sticks" with the learner so much better.<br /><br />Here's what this looked like with area and perimeter in my room last week. Had I used our math series in sequence, the progression would have looked something like this:<br /><br />1. Teach the formula for the area of a rectangle.<br />2. Teach finding the area of irregular shapes by decomposing into smaller rectangles.<br />3. Teach the formula for the perimeter of a rectangle.<br />4. Practice problems with area and perimeter.<br /><br />I've been doing this fourth grade thing a long time--and I know my students aren't ready for that yet. We still have a TON of misconceptions that need to be worked out before we move to formulas! For example, many students still aren't crystal clear on the difference between perimeter and area--so I certainly don't want to teach formulas for concepts that they aren't confident about!<br /><br />Also, students aren't ready to flexibly and correctly use labels (a "precision" issue!) related to units of length (ex. cm, in., m) as opposed to SQUARE units to measure area (we like to call it "squarea" to help with that!)<br /><br />I also know from the past that students really struggle to even COUNT the squares on the side of a shape and often get confused between "inside" and "outside" of shapes.<br /><br />There are other things that come up--there always are--but to jump right into formulas certainly doesn't give students time to explore, get these misconceptions corrected, and allow the time for them to build and deepen their own understanding. Here are a few snippets of what I did BEFORE we tackled some of the work in our math book!<br /><br />Our first investigation simply involved asking the students to build a rectangle using 12 tiles. Students were able to do this with ease--and then I asked them to measure their rectangles, jot the answer on a sticky note, and come up to the group to share. <br /><br />We had an amazing discussion about how to measure a rectangle! Some measured only one way ("Mine was 6 squares long.") and others used two dimensions ("Mine was 3 one and 4 the other."). I asked if anyone measured theirs and got 12. No one had. This led to a great chat about whether or not we should measure the INSIDE of a shape or the OUTSIDE--until we realized that BOTH could be valuable! We came up with all sorts of real world examples when we would need to measure the outside edge or "rim" (peRIMeter) like fences, wallpaper borders, door frames, and so on. We also then talked about times when we might need to measure the entire area ("SQUAREA") in units that take up space...like for carpet or tile or planting sod and so on. Once students were comfortable that there is more than one way to measure a rectangle, it was time to roll!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img alt="teaching area and perimeter" border="0" height="480" src="https://4.bp.blogspot.com/-DuBKHXjq7Rg/WNMVsV5SDVI/AAAAAAAAZOg/nJxPGMzYblkF1Rc52M6MPPFijRO50VVCgCLcB/s640/Photo%2BMar%2B18%252C%2B8%2B56%2B37%2BPM.jpg" title="area and perimeter lessons" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">We continued building rectangles with set areas (like 12 square inches) and finding all sorts of different ways to do it--and we then compared the perimeters. This was a great way for us to really stress the difference between measuring and counting the inches along the edge and the squares inside--two ways to "measure" rectangles. Students started to notice what happened when they built long and skinny rectangles versus short "chubby" ones--and even were using correct vocabulary words like "length" and "width" and "perimeter". We recorded our findings on a sheet and practiced using the correct labels--inches or square inches.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">When it was clear that we were in pretty good shape in this department, I wanted to test their group work and problem solving! This time, I told them they did NOT need to use rectangles--and that I wanted them to work in teams of 6 to solve a problem. We talked about the problems that can arise with big groups (people being "bossy", people getting off-task, etc) so we set goals to stay focused and to strive for equal participation. The task? Have each person in the group create a shape with an area of 24 square inches--where no two people have the same perimeter! This meant some people would have to give and take--and MAN it was interesting to watch some groups function (or NOT function as the case might be!) </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img alt="lesson plans area and perimeter" border="0" height="480" src="https://4.bp.blogspot.com/-Ww9KNRYaAYE/WNMVq4R1ppI/AAAAAAAAZOU/0xtWgZKpI00WhLcDaRGHq_loJ13C61vqQCEw/s640/Photo%2BMar%2B18%252C%2B8%2B55%2B37%2BPM.jpg" title="area and perimeter investigations" width="640" /></a></div> It was so cool to listen to their discussions, the hints they gave each other, and the questions they asked. Check out the shape one student came up with--which led to quite a debate within the group. Can you do this? Can there be a "void" (a student's word, not mine!) in the middle? I listened to the debate for quite a while and then we agreed to solve it by agreeing that we would NOT count "voids"--and that all shapes had to be solid figures. We called the other groups over to chime in--and then we reached consensus that we would proceed with that new rule.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img alt="teaching area and perimeter" border="0" height="480" src="https://1.bp.blogspot.com/-XzGM7YLNmkQ/WNM3_J-xquI/AAAAAAAAZO8/h1Aab_TamUsdFtA3W4alzCTRs7yN5xhVwCLcB/s640/Photo%2BMar%2B22%252C%2B8%2B02%2B42%2BPM.jpg" title="area and perimeter misconceptions" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">As the groups solved the task and could prove that all 6 figures had different areas, they transferred their solution over to a grid page...</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img alt="teaching area and perimeter" border="0" height="480" src="https://2.bp.blogspot.com/-rOl4PKccWP4/WNMVqN4IfxI/AAAAAAAAZOM/1XlvjBsuirwZhLraxr66RmD6g8heaSmPgCEw/s640/Photo%2BMar%2B18%252C%2B8%2B55%2B19%2BPM.jpg" title="area and perimeter unit" width="640" /></a></div> Colored it...cut it...<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img alt="teaching area and perimeter" border="0" height="480" src="https://2.bp.blogspot.com/-te1r-9HTz8c/WNMVq9wSv1I/AAAAAAAAZOQ/FyDVynkmIW8W2EOMkfn8UzrGFRXda_CnwCEw/s640/Photo%2BMar%2B18%252C%2B8%2B55%2B58%2BPM.jpg" title="hands on area and perimeter" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">I mounted them on black paper and hung them in the hall. They have been receiving lots of attention from passers by!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img alt="area and perimeter lessons" border="0" height="480" src="https://1.bp.blogspot.com/-Gwfq3J-YG2s/WNMVoxkO6bI/AAAAAAAAZOI/61m8NSS-ehcZCgKPmejS3tu_opp3MeJNQCEw/s640/Photo%2BMar%2B18%252C%2B8%2B53%2B47%2BPM.jpg" title="area and perimeter investigations" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">The next day, I knew I wanted to continue to push their thinking before we dug into the formula, so I used this task--find three different rectangles that meet specific area and perimeter guidelines. I reminded them that we have different tools in our classroom...tiles, graph paper, and so on--and sent them off to explore with their partners.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img border="0" height="480" src="https://4.bp.blogspot.com/-JQO22XTbnCE/WNMVsQBwo1I/AAAAAAAAZOc/_HtIgnDWPd0uBW0QNxBe1f9No0h1qnplgCEw/s640/Photo%2BMar%2B18%252C%2B8%2B56%2B57%2BPM.jpg" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">The discussions were amazing--and again, I reminded them to use the vocabulary list we had started on the board (I love to do this to keep that academic vocabulary fresh and accessible!) as they talked. I circulated and asked questions, asked groups to show me their strategies, and so on. Once they felt they had a solution, I told them to actually BUILD their rectangles! Once they had their exact dimensions, it was time to replicate them with paper strips!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img alt="hands on math" border="0" height="640" src="https://3.bp.blogspot.com/-QgEhrOtfumg/WNMVonzNUUI/AAAAAAAAZOE/6TWOecKaQS0nEmjkmRkM2HwNQNi7_vPXQCEw/s640/Photo%2BMar%2B18%252C%2B8%2B54%2B51%2BPM.jpg" title="area and perimeter activities" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img border="0" height="640" src="https://1.bp.blogspot.com/-rLHQIy_uXF8/WNMVofncq7I/AAAAAAAAZOA/cJhbL2e0YaYdWdlKBiWcWyjO-_BRykyUgCEw/s640/Photo%2BMar%2B18%252C%2B8%2B54%2B23%2BPM.jpg" width="480" /></a></div><div class="separator" style="clear: both; text-align: left;">It was amazing...as they worked, even MORE questions came up...some struggle with making right angles...some needed ruler help. It was fascinating to watch--and I was able to do some "just in time" interventions. The end product? More "Area Art" to hang in the hall!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img alt="area and perimeter" border="0" height="640" src="https://2.bp.blogspot.com/-wkxkEHRp7B8/WNMVr_Gno8I/AAAAAAAAZOY/e4OXbH4YabUcNRMOnXaYdtg_MeCJBgxrwCEw/s640/Photo%2BMar%2B18%252C%2B8%2B56%2B13%2BPM.jpg" title="constructivist math lessons" width="480" /></a></div><div class="separator" style="clear: both; text-align: left;">By this point, I was feeling pretty confident that we understood the key differences between area nad perimeter and could find the area and perimeter of rectangles. That lesson in our math series where I was supposed to TELL them the formulas? Yeah...wasn't necessary. They EASILY figured out the area and perimeter formulas as they worked through these investigations. When I showed them the lesson, they laughed! I heard things like, "Of course you multiply the length and width to get the area." and "There are lots of formulas to find the perimeter--not just the one in the book!". We had fun making a list of all the formulas we could think of--and then evaluated which ones made the most sense to us!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">There was a lesson in the book that was worth our time--finding the area of irregular shapes--but the students were SO comfortable with rectangles that they idea of "decomposing" these odd shapes was absolutely no big deal....but I want to talk more about that later because this post is already ridiculously long! Thanks for sticking with me...I always just get so excited when I see learning make sense to my students--and that they can enjoy that learning process!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Want to see these activities and more? Just click the image below.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img border="0" height="282" src="https://1.bp.blogspot.com/-hzLdbjwzsOM/WNRxkyLpzWI/AAAAAAAAZQA/WLlm17nJaeQkHwOTV9TnCq636okET78kwCLcB/s320/area%2Band%2Bperimeter%2Bad.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">Want to pin this post for later? Here you go!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Area-and-Perimeter-Activities-5-Activities-to-Deepen-Understanding-1761804?utm_source=http%3A%2F%2Fwww.theteacherstudio.com%2F&utm_campaign=Area%20and%20Perimeter%20Blog%20post%20March%2023%202017"><img alt="area and perimeter" border="0" height="640" src="https://4.bp.blogspot.com/-vM7dR0reMQQ/WNRxZ2gLHlI/AAAAAAAAZP8/WsRrRUIXr9Mich3F6BARrjAhou_LHNWZQCLcB/s640/pin%2Bimage%2Barea%2Bperimeter%2Bblog%2Bpost%2Bmarch%2B23%2B2017.jpg" title="constructivist math" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Thanks for stopping by--and check back for "part two"!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br />The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com1tag:blogger.com,1999:blog-8072938188438508721.post-41736320047706804452017-03-12T08:35:00.004-05:002017-03-12T16:11:21.768-05:00Academically Rich Test Prep: 6 Ideas for a Realistic, Logical Approach<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pausing-Points-Test-Taking-Strategies-1738271"><img alt="standardized testing" border="0" height="332" src="https://2.bp.blogspot.com/-alcoS7zF7V0/WMVLewY1lXI/AAAAAAAAZKk/HXmqLXqPO7cYTb971ikV6CSpZdSsWK6awCLcB/s640/test%2Bprep%2Bpost%2Bmarch%2B12%2B2017.jpg" title="test prep" width="640" /></a></div>Before we begin, I want to address the issue of standardized testing. It is getting a pretty bad rap in the media and among teachers--and for good reason. We test more than ever. We spend more time PRACTICING to test than ever. The stakes are higher than ever. And this saddens me...because standardized testing DOES have a purpose when done in a reasonable way. The simple truth is, we DO need a way to monitor our schools and our programs. If my district finds that its elementary scores in fractions are dropping--we need to look at why. If we notice trends in our special populations--we need to look at why.<br /><a name='more'></a><br />That being said, I am always so sad when I hear stories about teachers spending weeks and weeks on test prep...or students who are totally stressed out about testing...or any number of other "horror" stories. It just doesn't need to be that way--and we, as teachers, have the ability to lower the stress for everyone involved. Now I get it--you can't control certain things in your school or district--but you CAN take some control in your own classroom (or with your own children!). Here are some of the things I do to help keep the testing madness somewhat under control!<br /><h4>1. Build a culture of a growth mindset and positive attitudes.</h4>First of all, students pick up on our mindsets and attitudes, so I make sure to always model a positive attitude about the testing process and make sure my students know why we do them--and that they are only one way that teachers can learn about students and what they know and can do. We also work ALL YEAR on developing that "I can do this!" spirit and nurturing a growth mindset so they can the right perspective going into the testing.<br /><br />After all, helping students to understand how their mindset can affect their success is important for LIFE, not just testing. I use this resource at the beginning of the year, and "testing season" is a great time to pull it back out, revisit it, and talk about how it applies to the big tests. Seriously, my student finish their testing (and we have to do a LOT in fouirth grade!) and, for the most part, say things like, "That was way better than I thought it would be!" or "I think I did great!". I'll take it.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Growth-Mindset-Bulletin-Board-and-Activity-Set-2021181"><img alt="teaching a growth mindset" border="0" height="320" src="https://3.bp.blogspot.com/-IHRFycdxL24/WMRQz2pnbPI/AAAAAAAAZJg/uf1nWI9uiiEUwcbyod54mVdLvV_dB5dAACLcB/s320/growth%2Bmindset%2Bcover.jpg" title="growth mindset" width="320" /></a></div><br /><h4>2. Get students comfortable with experimenting and trying things in different ways.</h4>One thing that I have noticed over the years is that students who are successful at testing are willing to tackle problems--even if they aren't sure what they are being asked to do. They have a toolbox of strategies to use when encountering new and novel situations. This makes them feel they have some control! We can't teach every question they encouter on the test--nor should we. Students who are willing to just dig in and "decode" the test...to see what they think the question is asking and draw from thier strategy bank to dig in, will do just fine. All year long we practice with tough problems and I coach them on how to tackle them. One of my favorite lines? "What would you do first if you knew what to do?" You would be AMAZED at how this unlocks students!<br /><br /><h4>3. Help students learn to "prove" their ideas by looking back at the text or graphics.</h4>Another thin I have learned is that the most successful test takers are those students who are willing to slow themselves down and prove their answers. This means we need to work ALL YEAR on having our students defend their thinking with examples, by having them look back in texts to provide evidence for their thinking, and to have them avoid saying "I guess" or "I think" when they can say, "It shows right here..." or "I knew it when I saw..." Again, these are not skills important only for testing--these are simply GOOD instructional strategies. Students should be asked to defend their thinking, provide evidence, and refer back to the text because it makes sure they are accurate and precise--it just so happens that students who do this tend to do better on standardized tests. <br /><h4>4. Basic test taking strategies should be taught and practiced</h4><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pausing-Points-Test-Taking-Strategies-1738271"><img alt="test taking strategies" border="0" height="426" src="https://4.bp.blogspot.com/-Sj2tJ0G1-pU/WMRtEh0YhyI/AAAAAAAAZJ8/Fb0aovEJNQEpRbT2zmxGi3JteqvJJKZcwCLcB/s640/test%2Bimage.jpg" title="standardized testing" width="640" /></a></div><div><br /></div><div>Let's be honest--there are certain test taking skills that simply need to be taught and practiced to make sure students have every opportunity to be successful. I have included a partial list of some of those strategies that I try to touch on throughout the year--and then do a little "booster" review before the actual test.</div><div><ul><li>Reading all answer choices before choosing</li><li>Try inserting answer choices into the question to see if they make sense</li><li>Rule out bad choices and choose the best of the remaining ones</li><li>Use scratch paper rather than relying on your memory</li><li>Read and reread</li><li>Answer constructed response questions fully</li><li>Look for multiple part questions</li><li>Use graphics, maps, charts, and graphs carefully and look for all the details included in them</li><li>How to ignore tricky words and names</li><li>Rereading and revising written answers</li><li>Double checking to make sure all questions have been answered</li><li>and more!</li></ul></div><h4>5. I make sure my students have the technology experiences needed to be successful.</h4><div>Our testing is done on the computer, so one of the best uses of my time is to make sure that technology skills do not get in the way of student success. For me, this includes making sure that ALL YEAR we work on keyboarding and other skills so that no matter what the question, they are equipped to navigate it. Using the keypad to drag and drop, highlighting text, and using online manipulatives are all great ways to build that confidence. If your testing is done online, there are online practice tests that I highly recommend to build students' familiarity with the tools and resources they will be using. This is all a part of that risk-taking as well--students with lots of tech practice are more likely to dig in and attack questions--even if they haven't seen them before.</div><div><br /></div><div>If you take paper and pencil tests, students do need to know how to fill in the bubbles, make sure they make no other marks, use their scratch paper for work, and then transferring their answers to the book. Whatever "test technology" you use, we want to make sure that the students don't make mistakes BECAUSE of it.</div><h4>6. Good readers and thinkers are good test takers; providing quality instruction all year is the key to successful test taking!</h4>I think if you were to summarize my thoughts about test prep, you would find something like this:<br /><br /><ul><li>Good instruction ALL YEAR is more effective than trying to cram in review material before the test.</li><li>Building the climate for success and valuing effort and hard work are better than building up the "worry" and high-stakes nature of the tests.</li><li>There are easy test-taking strategies that are useful and worth teaching.</li><li>"Real world" reading skills such as rereading, using graphic and images, and "proving" ideas by revisiting text is not just good for test-taking--but just overall good reading.</li><li>"If you teach it, they will come" is my motto--I'd rather make sure I teach well all year and know it will pay off in good thinkers, confident students, and a testing climate that is low stress and reasonable.</li><li>Students need exposure to great reading, great writing, amazing science and social studies, and they need to WANT to show what they know. It's a climate and culture of learning and achievement. We can impact that!</li><li style="text-align: center;">Providing some low-pressure review materials never hurts. For example, I use these task cards as warm ups to just get students talking about different math concepts in those few weeks before the test just to get some of those different problem types back in front of them.<a href="https://www.teacherspayteachers.com/Product/Spiraled-Math-Foundation-Station-Task-Cards-Grade-4-Sets-1-3-BUNDLE-2474489"><img alt="math test prep" border="0" height="400" src="https://4.bp.blogspot.com/-TLT6WgOU66Y/WMRrX9xO0aI/AAAAAAAAZJw/d9FyyHjHBdYXbP5blzI2G0WZQzvyfWImQCLcB/s400/spiral%2Btask%2Bcard%2Bgrade%2B4%2Bbundle%2Bset%2B1-3.jpg" title="sprialed math review" width="400" /></a></li><li>Finally, remember that our students are little sponges who absorb whatever vibes we send out to them! No matter what pressures you are feeling from administration, the public, social media, or yourself, walk through that classroom door and make sure that you send a positive, controlled, "We GOT this!" message to your students.