tag:blogger.com,1999:blog-2746943698272861892015-09-16T13:53:06.783-07:00Pe^rt PlusMrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.comBlogger20125tag:blogger.com,1999:blog-274694369827286189.post-34377748027295860582014-07-13T12:10:00.000-07:002014-07-13T12:10:00.072-07:00Maryland Common Core Summer Institute for Algebra Continuing my professional learning July, I had the privilege of attending a week long institute devoted to learning more about instructional strategies for better teaching Common Core Algebra. The session was led by two professors at Towson University, and the insights they shared, especially pertaining to instructional tasks, was invaluable.<br /><br />To start the first day we were paired with another attendee and instructed to place yarn handcuffs on our wrists so that the respected yarn strands crossed one another. We were then tasked with figuring out a way to uncross our yard without cutting or removing the cuffs. This served as a nice awkward ice breaker, as my partner and I tried everything that we could think of, including stepping inside of each other's yarn to see if that would allow us to get uncrossed. This was a nice problem solving exercise as it had a solution, but it was far from obvious and required some outside of the box thinking to solve. After a while, the instructors started providing hints and support. This was very much needed, and it helped the groups to be able to support each other. As one group figured out how to do it, we could then support other groups who were still trying to figure things out.<br /><br />The yarn handcuffs exercise taught me two main lessons. 1) It is important to balance when to provide support, so as to maintain student sovereignty of their solving process, while preventing frustration and shut down, and 2) utilizing student ambassadors to help support other groups in the classroom is a valuable technique to make sure that support is more widely spread throughout the class while allowing students to have the opportunity to teach others, which solidifies their own understanding.<br /><br />After the handcuff activity we watched a video about Austin's Butterfly. It was about a third grader who was tasked to draw a picture of a butterfly as a scientist would. He drew the first picture, and while it was clearly a butterfly it was not precise. From his first attempt his classmates gave him specific and focused feedback on how he could improve his drawing. The emphasis here was for the students to kindly provide constructive feedback with the goal of Austin drawing the most accurate depiction of the butterfly. He continued to adjust his drawings, completing four drafts before adding color, and through the process using the feedback to improve from one draft to the next, Austin was able to produce a much more scientific drawing of the butterfly.<br /><br />The lessons learned from Austin's Butterfly that were emphasized throughout the week were to create an environment where students are comfortable giving a receiving feedback, for feedback to be constructive and focused, and begin with a focus on what is going right, keep in mind the goal of any project, and attempts should be thought more of as drafts that are meant to be constantly improved.<br /><br />The next opportunity to problem solve with my peers came in the form of a sort of puzzle. The set up is there is a sheep named Eric waiting in a line to get shorn. There are 50 sheep in front of Eric, and he is very impatient. Each time that a sheep is shorn, Eric skips ahead of two sheep. If this continues, how many sheep will Eric need to wait for before he is shorn?<br /><br />Working through this puzzle was a terrific experience. Not only was the puzzle interesting, especially the extensions available if he skips more sheep or if more sheep are shorn at a time, it was great to be able to work through a problem with other teachers. It was very rewarding to be able to bounce ideas off of one another, and I think that as teachers we take that for granted too often. Another great lesson from this task was the availability of having manipulatives to work with. Being able to model the scenario using chips proved invaluable. While getting students to act out the situation is engaging and helps to introduce the problem, it is not efficient for them to work through multiple cases. I also learned about floor functions, as well as alternate scenarios for the problem such as a lunch line or traffic setting for the problem. The big question remaining after working through the problem, is there a function that would represent the relationship between the number of sheep Eric would have to wait for given n sheep shorn and k sheep skipped.<br /><br />The remainder of day one was spent working through developing a task within groups. While working to develop a task we focused on trying to come up with a puzzle or trick that the students were trying to figure out, and trying to make sure that there was a need for students to work through the math. For instance, if I wanted students to use a table or come up with an equation, I need to provide a need for those strategies to be useful.<br /><br />On the second day we spent time talking about exponents, fractions, and ratios. The goal in it all was to work to get to the why behind certain properties that have traditionally been overlooked or taken for granted. Students need to see why things are as a means to build their conceptual understanding. In this way math will no longer seem to be a sort of magic to students, and they can be active participants in the process, rather than passive observers of a mystic power in the hands of experts. The theorem we tried to prove was that a/b < (a+c)/(b+d) < c/d . A good endeavor that any teacher of math should be able to execute.