</li></ul><br />If you are interested in another post I wrote about test prep, just <a href="http://www.theteacherstudio.com/2015/03/constructivist-test-prep-you-bet.html">CLICK HERE.</a> If you are interested in the resource that I work from as a part of my "minimalist" test prep, you can click the image below.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pausing-Points-Test-Taking-Strategies-1738271"><img border="0" height="320" src="https://3.bp.blogspot.com/-h5YvW2GYKXU/WMSZEgTvmpI/AAAAAAAAZKU/k1m3CpaGwr02GVN-D3Mx8Exvb-2-gqD9wCLcB/s320/pausing%2Bpoint%2Btest%2Bprep.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Interested in pinning this post for later? Here you go!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pausing-Points-Test-Taking-Strategies-1738271"><img alt="test prep ideas" border="0" height="640" src="https://3.bp.blogspot.com/-UDCsHon20Vo/WMVMHuHcclI/AAAAAAAAZKo/vHlfuMUZMzwt_2842qt4QGpAD6zQ4WP_ACLcB/s640/test%2Bprep%2Bpin%2Bpost%2Bmarch%2B12%2B2017.jpg" title="standardized testing" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;">Thanks for stopping by!</div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com2tag:blogger.com,1999:blog-8072938188438508721.post-61280015032494379322017-03-10T19:23:00.000-06:002017-03-12T16:11:32.848-05:00Multiplication Estimation Sorts <div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img alt="teaching estimation lessons" border="0" height="332" src="https://3.bp.blogspot.com/-0A95xg9phg8/WMNNkRXCTwI/AAAAAAAAZJA/vumlHIGUy84UyLFWEYfGLPQdCXE6rv2sQCLcB/s640/multiplication%2Bconcept%2Bsort%2Bpost%2Bmarch%2B10%2B2017.jpg" title="estimation with multiplication" width="640" /></a></div>So...as you may know, using math concept sorts is one of my absolute favorite strategies to get students thinking and talking about math. I often used them sporadically in my units....sometimes as a "kick off" to see what they know...sometimes in the middle...sometimes as a review.<br /><br />Today I thought I'd use one of my sorts that we didn't get to earlier as a great test prep review of multiplication and estimation. I thought, "This will be an easy one...a good 25 minute warm up."<br /><br /><a name='more'></a>False.<br /><br />What I had planned to be a basic warm-up turned into a 45 minute, in-depth study! It was SO much more challenging than I thought it would be. Here's what we did.<br /><br />This particular sort is a little unusual...it has 24 cards of multiplication problems; students are asked to use estimation to find 12 pairs that have similar estimated products. Simple enough, right? I encouraged students to jot down their estimated numbers to help them--and figured it would be a pretty quick task!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img alt="estimation" border="0" height="480" src="https://2.bp.blogspot.com/-666E8MptTtY/WMM6spiZ7_I/AAAAAAAAZIM/RzvhSrlHurAsq_pOSYcDH_EXQr0wiTO6wCLcB/s640/Photo%2BMar%2B10%252C%2B5%2B38%2B24%2BPM.jpg" title="teaching multiplication" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img alt="estimation" border="0" height="640" src="https://1.bp.blogspot.com/-Sdv6pkNH8dE/WMM6s-OA0rI/AAAAAAAAZIQ/2WKrqZi87EoWfNzDToowYvu1iGw3AKR5wCLcB/s640/Photo%2BMar%2B10%252C%2B5%2B38%2B44%2BPM.jpg" title="teaching multiplication" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">Groups started to find pairs (some faster than others, of course) as I circulated to encourage groups to stay on task and for ALL three members of the group to participate actively. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img alt="estimation" border="0" height="480" src="https://2.bp.blogspot.com/-pSDxk1CkI7I/WMM6s_NXKfI/AAAAAAAAZIU/HnIwwhzhLHg9EaBKSbdhOMYMlNWONIaJACLcB/s640/Photo%2BMar%2B10%252C%2B5%2B39%2B11%2BPM.jpg" title="teaching multiplication" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img alt="estimation" border="0" height="480" src="https://2.bp.blogspot.com/-MXmspcfp1eE/WMM6tUC7zkI/AAAAAAAAZIY/RMiIix8WKAgZyleGnIWkxAaT8l0ZGJiDACLcB/s640/Photo%2BMar%2B10%252C%2B5%2B39%2B34%2BPM.jpg" title="teaching multiplication" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">I started to notice that groups were having a hard time finding pairs...that they seemed to be really struggling to find a strategy to help them be methodical. I brought them back together as a group to do some talking about how to work in an organized fashion--encouraged my groups having success to share their ideas, and then sent them back off to work.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img alt="standards for mathematical practice" border="0" height="480" src="https://3.bp.blogspot.com/-3LdR6d4ziE0/WMM6uRTPq4I/AAAAAAAAZIc/Gc3WPhP4kBsrgSQatzajDH1TDV3PH6S9ACLcB/s640/Photo%2BMar%2B10%252C%2B5%2B39%2B50%2BPM.jpg" title="teaching multiplication" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Things started going a little bit more smoothly but students were still having a harder time than I thought coming to consensus on how to best round each number. I walked around and did a little more coaching and encouraged easier rounding (not 410 x 30...but 400 x 30) to speed things up.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">After a few more minutes I called "time" and told them to glue down all the pairs they had completed and asked them to take on step 2....deciding WITHOUT SOLVING EXACTLY which card in each pair was larger. I reminded them to really think about what we know about estimating (for example, if both numbers rounded UP, that estimate may be way too high compared to a problem where one rounds up and one rounds down). I circulated to listen to their discussions and how they worked to come to agreement on which of the two cards truly was larger. Lots of great math talk!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img alt="multiplication activities" border="0" height="640" src="https://4.bp.blogspot.com/-RbdmiEXF05w/WMM6ujoP33I/AAAAAAAAZIg/C71VlbuN23UZnlel7jSGom4STkqoKSwxgCLcB/s640/Photo%2BMar%2B10%252C%2B5%2B40%2B08%2BPM.jpg" title="standards for mathematical practice" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img alt="multiplication activities" border="0" height="640" src="https://3.bp.blogspot.com/-P3ivU7hu9nw/WMM6v9TBLOI/AAAAAAAAZIs/_K6UJaFuO9IHPen1gzYooNXG_EGFxLUFwCLcB/s640/Photo%2BMar%2B10%252C%2B5%2B41%2B31%2BPM.jpg" title="standards for mathematical practice" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">A few groups were struggling so I gathered everyone back at the easel (note the "math in real life" easel...no fancy anchor chart! This is math in the trenches!) to do a few samples where we played with numbers a little bit to see how altering our estimates can impact the product. For example, the top problem we looked at the difference between rounding the 76 to 80 and using 75, another easy number. We had some great discussions! I sent them back to their groups for a few more minutes of experimenting and then asked them to do the final step.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img alt="estimation with multplication" border="0" height="480" src="https://1.bp.blogspot.com/-Oe1MBJjQ8pM/WMM6uyVeBII/AAAAAAAAZIk/eCtb1MPF8GIBGvrhEmSL8klnq3-n2I9LACEw/s640/Photo%2BMar%2B10%252C%2B5%2B40%2B22%2BPM.jpg" title="standards for mathematical practice" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">After a few minutes, I asked them to each pick one or two of their "pairs" to solve exactly--and to look at their actual products as compared to their estimated products. It was fascinating to see how many teams found errors in estimating as they worked and had some new insight about WHY their estimates were either close--or not--to the actual product.</div><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img alt="two digit multiplication" border="0" height="480" src="https://4.bp.blogspot.com/-jGUcMrF27rs/WMM6vcLiYaI/AAAAAAAAZIo/ykD9nf8TwtEYy2pvJVDmBKa3lamHeGUUACEw/s640/Photo%2BMar%2B10%252C%2B5%2B40%2B46%2BPM.jpg" title="standards for mathematical practice" width="640" /></a><br /><br /><div class="separator" style="clear: both; text-align: left;">As is often the case, the result of this lesson didn't look exactly like I had planned--but we definitely got some amazing learning and thinking out of it! This is one of the sorts in my Multiplication Sort resource...the other sorts cover a variety of multiplication processes from basic facts to extended facts to prime and composite numbers and more! Just click the image below if you want to see more. I just love how sorts allow you to not just teach important MATH concepts--but those ever important math processes like discourse, modeling, patterning, and more. This set is all multiplying--but I have others for fracitons, geometry, angles, algebra thinking, and more!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img border="0" height="320" src="https://2.bp.blogspot.com/-UHOBFSub7dQ/WMM1hR3-GnI/AAAAAAAAZIA/INLztBJ6CaUB2BGxPS9cQLOeGUGV8GNMACEw/s320/concept%2Bsorts%2Bmultiplication%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Want to pin it for later?</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-Concept-Sorts-A-Set-of-5-Multiplication-Sorts-for-Grades-4-and-5-1519691"><img alt="teaching multiplication" border="0" height="640" src="https://3.bp.blogspot.com/-T6k2w-jpt5E/WMNQPsF43lI/AAAAAAAAZJM/08s25nu-F7op8WZM5EUB_zYGhaKnfhY1wCLcB/s640/estimation%2Bmultiplication%2Bconcept%2Bsort%2Bpost%2Bpin.jpg" title="estimation with multiplication" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-78246442932415099042017-03-07T22:06:00.001-06:002017-03-12T16:11:42.274-05:00Why Line Plots? Deep Thinking, Test Prep, and More!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Line-Plot-Toolkit-Activities-Investigations-and-Assessments-3045828"><img alt="measurement" border="0" height="332" src="https://1.bp.blogspot.com/-YCVEbx5u7d4/WL3uLw3FmXI/AAAAAAAAZGM/XK_jWpg8cd4EQMbLurwe1M7yoeDAA7Q4gCLcB/s640/line%2Bplot%2Bpost%2Bimage%2Bmarch%2B6%2B2017.jpg" title="teaching line plots" width="640" /></a></div>Chances are, if you teach third through fifth grades, the term "line plots" has become a part of your vocabulary. If you give standardized tests, you've probably realized that test makers love them! Unfortunately, many textbooks and other resources really don't seem to provide many rich and meaningful experiences with line plots. Most activities are simple "create the plot" activities or are sets of questions that ask very basic information about the plots. I wanted to find a way to make line plots more meaningful to my students, so I started by thinking of the following questions:<br /><a name='more'></a><br /><b>1. When are line plots meaningful?</b><br /><b>2. What misconceptions do students have regarding line plots?</b><br /><br />I started by thinking of real-world situations where we could explore line plots in a fun way (knowing that our test and our standards want students to be able to plot data with both whole numbers and fractions). I know my students love to move and love to be engaged and busy--so I set to work brainstorming. I know that our current unit of measurement was a GREAT place to start--we could tie in our metric conversions and really make this a great learning experience.<br /><br />I decided to set up some stations where we would collect data...we measured the length of our feet to the nearest 1/2 inch. We measured our wrist circumference to the nearest 1/2 cm. We measured our standing broad jump to the nearest 1/4 foot. We measured how far we could blow a cotton ball with a straw to the nearest cm. <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Line-Plot-Toolkit-Activities-Investigations-and-Assessments-3045828"><img alt="measurement lesson" border="0" height="640" src="https://1.bp.blogspot.com/-CtmUYB-xjNM/WL9-Yd1ncMI/AAAAAAAAZG0/HubENtjXyXgCyHe1BTyyA9V_f4LjYsjHwCLcB/s640/Photo%2BMar%2B07%252C%2B9%2B43%2B04%2BPM.jpg" title="teaching line plots" width="552" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Line-Plot-Toolkit-Activities-Investigations-and-Assessments-3045828"><img alt="measurement lessons" border="0" height="480" src="https://1.bp.blogspot.com/-g3x9yxJDhOg/WL-BHn0c5EI/AAAAAAAAZHQ/iwOAq4V6ktwjx-QpI67fLBuU0kmEBjemACEw/s640/Photo%2BMar%2B07%252C%2B9%2B55%2B45%2BPM.jpg" title="teaching line plots" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Line-Plot-Toolkit-Activities-Investigations-and-Assessments-3045828"><img alt="test prep" border="0" height="480" src="https://2.bp.blogspot.com/-zSWwM5sZ_kA/WL9-W_N1xHI/AAAAAAAAZGo/grhZdsyoZhADJeJ2Qf3BKclltxrQkTnfACLcB/s640/Photo%2BMar%2B07%252C%2B9%2B40%2B22%2BPM.jpg" title="teaching line plots" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Line-Plot-Toolkit-Activities-Investigations-and-Assessments-3045828"><img alt="test prep" border="0" height="480" src="https://3.bp.blogspot.com/-2-iNQykJT8o/WL9-YetJyOI/AAAAAAAAZGw/u3Q-d60fj1Apk9Hsm8UgaKfmBZ5ZyIY1ACLcB/s640/Photo%2BMar%2B07%252C%2B9%2B39%2B38%2BPM.jpg" title="teaching line plots" width="640" /></a></div>At each station, I made a big line plot for students to add data to...and then we got ready to roll! We met together to talk about some key measuring factors and expectations and reviewed how to measure to fractions of units. We talked about sportsmanship (positivity only!), rule following, and then I asked the question, "How can we make sure we work with as much precision as possible?"<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Line-Plot-Toolkit-Activities-Investigations-and-Assessments-3045828"><img alt="test prep" border="0" height="480" src="https://3.bp.blogspot.com/-QoUJjT0Kwqg/WL9-XSQElvI/AAAAAAAAZGs/JI1dpnjnYnsIjL2AswLm5BAsuF7Et-yEACEw/s640/Photo%2BMar%2B07%252C%2B9%2B39%2B59%2BPM.jpg" title="teaching line plots" width="640" /></a></div>We had a great discussion about consistency, about coming to an agreement about techniques (left foot or right foot? Shoes on or off? Standing or sitting?) so we could make sure we were as fair and scientific as possible. Once all the questions were answered, we were off! It was actually a great piggyback discussion to our science work from a few weeks back about keeping things "constant"! At each station, I had students record in a different way...just a marker to make an "X" at one, orange sticky dots at one, and stickers at another. I want them to realize that HOW the data is recorded isn't as important as the data itself.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Line-Plot-Toolkit-Activities-Investigations-and-Assessments-3045828"><img alt="test prep" border="0" height="480" src="https://3.bp.blogspot.com/-ngUHV5INoMg/WL-BHywnI4I/AAAAAAAAZHU/Ug-3WeTzQcQ3anXqUPcN-SzqjcHOh4skACLcB/s640/Photo%2BMar%2B07%252C%2B9%2B55%2B28%2BPM.jpg" title="teaching line plots" width="640" /></a></div>I had a blast walking around the stations, talking to them, asking them questions, helping them make predictions, and watching and reminding students to record their data on the line plots. When we were finished, it was time to bring the plots up to the easel and analyze them!<br /><br />We had some amazing discussions...we talked about what data we COULD find...what data we could NOT find...we talked about the term "outlier" and discussed all the reasons a data point (or more) might not fit the rest of the plot--from operator error to just unusual data! I started to ask them trickier questions...like if all the students who jumped 5 1/4 feet added their jumps together, how far would it be? One student asked a question that brought me back to my questions from the beginning--why are line plots meaningful (I think the students bought into that!) and then the idea of misconceptions--and I realized that not all my students realized a very key thing about line plots--that every mark on the plot represents one "vote" or one "person" or one piece of data. It seemed so obvious to me...but it wasn't to all. It was an easy fix--and then I found my second misconception--the idea of "most".<br /><br />On a line plot, you can ask two big question related to "most"...which category had the most "votes" (the "winner"...the tallest bar in a bar graph, etc) but also the "most" might refer to the biggest category...the biggest foot, the longest jump, and so on. We had quite the discussion about how important it is to read the question and to think about what is being asked; the greatest "jump" is very different than which CATEGORY got the greatest number of tallies.<br /><br />I think we are ready to try some trickier problems...so I am ready to sprinkle some line plot practice in over the next weeks to keep these ideas fresh in their minds before we do our state testing in April. I think they'll have a much deeper understanding now!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Line-Plot-Toolkit-Activities-Investigations-and-Assessments-3045828"><img alt="test prep" border="0" height="240" src="https://3.bp.blogspot.com/-WLfXly4B6Jg/WL9_vPyfnvI/AAAAAAAAZHA/uZIEMfYCaHEFkj9rbYsF3H_mi_TTeNrNgCLcB/s320/Slide10.JPG" title="teaching line plots" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Line-Plot-Toolkit-Activities-Investigations-and-Assessments-3045828"><img alt="test prep" border="0" height="240" src="https://1.bp.blogspot.com/-2dYrwiLGOXI/WL9_vAUnkLI/AAAAAAAAZG8/zysE2slqAqci3mVuE4j9Fg17TMWYmwM8ACLcB/s320/Slide49.JPG" title="teaching line plots" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">I put all of the hands-on activities, the line plot recording sheets, and a ton of practice pages, teaching tips, and assessment pages together in toolkit if you are having a hard time finding good line plot resources like I was. </div><div class="separator" style="clear: both; text-align: center;">See what you think!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Line-Plot-Toolkit-Activities-Investigations-and-Assessments-3045828"><img border="0" height="320" src="https://2.bp.blogspot.com/-f5zMMUraAwI/WL9_-un88JI/AAAAAAAAZHE/YP2WhkLrbicGrrchYKDwG5UZUgdK6HeMQCLcB/s320/line%2Bplot%2Btoolkit%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Want to pin this post for later?</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Line-Plot-Toolkit-Activities-Investigations-and-Assessments-3045828"><img alt="test prep" border="0" height="640" src="https://2.bp.blogspot.com/-tRGWMC288uk/WL-FrA2Vx6I/AAAAAAAAZHg/idaSRXXfZYYAOvr79WcEWZ6BHxh5-Aj8ACLcB/s640/line%2Bplot%2Bblog%2Bpost%2Bmarch%2B7%2B2017.jpg" title="line plots" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-76085248719930436042017-02-27T21:58:00.000-06:002017-03-12T16:11:51.990-05:00Teaching Dialogue and Why It's So Important!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-the-Power-of-Dialogue-Creativity-Task-Cards-1697095"><img alt="teaching narrative writing" border="0" height="332" src="https://2.bp.blogspot.com/-XMw3kkWxbdU/WLTMbsYcxII/AAAAAAAAZEg/gZMm4MNuyNw39cA43KTrq1Yme6veeTZBACLcB/s640/dialogue%2Bblog%2Bpost%2Bimage%2Bfebruary%2B27%2B2017.jpg" title="teaching dialogue" width="640" /></a></div>We are digging into a fun narrative writing unit to complement our historical fiction unit. I know many of you write personal narratives...many write realistic fiction...mysteries--you name it. One of our fun writing projects is to take a scene from one of their historical fiction book club books and rewriting it through the eyes of a different character. It's so much fun to talk about point of view and how we can take a very "known" event and make it our own.<br /><a name='more'></a><br />In order to really tie back to our writing standards, I use parts of the same planning guide I used earlier in the year--but without having to create the character. (Not sure what I'm talking about? Check out <a href="http://www.theteacherstudio.com/2016/10/loving-our-narrative-writing-unit.html">this post</a>). We brainstormed those ever important setting clues (which they were quite familiar with since they just finished reading the book!) and then dug into planning their stories. Watch for a post on the drafting process soon!<br /><br />Before we dig into writing, I wanted to do a quick review on dialogue--both the reasons WHY writers use dialogue and HOW they punctuate/write it correctly. It's a tough writing skill for intermediate students--especially with all the different ways one can punctuate and format it!<br /><br />To start, I wanted my students to really study the WHY--something we started with our book clubs and our read aloud. We talked about how dialogue should have a purpose; we've all heard stories that unfold a little something like this.<br /><br />"Hey. What are you doing?"<br />"Going to the park."<br />"Why?"<br />"For baseball."<br />"OK."<br />"What are you doing?"<br />"Nothing" <br /><br />(Kind of reminds me of teenagers texting, to be honest!)<br /><br />Is it dialogue? Yes. Is it adding meaningfully to a story? Not so much. We talked about all the things dialogue can help an author do...this list is just a smattering of ideas--certainly it is not meant to be all-inclusive, but I think it's interesting for students to see that dialogue has a purpose--and they can experiment with these as they begin drafting!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-the-Power-of-Dialogue-Creativity-Task-Cards-1697095"><img alt="dialogue anchor chart" border="0" height="640" src="https://4.bp.blogspot.com/-kzZW9dHytUE/WLS8kTaKKVI/AAAAAAAAZEI/mL9s6qugipIBopAFEcGrDBTOvzHVTdqAgCEw/s640/Photo%2BFeb%2B27%252C%2B5%2B48%2B52%2BPM.jpg" title="teaching dialogue" width="480" /></a></div>In fact, as I read my read aloud now, I will highlight certain examples of dialogue for us to consider how it is helping the author convey the big ideas of the story. There are TONS of great examples in Number the Stars, our current read aloud! I think it's really valuable for students to realize that writers are intentional with things like this--and that understanding this can help them not only improve their WRITING--but understand their reading more deeply as well.<br /><br />The next thing I wanted to review is the actual "rules" for punctuating dialogue. We had done lessons on this earlier this year, but it is definitely something that needs lots of repetition. We reviewed by using the following anchor chart and I put up several examples of dialogue. We highlighted each of these features with different colors. I forgot to take a picture of that! Sorry!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-the-Power-of-Dialogue-Creativity-Task-Cards-1697095"><img alt="teaching dialogue" border="0" height="640" src="https://1.bp.blogspot.com/-P56bLadOOtI/WLTiDlFEG3I/AAAAAAAAZFc/4ZWic7Ej4zcyP2j5a2pYB3R7NackIiD9ACLcB/s640/Photo%2BFeb%2B27%252C%2B8%2B34%2B57%2BPM.jpg" title="dialogue anchor chart" width="480" /></a></div>After we had reviewed, I wanted to model some dialogue writing with my own "think alouds" to show how to punctuate it. I pulled out my dialogue writing cards that we had used earlier this year and told my students that we were going to get creative. I reminded them of how SERIOUS our historical fiction stories are--so this was our chance to let loose a little!<br /><br />I started with this card and had them talk in trios about what Melanie could possibly say to a lifeguard...and we had some hilarious ideas. I picked one and wrote it down under the document camera. <br /><br />We then went back to our groups to discuss what the lifeguard could say back--and we had so much fun! I then had the students try their own versions of this same dialogue--with the reminder to be appropriate!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-the-Power-of-Dialogue-Creativity-Task-Cards-1697095"><img alt="writing task cards" border="0" height="480" src="https://2.bp.blogspot.com/-ddU4Fq_ruJ4/WLS8kOWtwfI/AAAAAAAAZEE/hFuMmn2iBOkvr2uRkfHw1x-riQHMkeaSACLcB/s640/Photo%2BFeb%2B27%252C%2B5%2B50%2B05%2BPM.jpg" title="teaching dialogue" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-the-Power-of-Dialogue-Creativity-Task-Cards-1697095"><img alt="writing lesson ideas" border="0" height="480" src="https://4.bp.blogspot.com/-R_pkdtUNt0k/WLS8hiPv7DI/AAAAAAAAZD8/UqKqYU8C5740BfijOn-BVJkcmhiSj_iLACEw/s640/Photo%2BFeb%2B27%252C%2B5%2B46%2B00%2BPM.jpg" title="teaching dialogue" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">After that, I added three more cards under the document camera and let students do a "four corners" type activity where they chose which card they wanted to work on--more work with the lifeguard card or one of the other three. They broke off into groups and got to work. I reminded them to refer to our model on the board for correct punctuation and capitals, and I circulated and coached.</div><a href="https://www.teacherspayteachers.com/Product/Teaching-the-Power-of-Dialogue-Creativity-Task-Cards-1697095" style="margin-left: 1em; margin-right: 1em;"><img alt="teaching dialogue" border="0" height="480" src="https://3.bp.blogspot.com/-rPybVLCWmjw/WLS8hSQSE5I/AAAAAAAAZD4/nfK8_apng3sSZDcILB9Df2NEYEQ7FD9cwCEw/s640/Photo%2BFeb%2B27%252C%2B5%2B47%2B51%2BPM.jpg" title="writing lesson ideas fourth grade" width="640" /></a><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-the-Power-of-Dialogue-Creativity-Task-Cards-1697095"><img alt="fourth grade writing lessons" border="0" height="480" src="https://3.bp.blogspot.com/-P92YKjQWy3Y/WLS8hSBc-_I/AAAAAAAAZD0/B588MV_kBX4DlANcb4aIur0shfFcsHblwCEw/s640/Photo%2BFeb%2B27%252C%2B5%2B47%2B25%2BPM.jpg" title="teaching dialogue" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">Overall, it was a great review lesson that also served to spark excitement for infusing dialogue into their historical fiction stories. Watch for a blog post about how we took our planning and turned it into a draft!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;">Want to pin this post for later?</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-the-Power-of-Dialogue-Creativity-Task-Cards-1697095"><img alt="writing lessons" border="0" height="640" src="https://1.bp.blogspot.com/-EyYGchLtoNA/WLTRaW5WkeI/AAAAAAAAZE0/KTuifW5Yi0wum78_O4zaTbG7ZfC1OJATACLcB/s640/teaching%2Bdialogue%2Bpost%2Bfebruary%2B27%2B2017%2Bpin.jpg" title="teaching dialogue" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Interested in the task cards shown above? Click the image below to see more. This resource is also a part of a discounted Teaching Tandem available by clicking <a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Teaching-Dialogue-2375552">HERE</a> and a set of four narrative writing resources which can be found by clicking <a href="https://www.teacherspayteachers.com/Product/Narrative-Writing-BUNDLE-Helping-Students-Write-Quality-Narratives-Grades-3-5-2810248">HERE</a>.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-the-Power-of-Dialogue-Creativity-Task-Cards-1697095"><img border="0" height="320" src="https://3.bp.blogspot.com/-FAwlZZybv4Y/WLTT-rM6FMI/AAAAAAAAZFE/Ffh8mXwcL60CZzk8bbq1APCpmD6dgvgbgCLcB/s320/creativity%2Bdialogue%2Btask%2Bcards%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-22549810884781517062017-02-23T18:42:00.000-06:002017-03-28T15:58:55.923-05:00Building Math Confidence: Revisiting Familiar Tasks<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Algebra-Thinking-Balancing-Equation-Problem-Solving-Task-Cards-2787290"><img alt="math process standards" border="0" height="332" src="https://3.bp.blogspot.com/-nxGVk76GfFs/WK-XXaTTOKI/AAAAAAAAZDU/_TwA1LcaMmADAUh3xQ7OujqtXdn9MYNEgCLcB/s640/building%2Bmath%2Bconfidence%2Brevisiting%2Bblog%2Bpost%2Bfebruary%2B23%2B2017.jpg" title="algebra thinking" width="640" /></a></div>When you have students that struggle, they spend an awful lot of time feeling frustration with the lessons and other activities we do. They often "check out"--and the cycle continues.<br /><br />One thing I have started to do about this time of year is to go back to some of the activities earlier in the year that I know some of my less able students really struggled with--and weren't even willing to try doing and pull them out again--sometimes with a new twist, but always with a "You know...this fall, I know this was tricky for you, but I have seen how much you've grown and I know you're ready for it now!" type of comment.<br /><a name='more'></a><br />That was the case way back at the beginning of the year when I was working on some algebra thinking concepts with my students, and I introduced them to my algebra thinking "balance" task cards. After the first card or two, they checked out. I mean--CHECKED OUT. I tried encouraging them, got out counters--but, alas, I had no success.<br /><br />Well, we've come a long way in both our math thinking and our math confidence, so I decided it was time again! I broke out the cool jewel counters and pulled a group of four over to re-introduce them to the task.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Algebra-Thinking-Balancing-Equation-Problem-Solving-Task-Cards-2787290"><img alt="math task cards" border="0" height="480" src="https://3.bp.blogspot.com/-v2Q_8VzHdhk/WKoN633jaUI/AAAAAAAAZAc/C-eQP5sFBLwGXa67QMntzlMFQlcW-OJ3QCLcB/s640/Photo%2BFeb%2B19%252C%2B4%2B22%2B11%2BPM.jpg" title="perseverance and math practices" width="640" /></a></div>As I suspected, they "sort of " remembered doing these cards but had no clue what to do. I reminded them of the concept of "equal" that we have been doing all year...and that I was SO confident that their reasoning and thinking skills were SO much better that they could tackle these now when before they seemed impossible.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Algebra-Thinking-Balancing-Equation-Problem-Solving-Task-Cards-2787290"><img alt="algebra thinking" border="0" height="480" src="https://3.bp.blogspot.com/-OnwBQw_0d6Y/WKoN9PTaTyI/AAAAAAAAZAg/wAVDZvS8HeAEmBjKtHqMa6kDhYckhWltACLcB/s640/Photo%2BFeb%2B19%252C%2B4%2B22%2B30%2BPM.jpg" title="perseverance and math practices" width="640" /></a></div>Step 1: We talked about the idea of "balance"...and if there are 20 TOTAL jewels, how many would be on each side? Earlier this year, these kiddos did NOT know how to divide numbers larger than 10 in half...so our first accomplishment was noted! Because I knew that this was going to need to be visual, we divided our 20 jewels and showed how they would balance.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Algebra-Thinking-Balancing-Equation-Problem-Solving-Task-Cards-2787290"><img alt="task cards" border="0" height="480" src="https://1.bp.blogspot.com/-gA8LW_jG6-0/WK9qCVvqI6I/AAAAAAAAZCM/qsnDvRUrtS4kR03O_XZvRh9KbhDpEiSRACLcB/s640/Photo%2BFeb%2B23%252C%2B4%2B53%2B17%2BPM.jpg" title="perseverance and math practices" width="640" /></a></div> Next, we looked at the next rule (we had already discussed how no two colored jewels could be the same weight, etc) which stated that "green plus green equal purple". We brainstormed some possible ways to make that happen--and then started using "guess and check" to try them out. It was so much fun to watch them try something, rule it out,, and then adjust. They had a ball!<br /><br />On attempt number 4, they got it! There were high fives all around--and "Can we do more?" Ummmm...YES, yes you can. I sent them off to try another one in pairs and I heard some of the greatest math talk and cooperation. I think so often we want to "skill and drill" our strugglers and forget to take the time to immerse them in real number sense and algebra thinking experiences--and they will absolutely need these skills as they move to more difficult math.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Algebra-Thinking-Balancing-Equation-Problem-Solving-Task-Cards-2787290"><img alt="teaching algebra thinking" border="0" height="480" src="https://4.bp.blogspot.com/-e4sh3z45xf8/WK9qFTVSbyI/AAAAAAAAZCQ/sImJQs04NnYNTPFipnEzXfhMWVCQrIocQCLcB/s640/Photo%2BFeb%2B23%252C%2B4%2B53%2B42%2BPM.jpg" title="perseverance and math practices" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">The best part of this whole intervention group was watching their faces absolutely GLOW with the realization that they DID IT...they didn't think they could, but by thinking deeply and guessing and checking, they were able to logic their way through it. I reminded them that "math makes sense" and they actually agreed! I can't wait to revisit some other tasks that I know stumped them earlier this year to show them how much their math thinking has grown.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Want to try one of these challenges with some of YOUR kiddos?</div><div class="separator" style="clear: both; text-align: center;">I have a free sample and a resource with a bunch of them if you think this kind of activity would be good for your students. Here is the link to the free one...click any other image in this post to go to the full resource. I'd love to know if you try it, how it goes!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Algebra-Thinking-Balancing-Equation-Task-Card-FREEBIE-3023518"><img border="0" height="320" src="https://3.bp.blogspot.com/-4U6b3G3Uhc4/WK9zSeLgueI/AAAAAAAAZDA/T6A6wm3NHLU4F5XN12SOtdcrj3Fly4EeQCEw/s320/balance%2Btask%2Bcard%2Bfreebie%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Want to pin it for later? Here you go!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Algebra-Thinking-Balancing-Equation-Problem-Solving-Task-Cards-2787290"><img alt="perseverance and math practices" border="0" height="640" src="https://4.bp.blogspot.com/-rQ-SWtpwVGg/WK9t_rk5JtI/AAAAAAAAZCg/2XteVjneN2wmA68zrSl3Fc1igaD7-0WlwCEw/s640/revisiting%2Bchallenges%2Bpost%2Bfebruary%2B23%2B2017%2Bpin.jpg" title="math challenge" width="320" /></a></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com2tag:blogger.com,1999:blog-8072938188438508721.post-64126751613287326752017-02-19T11:10:00.000-06:002017-03-12T16:16:20.329-05:00Fraction Concepts Day 2! Conceptions, Misconceptions, and Mathematical Language<div style="text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="teaching fractions" border="0" height="640" src="https://2.bp.blogspot.com/-lxNiLZUqtdU/Vj0OHN6_7MI/AAAAAAAAO_o/InaiVGr-n8E/s640/fraction%2Bblog%2Bpost%2B2.jpg" title="fraction understanding" width="394" /></a></div><span style="font-size: large;">Well, things got even more interesting as my fraction unit unfolded on day 2! For those of you who read my first fraction post, I discussed how we used paper folding to get our fraction concepts unit "launched", and we ran out of time to finish the investigation. I gave them another 25 minutes today to work on folding their different fractional amounts and then asked them to spend some time writing in their math notebook on any of the following:</span><br /><span style="font-size: large;"><br /></span></div><div style="text-align: center;"><span style="color: #3d85c6; font-size: large;">What did you notice?</span></div><div style="text-align: center;"><span style="color: #3d85c6; font-size: large;"><br /></span></div><div style="text-align: center;"><span style="color: #3d85c6; font-size: large;">What was challenging?</span></div><div style="text-align: center;"><span style="color: #3d85c6; font-size: large;"><br /></span></div><div style="text-align: center;"><span style="color: #3d85c6; font-size: large;">What was easy?</span></div><div style="text-align: center;"><span style="color: #3d85c6; font-size: large;"><br /></span></div><div style="text-align: center;"><span style="color: #3d85c6; font-size: large;">What patterns did you discover?</span><br /><a name='more'></a><span style="color: #3d85c6; font-size: large;"><br /></span></div><span style="color: #3d85c6; font-size: large;"></span> <br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fraction unit" border="0" height="480" src="https://4.bp.blogspot.com/-K0THsvM6jlo/UQmnhO_e53I/AAAAAAAABXA/rRi3lTFUSaA/s640/IMAGE_34264EBE-047C-4789-93A7-280C59A6F298.JPG" title="teaching fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">First I gave the students "alone" time to write and then let them go compare notes with their partner from the investigation...</a><br /><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><br /></a><br /><div style="text-align: left;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><br /></a></div><div style="text-align: left;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">After the students had their work time, we had a discussion about the things that they noticed...I jotted down their ideas on the Smartboard...</a></div></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="font-size: x-small;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fractions" border="0" height="480" src="https://3.bp.blogspot.com/-biGMRFKJbU0/UQmnrCmHvJI/AAAAAAAABXQ/WbpgCRutvH8/s640/IMAGE_422F20E2-1766-42FC-B56C-A0AB71AF9499.JPG" title="fraction lessons" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Not a great photo...not great handwriting...sorry!</a></td></tr></tbody></table><div style="text-align: left;"><div style="text-align: center;"><span style="font-size: 13px;">What really stood out to me was the very NEBULOUS (vocabulary word!) math language I was hearing. A phrase that kept coming up was "small fractions" as in <span style="color: #0b5394;">"It was harder to fold the small fractions."</span></span></div></div><div style="text-align: left;"><div style="text-align: center;"><br /></div></div><div style="text-align: left;"><div style="text-align: center;"><span style="font-size: 13px;">So, being the pesky and annoying teacher that I am, I presented this question to the class:</span></div></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fractions" border="0" height="480" src="https://1.bp.blogspot.com/-XarrcITBTIg/UQmnlQrlG-I/AAAAAAAABYA/faI9iFuE1yQ/s640/IMAGE_B974EDB7-CBB3-4187-B3D1-7F824486CA6C.JPG" title="fraction thinking" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Tee hee...I love to ask questions like this! </a></td></tr></tbody></table><div style="text-align: center;">I didn't let the students talk . . . I just said that I was hearing MANY students use this phrase, so I thought we had better made sure we all knew what it meant. I asked each student to write the answer to that question on a post it note and come slap it on the easel.</div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="mathematical thinking" border="0" height="480" src="https://1.bp.blogspot.com/-oV9aoliDOIU/VjGJVPp32UI/AAAAAAAAO8U/H6Z3mvpCuWM/s640/day%2B2%2Bfraction%2Bpost%2Bpinterest%2Bimage.jpg" title="fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><div style="font-size: 12.8px;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Being the obedient students that they are, they did.</a></div></td></tr></tbody></table><div style="text-align: center;">And--seriously--I only wish I had taken some photos of the notes up close. SERIOUSLY! I had everything from . . .</div><div style="text-align: center;"><br /></div><div style="text-align: center;">64</div><div style="text-align: center;"><span style="color: #741b47;"><br /></span></div><div style="text-align: center;"><span style="color: #741b47;">to</span></div><div style="text-align: center;"><br /></div><div style="text-align: center;">1/100th</div><div style="text-align: center;"><br /></div><div style="text-align: center;"><span style="color: #741b47;">to</span></div><div style="text-align: center;"><br /></div><div style="text-align: center;">"When you make it smaller"</div><div style="text-align: center;"><br /></div><div style="text-align: center;"><span style="color: #741b47;">to</span></div><div style="text-align: center;"><br /></div><div style="text-align: center;">"Small fractions are like tenths"</div><div style="text-align: center;"><br /></div><div style="text-align: left;"><div style="text-align: center;">At this point, any concerns I had about backing up this far and moving this slowly were GONE! I read off the notes to the students and then asked what we had learned about what a "small" fraction is and one of my delightful yet very shy students called out, "ABsolutely nothing!" and we all laughed hysterically.</div></div><div style="text-align: left;"><div style="text-align: center;"><br /></div></div><div style="text-align: left;"><div style="text-align: center;">So where do we go from here? I reminded the students about how we have been talking about the Common Core and how important it is to use precise mathematical language. I asked if "small fraction" was precise enough that anyone else would know what we meant. . . and we had complete agreement that it was not. I asked them if, on our 4, 3, 2 , 1 rubric we were evaluate how clearly we communicated, we agreed that all our post its were 1's with a few 2's sprinkled in . . . until "T" asked, "If there really isn't an answer, how could someone get a 4 on this?" Have I mentioned how much I love fourth graders? He honestly asked--and honestly wanted to know! I told him I had to think about it. . . always a good strategy for the tricky questions! Don't answer too soon!</div></div><div style="text-align: left;"><div style="text-align: center;"><br /></div></div><div style="text-align: left;"><div style="text-align: center;">So I set the students to work on a little activity to set them up for tomorrow's lesson...I asked them to work completely alone to answer the following question:</div></div><div style="text-align: left;"><div style="text-align: center;"><br /></div></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fraction misconceptions" border="0" height="480" src="https://1.bp.blogspot.com/-BEBAfUDt0WE/UQmnzyw4VXI/AAAAAAAABXo/4aU7aY5VgTQ/s640/IMAGE_F816EE65-7378-4B5F-94D0-2E9D9B63CEE6.JPG" title="fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">If it is too small to read, the question asks "Is this shape divided into fourths? Explain your thinking."</a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">I let them work for a few minutes and then on their way out to recess made them commit to either a "yes" or a "no" response . . . and it will be our kickoff "debate" tomorrow! Remember, one key element of the Standards for Mathematical Practice is the ability to explain one's own work and to critique the reasoning of others . . . so tune in tomorrow to see how it all shakes out!