<br /><br />From there the focus turned to the eight standards of mathematical practices. The two main tasks that we had worked through encompassed all eight math practices, and they gave us the opportunity to experience what it means to persevere, to reason, to construct arguments, to model, to use tools, to be precise, to look for structure, and to look for patterns. Seeing and doing those things in a focused and targeted way, helped us as teachers to realize what it is that we want our students to do, use, and think about as they become proficient in making use of the math practices. It was also emphasized that the practices to not take a back seat to content standards, as they go hand in hand in developing mathematically literate problem solvers.<br /><br />We were given a presentation regarding the new PARCC assessments. This was informative as it provided us with details regarding the format and layout of the new tests. I like how the new tests will provide students with a way to show their thinking, and I like that the rigor of the test is meant to match the rigor that should be taking place in the classroom. There will definitely be an adjustment for teachers and students to get used to the different types of questions and the new technology meant to assess students' proficiency, but I hope that teachers will focus more on the content standards and standards of math practice more than they will on the format of the assessment tool.<br /><br />Another problem solving task that we worked through was about two lines of people. Two lines of three people on their own block with a center block between the two lines, and the two lines facing each other. The rules of the game are that people can only move through a slide or a jump. A slide can be done one block at a time, and a person can only jump over one person at a time. Each move requires that the people are still facing the same direction, and the goal is for the two respective groups of three people to be on the opposite side of the center block in as few moves as possible.<br /><br />This was an interesting puzzle, and it allowed for the group to work through a multitude of problem solving strategies. We tried to work out a simpler problem, starting with one person, then two, and so on. We modeled the problem working with chips instead of continuing to move people around. We made sure to record our findings, and we looked for patterns that we noticed that might help lead to a solution. Once we found the correct order in which to execute the jumps and slides, we worked to find a function that might represent the relationship. This was a nice exercise as it yielded a non-linear function, and with the shift in common core Algebra, non-linear functions are going to be emphasized more.<br /><br />The other puzzle that we worked through dealt with the famous Tower of Hanoi problem. we tried to find the relationship between the number of moves as a function of the number of puzzle pieces. This was another nice problem because it dealt nicely with recursion, as well as exponential relationships. Both of which are also focused heavily in the common core standards. <br /><br />The major lesson learned from a lot of the tasks and other demonstrations we had was to try to provide as many visual representations of concepts as possible. A great example of utilizing visual and tactile representations of concepts was the use of algebra tiles to demonstrate factoring and completing the square. The presentations make me want to invest in Algebra Tiles, and the entire institute makes me want to get chips and other items that students can make use of as they work through problems.<br /><br />The final day of the institute was spent presenting our tasks that we developed in our respective groups. This was a terrific experience as there were six products that were presented that I am planning on using with my students. Most everyone tried to make use of the similar puzzles and problems that nicely incorporated multiple solution paths and techniques. There was a dice trick, systems stations, the locker problem, an outbreak of Algebritis, a field trip, and profit comparison all of which provided me with ideas that I can take back to my classroom.<br /><br />The entire week served to invigorate my creative flow, and it makes me very excited to try out different approaches while working to hone my execution of the approaches that already know and use. I am excited for the next institute pertaining to the Common Core Number and Quantity standards, and I can't wait to see the new ideas and tasks that I can bring back to share with my colleagues. <br /><br /><br /> MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-10999666447387558502014-07-06T12:27:00.001-07:002014-07-06T12:27:22.086-07:00Conference Day 2: STEMnetAs a part of my reflection process from the sessions I attended at the Maryland College and Career Readiness, this is my final eighth session reflection. The final reflection is from the session devoted to resources from STEM net. <div><br></div><div>The main goal of the site is to ensure that teachers have a direct line to resources for providing students with valuable opportunities to engage in real world problem solving. One example of these resources is in the Scholars Speakers Bureau that is available. Students and professionals in STEM fields can come to schools and speak to students as a means to increase interest in science technology engineering and mathematics. </div><div><br></div><div>Another