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">After they worked for a few minutes we gathered back together to talk about T's question . . . is it possible to get a 4 on a question with no answer? Maybe I should save that for another blog post . . . this one is already plenty long--but I told him that yes, I do believe you can get a 4 on a question with no answer. I reminded him that we are stressing explaining our thinking, and we could certainly do that with this question. I modeled something sort of like this (this was done aloud, not in writing . . . I'm just trying to give you the gist of it)</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #a64d79;">"I know that there are different ways to look at the idea of being small. Some people might think the numbers should be small--like in 1/2. Some people might look at the size of the pieces to determine what a "small" fraction is. Still others might think a small fraction is one where you only look at one piece of a whole--like 1/3 is small where 2/3 is big. So for the question "What is a small fraction?", it is very important to understand that there might be more than one way to answer it."</span></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #a64d79;"><br /></span></div><div class="separator" style="clear: both; text-align: center;">Would I expect a fourth grader to be able to answer like this? Maybe not today . . . but now that it has been modeled--perhaps. We must push their thinking, push their comfort level, and push them into the rigor that is required. If we make it meaningful, they can do it! Thanks for sticking with me again--sorry these are getting so long! Stay tuned to see how our debate works out . . . <span style="color: magenta; font-size: large;">I'll give you a hint--the vote was 9 "yes" to 13 "no"!</span></div><div><div><div style="text-align: left;"><span style="font-size: 13px;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"></div><div style="text-align: left;"><span style="font-size: 13px;"><br /></span></div></div></div><div class="separator" style="clear: both; text-align: center;">***UPDATE***</div><div class="separator" style="clear: both; text-align: center;">This blog post is now a part of my comprehensive fraction unit available by clicking the image below. Hundreds of teachers have now used it to change the way they teach fractions! </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img border="0" height="320" src="https://3.bp.blogspot.com/-2HwOoDzAH_4/VjGFvrklnCI/AAAAAAAAO74/RHKpd66BMSA/s320/fraction%2Bunit%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: left;"><br /></div><br />The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com7tag:blogger.com,1999:blog-8072938188438508721.post-75500235571337500342017-02-18T17:47:00.000-06:002017-03-12T16:15:51.329-05:00Fraction Folding--discovery learning<div style="text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="hands on fraction activities" border="0" height="640" src="https://3.bp.blogspot.com/-wuY79DWAyb0/Vj0Ml4XHCoI/AAAAAAAAO_g/FYGjVd02Gus/s640/pinterest%2Bimage%2Bfraction%2Bpost%2B1.jpg" title="fractions" width="394" /></a></div>Today we kicked off our fraction unit, and I think I am going to really try to do a lot of blogging about it over the next few weeks--because I will be immersed in it AND because it is such a critical component of the Common Core for intermediate grades. I think it is vital that we dialogue about ways to help students <b>build their understanding of fractions</b>, so I invite you to share along with me as I "trace" the path of our unit as it unfolds. I'll try to be clear--but you know how I tend to get wordy! I'll try to include lots of photos and work samples as I go, and I am hopeful that the rest of you will share great ideas and resources that have been successful for you.<br /><br /><a name='more'></a><br /></div><br />Again, knowing that the CCSS places a great deal of importance on fractional understanding, our district math team made a decision to build in<span style="color: cyan;"> two</span> fraction units into our year--this one and another one later which will work to tie together decimals, fractions, and a more sophisticated level of understanding.<br /><br />Today I started by asking students to reflect on what they already know about fractions and to rate their overall confidence (using our 4 3 2 1 ) scale <a href="http://fourthgradestudio.blogspot.com/2013/01/self-assess-4-3-2-1.html" target="_blank">(Click here to revisit earlier blog post about this!)</a> and the results were quite amazing! In a ten minute writing time, I got to witness a number of misconceptions, poorly explained reasoning, and a bunch of "3's" and "4's" in confidence! Good thing I had planned on starting slowly! Today we started our new math notebooks, and I explained to the students that we are "raising the rigor" one level more (poor things have heard this all year) and we are going to work hard to use our new notebooks to both record our thinking, our practicing, and our new learning. I am going to try a version of interactive notebooks, knowing that I cannot do it in true form as some teachers do . . . I'm just not quite there yet. I'll blog more about this later as it unfolds! For today, we started the section we called "Fraction Concepts" and even talked about what the word "concept" means. Fascinating! I told the students that our job through this unit would be to determine some things we could determine to be "true" about fractions and that we would be working our way through a number of these "truths" during the unit.<br /><br />Today's "truth" involved ensuring that students understand that fractions represent equal parts of something (I didn't really want to use the term "whole" yet--I don't really like to treat fractions of "objects" and "sets" differently until I have to!) and that we would be spending some time creating equal parts.<br /><br />I put the students into pairs (I love popsicle stick picking!) and gave them each 3 minutes to find a classroom object that was either a square, rectangle, or circle and was bigger than a deck of cards and smaller than a book. Each team was then assigned a color of paper and the following task:<br /><br /><span style="color: #351c75; font-size: large;">With your partner, trace and cut out your shape. You will need many of these as the investigation unfolds. Your job is to find ways to divide your shape into equal parts. . . first in two equal parts, then three, and so on. </span><br /><span style="color: #9fc5e8; font-size: large;"><br /></span><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="fraction unit" border="0" height="480" src="https://1.bp.blogspot.com/-Jm4wOnPw-ss/UQgcwI6zgMI/AAAAAAAABVU/OE3Z9Eng76U/s640/IMAGE_78FEF0C3-6C33-4308-A102-F99FE1C16AC4.JPG" title="teaching fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571">I made sure we had some circles, some rectangles, and some squares...</a></td></tr></tbody></table><span style="color: #9fc5e8; font-size: large;"><br /></span>I then showed the students the following charts--each is labeled "halves", "thirds", "fourths", and so on. As they discovered a way to fold their shape, they were asked to put it on the correct chart. . . and I was on the prowl for work that was not accurate and precise.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="teaching fractions" border="0" height="480" src="https://2.bp.blogspot.com/-ZIGgqJjqZcc/UQgctjZoICI/AAAAAAAABVE/c48UkyPOGZg/s640/IMAGE_C1ED33AF-10B1-4CB9-8FB1-CAAD470A1B74.JPG" title="hands on fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Voila! Posters are taped to the ground with deliberate "aisles" so they don't get trampled on!</a></td></tr></tbody></table><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fractions" border="0" height="480" src="https://4.bp.blogspot.com/-YQOkBkLPn7g/UQgcu4IzA0I/AAAAAAAABVM/BTL9A0J8l8o/s640/IMAGE_7039F0C0-42C7-421D-86E3-FC0E14CB2E59.JPG" title="fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Each poster is labeled with the word for the fractional part--I will use the words and different symbols interchangeably throughout the unit. NOTE: The chart does NOT say "1/3" because we were not identifying 1 out of 3 parts.</a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div>Students dug into their work and did need some frequent reminders about using straight edges, working carefully, and so on (I know--shocking!), but the were very engaged and thoughtful. I heard some pretty nifty stuff like:<br /><div style="text-align: center;"><span style="font-size: large;"><br /></span></div><div style="text-align: center;"><span style="color: magenta; font-size: large;">"Hey--as you try to get more pieces, the pieces get smaller!"</span></div><div style="text-align: center;"><span style="font-size: large;"><br /></span></div><div style="text-align: center;"><span style="font-size: large;">and </span></div><div style="text-align: center;"><span style="font-size: large;"><br /></span></div><div style="text-align: center;"><span style="color: #0b5394; font-size: large;">"Man--it's a lot harder to fold the odd numbered pieces!"</span></div><div style="text-align: center;"><span style="font-size: large;"><br /></span></div><div style="text-align: center;"><span style="font-size: large;">and</span></div><div style="text-align: center;"><span style="font-size: large;"><br /></span></div><div style="text-align: center;"><span style="color: magenta; font-size: large;">"If you fold it in half and then in half again, each half gets cut in half!"</span></div><div style="text-align: center;"><span style="color: cyan; font-size: large;"><br /></span></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.blogger.com/goog_311145528"><img alt="fraction unit" border="0" height="480" src="https://3.bp.blogspot.com/-XNs8200vPmg/UQgcxyrA0VI/AAAAAAAABVc/MgMP94FVmFM/s640/IMAGE_DE39FD3F-C2DF-4B3D-B464-7A74C1AEF7E5.JPG" title="teaching fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Tracing...</a></td></tr></tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fraction activities" border="0" height="480" src="https://4.bp.blogspot.com/-9_thfzSmoaY/UQgc3b84jsI/AAAAAAAABV0/8sNpAwG-LB8/s640/IMAGE_2DB9AA2B-1FDD-4CA5-9B3C-76A9CCDA3EC2.JPG" title="teaching fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Using a straightedge for precision...</a></td></tr></tbody></table><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fraction lessons" border="0" height="480" src="https://3.bp.blogspot.com/-gTomHc6iyx0/UQgc1BQ21JI/AAAAAAAABVs/Dybbbb1kiR4/s640/IMAGE_EFF50082-BFEB-4010-BDFB-F3BE0E18AA47.JPG" title="folding fractions" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">Circles are the toughest as this team found!</a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">As the period unfolded (and it became clear that this was going to be a TWO DAY investigation!), our charts began to fill up and things moved a little faster.</div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img alt="fraction lessons" border="0" height="480" src="https://2.bp.blogspot.com/-SSKGqo8mQnw/VjGIYfQVgiI/AAAAAAAAO8E/mGg-rnvK-xw/s640/fraction%2Bday%2B1%2Bpinterest%2Bimage.jpg" title="fraction activities" width="640" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: 12.8px;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571">The charts started to fill...first halves and thirds, then fourths and eighths...we'll see how it "unfolds" tomorrow! Got to love a little math humor, right?</a></span></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;">Tomorrow we will finish up our investigation and then ask ourselves if we have discovered any new "truths" to record in our notebooks. Although I am pretty confident that my students would have been able to answer correctly if given a sheet of "shaded fractions" to identify, today's activity showed me that many students are missing some very critical understandings about equal parts and about patterns that arise when dividing shapes. I'm pretty sure that the work we will do over the next few days is going to be very important to build a foundation for the more advanced skills coming. If you aren't familiar with what the CCSS requires from students regarding fractions, I would encourage you to dig in and follow along with us as we try to construct meaning over the next few weeks!</span></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;">***UPDATE***</div><div class="separator" style="clear: both; text-align: center;">This blog post is now a part of my comprehensive fraction unit available by clicking the image below. Hundreds of teachers have now used it to change the way they teach fractions! </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Fraction-Unit-Grades-3-5-625571"><img border="0" height="320" src="https://3.bp.blogspot.com/-2HwOoDzAH_4/VjGFvrklnCI/AAAAAAAAO74/RHKpd66BMSA/s320/fraction%2Bunit%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: left;"><br /></div><br />The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com6tag:blogger.com,1999:blog-8072938188438508721.post-53463456303827359882017-02-15T06:02:00.000-06:002017-03-23T20:21:53.047-05:00Studying Dialogue to Improve Reading AND Writing<div class="separator" style="clear: both; text-align: center;"><a href="http://www.upperelementarysnapshots.com/2017/02/studying-dialogue-to-deepen.html"><img alt="teaching dialogue" border="0" height="332" src="https://3.bp.blogspot.com/--1yUQwl3aWQ/WKPOya1rn6I/AAAAAAAAY9c/sXnYLpF1zaYgtNZNPtNuN_SRyauG_HQIgCLcB/s640/close%2Breading%2Bstudying%2Bdialogue%2BUES%2Bpost.jpg" title="close reading" width="640" /></a></div>Today is my day to post over at Upper Elementary Snapshots, and I hope you'll head over to read about a lesson I did last week to help slow down my readers and get them thinking more deeply about the books they read. I am excited to see if our dialogue studies transfer to their writing next week--so stay tuned! Want to learn more about what we did? Just click the image above and check it out!<br /><br /><a name='more'></a><br /><br /><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-41126639554257481812017-01-30T06:00:00.000-06:002017-02-23T19:16:48.643-06:00How To Keep The Class Learning While You Pull Small Groups<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Valentines-Day-Product-Bundle-Grades-3-5-1077961"><img alt="teaching math" border="0" height="332" src="https://4.bp.blogspot.com/-lxGKcOgZJ1U/WI55-hgktGI/AAAAAAAAY4o/JCIayVTQezMelTwfLlKt7VsnqYeweIUXgCLcB/s640/keep%2Bthem%2Blearning%2Bwhile%2Byou%2Bpull%2Bsmall%2Bgroup%2Bpost%2BFB%2Bimage.jpg" title="small group math" width="640" /></a></div>This week we are starting our "big multiplying" unit. Not facts--but "big" multiplying. Our standards state that our students must be able to multiply up to 1 x 4 and 2 x 2 digit multiplication, and for some of my students--I know this is going to be a biggie.<br /><br />Because of that, in my planning this week I am planning ahead to be ready to free myself up to pull small groups as much as possible. I know that some students already know the standard algorithm--and others are still not really even confident with arrays. This is going to take some navigating and planning! If you are interested in any of the resources pictured in this post, simply click the image to learn more about it.<br /><br />Here are a few of my "rules to live by" when faced with this type of situation. After all, if I'm going to be working with a small group--I want to do way more than just keep the other students "busy". Right?<br /><br />1. Know where your students are and where they need to be. Make sure you are clear on your content--and have a plan for assessing students formally and informally throughout your teaching so you can really target your instruction to exactly what they need. I'm not a huge fan of pretesting (I think it's tough to make decisions about concepts based on one or two problems) but I am a HUGE fan of formative assessment along the way. If a student can demonstrate mastery, they may need SOME work to build fluency--but their time is better spent doing other things. I use my <a href="https://www.teacherspayteachers.com/Product/Formative-Assessment-Toolbox-Multiplication-and-Division-Grades-3-5-1231073">formative assessment resources</a> all the time to take quick snapshots of progress. <br /><br />2. So what if they need that "something else"? I love to immerse my students in challenging, open-ended tasks. For this unit, I am presenting my <a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Valentine-Celebration-Math-Project-Grades-3-5-1629653">Thinker Task Valentine Challenge</a> to the class as one of these options. Notice that I said TO THE CLASS. I make sure ALL students have access to these quality problems. Some students may not get as far into the challenge as others--but we so often "dumb down" our instruction for our struggling students and don't give them access to rigorous and meaningful tasks. I might encourage them to use a calculator...to work in teams...or to use the easier version (I love that these have 2 levels for just this reason!). Again--if I am pulling small groups, there will be time for students to do other work--and this is a great way for students to ALL have a common task. <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Valentine-Celebration-Math-Project-Grades-3-5-1629653"><img alt="Valentine problem solving" border="0" height="480" src="https://2.bp.blogspot.com/-lruOTx2Y_GU/WI5jilFNX1I/AAAAAAAAY4U/VWEJhC-dhDAw7su2cG4phgqBx-KX6uuuwCLcB/s640/Photo%2BJan%2B29%252C%2B3%2B46%2B41%2BPM.jpg" title="Valentine math project" width="640" /></a></div>3. Building fluency is another great thing to do when not in teacher-led groups. Playing games can be a great thing--as long as the students are working on games that are "just right" for them. If students are already fluent with facts, their games should involve some strategy. If they AREN'T fluent, make sure they actually are ready for the skill on the test. There is nothing worse than asking a child to play a game to build fluency and for them to not have the strategies to do it--instead, they spend time practicing wrong! I certainly don't want students who don't know their multiplication facts to practice them incorrectly because I need them to be independent. I'll have to find another skill for them to do independently. For the next two weeks, I am making these multiplication fact fluency games available--each at two levels of challenge. They aren't right for ALL of my students, but they are for MOST.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Valentimes-Math-Games-Set-of-3-Differentiated-Multiplication-Games-1077903"><img alt="multiplication game" border="0" height="480" src="https://4.bp.blogspot.com/-J1XxUPu4sU4/WI5hrXLAnvI/AAAAAAAAY38/NCdeRONQhGUXPidDc-HoZ4PjKsa5hVsZQCLcB/s640/Photo%2BJan%2B29%252C%2B3%2B39%2B06%2BPM.jpg" title="Valentine math game" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">4. Another great thing for students to work on when they aren't with you is word problems. Whether you have them try them alone or work in partners--problem solving is NEVER a bad use of time! Try to find problems that will be engaging (these all have a February or Valentine's Day theme) and are at a variety of levels. I keep mine cut apart and in a pocket chart on my wall and try to put the easier ones toward the top. Many of these also have an "extra" component so students can tackle that piece if it is a good fit for them. As I transition between groups, I'll do some laps around the classroom checking student choices and doing some coaching along the way--but they really do a nice job of coaching each other!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Seasonal-Word-Problem-Collection-Valentines-Day-Grade-3-5-1047616"><img alt="Valentine problem solving" border="0" height="480" src="https://1.bp.blogspot.com/-_h2wXt27xVk/WI5hxZSl8cI/AAAAAAAAY4E/LW03cYV479MA_zuEEXJhfh4gP0BQmDCWQCLcB/s640/Photo%2BJan%2B29%252C%2B3%2B08%2B01%2BPM.jpg" title="Valentine word problems" width="640" /></a></div>5. One more option is to provide the class with a meaningful "warm up" problem or set of problems. By starting off a class like this, you can make sure students understand the task and that they can be productive while you work to pull other groups. <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Valentines-Day-Fun-Learning-Activities-for-Grades-3-5-1050286"><img alt="Valentine printables" border="0" height="480" src="https://2.bp.blogspot.com/-PANtiCRJMXU/WI5h3INzYcI/AAAAAAAAY4I/4MxoJALJEY4t7P7HI48Qlbaf5jnPoCiFACLcB/s640/Photo%2BJan%2B29%252C%2B3%2B07%2B41%2BPM.jpg" title="Valentine word problems" width="640" /></a></div>So...as you are planning for instruction you know might be difficult where you might need to do some focused attention, think about what kind of MEANINGFUL activities you can provide for your students. I can almost guarantee--if you give them engaging things to do, the management concerns all but disappear and you are free to work your magic! <br /><br />Want to pin this for later? Here you go!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Valentines-Day-Product-Bundle-Grades-3-5-1077961"><img border="0" height="640" src="https://4.bp.blogspot.com/-zup-1mKUQdY/WI56DASVxjI/AAAAAAAAY4s/75MpNgeDNdgHXsQuRmhDg1RVuWum4BvKwCLcB/s640/keeping%2Bstudents%2Bworking%2Bwhile%2Byou%2Bpull%2Bsmall%2Bgroups%2Bpin.jpg" width="320" /></a></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-16874980269498660392017-01-28T22:02:00.001-06:002017-02-23T19:17:00.601-06:00More Fraction Number Lines: More Critiquing Reasoning!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction number lines" border="0" height="332" src="https://3.bp.blogspot.com/-_jeylZ4BQhQ/WI1iPlkqpvI/AAAAAAAAY3M/KvMQ3pWNMoI8-J3_swM1tuvbZUwf6x7OwCLcB/s640/fraction%2Bnumber%2Bline%2Bpost%2B2%2BFB%2Bimage.jpg" title="critique the reasoning of others" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">If you missed my post the other day about using number lines to improve fractional reasoning, you might want to take a peek at it before digging into this post! Just <a href="http://www.theteacherstudio.com/2017/01/fraction-number-sense-and-math.html">CLICK HERE</a> if you missed it...because I want you to know that the lesson featured today was not the FIRST time my students had worked with this number lines....and the lesson is one that should come after they have had some other experiences using number lines and having conversations about them.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">So let's dig in! </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Step one--present students with a number line task. As I mentioned the other day, even a number line task can be simplistic and obvious. I am partial to a more "open" number line--where partitions are not already drawn. When you include those partitions, you've done so much of the thinking FOR the students! Remember, I always ask students to THINK before they pick up their pencil so they have a starting point.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="teaching fractions" border="0" height="480" src="https://3.bp.blogspot.com/-wSlggWVBJnU/WIwVecQkEfI/AAAAAAAAY18/EzIrRFJCEgwCXzRO0r8veH9KSLNdRCWAQCLcB/s640/Photo%2BJan%2B27%252C%2B9%2B45%2B34%2BPM.jpg" title="fraction number line" width="640" /></a></div>As students worked, I walked around and checked out their work and hunted for misconceptions. I would make note of how they were organizing their work or strategies they used that I thought might be worth talking about. In my last post, the next step involved pairing up and having discussions together and coming to consensus. Today? Not so much!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="standards for mathematical practice" border="0" height="460" src="https://1.bp.blogspot.com/-ctgzKOHvFN8/WIwVebZrpbI/AAAAAAAAY2A/rc-fEF5Ik1MJeCf53PPJAuB3dp2lBGqjgCLcB/s640/Photo%2BJan%2B27%252C%2B9%2B50%2B56%2BPM.jpg" title="fraction number line" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">My next step was to ask students to come up and place a blue dot on this "class number line" to show where they had marked in in their math journal. I reminded them to NOT change their answer based on what they see--because they need to trust their gut!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction number lines" border="0" height="480" src="https://1.bp.blogspot.com/-hSWjh_2-m4w/WIwVktxgAhI/AAAAAAAAY2E/wJmhXhac36YEYckLz1uvrFjEBkDF7A2uACEw/s640/Photo%2BJan%2B27%252C%2B9%2B45%2B15%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">By the time all the dots were up, it was time to have a discussion where we "critiqued the reasoning" and defended our thinking. We had to use math language and vocabulary with our sharing--so I heard things like...</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">"The dots on the far left can't be accurate because they would really be past 0 and into negative numbers."</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;">and</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">"I think [pointing to a dot] this isn't possible because there is no way that you can keep equal parts."</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">and</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">"It was more clear to me when I put in all the whole numbers so I could find where they 1/3 really should go."</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction lesson " border="0" height="480" src="https://4.bp.blogspot.com/-u7698YC-UbE/WIwVklnksiI/AAAAAAAAY2M/0Qq-ZrILzIcEoMbkAWyQoNy8Dkp8vhaGQCLcB/s640/Photo%2BJan%2B27%252C%2B9%2B44%2B55%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">Some students needed some convincing--and we had frequent "turn and talks" throughout to get EVERYONE involved in discussion the ideas people shared. It was great to see some light bulbs REALLY go off! After our discussion, I sent the students back to their own notebooks to study what they had done and to "revise" their thinking if necessary. SUPER powerful stuff!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">This was a very nice and quick warm up for our lesson--and the process can be used not just with number lines but with ANY problem type! Stay tuned for another post coming soon with more fraction fun!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Want to see the resource that these number line problems are from? Lots of different problems and options...</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img border="0" height="320" src="https://1.bp.blogspot.com/--sAvqVEoPys/WI1H6kkM4XI/AAAAAAAAY24/bMbP_kVl3kgQQA2N1X-Ne82Y8zW74kh3QCLcB/s320/number%2Bsense%2Bwith%2Bnumber%2Blines%2Bfractions%2Bdecimals%2Bcover.jpg" width="320" /></a></div>Also available bundled with whole numbers to 1,000 and whole numbers to 1,000,000.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Grade-3-5-BUNDLE-2957028"><img border="0" height="320" src="https://2.bp.blogspot.com/-Vx1ZvvSwSRk/WI1H7rAMX9I/AAAAAAAAY28/ol5UCwilxe0x2YipEo_1LLrvp7tQQQcxwCLcB/s320/number%2Bline%2Bresource%2Bbundle%2Bcover.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Want to pin this for later? Here you go!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-ScSDXQHPpHg/WI1iXuQcnJI/AAAAAAAAY3Q/cQ8OcsST-9EG_7lg48lLLBrLk01z3wwFwCLcB/s1600/fraction%2Bnumber%2Bline%2Bpost%2Bpart%2B2%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="fraction number lines" border="0" height="640" src="https://1.bp.blogspot.com/-ScSDXQHPpHg/WI1iXuQcnJI/AAAAAAAAY3Q/cQ8OcsST-9EG_7lg48lLLBrLk01z3wwFwCLcB/s640/fraction%2Bnumber%2Bline%2Bpost%2Bpart%2B2%2Bpin.jpg" title="critique the reasoning of others" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-77739064865823649142017-01-26T22:48:00.000-06:002017-01-28T08:58:13.017-06:00Fraction Number Sense and Math Discourse Part 1<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction number lines" border="0" height="332" src="https://1.bp.blogspot.com/-4YVNXr8swM0/WIrOV7RxHeI/AAAAAAAAY1g/eMeYl06hsyAwu1aKw5hceTx2p5fsB2MRQCLcB/s640/fraction%2Bnumber%2Bline%2Bpost%2BFB%2Bimage.jpg" title="teaching fractions" width="640" /></a></div>It seems like I have picked a few topics lately that just don't fit into one blog post! I wanted to share two different "warm ups" I did with fraction number lines--and two different types of "math talk" that resulted from them. Give these two lessons a try and see what you think! I went kind of "photo journalism" style because I thought the pictures helped tell the story! Watch not just for the important fraction understanding--but the immersion in the Standards for Mathematical Process as well!<br /><br />First of all...if you have followed me for long, you know I love number lines--especially number lines that think "outside the box"--even number lines can be rote and low level--so we want to watch for that!<br /><br />The other day I gave my students this one...it had the 0 and the 2 marked--and asked student to identify what number they felt that "dot" was showing. My first step is always to ask them to THINK before they even pick up their pencil. While they think, I remind them to consider what they know and can tell from just looking at it. I really think slowing them down before they start writing can lead to deeper understanding and reduce careless errors. Plus--for those students who ARE slower processors...not having to watch 20 other students get to work feverishly while they sit is SO refreshing and validating for them. After some think time, they were off!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="teaching fractions" border="0" height="480" src="https://4.bp.blogspot.com/-F05qvgCeXdc/WIa5x5gC9lI/AAAAAAAAYzw/7XV__LKTlusi6m9fWSYshMAsH11HA4SFwCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B54%2B07%2BPM.jpg" title="fraction number lines" width="640" /></a></div> Some asked if they could use rulers...I simply said, "If you think it will help..."<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="Standards for Mathematical Practice" border="0" height="480" src="https://1.bp.blogspot.com/-QLS2w5HMGLw/WIa5yD5leZI/AAAAAAAAYz0/QNdFUoCm8B0DFvsEq2lHMJ7TXLGV5sLMACLcB/s640/Photo%2BJan%2B23%252C%2B7%2B54%2B23%2BPM.jpg" title="fractional reasoning" width="640" /></a></div> I noticed that some students seemed to be putting fractions on their number lines WITHOUT adding the whole numbers first. I asked, "Are you sure 1/4 goes there? How do you know?" Their answers told me a ton about their level of understanding. Some had already visualized where the "1" went--others were simply putting it "where it looked right".<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="number lines and number sense" border="0" height="640" src="https://4.bp.blogspot.com/-pVAUmf63ShQ/WIa5yKwVQII/AAAAAAAAYz4/YQ-RrNF-LEob53FcvYguuwNV4gVHFwmWgCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B54%2B41%2BPM.jpg" title="teaching fractions" width="480" /></a></div> As with all my number line work, I want them to be able to explain their reasoning both in writing and orally. As students were working to finish, I had students begin to write their ideas down so they were ready to buddy up.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="critiquing reasoning" border="0" height="640" src="https://1.bp.blogspot.com/-oYiPfLN87Vk/WIa5yk5eNZI/AAAAAAAAYz8/SWF6gXKAxsk4LgbAUyFXU7e-evZREJM3gCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B55%2B17%2BPM.jpg" title="teaching fractions" width="480" /></a></div> When we were all in a good place (in other words, essentially finished), I put students in pairs and trios and gave them the following direction:<br /><b><br /></b><b>You must all come to consensus about what fraction you will assign your dot. When you are all in agreement </b>(and this took SOME debate in some groups!)<b>, you will mark it on the white copy and start explaining your thinking. When you present, I will call on whoever I want so make sure everyone is accountable for the information and explanation.</b><br /><br />(or something to that effect)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="teaching fractions" border="0" height="480" src="https://2.bp.blogspot.com/-vXEnJBCLOHM/WIa5zaAM76I/AAAAAAAAY0A/REPrkjzHE3YJaLNuw_-LsBpNWRQZIN6uACLcB/s640/Photo%2BJan%2B23%252C%2B7%2B55%2B52%2BPM.jpg" title="math discourse" width="640" /></a></div> I circulated and listened and coached and looked for misconceptions and mistakes. I also looked to see the variety of strategies shown so I could have a variety of ideas to share under the projector.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="math talk" border="0" height="480" src="https://1.bp.blogspot.com/-KRGNhVR2gH4/WIa5ziGkhKI/AAAAAAAAY0E/jIpS3aicMcYcuyU3TEwUqg8PyPPsyFfDwCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B56%2B12%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">For this particular problem, we had some debate. About half the groups believed the dot to be at 3/4 while the other groups had a variety of answers. One by one, they presented their solution and defended their logic. Along the way, there were a few "a-ha's"...and a few stubborn souls who stood their ground despite very good arguments from others!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="math discourse" border="0" height="484" src="https://2.bp.blogspot.com/-uRaijxm5H8U/WIa50H_LL9I/AAAAAAAAY0M/-IzL0WtyQ9c-A3h9WwsEH-MBQUt93rGGQCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B58%2B53%2BPM.jpg" title="teaching fractions" width="640" /></a></div> At one point, we put two different solutions up and had students try to determine which one they felt was "more right"...and which explanations seemed most plausible.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction number line" border="0" height="460" src="https://1.bp.blogspot.com/-TLYr4Q_msK0/WIa5z7V7_eI/AAAAAAAAY0I/k4qb7i_T8X0wJiTwfAqgDvtxw08KVrTkwCLcB/s640/Photo%2BJan%2B23%252C%2B7%2B58%2B31%2BPM.jpg" title="critiquing math reasoning" width="640" /></a></div> We also showcased different strategies that seemed to help some groups. This group used different colors for each step along the way--and other groups agreed that this seemed to make their explanation easier to follow.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="standards for mathematical practice" border="0" height="482" src="https://4.bp.blogspot.com/-aQ2sPtcZAK0/WIa50s9-y6I/AAAAAAAAY0Q/Ku1IFMboVh4MEAuL6it0Cp1L24r-PMMeACLcB/s640/Photo%2BJan%2B23%252C%2B8%2B04%2B04%2BPM.jpg" title="teaching fractions" width="640" /></a></div> Finally, we ended up grabbing a spare number line and doing some folding to find those midway points and really "prove" what the 3/4 teams were proposing. We had a great discussion...and SO much learning happened--and the students did it ALL! Consider trying the strategy:<br /><br />1. Think time<br />2. Independent time<br />3. Partner/consensus time<br />4. Whole group sharing and debating time<br /><br />Watch how engaged your students will be...and let me know how it goes!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img alt="fraction lesson ideas" border="0" height="480" src="https://3.bp.blogspot.com/-gGl4c4We6ik/WIa51PCO3AI/AAAAAAAAY0U/JHxPsGHyaTMkIP_EeSfEMujste9ZQD5uACLcB/s640/Photo%2BJan%2B23%252C%2B8%2B04%2B31%2BPM.jpg" title="teaching fractions" width="640" /></a></div>Looking for the fraction number line resource pictured?<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img border="0" height="320" src="https://3.bp.blogspot.com/-UBw4RDayXe4/WIrK7EY36uI/AAAAAAAAY1Q/PYXlJXarJCUqZhbHU0cyCSg46p7fXk67ACLcB/s320/number%2Bsense%2Bwith%2Bnumber%2Blines%2Bfractions%2Bdecimals%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;">I also have two other number line resources and a bundle of all three...see what you think! I use them ALL year long.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Grade-3-5-BUNDLE-2957028"><img border="0" height="320" src="https://4.bp.blogspot.com/-ZLgjYUaNn2c/WIrK_weQBLI/AAAAAAAAY1U/lZKpnZIRcTET7PprCwW0En-Dvm2CPrZdgCLcB/s320/number%2Bline%2Bresource%2Bbundle%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;">Want to pin this post for later? Here you go! And watch for several more fraction posts coming soon!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Number-Sense-with-Number-Lines-Fraction-and-Decimal-Understanding-2956695"><img border="0" height="640" src="https://1.bp.blogspot.com/--NCWSTNFfH0/WIrPlubl0bI/AAAAAAAAY1o/i_mh74Tl9JQZRdtZn7U3iUa-dCjewmeHgCLcB/s640/fraction%2Bnumber%2Bline%2Bpost%2Bpin.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Looking for an entire fraction UNIT to get students thinking and talking? Check this one out! </div><div class="separator" style="clear: both; text-align: center;">(the number lines are not a part of this resource)</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img border="0" height="320" src="https://3.bp.blogspot.com/-dfBRzNE0z2g/WIyxT7dCntI/AAAAAAAAY2k/f80T2OP5bMUzhyFZAN4P1jWLR0Gif3XAgCLcB/s320/fraction%2Bunit%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-74769021682304230182017-01-19T20:36:00.003-06:002017-03-12T16:15:18.686-05:005 Tips for Helping Students Make Sense of Word Problems<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="teaching word problems" border="0" height="332" src="https://4.bp.blogspot.com/-2ps40JOSuMo/WIFzPXjG3xI/AAAAAAAAYyo/CNX6e26S_ssSZoHBN1aD-uE9Mffx3sRcgCLcB/s640/making%2Bsense%2Bof%2Bproblems%2Bdigging%2Bin%2Bpost%2Bimage.jpg" title="problem solving" width="640" /></a></div>How many of you have ever given your students a challenging problem and within SECONDS heard something like...<br /><br /><div style="text-align: center;"><b>"I don't get it." </b></div><div style="text-align: center;"><b><br /></b></div><div style="text-align: center;">or</div><div style="text-align: center;"><b><br /></b></div><div style="text-align: center;"><b>"What are we supposed to do?</b></div><br />This is the point where every teacher sighs and wonders where they went wrong as teachers--or where the students have been during the last months of teaching! I think part of the problem comes from the fact that we too often make assumptions about what our students know about "tackling" problems. Whether they struggle with reading--or maybe with motivation--looking at a problem can often lead to shut down from some students. I have a few tips that I have found to be successful. See what you think!<br /><br /><a name='more'></a><br /><br />1. Sometimes it's ok to read the problem to the class (or to a small group or individual). Yes, part of math is being able to make sense of a problem independently, but we also need to remember that separating the reading from the math provides equal access for all students. Let's not make all our struggling readers math deficient as well! Reading problems aloud can get students' brains working, focused and ready. Think about your goal--if your goal is "Students will independently be able to read and make sense of a problem", then this tip is not useful. If your goal is more math oriented--like "Students will work to solve multi-step problems." or "Students will use estimation strategies to check their work.", reading certainly can be taken out of the equation (pun totally intended).<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="problem solving" border="0" height="480" src="https://2.bp.blogspot.com/-fKAF2qAheeM/WIAKHtbp1xI/AAAAAAAAYx8/frBRo-DRagUL_C73NDr7bfYjo6ZLjjPigCLcB/s640/Photo%2BJan%2B18%252C%2B6%2B33%2B36%2BPM.jpg" title="helping students with word problems" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">2. Encourage students to take "Think Time" before putting pencil to paper or before working in groups. Ask them to reread the problem. Ask them to imagine or "visualize" what is happening. This could be a great time to ask students to find the question or think about what they need to do or what operations they might need to use. After some think time, ask them to work a bit independently--even if you DO plan on having them work together. By each getting started on their own, they bring something to the table for their group to discuss. This really helps minimize having one partner or team member completely take over--because everyone has SOME sort of start to talk about.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="cooperative problem solving" border="0" height="480" src="https://2.bp.blogspot.com/-h0WdOYo_Li0/WIAKGlUverI/AAAAAAAAYx0/Lob-i9aPa2slvCa9CmiWRc1vYPwc4P1EwCEw/s640/Photo%2BJan%2B18%252C%2B6%2B33%2B21%2BPM.jpg" title="problem solving" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">3. Remind students that sketches, drawings, and charts can help them get key ideas or details down on their paper so they can start making sense of them. Simply rewriting key information or labels can help too--it can help students get started processing the information. ALL students can do this--they can all start looking for key information to record.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="problem solving" border="0" height="480" src="https://1.bp.blogspot.com/-cQ2_gmhlc14/WIAKGjxC1tI/AAAAAAAAYx4/n1yfI2kj5_0-1l2xTw3_uA5xgBjqSa-8wCEw/s640/Photo%2BJan%2B18%252C%2B6%2B33%2B03%2BPM.jpg" title="word problems" width="640" /></a></div> 4. Two heads are better than one! Cooperative problem solving can be SUCH a game changer for students who tend to sit back passively. That being said, it does take some work up front with students to learn the art of partnering. I have a blog post from this fall about it if you are interested. Just <a href="http://www.upperelementarysnapshots.com/2016/09/making-partner-work-perfect.html">CLICK HERE</a> to read it! Some students navigate this seamlessly with minimal coaching and others need help. Put your observation "lens" on and watch to see how students work together--and giving reminders about what is expected in partnerships is a great idea. Creating an anchor chart together about how partnerships work gives you a visual to refer to all year long.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="problem solving" border="0" height="480" src="https://4.bp.blogspot.com/-L-iIlqWqmVE/WIAKGkx4uHI/AAAAAAAAYxw/iuXIKNq3qVQ7L53CdhAzJI-NndvMp0rFwCEw/s640/Photo%2BJan%2B18%252C%2B6%2B31%2B36%2BPM.jpg" title="perseverance in math" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;">5. Finally, sharing ideas and talking about problems AFTER students finish can give new insight as to ways to organize work, alternative strategies, and more. If students are already in pair, match two pairs together to share out their strategies and solutions. Hear something interesting as you circulate? Bring it back to the entire class so everyone can benefit.