similar resource is for STEM specialists to visit and cooperatively work with teachers n schools to enhance the STEM experiences being delivered to students. The main emphasis is to help students connect the fields of study to possible careers of interest. </div><div><br></div><div>The most exciting resource that is available through the STEM net are STEM Challenges. Businesses are contacted to provide current problems they are facing that students could tackle. From there the problems are connected to content that is being taught in schools. Then students can submit their ideas and solutions, and get recognized for their efforts with an opportunity for internships with the companies. </div><div><br></div><div>In addition to these resources, there are also lessons and project ideas that are aligned to common core content standards. All of these resources in conjunction with the network of educators, energize me to begin incorporating STEM projects regularly in my teaching. </div><div><br></div><div>My main goals after attending this session are to make effective use of the resources including the STEM Challenge, and I want to continue promoting true STEM for all experiences for all students in my district instead of a select few. </div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-38419424237584699522014-07-06T11:13:00.005-07:002014-07-06T11:13:53.981-07:00Conference Day 2: Facilitation Skills for LeadersThe second session on the second day of the Maryland College and Career Readiness Conference was targeted to improving the skill of facilitation in leaders. <div><br></div><div>Facilitators serve three main roles in their work with groups of professionals. They are designers who develop an agenda and a vision for the group. From designing facilitators then become pilots who lead the course of discussion and brainstorming, as well as landing the productive plane with an action plan that brings everyone to a common purpose. Continuing the group's travels the facilitator becomes a guide if the group through the action plan. As an expert, the facilitator uncorporates the valued opinions of the entire group in the discussion and execution of the process. </div><div><br></div><div>This metaphor was very helpful in connecting the many differ bet hats of the facilitator as a leader of others. The main skills that stuck with me were as follows; listening and responding effectively, guiding others, attending to the conten and process keeping the group focused, being in service of the group, and creating conditions that bring people together. </div><div><br></div><div>When working with a divers group of people towards a common purpose it important for the facilitator to maintain a sense ofcommunity and goal oriented focus. I connected this to how we as teachers organize our students in the work toward a common goal. </div><div><br></div><div>My goals after attending this session are to engage in facilitation with a group of professionals, and to improve the facilitation of my students in their problem solving. </div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-65856374809634258522014-07-06T11:13:00.003-07:002014-07-06T11:13:43.772-07:00Conference Day 2: Integrating STEMContinuing my reflection from the sessions I attended at the Maryland College and Career Readiness Conference, I am beginning to look back on day two. The first session I attended was about integrating STEM standards into middle school. I was very interested in this session because a major goal of mine is to provide STEM experiences for all students instead if te select few who get those opportunities through the STEM academy. <div><br></div><div>The main emphasis of STEM centric teaching is to connect to careers, incorporate STEM standards, connect to the real world, and have the work be a natural fit in the disciplines. Projects and problems shouldn't feel out of place or disconnected, and there should be a connection to at least two of the STEM fields as often as possible. </div><div><br></div><div>The process of designing a STEM centric lesson starts with the content and STEM practices. What is the content being taught? </div><div><br></div><div>From there the task shifts to finding a real world connection to the content. What is a problem or projects that professionals in the field are tackling that connects to the content?</div><div><br></div><div>Once the project idea is put together, a connect to at least two of the Science Technology Engineering and Math standards. What science connects, technology uses, engineering opportunities, and mathematical thinking will students be doing? </div><div><br></div><div>An abbreviation to which I was unfamiliar was the "5Es"; engagement, evaluation, exploration, entension, and explanation. The idea is for all five to be incorporated, so that students are working through all five skills throughout the process of the project. </div><div><br></div><div>The connections and the resources presented in the session were very informative, and I left very excited to start preparing lessons through a STEM lenses on a continuous basis for all of my classes. This leads me to the main goals after attendng this session. I want to develop STEM lessons and projects for my 8th grade math class specifically, I want to incorporate hands on projects for students to work on often in all of my classes, and I want to promote the ideal that every student should have the STEM opportunities on a regular basis at the county level. </div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-87776867993672491332014-07-06T11:13:00.001-07:002014-07-06T11:46:14.619-07:00Conference