</div><div class="separator" style="clear: both; text-align: center;"><br /></div>So...we really need to put our students in positions where they can take some ownership and dig in without us "'spoonfeeding" them and coaching too much! Coming soon--a blog post about how to do just that! Want to see another blog post about helping students makes sense of problems? Just click the image below to take you there!<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://www.theteacherstudio.com/2016/10/helping-students-make-sense-of-problems.html"><img alt="" border="0" height="640" src="https://2.bp.blogspot.com/-N5P1qSGqMdg/WIFvktkxuhI/AAAAAAAAYyY/Nd-2YAXfsbIz5yw3sxCGdZqBMUPctJVqgCLcB/s640/making%2Bsense%2Bof%2Bproblems%2Bpost.jpg" title="problem solving" width="320" /></a></div><div style="text-align: center;">The problem pictured in this post is from the following resource if you are interested in checking it out!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img border="0" height="320" src="https://1.bp.blogspot.com/-u8MDXiGPdpw/WIFvS6Ev3EI/AAAAAAAAYyU/8do1Mmmj6bwzNMh4KY4dNfZWEKM3sa21ACLcB/s320/perseverance%2Bproblem%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;">Would you like to pin this post for later? Here you go!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Digging-Deeper-into-Problem-Solving-A-Resource-to-Teach-Perseverance-997255"><img alt="math strategies for word problems" border="0" height="640" src="https://3.bp.blogspot.com/-A5VNoczYpts/WIF129Q_2AI/AAAAAAAAYy0/_5cpeBW_bcQGL-Gkx7LwPYaXd-Wf-SdbACLcB/s640/making%2Bsense%2Bof%2Bproblems%2Bpost%2B2%2Bperseverance%2Bpin.jpg" title="problem solving" width="320" /></a></div><br /><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-10940935963176472322017-01-08T07:00:00.000-06:002017-02-23T19:17:22.283-06:00Angle Studies Part 2<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Geometry ideas" border="0" height="332" src="https://3.bp.blogspot.com/-EhiTYCI2Dq8/WHFyNGLRqzI/AAAAAAAAYwE/JqH1J2a8t0weuWnp4mReoR3Z5AVxR2HeACLcB/s640/angle%2Bpost%2B2%2Bimage.jpg" title="Angle lesson ideas" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">So, yesterday I showed you how I got my angle studies kicked off with my students--how I solidified understanding of "right angle". We had lots left to accomplish--so I'll try to share some of the different lessons and activities we did over the next days!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Tip 1: If you can get your hands on thin drinking straws....like the kind you might get in a school cafeteria...taking 2 of them and threading a twist tie between them. (I forgot to snap a picture at school so I did a mock up at home--but these are big straws. The skinny ones are WAY better.) These "magic angle makers" are great for showing students different angles, how they can "get smaller" and bigger. Students often don't realize that a "big" angle means it is open more--not that they rays are longer. These little buggers are great for helping show that.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="teaching geometry" border="0" height="640" src="https://3.bp.blogspot.com/-dCni1CI49Wg/WHF_DPgmcDI/AAAAAAAAYwk/d7U2dkOdynIRfUhnA62YZN0jS0lgQm_ywCLcB/s640/Photo%2BJan%2B07%252C%2B5%2B50%2B41%2BPM.jpg" title="Angle lesson ideas" width="578" /></a></div><div class="separator" style="clear: both; text-align: center;">So we worked on building acute, right, and obtuse angles...went hunting around the room for them...sketched them...made our bodies into them...you get the picture. We also worked to develop our mathematical rules for them--that acute angles are less than 90 degrees, and so on.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Because we had done our folded circles earlier (Missed it? <a href="http://www.theteacherstudio.com/2017/01/teaching-angles-part-1.html">CLICK HERE</a> for that post), my students were ready to do a little more estimation practice. We had done the right angle concept sort yesterday, but today I wanted them to use their "reasoning" to estimate the relative size of different angles. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Angle-Activities-3-Activities-to-Deepen-Understanding-1611117"><img alt="Angle lesson ideas" border="0" height="480" src="https://3.bp.blogspot.com/-2rjMll7Z4G4/WHFPnyUlceI/AAAAAAAAYuc/B_j-4bYOYtkytM-kOFP4uMiBk1KP3ac9QCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B17%2B17%2BPM.jpg" title="Fourth grade geometry lessons" width="640" /></a></div> I loved walking around and hearing the math talk! I did quite a bit of prompting and cuing to help them use their prior knowledge to explain their thinking--but overall it was GREAT to see that they were able to handle this task!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Angle-Activities-3-Activities-to-Deepen-Understanding-1611117"><img alt="Angle lesson ideas" border="0" height="480" src="https://1.bp.blogspot.com/-r4V_cCmziGs/WHFkhMCl2aI/AAAAAAAAYvM/IEFX9jUNxxE2lmDv3BKFkn-UPMTzSE_SwCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B13%2B39%2BPM.jpg" title="Teaching fourth grade geometry" width="640" /></a></div> I wanted to give my students something concrete to continue their work with acute, right, obtuse, and straight angles, so it was time for some angle art! (Both of these activities are a part of my Amazing Angle Activities resource available <a href="https://www.teacherspayteachers.com/Product/Angle-Activities-3-Activities-to-Deepen-Understanding-1611117">HERE</a>.)<br /><br />I wanted students to show their understanding by folding paper strips into the different angle types. They spent some time arranging them on their page, had to "prove" to a classmate that they had all four angle times, then glued them down and made a key.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Angle-Activities-3-Activities-to-Deepen-Understanding-1611117"><img alt="Fourth grade geometry lessons" border="0" height="640" src="https://2.bp.blogspot.com/-66q3Mp_Za6I/WHFwE3H83lI/AAAAAAAAYvs/Op_nELgHDtAhLV1foqVebbDZyqkwpMiKQCLcB/s640/Photo%2BJan%2B07%252C%2B4%2B43%2B58%2BPM.jpg" title="Angle lesson ideas" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Fourth grade angle lessons" border="0" height="482" src="https://2.bp.blogspot.com/-da3tBNnCS0M/WHFwE7oU-OI/AAAAAAAAYvw/S_VAhop_-l0OH5Pr1vGgBOI1i8LWrTFEgCLcB/s640/Photo%2BJan%2B07%252C%2B4%2B45%2B26%2BPM.jpg" title="Angle lesson ideas" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">We think they look pretty cool!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Geometry projects" border="0" height="480" src="https://1.bp.blogspot.com/-xrZk7ZA74aw/WHFkhOzEveI/AAAAAAAAYvI/tf6rGUK5igUX-sm6iXEvjku-SDXBXHV7QCEw/s640/Photo%2BJan%2B06%252C%2B7%2B13%2B12%2BPM.jpg" title="Angle lesson ideas" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">The next step in our journey was to actually break out the protractors and learn how to use them. If you have ever taught this skill, you know it can be really tricky for some students. Here are a few of my tips in case this is on your agenda for this year!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">1. Work with students in small groups. I worked with 4 at a time and it makes such a difference. In 15 minutes, a group of 4 can master it pretty quickly...and if they can't, you sure can tell who is struggling to work with more later!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">2. Stress the importance of estimating. With most protractors, the two sets of numbers can be very confusing. If students always ask themselves, "Is it smaller or larger than 90?", it can be really helpful.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">3. I try to keep my directions very simple--a phrase you here in my classroom a lot is "Dot on the dot, line on the line" which means, "Line up the vertex on the center dot and make sure the ray is on the protractor line pointing to 0.". </div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">4. Make sure you explicitly teach students how to measure angles facing in different directions, angles that are part of shapes like triangles and quadrilaterals (MUCH harder than just two rays), and that you have students DRAW and correctly label angles as well. Some students struggle with the drawing part--so spending some time on that is certainly valuable.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">5. Working in partners is SUCH a meaningful way to work with angles. Having students draw angles for each other, measure them, and try to get within 2 degrees is a great way to tackle precision and get tons of practice in! If they don't get within 2 degrees, have them work together to figure out why. I love to hear the coaching they do with each other!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Angle lesson ideas" border="0" height="480" src="https://4.bp.blogspot.com/-Rw7_4TVLpME/WHFkhYtuSOI/AAAAAAAAYvQ/ktE1MGNfh6MLwxDyiueoL7sHMIzLJDPxgCEw/s640/Photo%2BJan%2B06%252C%2B7%2B13%2B56%2BPM.jpg" title="Teaching protractor skills" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Teaching protractor skills" border="0" height="480" src="https://3.bp.blogspot.com/-u0OQS0ib8YQ/WHFkiXAAGwI/AAAAAAAAYvY/iCqHsDCuc2I9zkOxM6JRqzdwFhZa7Xg4wCEw/s640/Photo%2BJan%2B06%252C%2B7%2B14%2B12%2BPM.jpg" title="Angle lesson ideas" width="640" /></a></div> 6. Provide lots of different opportunities for practice. I love these big cards printed on bright cardstock. They are easy for students to use and can also be used as an assessment tool. I use the sheet that is included to help practice estimation as well (This is also a part of my angle resource mentioned above).<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Using a protractor" border="0" height="540" src="https://2.bp.blogspot.com/-lFQUWRSGg0s/WHFkgN_pLrI/AAAAAAAAYvE/Dv6cx_JBQK0pP3b2KRxcePqEPSsRzRAAACEw/s640/Photo%2BJan%2B06%252C%2B7%2B09%2B20%2BPM.jpg" title="Angle lesson ideas" width="640" /></a></div> Along the way, I did some formative assessment to check on student progress. (I made this into a freebie in my store if you want to grab it--just click the picture below!)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Angle-Studies-Using-a-Protractor-Formative-Assessment-Freebie-2950274"><img alt="Angle lesson ideas" border="0" height="480" src="https://3.bp.blogspot.com/-FXHUCmxT_4I/WHFkfmwJ2rI/AAAAAAAAYvA/-I8egikLFtsXA6VIcRm4Ui_8sX0hGxDaACEw/s640/Photo%2BJan%2B06%252C%2B7%2B08%2B58%2BPM.jpg" title="Protractor skills" width="640" /></a></div> The next steps of our angle studies involved composing and decomposing angles. We started to tackle this that first day when we divided our circle...students started to see from the beginning that angles can be divided into other angles. Each day, we "played" with this idea a little bit more. <br /><br />"If I divide a right angle into two angles and one angle is 34 degrees, how much is the other one?"<br /><br />"If I divide a 180 degree angle into three equal angles, how big will each be?"<br /><br />"What are three different ways to divide a 360 degree circle into 4 different angles?"<br /><br />My students were loving these problems so I decided to come up with something more for our Angle Art wall...I simply told the students one fact. I told them that the small angle on a tan pattern block is exactly 30 degrees. From that point, I asked them to spend some time playing with pattern blocks and making discoveries. Students quickly began to make connections....the green pattern block had 3 equal angles of 60 degrees. The blue pattern block had two 60 degree angles and two 120 degree angles. Light bulbs were going off like crazy!<br /><br />So I decided to push them a little bit. We have an Ellison machine with the die cuts for pattern blocks so I went and cut a bunch. I told the students to take 10-15 shapes and build a design of their choosing. When they finished, we went on a "hunt" for angles--by combining angles and looking for ways to "compose" 360 degree circles! They had so much fun--and now our hallway has even more math art for our friends to check out!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Angle lesson ideas" border="0" height="480" src="https://2.bp.blogspot.com/-nuoxgajeA40/WHFkfIH9B3I/AAAAAAAAYu4/O1PfOM0afFUbUG5ubSavBhA6frwVDWdbwCEw/s640/Photo%2BJan%2B06%252C%2B7%2B08%2B31%2BPM.jpg" title="Geometry problem solving" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="Geometry problem solving" border="0" height="640" src="https://1.bp.blogspot.com/-OUHB9PnXiRA/WHFkfXH9iYI/AAAAAAAAYu8/fhdMgKNxs_oXHePKnoH19qJox1XL_x9UgCEw/s640/Photo%2BJan%2B06%252C%2B7%2B08%2B00%2BPM.jpg" title="Angle lesson ideas" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">After our in depth work, I think they are ready for our summative assesssment next week! We will revisit these concepts again later this year when we work more with 2D shapes, but I think for now we are in great shape! Want to see more angle ideas? Just click below.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img border="0" height="320" src="https://4.bp.blogspot.com/-OjfWb0XKxQ0/WHF2yHAtNtI/AAAAAAAAYwU/1aaMiud8p7Icgja-Iik_i0zyu2JUQgG8gCLcB/s320/Slide1.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img border="0" height="640" src="https://1.bp.blogspot.com/-ewQf2rMWfAo/WHFxjxWaeRI/AAAAAAAAYv8/qJQIYQuSooAqyI2BbgcnCpHMyc1L67GrACLcB/s640/angle%2Bstudies%2Bpart%2B2%2Bpin.jpg" width="320" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-9236442999860277022017-01-07T11:28:00.000-06:002017-01-07T11:28:19.817-06:00Teaching Angles: Part 1<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="geometry angles" border="0" height="332" src="https://4.bp.blogspot.com/-u_99e6Z1mV8/WHEh7PSSelI/AAAAAAAAYt8/mWBGxhEfeoATcvwFtOOCPb5nchtACZSfACLcB/s640/angle%2Bpost%2B1%2Bimage.jpg" title="teaching angles" width="640" /></a></div>This week was "Angle Week" in my classroom...a week of intense work with angles to help us prepare for later work with geometry! I love this unit for a bunch of reasons--one, many students who struggle with computation-based concepts shine with more "spatial" concepts. I love it!<br /><br />Another reason I find angle studies to be so much fun is that I LOVE watching students start to make connections between all the other work we have done and a brand new topic. Composing and decomposing? CHECK! Estimating? CHECK! Connecting to fractions? CHECK!<br /><br />So the first thing I did to kick of this unit is to make sure that students understood the third grade concept of "right angles". You see, in the past, I have found a number of misconceptions related to this and this year was no exception. Many textbooks and worksheets present right angles looking the same way...something like this:<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle misconceptions" border="0" height="332" src="https://3.bp.blogspot.com/-6nHHeHrsv9c/WHEGYkebGCI/AAAAAAAAYtU/Is4In2_Ujv84clwMdwVIX9GivlC208UAgCLcB/s640/right%2Bangle%2Bimage%2B1.jpg" title="teaching angles" width="640" /></a></div>Which is fine--it certainly is a right angle. But what I have found is that students don't always generalize....so when they see THESE images, I get some of the following comments!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle lesson plans" border="0" height="332" src="https://3.bp.blogspot.com/-sfPPomUY8XU/WHEGsykEqVI/AAAAAAAAYtY/-U1B5LIVxggFNV937NROXjjpQnWx1nmzgCLcB/s640/right%2Bangle%2Bimage%2B2.jpg" title="teaching angles" width="640" /></a></div>So you can see--there is a huge danger in creating misconceptions if we don't dig in. Here was our first activity. I gave each student a circle of paper and, under the document camera, modeled the following. I'm giving you the abbreviated version...hopefully you can visualize how this unfolded (literally AND figuratively!)<br /><br />We first wrote "360 degrees" on the back to remind us of our "whole" circle.<br /><br />Then we folded in half, traced that fold line, colored one half, and labeled it with "180 degrees". We talked about the concept of "straight angles" and noted that a full circle is comprised of two 180 semicircles. I had them fold again, trace the fold line on half of it, color a new color, and asked how many degrees it must be (they easily knew 90). Again, we tied it back to the full circle...being 1/4...1/2 of a 1/2...and so on. We then folded the circle into it's fourths so only the right angle was exposed and we went on a "hunt" around the room to find examples of right angles. We found them everywhere--the corner of the whiteboard, the lights, the door, their name tags...students were turning their "right angle finder" at all sorts of angles to find them! We then came back and folded our circle in half AGAIN to find a 45 degree angle and went back on a hunt!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="teaching angles" border="0" height="640" src="https://2.bp.blogspot.com/-jcyOxcg0CeY/WHBRKysQToI/AAAAAAAAYso/-OdqnkdaY5oaBJkyL-svybEP6s_nA-b1QCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B16%2B38%2BPM.jpg" title="geometry lessons" width="640" /></a></div> Students found angles in letters, in the angle our easel was set at, and in dozens of other places! I loved watching them really start to "see" how big these different angles are--a huge help in our ability to estimate relative sizes and to check for reasonableness.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle lesson plans" border="0" height="480" src="https://3.bp.blogspot.com/-IYlNapmkEiM/WHBRKljE5iI/AAAAAAAAYss/EotKuGjzSQ4shcHAZSQTr0WNajyUbOdtgCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B14%2B39%2BPM.jpg" title="teaching geometry" width="640" /></a></div> So after I was pretty sure we were in good shape with right angles, I knew I wanted to test it with a concept sort. If you aren't familiar with concept sorts, I have a bunch of blog posts about them so I won't bore you here with the details. Just search in the right side bar for "concept sorts" if you want to find more posts.<br /><br />This one was simply geared toward getting students talking about right angles and defending their thinking based on the foundation we had gotten with our folding activity.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="geometry lessons fourth grade" border="0" height="640" src="https://2.bp.blogspot.com/-sOKMHOXPp1k/WHBRNPWCU1I/AAAAAAAAYtA/yFds62VzQgY4yUKC58akANIamd3qPHV3QCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B19%2B31%2BPM.jpg" title="teaching right angles" width="480" /></a></div> One of my rules for concept sorts is that nobody can place a card in a category without the team agreeing...it is super easy for students to grab cards and start sorting quickly--meaning that the assertive, confident students get the work! <br />No thank you!<br /><br />Groups are required to go one card at a time and take turns leading the discussion. I circulate and ask probing questions, ask them to "prove" it to me, and so on.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="teaching angles" border="0" height="480" src="https://2.bp.blogspot.com/-IyL52252eY8/WHBRL7PtO6I/AAAAAAAAYs0/KLv7Lm5r_FoBa62ke1EAivbcIvfgkfd0QCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B18%2B02%2BPM.jpg" title="fourth grade geometry" width="640" /></a></div> For this sort, some students asked if they could use "tools". I shrugged and told them that I didn't care how they did it--as long as they all agreed!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle lesson plans" border="0" height="480" src="https://1.bp.blogspot.com/-jj7xFG1qweM/WHBRNZEw4rI/AAAAAAAAYtE/PhvCz8SYGng2jzfitWvBk2SRoz35qiVfACLcB/s640/Photo%2BJan%2B06%252C%2B7%2B19%2B55%2BPM.jpg" title="fourth grade geometry" width="640" /></a></div> After about 10 minutes of sorting, I passed out a different colored crayon to each group. I gave them about 5 minutes to do a gallery walk to see what others did--and then mark an "x" on any cards that they disagreed with. Those were the ones that we then projected under the document camera and discussed.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle lesson ideas" border="0" height="480" src="https://1.bp.blogspot.com/-TpNSqY0YrRw/WHBRMbLiX2I/AAAAAAAAYs8/1JVLnfkYDZwW7f0WqmBKtCcge16kaLk8QCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B18%2B41%2BPM.jpg" title="fourth grade geometry" width="640" /></a></div> As we talked about the tricky ones, students had to work on using their specific math language (a big part of "precision") until we could all come to an agreement about whether or not the angle was truly a 90 degree angle.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img alt="angle lesson ideas" border="0" height="480" src="https://2.bp.blogspot.com/-L9yrNb8WOsQ/WHBRMdguoYI/AAAAAAAAYs4/KwNjeO0bgpktXWZPOlLFCieig2lXmizwQCLcB/s640/Photo%2BJan%2B06%252C%2B7%2B19%2B10%2BPM.jpg" title="fourth grade geometry" width="640" /></a></div>Next steps? Acute, obtuse, and reflex angles....protractor use...and composing/decomposing angles. Stay tuned for that post coming soon!<br /><br />Looking for angle help in your classroom? Check out this teaching tandem and see what you think!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Teaching-Tandems-Angle-Studies-2284366"><img border="0" height="320" src="https://4.bp.blogspot.com/-EgAaQv3vGjc/WHEQPpFr8lI/AAAAAAAAYts/8v3ixseimqEX6oGdmWjh7uTIu3fLOs1PgCLcB/s320/Slide1.JPG" width="320" /></a></div><div style="text-align: center;">Want to pin it later? Here's a pin for you!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-N6odlf7Fo6Q/WHElA10AzNI/AAAAAAAAYuI/As1NvHFK_es47WQcdxPxVkKIs5tc6OufgCLcB/s1600/angle%2Bstudies%2Bpart%2B1%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://3.bp.blogspot.com/-N6odlf7Fo6Q/WHElA10AzNI/AAAAAAAAYuI/As1NvHFK_es47WQcdxPxVkKIs5tc6OufgCLcB/s640/angle%2Bstudies%2Bpart%2B1%2Bpin.jpg" width="320" /></a></div><br /><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-37796126524433531432016-12-31T06:00:00.000-06:002016-12-31T06:00:21.569-06:00Chilling With a Good Book <div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="snowman bulletin board" border="0" height="332" src="https://2.bp.blogspot.com/-Wi1Ji3X0jS8/WGb2QOE24gI/AAAAAAAAYqs/YHafQ9MfqKASjFWIThhhH0G4y4sRSKKsgCLcB/s640/chilling%2Bwith%2Ba%2Bgood%2Bbook%2Bpost%2Bcover%2Bimage%2B2016.jpg" title="book report" width="640" /></a></div>Teaching minutes are precious, so being able to teach real content while still engaging our students' creativity is key! Check out this book review project that reinforces opinion writing, reading, revising and editing--and creates a beautiful bulletin board as well! I asked my students to think hard about one of the BEST books they have ever read (or heard)--because I wanted them to be ready to write about it. I gave them a few days to think and talk about it so they all had an idea ready.<br /><br />As a class, we talked about what we remembered about OPINION writing--and how good opinion has a clearly stated thesis statement, so students worked to craft quality first sentences that would state their opinion about their book. We did our drafting in our writer's notebooks and then did some peer revising and teacher editing. I had asked students to only write 3-5 sentences which kept them on topic AND made it easy for me to get to everyone for editing!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="winter bulletin board" border="0" height="480" src="https://2.bp.blogspot.com/-sYBvfb0WJ1Q/WGbqki4gj7I/AAAAAAAAYqA/h-wZb5dijpEiYVVQ99ZY6B58uYjLu5VxQCLcB/s640/Photo%2BDec%2B30%252C%2B5%2B09%2B58%2BPM.jpg" title="winter book report" width="640" /></a></div> After they finished writing, self-revising, and peer revision, they put their names on the "teacher time" list on the white board and got ready to "build" their snowman! I had a variety of circle tracers set out as well as colored paper. I explained that they could create their snowman while they waited for their edits--and then they could do their final copy to add to their project. It was fun to see so many students design their snowman to "match" the book they chose!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="winter bulletin board" border="0" height="480" src="https://3.bp.blogspot.com/-dbvh56EkOms/WGbqlVF7eLI/AAAAAAAAYqI/lQEh0Y4IgAEHFpThS_b45kENKe0PAQelgCLcB/s640/Photo%2BDec%2B30%252C%2B5%2B10%2B51%2BPM.jpg" title="snowman book report" width="640" /></a></div> When their snowman was built and their final copy done, it was time to finish the project!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="book report project" border="0" height="640" src="https://1.bp.blogspot.com/-6C9CznpqBNs/WGbqmUA7ZGI/AAAAAAAAYqM/VXCua1LBnJ87Whs_bqAOC4j6rUtrKhXNQCLcB/s640/Photo%2BDec%2B30%252C%2B5%2B11%2B13%2BPM.jpg" title="winter bulletin board" width="480" /></a></div> How stinkin' cute is this one? She worked SO hard and was so proud of it!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="snowman project" border="0" height="640" src="https://1.bp.blogspot.com/-Oo0GTfGEXdQ/WGbqm90mOvI/AAAAAAAAYqQ/c2vosY8eMi0HaQj-1V2p15T450nOkNQ6ACLcB/s640/Photo%2BDec%2B30%252C%2B5%2B12%2B24%2BPM.jpg" title="winter bulletin board" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">After they were all finished, I tore a paper snowhill out of bulletin board paper and hung our new friends above our lockers. The students had a blast...got some great writing practice...and I have a beautiful new display that can be up for a VERY long time! </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img alt="snowman book report" border="0" height="348" src="https://1.bp.blogspot.com/-I_O8q3nWP0I/WGbqkjL8ngI/AAAAAAAAYp8/I4J-nbBfmr8NnsM7Oe8mvNO_RQar26XDwCEw/s640/Photo%2BDec%2B29%252C%2B5%2B28%2B27%2BPM.jpg" title="winter bulletin board" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Interested in the letters and the template? Here you go!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img border="0" height="240" src="https://3.bp.blogspot.com/-F2nSOk_vDII/WGbq1ThhGVI/AAAAAAAAYqU/xGnx16Y63vsWF643szYoScqSPlzyJggcgCLcB/s320/Slide1.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Want to pin it for later?</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Chilling-with-a-great-book-Winter-Bulletin-Board-Project-1011827"><img border="0" height="640" src="https://4.bp.blogspot.com/-dzCLOs3LslQ/WGb3xVqI22I/AAAAAAAAYq4/J62vqTGTiXwFMfbTmz4HwKkPLlG0uFrfACLcB/s640/chilling%2Bwith%2Ba%2Bgood%2Bbook%2Bpin%2B2016.jpg" width="320" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com2tag:blogger.com,1999:blog-8072938188438508721.post-67177532536603749222016-12-30T13:09:00.000-06:002016-12-30T13:21:29.634-06:00Pioneer Research! Learning Collaboratively <div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img alt="fourth grade social studies" border="0" height="332" src="https://1.bp.blogspot.com/-YPuv1JrRucw/WGWs_puHIRI/AAAAAAAAYos/GKMrFnHPGg4jOTbCWYF5YU_DPwXFfNk4gCLcB/s640/pioneer%2Bresearch%2Bpost%2Bimage.jpg" title="pioneer westward expansion activities" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">One thing that I love to do is immerse my students in resources on a topic we have in our curriculum--with a specific task to accomplish. If your school is like mine, social studies and science time are getting reduced more and more, so we need to be constantly searching for meaningful ways for students to incorporate this real world learning into our language arts curriculum. Informational research "mini projects" are a great way to combine the two!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">This book by Christopher Lehman is a really great way to think about research in a little different way...it's FULL of strategies that are super helpful in getting students to master key elements of research. For this little project, I focused on a strategy he calls, "Slow and Steady Wins the Race" where he stresses the importance of helping students pause before writing notes to make sure they read, stop, cover the information, and then jot notes. This really helps reduce the direct copying. I add one more layer to the process by having students read, cover, then explain to a partner where the two together decide if the information is important enough to write down. If you are interested in more of his strategies, I put an affiliate link to his book at the bottom of this post. It's short and easy to read--and I have it FULL of sticky notes with ideas!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">So here is what we are doing...I went to our library and got all the books possible on pioneer life and westward expansion--the next step in our social studies curriculum. The textbook is another option, and I will be using it as well--but I really want my students to understand that true research uses multiple sources. True research also involves students generating their research questions--and this project is too small for that. What I really want is for students to practice their paraphrasing skills and to refine their ability to find facts that are most important. To keep the project small in nature, I gave the students categories to "collect" facts about...and to record in this research guide. We used the textbook, the library books, and even some ebooks that our library has (if you haven't looked at TrueFlix, check it out!). I gave the students two work times to work together to gather facts, practice paraphrasing orally and then in writing, and then we prepared to select the most important information to display.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img alt="pioneers" border="0" height="426" src="https://2.bp.blogspot.com/-sN-nIGiH8Oc/WGWwth4NN1I/AAAAAAAAYpA/SCNJ6YIoy_sf4kDSb_luAf7gqtvTDGSvACLcB/s640/Slide11.JPG" title="fourth grade research" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">I then show my students a sample of how the lap book can be arranged--and tell them that it is their job (with the input of their partners) as to what is the most important information to include on each flap. Students take their notes, explain in their own words, and then get creative!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img alt="fourth grade history" border="0" height="426" src="https://2.bp.blogspot.com/-DbWBJUUz_-c/WGWwtr6lRRI/AAAAAAAAYpE/bmy7Q5xkRoghNyskqq2STwJFMZIO-UEEgCEw/s640/Slide9.JPG" title="pioneers" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img alt="interactive notebook lapbook" border="0" height="426" src="https://4.bp.blogspot.com/-2toXOei92nE/WGWwthGWmkI/AAAAAAAAYo4/ZmBSv--4MeUo1LaqdPxdVZ3jvPwOVNpPQCEw/s640/Slide12.JPG" title="pioneers" width="640" /></a></div>It's fun to watch students take on this project and get creative...and the best part is I know that they are learning the content, working together, and learning more about informational reading and writing. I love watching them share their "lap books" in small groups and compliment each other on how they did things!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img alt="interactive notebook lap book" border="0" height="426" src="https://1.bp.blogspot.com/-zGxHkCE3bqM/WGWwtvE-bzI/AAAAAAAAYo8/2Tc7vFELHR0wkyrCrfJcb9_oAH0Q8s0pgCEw/s640/Slide10.JPG" title="pioneers" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">Interested in the lap book (or you can use as a part of an interactive notebook) resource? Here it is!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img border="0" height="320" src="https://3.bp.blogspot.com/-Bc3JtI29GOM/WGZ_IdL7X2I/AAAAAAAAYpc/wYunqPSBEZ4x8SvZ4gL7BPZ1Z_mnfGCxgCLcB/s320/Slide1.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;">Here is the Christopher Lehman book that I love!</div><div style="text-align: center;"><iframe frameborder="0" marginheight="0" marginwidth="0" scrolling="no" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ac&ref=qf_sp_asin_til&ad_type=product_link&tracking_id=theteastu0e-20&marketplace=amazon&region=US&placement=0325043574&asins=0325043574&linkId=d936b171f8f12c4983500993bff86758&show_border=false&link_opens_in_new_window=false&price_color=333333&title_color=0066c0&bg_color=ffffff" style="height: 240px; width: 120px;"> </iframe></div><div style="text-align: center;">Thanks for stopping by!</div><div style="text-align: center;"><br /></div><div style="text-align: center;">Want to pin this for later?</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Pioneer-Research-Lap-Book-or-Interactive-Notebook-Resource-2304191"><img border="0" height="640" src="https://3.bp.blogspot.com/-4cxB_wlHKfY/WGau5lKoluI/AAAAAAAAYps/BZU_NTXFBbUIwI5maJXb8UDlaMWkSsZDwCLcB/s640/pioneer%2Bresearch%2Bpost%2Bpin.jpg" width="320" /></a></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-19091204821151044452016-12-27T14:36:00.000-06:002016-12-27T14:36:00.395-06:005 Teaching Resolutions for the New Year!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Store/The-Teacher-Studio"><img border="0" height="332" src="https://4.bp.blogspot.com/-pp8lkj9MAbI/WGLMBENWrGI/AAAAAAAAYnw/0CVYlWuINpgWN2lcg0XfVPAWNlbjZqxeQCLcB/s640/resolution%2Bpost%2Bimage.jpg" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">As 2016 wraps up, I--like many others--start to think about things I want to do better in 2017. I have tons of personal goals (get healthy, get more organized, etc), but today's post has a few musings about some classroom goals I have to better meet the needs of my students in the new year. </div><div class="separator" style="clear: both; text-align: center;"><b>Ready for five of them?</b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-33XaWN3hgok/WGKi22lTGdI/AAAAAAAAYlo/d6sahbzFgNc-xyZuDsbQMpuFfOf8qUCswCLcB/s1600/Slide1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://4.bp.blogspot.com/-33XaWN3hgok/WGKi22lTGdI/AAAAAAAAYlo/d6sahbzFgNc-xyZuDsbQMpuFfOf8qUCswCLcB/s200/Slide1.JPG" width="200" /></a></div> My first "resolution" is to incorporate more deliberate instruction on how to write about math. My students have really struggled with this...they seem to be conditioned to "write the algorithm" and instead of explaining their THINKING, they simply tell me what they did. They might write:<br /><br />I put the 483 under the 820. I crossed out the 8 to get more ones... (you get my drift)<br /><br />What I WANT them to do is explain WHY they did what they did...and to look for patterns...and to make connections. I made this anchor charts a few weeks ago but haven't done nearly enough with it. <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-bxzE7MrlEKo/WGKxEhQPzVI/AAAAAAAAYmM/we_DwfrVlyoYDmmGBHEhsU0Ads4a_kbfgCLcB/s1600/Photo%2BDec%2B27%252C%2B11%2B33%2B49%2BAM.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://4.bp.blogspot.com/-bxzE7MrlEKo/WGKxEhQPzVI/AAAAAAAAYmM/we_DwfrVlyoYDmmGBHEhsU0Ads4a_kbfgCLcB/s640/Photo%2BDec%2B27%252C%2B11%2B33%2B49%2BAM.jpg" width="592" /></a></div>I am going to use the problems in this resource to help--because each problem is available in three formats--one of which requires students to explain their thinking!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-hY7-qyUzu18/WGKyZe2crgI/AAAAAAAAYmg/2qY6Jj6YY_odx50DsibY0vUNq-c3KYo1ACLcB/s1600/grade%2B4-5%2Bword%2Bproblem%2Bcover.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://1.bp.blogspot.com/-hY7-qyUzu18/WGKyZe2crgI/AAAAAAAAYmg/2qY6Jj6YY_odx50DsibY0vUNq-c3KYo1ACLcB/s400/grade%2B4-5%2Bword%2Bproblem%2Bcover.jpg" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-NNHjTKXpr7Q/WGKi3FLPWQI/AAAAAAAAYlw/fc_3THteg90U1KQUwEQtXtRV8C6t03zvACLcB/s1600/Slide2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://2.bp.blogspot.com/-NNHjTKXpr7Q/WGKi3FLPWQI/AAAAAAAAYlw/fc_3THteg90U1KQUwEQtXtRV8C6t03zvACLcB/s200/Slide2.JPG" width="200" /></a></div> Another big goal for me is to spend more time conferring with students about their reading. I have so many strugglers--and I find myself scrambling to pull together intervention groups and lessons. I need to make sure to not ignore my top readers, so I am really going to make a concerted effort to keep up with my status of the class and anecdotal records. It's such a nice time with students--even a few minutes a week helps keep me really connected to what they are reading and how they are doing. Here is a blog post with more details about what I do...just <a href="http://www.theteacherstudio.com/2015/12/refocusing-on-reading-behaviors.html">CLICK HERE</a>!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Reading-Status-and-Anecdotal-Records-Calendars-2016-2017-for-Readers-Workshop-444716"><img border="0" height="480" src="https://2.bp.blogspot.com/-UfamdwZAhwU/WGK7jbu8hKI/AAAAAAAAYnA/Xmsbi8nCBWMPCO0iNVzu85t9gCF2X8iCACLcB/s640/Slide3.JPG" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Reading-Status-and-Anecdotal-Records-Calendars-2016-2017-for-Readers-Workshop-444716"><img border="0" height="300" src="https://3.bp.blogspot.com/-qUaSE9leKvg/WGKxUg5OiVI/AAAAAAAAYmQ/mv1g60a6LIQs9P9qWxpNkNBGcUsOPUrmgCLcB/s400/Reading%2BStatus%2BCalendar%2B2016%2B-%2B2017%2Bcover.jpg" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-bR8D3yStzwU/WGKi3MnSwNI/AAAAAAAAYls/b8fTwFISDcQJcStWOnjUcS5IGavwAClUwCLcB/s1600/Slide3.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://4.bp.blogspot.com/-bR8D3yStzwU/WGKi3MnSwNI/AAAAAAAAYls/b8fTwFISDcQJcStWOnjUcS5IGavwAClUwCLcB/s200/Slide3.JPG" width="200" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Another goal I have is to do a better job giving students feedback on their writing. I feel I do a pretty decent job TEACHING writing...but I know I have a long way to go in giving them timely feedback on what they do. Each student is, of course, at an entirely different place with their writing, so simply doing great whole-class lessons isn't enough. I need to do more quick collections of work with a fast turnaround time. Even ONE piece of specific feedback can make such a difference. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Writing-Demand-Prompt-Assessments-Bundled-Set-1669124"><img border="0" height="640" src="https://3.bp.blogspot.com/-Zeia7A6IZyA/WGLBFStochI/AAAAAAAAYng/nIR3UKmwlAcKL-3C-dZOxlOFzu3NDGVmgCLcB/s640/Photo%2BDec%2B27%252C%2B1%2B27%2B16%2BPM.jpg" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Writing-Demand-Prompt-Assessments-Bundled-Set-1669124"><img border="0" height="400" src="https://1.bp.blogspot.com/-kU2sr1Nmcwg/WGKxePeQHiI/AAAAAAAAYmU/GO1DF7MP1cE_ml6q_D-5NXFkme24-gIuQCLcB/s400/Great%2BEight%2BBundle%2BInformation%2BCOVER.jpg" width="300" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-NDrRkrWTr5w/WGKi3Efl5OI/AAAAAAAAYl0/Kczu2Ko2GIcblGRySeG1yQzR3OoVO4CfQCLcB/s1600/Slide4.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://2.bp.blogspot.com/-NDrRkrWTr5w/WGKi3Efl5OI/AAAAAAAAYl0/Kczu2Ko2GIcblGRySeG1yQzR3OoVO4CfQCLcB/s200/Slide4.JPG" width="200" /></a></div> A fourth resolution for me is to build in more time for creative thinking activities. Before break, we did a few different things in class and my students were SO engaged and had some AMAZING discussions. It doesn't take long--and the benefit of thinking outside the box carries forward into other learning. I also love these exercises because it allows some students who are less confident with our academic content to really shine and be actively engaged in what we are doing. It was great for community building AND to get those neurons firing in new ways!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinking-Outside-the-Box-Exercising-Creative-Minds-Bundled-Set-1217847"><img border="0" height="640" src="https://4.bp.blogspot.com/-E8g-KBElFtE/WGK9uuaJ3DI/AAAAAAAAYnU/SJBySHOvtuE9l0QqUBxyazxJAzWqDr4xQCLcB/s640/Photo%2BDec%2B23%252C%2B5%2B45%2B42%2BAM.jpg" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinking-Outside-the-Box-Exercising-Creative-Minds-Bundled-Set-1217847"><img border="0" height="320" src="https://2.bp.blogspot.com/-U96YCOKX2Q8/WGKy0aDlhpI/AAAAAAAAYmo/UN4DxEXghHkNp2rlzqr_1Qzmw9FFcp-VACLcB/s320/creativity%2Bbundle%2Bcover.jpg" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-C6rTJWQvreQ/WGKi3PhoSII/AAAAAAAAYl4/lpOjb8jFlOAODs34t51VAs8_hWfnF_EfQCLcB/s1600/Slide5.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://3.bp.blogspot.com/-C6rTJWQvreQ/WGKi3PhoSII/AAAAAAAAYl4/lpOjb8jFlOAODs34t51VAs8_hWfnF_EfQCLcB/s200/Slide5.JPG" width="200" /></a></div><div style="text-align: center;">Finally, I am going to rework my math workshop time to find more minutes for EXPLICIT fact strategy instruction for my students who need it--and it's QUITE a few of them. I started off in the fall pretty strong working with those students who needed review on doubles, tens, and fives but then things kind of fell apart. I NEED them to be more fluent with their facts before we get into big multiplying, so I am really going to be diligent about working with them. They love the activities...it's matter of ME doing a better job scheduling my time!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Multiplication-Facts-Instruction-and-Intervention-Resource-Kit-2623243"><img border="0" height="480" src="https://1.bp.blogspot.com/-CYTHSc19vfs/WGK73nfnilI/AAAAAAAAYnE/6Loe3xazHmck_ZzFpy-JiRxk6Urq49SWgCLcB/s640/Photo%2BOct%2B28%252C%2B8%2B14%2B37%2BPM%2B%25281%2529.jpg" width="640" /></a></div><div style="text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Multiplication-Facts-Instruction-and-Intervention-Resource-Kit-2623243"><img border="0" height="320" src="https://4.bp.blogspot.com/-xn1YKsnQdTw/WGKy5V1fpZI/AAAAAAAAYms/WbHC5m1rnBUdPiU30650LO7Si7Csq-FCACLcB/s320/math%2Bfact%2Bintervention%2Bresource%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;">So...in case YOU want to set any of the same resolutions as me, I am marking these five products on sale until January 1! Grab them and make a difference in your teaching for 2017!</div><div style="text-align: center;"><br /></div><div style="text-align: center;">Want to pin it for later?</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Store/The-Teacher-Studio"><img border="0" height="640" src="https://1.bp.blogspot.com/-uhCW1IShoNc/WGLQP_NkyXI/AAAAAAAAYn8/LAcohklsZrQSpWaqNU2qctHidbXvTwCvwCLcB/s640/resolution%2Bpost%2B2016.jpg" width="320" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com2tag:blogger.com,1999:blog-8072938188438508721.post-8013939535558944192016-12-18T08:29:00.003-06:002016-12-18T08:55:05.840-06:00More work with fractional reasoning!<div class="separator" style="clear: both; text-align: center;"><a href="http://www.upperelementarysnapshots.com/2016/12/critiquing-fractional-reasoning.html"><img alt="fraction lessons" border="0" height="640" src="https://2.bp.blogspot.com/-xVRnQ1G-Iyo/WFaal8xsrgI/AAAAAAAAYkw/P2o8ikBctpcIAZBrqhkEtCuIjl6JxK2lwCLcB/s640/UES%2Bfraction%2Breasoning%2Bpost.jpg" title="teaching fractions" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Today is my day to blog over at Upper Elementary Snapshots--so I hope you will stop by and check out this fun lesson we did last week...and REALLY showed me where my students were with their math thinking! Just click the image above to check out the details.