Day 2: PLCLooking back on the Maryland College and Career Readiness Conference, I have been reflecting on the sessions. The third sessions from the second day of the conference was one I was very interested as it pertains to goals that I have for my department, Keeping the Learning in PLC. <div><br></div><div>This session focused on keeping PLCs as a tool for ongoing rigorous growth for improving student achievement. The key features of a PLC include research, examining student work, enhance pedagogy, and providing time for reflection. All of there can be present in any Professional Learning Community. </div><div><br></div><div>One of the key components needed for any development to take place is to ask why. Why are we doing research, why are we looking at student work, why are we trying to enhance instruction, why are we reflecting, why are we doing anything to grow professionally? The why is the key, for without a satisfying understanding of the why, we will have trouble defining an action plan or vision forward. </div><div><br></div><div>The session took a step towards distinguishing between dialogue and discussion. Dialogue is meant to provide a means for a group to talk while reserving judgement, promote inquiry and examination, and listening. Discussion is meant to advocate for a position, convince others of an idea, and solutions are not necessary. This was an interesting day crib to make, and we discussed that both forms of communication are appropriate depending on the situation. </div><div><br></div><div>The main goal that I have moving forward frm this session are to effectively organize and participate a PLC in my department. I have noticed that meetings among colleagues tend to be too focused on administrative details and not focused enough on learning and improving practice. I would like for meetings to be regular and to address a goal of the collective department. </div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-56114283743188108172014-07-06T09:39:00.003-07:002014-07-06T09:39:39.098-07:00Conference Day 1: Aligning Tasks to StandardsAs part of my reflection process from the Maryland College and Career Readiness Conference, I am recording my thoughts and goals following each session. This session focused on using four main protocols meant to aid instructors, publishers, and curriculum specialists in determining how well curriculum materials are aligned to math and language arts common core standards. <div><br></div><div>The tool that I worked on dissecting was the EQuIP tool. This process was structured as a rubric meant t measure the enxtent to which lessons and units effectively incorporate appropriate depth, conherence, rigor, differentiation, and assessment. The main goals are to make sure that materials are aligned with an emphasis on performance based assessment as evidence if effective lesson design. </div><div><br></div><div>The five steps of the protocol are to review the materials, analyze the purpose as determined solely by the directions presented, compare the content to the standards, diagnose student work looking for patterns, and making suggestions on how to improve the materials. Through those five steps the EQuIP has a nice overall evaluative tool for units and lessons. </div><div><br></div><div>The other tools discussed were primarily mean for entire assessments, individual assessment items, and supplementary materials. I am very glad that I was given access to the entire toolkit, a hefty phone book sized document. </div><div><br></div><div>My goals after attending this session are to use the tools to evaluate materials that I am using in my own instruction, and I want to make administrators and supervisors aware of the tools in case they are not already, so that they can a way of making sure materials are appropriately aligned. </div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-90454805155607189712014-07-06T09:39:00.001-07:002014-07-06T09:39:31.057-07:00Conference Day 1: Coaching SkillsFollowing the Maryland College and Career Readiness Conference, and am continuing to try reflect on the eight sessions that I attended. <div><br></div><div>Staring the session, there was a distinction established between being a mentor and being a coach. The main separation between the two roles is that an instructional coach primarily asks prompting questions that are meant to empower teachers to solve their own problems, while mentors primarily consult teachers and work to problem solve for a mentee. </div><div><br></div><div>This was an important distinction, as most of the participants serve as coaches meaning to empower teachers. There are three stages of coaching that shift the approach of the coach. The first stage is a standard coaching relationship where the teaching is the main actor in the problem solving process. The second stage, which may be utilized depending on the level of capability of the teacher, is a collaborative relationship where the coach and teacher are working together to get through a problem. The third stage is meant to be a last resort where the coach takes on a consulting relationship with the teacher. This third stage is very similar to serving as a mentor. </div><div><br></div><div>The idea behind the distinction in the three stages of coaching is to provide a structure for coaching that is flexible based on the teacher's needs. </div><div><br></div><div>The most important skill that effective caches possess is being able to listen well. This took the session into a focus on determining what time of listener we are, so that we can better listen to teachers in order to better attend to their concerns. The key focus was to make sure that full attention and effective listening takes place no matter who the speaker is. In order for us to be effective coaches, the teachers need t know that we are listening fully, and devoting undivided attention to their needs in the moment. </div><div><br></div><div>From being an effective listener, the focus went towards being able to paraphrase effectively so that the teacher knows that you have accurately listened and understood their problem. The main ways to paraphrase depend on how well you as the listener understood what was said. The coach can either acknowledge and ask for clarification, summarize and organize the information, or shift the conceptual focus appropriaty to a productive way forward. The important feature of each method is to affirm for the teacher that their concerns have been heard and you are ready to help them work out a solution. </div><div><br></div><div>We had the opportunity to practice our coaching on a hypothetical dramatization of a teacher. This was a great exercise as it put us in the shoes of a coach trying to help possibly difficult clientels. After engaging in this practice I realized that, just as with students, if teachers do not see the need for change and growth none of your suggestions will really help them. They need to own the process. </div><div><br></div><div>After attending this session, my goals moving forward Into this year are to build trust from my colleagues and to improve my listening skills to better support teachers in ourcollective shift to new curriculum, strategies, and technologies. </div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-32028849757442104502014-07-01T19:56:00.001-07:002014-07-01T19:56:08.885-07:00Conference Day 1: Classroom Focused Improvement ProcessContinuing my reflection process following the Maryland College and Career Readiness Conference, I am going to focus on the second session I attended about CFIP. This protocol for analyzing data in continuos, timely, collaborative, and productive ways. <div><br></div><div>I found this session particularly useful as my school began ongoing data meetings where teams met to discuss student work on PARCC type assessments. I was able to connect the good things that are happening at these data meetings with the areas that the CFIP outlines for improvement. </div><div><br></div><div>Last years data meetings took place about once a month, while the CFIP suggests meeting at least every two weeks. Making the meetings more consistent will help make the shift of analyzing data in focused and collaborative ways more effective. Just as students need more exposure to puzzling and authentic problem solving tasks to get better, teachers need the same continuous process of engaging in meaningful dialogue about student work to better improve practices. </div><div><br></div><div> My big take aways from the session are as follows. </div><div><br></div><div>-Discussion about data needs to take place with team members on the same page with common understanding and common purpose.</div><div><br></div><div>-Discussion needs to stay focused and precise when discussing data and outcomes. </div><div><br></div><div>-It is important for teachers to separate what we do from who we are. It is easy for teachers to fall into taking comments about student work and suggestions for improving instruction personally. </div><div><br></div><div>-Data that does not serve to answer a question is not necessary. </div><div><br></div><div>- Decisions made about interventions and enrichment should be based on patterns in student work as present in the data. </div><div><br></div><div>In general this session was very informative in introducing the CFIP protocol, and it offered a lot of good ideas to take with me to my department and PLC. I look forward to using the common assessments that we are developing this summer with my PLC to improve instruction based on the data. </div><div><br></div><div>My main goals for the coming year are to establish norms regarding regular meetings that utilize the CFIP framework within my department and PLC. </div><div><br></div><div><br></div><div><br></div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-13287693119390041632014-07-01T16:36:00.001-07:002014-07-01T16:36:42.721-07:00Conference Day 1: Using Technology for Effective Formative Assessment
FeedbackThe first day of the Maryland College and Career Readiness Conference, and I have a lot of ideas ad information to take away. I am going to use this as a platform for reflection for each of the eight sessions I attended. The first session focused on using technology to more effectively assess student learning and provide timely and meaningful feedback. <div><br></div><div>A major goal of mine has been to find more efficient ways in which I can evaluate student work and provide timely feedback. The first few tools that were presented provided me with a means to accomplish that goal. I was very glad to have attended this session and now my goals have shifted to working on incorporating those tools into my instruction. </div><div><br></div><div>The first tool that caught my attention was Socrative. Very similar to Poll Everywhere, Socrative provides a resource where assessments can be developed and students can respond from any WiFi enabled device. This will be very handy given that I may not have a set of clickers next year, and I can utilize a bring your o an device policy for students in my room with varying devices.