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Missed any of my other fraction posts last week? Click <a href="http://www.theteacherstudio.com/2016/12/examples-counterexamples-and-more-with.html">HERE</a> and <a href="http://www.theteacherstudio.com/2016/12/using-our-fractional-reasoning.html">HERE</a> to check out a few more!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">Also...don't forget that I have a few holiday resources on sale for the next week for those of you who are still teaching--like me!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-IIxf02E9jp0/WFabVidfBII/AAAAAAAAYk4/yZXYXAwSBg82HCIWIC1k1xEttu9nx8ZnwCLcB/s1600/christmas%2Bsale%2Bitems.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://3.bp.blogspot.com/-IIxf02E9jp0/WFabVidfBII/AAAAAAAAYk4/yZXYXAwSBg82HCIWIC1k1xEttu9nx8ZnwCLcB/s320/christmas%2Bsale%2Bitems.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Feast-Math-Project-Grades-3-4-1531237">Holiday Cookie Task</a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Seasonal-Word-Problem-Collection-Christmas-Grade-3-5-1012901">Christmas Word Problems</a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Winter-Word-Problems-Algebra-Thinking-454583">Winter Algebra Thinking Task Cards</a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>If you are still teaching....hang in there! It's all we can do...keep joy in your heart as best you can!<br /><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-13784714101858354592016-12-14T19:26:00.001-06:002016-12-14T19:26:17.314-06:00Examples, Counterexamples, and More with Equivalent Fractions<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="equivalent fractions" border="0" height="640" src="https://1.bp.blogspot.com/-BX8rAFnvtQQ/WFHvYqCTu5I/AAAAAAAAYi8/llhj-CXe630G4kRiu8cjQLh3n3M3D2qjACLcB/s640/fraction%2Bpost%2Bequivalent%2Bexample%2Bcounterexample.jpg" title="teaching fractions" width="320" /></a></div>As I have been working to build my students' understanding of key fraction concepts, I wanted students to really work to deepen their understanding that fractions can have more than one name--and can be represented in more than one way.<br /><br />Today's "warm up" was geared toward reminding students that they can represent fractions in many ways...so I gave them 5 minutes to make a "mini poster" (literally 4 inches by 4 inches!) to show as many ways to show 1/2 as possible. After they worked, we did a little gallery walk. We came back together and had a discussion about what we saw...different shapes...number lines...fractions of sets...equivalent fractions...<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="equivalent fractions" border="0" height="480" src="https://1.bp.blogspot.com/-pihoUK_n1Pc/WFHYy_p6O7I/AAAAAAAAYiY/XVPu4WH50vA4CNXekXuUN74HfyhH6iQBgCLcB/s640/Photo%2BDec%2B14%252C%2B5%2B32%2B11%2BPM.jpg" title="teaching fractions" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="equivalent fractions" border="0" height="640" src="https://3.bp.blogspot.com/-O7l-WBVmqQk/WFHYz1gNtOI/AAAAAAAAYik/bzV6uTrEZ74nqm-m0vCZvDXI-LtNbzgrQCLcB/s640/Photo%2BDec%2B14%252C%2B5%2B34%2B08%2BPM.jpg" title="teaching fractions" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;">It was a good warm up to our main lesson which worked to help students derive the "computation" method for finding equivalent fractions. (If you missed my post yesterday about building that understanding, </span><a href="http://www.theteacherstudio.com/2016/12/using-our-fractional-reasoning.html" style="text-align: start;">CLICK HERE</a><span style="text-align: start;"> to read that one!). After our explorations, it wasn't that big of a stretch for students to recognize that multiplying or dividing the numerator and denominator by the same number generated new fractions that are equivalent. We proved it with some drawings, some manipulatives, and then moved to bare numbers.</span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;">So after working with equivalent fractions for a while, I wanted to put my students to the test to see how WELL they understood the concept! So often we give students a quick exit slip or something like that--a "fill in the blank" worksheet that follows whatever computation rule we have taught. If they fill in the blanks correctly, we assume understanding. It just isn't that simple.</span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: start;"><br /></span></div><div class="separator" style="clear: both; text-align: start;">To really get students talking, I asked them to do an activity in my big fraction unit....an activity where they need to first generate equivalent fractions (sometimes I do this activity where they can write fractions, draw fractions, etc like the warm up) but today I simply wanted them to use their new algorithm to make a set of 5-7 equivalent fractions for the "unit fraction" I assigned them. The group below was working to generate a list of fractions equivalent to 1/8.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="equivalent fractions" border="0" height="480" src="https://2.bp.blogspot.com/-KrnwWIod_Ls/WFHYzNrZlUI/AAAAAAAAYic/tarpB4GyymwkM5zX4SP5UKbfAE4g5ssUQCEw/s640/Photo%2BDec%2B14%252C%2B5%2B32%2B59%2BPM.jpg" title="teaching fractions" width="640" /></a></div> Here's where the fun (and really deep understanding) kicks in. The next task is to create ONE more fraction for their poster--that does NOT fit their "team"...in other words, that is NOT equivalent. I explained that they would be then traveling from team to team to try to find the "mystery" fraction. I had them write their "counterexample" on the back so students could check their work...and encouraged them to try to be as sneaky as possible when making their "outsider" so other students would really have to work! Some groups did an AMAZING job...and I heard some great math talk! This really immersed them in this idea of equivalent fractions and having to think hard about number patterns and the true meaning of equivalence. We came back together after their gallery walk and discussed their findings--and talked about some of the trickier ones. It was a ton of fun and a great use of time. The paper and pencil practice work we did after this was done in a snap--almost all students were really getting it, and those who weren't met with me for a little extra practice.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img alt="equivalent fractions" border="0" height="480" src="https://2.bp.blogspot.com/--afEnDzAXzY/WFHYzHnvYeI/AAAAAAAAYig/YESl29a37UAA4dtvM3w_AffGrDxJ6hCBgCEw/s640/Photo%2BDec%2B14%252C%2B5%2B33%2B27%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>I wrote about this a few years back with a slightly different twist if you want another idea. Just <a href="http://www.theteacherstudio.com/2013/02/fractions-day-4-example-counterexample.html">CLICK HERE</a> for that post! These ideas are a part of my full fraction unit which you can check out by clicking the image below. If you are looking for ways to deepen your students' understanding--plus have fun teaching, you might want to check it out!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Improving-Deep-Fraction-Understanding-A-Fraction-Unit-for-Grades-3-5-625571"><img border="0" height="320" src="https://2.bp.blogspot.com/-zpCzn_fLOE8/WFHsc3FQLNI/AAAAAAAAYi0/S2Kq3OydfNA772EZ4nSEQ02N0v9_YWoMACLcB/s320/fraction%2Bunit%2Bcover.jpg" width="320" /></a></div><br /><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-83735084447906267622016-12-13T22:50:00.000-06:002016-12-14T06:13:38.892-06:00Using Our Fractional Reasoning!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="fractions" border="0" height="640" src="https://1.bp.blogspot.com/-E6G-MMQq4Ho/WFDLgrICdsI/AAAAAAAAYh0/IOVkUZx1JpEGlFtcqfdHrL_A3XC5d71ggCLcB/s640/fractional%2Breasoning%2Bpost%2Bconcept%2Bsort.jpg" title="concept sort" width="320" /></a></div>We had a great concept sort today...and I just wanted to share a little about what we did!<br /><br />We are working on the concept of equivalent fractions...we have drawn pictures, told stories (If I had half a pizza but cut the half into two pieces, what fraction would I have?), and generated lists of equivalent fractions. What we DIDN'T do is what most math programs do right away--teach students to multiply the numerator and denominator by the same number. We'll get there-but first I really want students to use their reasoning to really show their understanding of some key fraction concepts.<br /><br />One of the Standards for Mathematical Practice involves the ability to "reason"--to create strong understanding of key concepts without merely computing. It states:<br /><br /><span style="color: #202020; font-family: "lato light"; font-size: 16.8px;"><b>"Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects."</b></span><br /><span style="font-family: inherit;"><span style="color: #202020; font-size: 16.8px;"><br /></span><span style="color: #202020; font-size: 16.8px;">By helping students learn to reason about fractions, they become better at understanding without relying on tricks and computation--which helps them with estimating and checking for reasonableness as the math gets more challenging. I love trying to help students VISUALIZE math and make sense of it before teaching them--so that's what today was all about!</span></span><br /><span style="font-family: inherit;"><span style="color: #202020; font-size: 16.8px;"><br /></span><span style="color: #202020; font-size: 16.8px;">Most students have a pretty decent understanding of the concept of "one half", so I wanted to experiment with a sort and see what my students could do. We've already talked about the concept of "unit fractions"--and how they can by used to "count" fractions...1/4, 2/4, 3/4 and so on. We also have used our reasoning to picture the relative size of these unit fractions...that even though "seven" is a bigger number than "three", sevenths are smaller than thirds because more parts must mean smaller parts!</span></span><br /><span style="font-family: inherit;"><span style="color: #202020; font-size: 16.8px;"><br /></span><span style="color: #202020; font-size: 16.8px;">This was really enough information for us to begin this sort--where students used what they know about fractions to sort them into three categories--greater than 1/2, exactly 1/2, and less than 1/2.</span></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="480" src="https://3.bp.blogspot.com/-UXbOl7xSd7Q/WFC4wsgNnMI/AAAAAAAAYhU/kATthHZFj00TYljJz_p_qSzdY71knN7NQCLcB/s640/Photo%2BDec%2B13%252C%2B9%2B09%2B06%2BPM.jpg" title="teaching fractions" width="640" /></a></div> One of our rules about concept sorts is that students work in small groups (usually trios) and must go one card at a time where they discuss together and make a decision about which category the cards fall in. If they have any debate, they set it aside for later.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="480" src="https://3.bp.blogspot.com/-Ue8TLcxtV4g/WFC40HY5H9I/AAAAAAAAYhk/JP-kJP53spgkJwzpLrTjVR6IiDfgQP1XACLcB/s640/Photo%2BDec%2B13%252C%2B9%2B09%2B55%2BPM.jpg" title="teaching fractions" width="640" /></a></div> While students are working, I'm circulating, asking questions, listening--and looking for misconceptions. Anything "interesting" gets thrown under the document camera at the end!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="640" src="https://4.bp.blogspot.com/-hN6KFP4qzpg/WFC4wQsP5kI/AAAAAAAAYhQ/nhW0KL6YA1grMuQREiVvdQ8YCbxj2OLewCLcB/s640/Photo%2BDec%2B13%252C%2B9%2B10%2B18%2BPM.jpg" title="teaching fractions" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">For groups finishing early, I ask them to write their OWN examples for each category...</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="480" src="https://2.bp.blogspot.com/--tMXb5Tk_ao/WFC4zoC5EBI/AAAAAAAAYhg/CVg7mL1xuoksK4kXXiNnNwKL_p-boW4kgCEw/s640/Photo%2BDec%2B13%252C%2B9%2B08%2B18%2BPM.jpg" title="teaching fractions" width="640" /></a></div> I LOVED hearing the discussion this group had--they write the example and then couldn't come to an agreement about which category! One of the students was trying SO hard to explain that HALF of 310 would be 155...so 149/310 HAD to be less than one half. The other two were NOT understanding her reasoning!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="640" src="https://2.bp.blogspot.com/-8fqX5lcrxAU/WFC4zgCTPpI/AAAAAAAAYhc/jZsL8nCxCAgmdfLUc77fH0kIwjGZGNLLwCEw/s640/Photo%2BDec%2B13%252C%2B9%2B07%2B55%2BPM.jpg" title="teaching fractions" width="480" /></a></div><div class="separator" style="clear: both; text-align: center;">After we worked for a while, I picked THIS fraction to discuss...and with NO computation about finding fractions equivalent to 1/2, we had two very justifiable explanations for why 7/15 is less than one half. One student came up and explained how it HAD to be less than one half because 7/14 would be one half...and fifteens are smaller than fourteenths--so 7/15 had to be smaller than 7/14. Pretty slick!</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">The other argument explained that the "halfway" point of fifteenths would have to be "seven and a half" of them...so 7 of them ha to be less than one half. Such GREAT math discussions...with no computation. This is a perfect example of why I love concept sorts...so much discourse. So much math. So much engagement. Tomorrow--we learn the algorithm for generating equivalent fractions...and I think they are more than ready for it!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img alt="equivalent fractions" border="0" height="480" src="https://2.bp.blogspot.com/-3lnQL3XqS1A/WFC4zbfjJkI/AAAAAAAAYhY/-QmQve0gVZkSZanFvTmiUGghpD3fA3SSwCEw/s640/Photo%2BDec%2B13%252C%2B9%2B07%2B29%2BPM.jpg" title="teaching fractions" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;">This sort is one of the five sorts in this resource. Check it out if you are curious!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Set-of-5-Fraction-Sorts-for-Grades-4-and-5-1036755"><img border="0" height="320" src="https://2.bp.blogspot.com/-6FDdle-Krhw/WFDODy4QOpI/AAAAAAAAYiA/WhcOP8NHVZocstVSmpv7XqTmXqcc6J8EQCLcB/s320/concept%2Bsort%2Bfraction%2Bcover.jpg" width="320" /></a></div><div style="text-align: center;"> <span style="text-align: center;">Looking for just a single sort to address equivalent fractions? Check out this one!</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Concept-Sorts-A-Single-Sort-Resource-for-Equivalent-Fractions-1601711"><img border="0" height="320" src="https://1.bp.blogspot.com/-VIocu33MMKU/WFDOHCGZ-qI/AAAAAAAAYiE/Chfs1t6ivL8MggSI_o5UeYd4VPrs5KsXgCLcB/s320/Slide1.JPG" width="240" /></a></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0tag:blogger.com,1999:blog-8072938188438508721.post-54223363885980454242016-12-10T15:39:00.000-06:002016-12-10T15:39:11.048-06:00Coming Up with a Math Plan, Teamwork, and Perseverance!<div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img alt="standards for mathematical practice" border="0" height="640" src="https://3.bp.blogspot.com/-wobDYJoenTI/WExwUo8cD6I/AAAAAAAAYgw/O8ARTKZGF-4E-NsGptVwcuHUvNRWi5megCLcB/s640/thinker%2Btask%2Bcookie%2Bpost.jpg" title="problem solving" width="320" /></a></div>I just wanted to share a quick blog post about what I am doing in math workshop over the next two weeks because my students are SO excited! We are digging into the next series of fraction lessons, and I know that some of my fourth graders are going to handle the material easily. To make sure they have plenty of meaningful work to do when they finish their learning, I introduced the holiday cookie task to them! They were thrilled! One even said, "Is this one going to challenge us even more than the Thanksgiving feast one?" and I just smiled and reminded him that different tasks provide different challenges for different people because we all bring different background to it. I was going to introduce it Friday and get started on Monday, but we had extra time and they begged and I was tired. So I caved.<br /><br />I told them that the main part of this project that I wanted them to focus on (always good to keep a simple focus on complicated tasks, I have found) was that with their partner(s), they needed to come up with a plan. This task has many solutions...but the key direction is to "make as many cookies as possible"...so I wanted my students to really be thinking about what they could do to "test" if they could possibly make more cookies than their first attempt showed them. I also told them that they would really have to remember all they know about basic fractions AND solving problems with more than one step--and they were ready.<br /><br />So they looked...<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img alt="problem solving" border="0" height="480" src="https://4.bp.blogspot.com/-h5pLqhHsC6Q/WEtFOp5gJcI/AAAAAAAAYgE/spbdDLBwt5MydbJZHCn0BW-U_kJiZ4oRgCLcB/s640/Photo%2BDec%2B09%252C%2B5%2B13%2B08%2BPM.jpg" title="word problems" width="640" /></a></div> And they read...<br /><br />I really like my students to read these complicated tasks on their own to try to "make sense" of problems without me spoon-feeding. Depending on the student, I may restate the task, ask THEM to restate the task, or let them proceed and then adjust along the way with questions like, "Hmmm...does it SAY that you can do that?" Great opportunities for teaching mathematical thinking sometimes require students to make mistakes and adjust--and they learn quickly to dig in deeply to find information. It's too easy when the teacher tells them everything they need to know! This is also a great way to push students toward better perseverance; when everything is "coached", they don't learn those critical skills needed to push themselves, ask good questions, and have great "math talk" with each other. I heard some of the GREATEST "arguments" as they were working to make sense of this problem--and THAT is exciting math!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img alt="preseverance" border="0" height="480" src="https://4.bp.blogspot.com/-BxBzLWcYDtI/WEtFOsDJ6lI/AAAAAAAAYgI/7uHNt38SJDoIZYtLvaE6GUbYHlOPj_RYgCLcB/s640/Photo%2BDec%2B09%252C%2B5%2B13%2B29%2BPM.jpg" title="standards for mathematical practice" width="640" /></a></div> And they started to record their ideas<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img alt="fraction problem solving" border="0" height="480" src="https://1.bp.blogspot.com/-yWBvNtcCaWc/WEtFOU-8exI/AAAAAAAAYgA/tVb3ODNVpgElfYYqOrm_l4iZ0sjJfj5jwCLcB/s640/Photo%2BDec%2B09%252C%2B5%2B13%2B47%2BPM.jpg" title="math problem solving" width="640" /></a></div> I love that some immediately went to abbreviations ("SC" for sugar cookie, etc), others drew pictures, some made tables...and they were off and running. As I circulated, I kept asking students to remember to have a plan to see if they are REALLY maximizing how many cookies they could make. I love the hum of collaborative math work...seriously. I sometimes just stand back for a few minutes and watch them ENJOYING math.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img alt="holiday word problems" border="0" height="640" src="https://2.bp.blogspot.com/-lJDMFOXV3n4/WEtFO1LFEZI/AAAAAAAAYgM/yYKIdtownk8V6OEu0S_TGZotBJZwjJC2QCLcB/s640/Photo%2BDec%2B09%252C%2B5%2B14%2B21%2BPM.jpg" title="fraction problem solving" width="480" /></a></div>As they worked to get going, I got some of the BEST questions...so I am super excited to see how the next few days unfold! "Can we cut recipes in half? What about fourths?" and "Is this a problem where we can work backwards?" Love it! I think when we finish, students who are interested will report back to the class how their strategies and plans changed and evolved throughout the process. Like my other Thinker Tasks, I know some students will get a lot farther into the project than others--but those discussions about planning and modifying and adapting are so important as students begin to realize that problem solving is about FAR more than the answer! Stay tuned!<br /><br />Interested in seeing more about this project?<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Tasks-Holiday-Cookie-Math-Project-Grades-3-5-1597440"><img border="0" height="320" src="https://4.bp.blogspot.com/-_oCgdSN5Z-A/WExtfNA_RUI/AAAAAAAAYgc/JG-w0CIQkvAntJ614b69jBXbTBldP95xgCLcB/s320/holiday%2Bcookie%2Bthinker%2Btask%2Bcover.jpg" width="320" /></a></div><br />Here is the discounted bundle of all my Thinker Tasks!<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Thinker-Task-Bundle-Differentiated-Open-Ended-Math-Tasks-1843282"><img border="0" height="240" src="https://4.bp.blogspot.com/-mPxt6ZXn7Cg/WExtkdKcDwI/AAAAAAAAYgg/gfi7cWtBmRU9_OMlXF9PaPnf11UZIfvUACLcB/s320/Slide1.JPG" width="320" /></a></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><img src="http://i1064.photobucket.com/albums/u378/designbychristi/blogs/megsig.png" /></div>The Teacher Studiohttp://www.blogger.com/profile/04936657056940797588noreply@blogger.com0