</div><div><br></div><div>Another tool that I am especially excited to use is Flubaroo. This tool allows me to utilize google forms, and as an add oo in the spreadsheet, Flubaroo will grade student submissions and email individual reports to each student. I have figured out how to have student responses graded automatically, but being able to send student progress in a timely manner is a great way to let students know their strengths and weaknesses. </div><div><br></div><div>I am excited to explore these tools and more like Three Ring and Video Notes along with a host of other tools that can help me gather student work more seamlessly and timely. </div><div><br></div><div>My goal after attending this session is to incorporate these tools into as many lessons so as to enhance instruction in meaningful ways. </div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-54599576121231419822013-09-27T20:30:00.001-07:002013-09-27T20:31:28.275-07:00Thank you 101qs.comThis past week was a humbling reminder that I still have a long way to go before I'm satisfied with my ability to be an effective teacher.<br /><div><br /></div><div>Nonetheless, I am feeling more comfortable with my ability to implement problem solving tasks with my students. I am very grateful for the wonderful community of resources that exists through the twitters and all of the blogs, and one in particular that I am excited to have started using is <a href="http://www.101qs.com/">http://www.101qs.com/</a>. </div><div><br /></div><div>I had started my seventh graders working on representing percentage using equivalent expressions, when I came across a<a href="http://www.101qs.com/1999-what-micheals-coupon-should-you-use" target="_blank"> picture that led to a really interesting question about deciding between two coupons. </a>The picture led to students noticing and wondering, which led to them thinking.<br /><br />Which coupons is better, 30% off the entire purchase or 40% off one regular item?<br /><br />Their first inclination was that, "it depends." Now came for the fun part, because they realized that they would be figuring out on what it would depend. What prices would cause you to choose one coupon over another? Does it matter how many items are in your cart?<br /><br />They were split up into groups of three, and most every group started working through different purchase situations. Most began to find that the 30% off coupon consistently won out, and this led to a prompt for them to find a situation when the 30% off coupon would not be the better deal.<br /><br />As groups worked through this portion, I could see the wheels really start turning. They were noticing different patterns, they were being strategic in the prices that they assigned to the one item on which the 40% off coupon would be used, they were thinking about the problem in creative and insightful ways.<br /><br />When a student first gave me his answer, I didn't quite know how to respond. I expected that the groups would find an answer, but I anticipated solutions to start popping up later based on the progress they were making at the time. For several of the groups to start noticing that the one item had to be more than 75% of the total purchase in order for the 40% off coupon to be a better deal, really impressed me.<br /><br />I was excited, and I was very proud to see them start with no more than a picture and some questions only to end with a powerful solution.<br /><br />The best part of the solution was the extension afterwards. Having the conclusion that the one item had to be worth more than three fourths of the total in order for the 40% off coupon to be worth using, led to students observing that 30/40 reduces to three fourths. Their problem now became one of verifying whether that result would continue for other combinations of discounts, or if it was merely a coincidence.<br /><br />All in all the problem was rich with great thinking and exploration, and so far it served as one of my best class sessions this year.<br /><br />I am still struggling to present the problems more consistently and effectively, but I won't be able to improve if I don't try new things. Here is to my own exploration and discovery. </div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-89547431274471509552013-09-06T20:55:00.000-07:002013-09-06T20:57:11.498-07:00Making "Real World" Problems Feel More RealThird week of school, and I am feeling more and more satisfied with the amount of problems on which students have been working. Starting with my Geometry classes working on the great<a href="http://mr-stadel.blogspot.com/2012/10/transversals-tape-and-stickies.html" target="_blank"> transversal tape and sticky</a> activity that I found on the wonderful <a href="https://docs.google.com/document/d/1E-HSbjWJ8A4xq0OPdosjcK_X20S9V1sKyK9DDvwxtn8/edit" target="_blank">problem based learning curriculum maps</a> (that I adore exploring). The activity didn't go quite as planned because I wasn't able to make copies of the handouts, but the students worked well none the less.<br><br>Those Geometry classes also had fun tackling some logic puzzles as we started talking about forming proofs and deductive reasoning. I was very thankful that my wife and I were able to visit her grandparents last weekend, and while there her grandmother gave me a book titled "<a href="http://www.amazon.com/The-Brain-Game-Rita-Aero/dp/0688019234" target="_blank">The Brain Game</a>." The book has 27 intelligence tests "that will reveal your unique abilities" like an IQ test. <div><br></div><div><div class="separator" style="clear: both;"><a href="https://lh4.googleusercontent.com/-qkQbK8Yu4VA/UiqkFKcpv8I/AAAAAAAAAR8/yewaBaU_W4w/s640/blogger-image--383430285.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh4.googleusercontent.com/-qkQbK8Yu4VA/UiqkFKcpv8I/AAAAAAAAAR8/yewaBaU_W4w/s640/blogger-image--383430285.jpg"></a></div><br><div><br></div><div><br></div><div>When I first saw it, I instantly thought of the possible problems and tasks I could pull from for the students, and thinking about the proof lessons coming up, I was look at the logic tests for some gems. One of the puzzles involved blue wombats, and it was a nice starter before we started proving angle relationships.<br><br>Moving to the Algebra 1 classes, I tried my hand at implementing a 3 Act task today with a<a href="http://mrpiccmath.weebly.com/1/post/2012/07/3-acts-pepsi-points.html" target="_blank"> Pepsi Points task </a> that I also found using those <a href="http://emergentmath.com/my-problem-based-curriculum-maps/" target="_blank">wonderful curriculum maps</a>. I am looking forward to talking with the kids on Monday about the <a href="http://en.wikipedia.org/wiki/Leonard_v._Pepsico,_Inc." target="_blank">court case involving the person who tried to redeem pepsi points for a jet</a>, and today they were really into estimating how much things cost and starting to figure out how many points it would take to get the jet. This was also a fun task because I got to talk about my experience with my dad riding in his van and stopping on the side of the rode to pick up pepsi bottles for the caps, so that he could redeem the points for stuff.<br><br>The fun did not end with Algebra, thankfully, as my seventh graders got to work on a problem about <a href="https://docs.google.com/document/d/1CW5CeA0cWmLTt5j-OB0oU6vi3lXEJiaX59TRzN0EbU4/edit?usp=sharing" target="_blank">designing a model of the solar system</a>, a <a href="https://docs.google.com/file/d/0B8hYicf5bKkaMlZYRy14MzdJekk/edit?usp=sharing" target="_blank">problem about McDonalds</a>, and a <a href="https://docs.google.com/document/d/1e6mKYYEF9AJ1XDX8TDwF6hhwRQWwlRmH-yZnVBbH-4A/edit?usp=sharing" target="_blank">problem about the Curiosity Rover. </a>They were working with exponent properties and scientific notation, and problems about space and the McDonald's serving 1% of the world's population seemed to fit. I loved showing them pictures of some really cool planets and stars, and they were really interested in <a href="http://www.jpl.nasa.gov/video/index.php?id=1103" target="_blank">how the Curiosity Rover landed</a>. Infecting kids with the wonders of space explorations is my favorite past time. The fun again came in when I was able to relate the problems to experiences from my life. They seemed to enjoy some funny stories from my childhood when my mom worked as a manager at McDonald's, and I would play around the store in the freezer, in the drive through (scrounging for dropped change for a small fry), and wearing the headsets listening to the drive through orders. One particular group of girls found the idea of a car coming through the drive through while I was looking for change quite funny.<br><br>I started thinking after having the chance to share the stories about myself to my students that being able to connect these problems to my life really seemed to help make the work we were doing more meaningful. The students weren't just working through problems from some foreign book, or even good problems that aren't related to anything. Not only were students given an opportunity to work on interesting and challenging problems, they were able to see these problems as something more than just a math problem. Through telling my little stories, I felt that I was able to make these "real world problems" more real.</div></div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-21054427060862200812013-08-31T10:25:00.002-07:002013-08-31T10:25:44.693-07:00Really Fun Moments from the First Week of SchoolThe first week of school has been a blast. This is my first year at a middle school, and I am really enjoying these seventh and eighth graders. They are an impressive bunch, and I am very excited for what is sure to be a great year.<br /><br />Starting off the year, I got the idea from a friend of mine to present a really nice counting problem. We started looking at a soda can pyramid picture that I found. The bottom row of the pyramid has 11 cans with each successive row having one less can until the single can at the top.<br /><br />The goal was to count the number of cans, and after students went through and added them all together, we tried to come up with a better way of counting that would be more efficient. A few students picked up on the trick commonly credited to Gauss, which was fun because I was able to show them a nice <a href="http://youtu.be/Dd81F6-Ar_0" target="_blank">numberphile video </a>about the counting problem after they worked it out.<br /><br />The fun began when they were faced with a pyramid that has 50 cans at the bottom. They thought about it independently for a couple of minutes, then they were split into six groups to work out the problem on big white boards. Below are some of the great ideas they came up with and presented to the class.<br /><br /><span id="docs-internal-guid-2f915ff8-d560-e687-5a4f-05f8a1124ee5"><img height="271px;" src="https://lh6.googleusercontent.com/4mJAVqZeBq1eXabSnAG1ardk_2D2e6Bw_ScouDB4VF_2LpnMkGZ3722UcnqN90w4IMP4jISgLuhpeRhYdTONKZ2vBMyMRPYY7KqhC-cfpgbB4CLTIySraHCR99LLqQ" width="452px;" /></span><br />This idea was about turning the pyramid into a square and subtracting off the area. The coolest part about this idea was that the group accounted for the single can at the top of the pyramid.<br /><br /><span id="docs-internal-guid-12922758-d561-04cd-f554-85e8ff91f0da"><img height="227px;" src="https://lh6.googleusercontent.com/yoQlkchR2yU-CXJdTImGjErjZ_BGuyVJ6eY9EDhWWe4OmCr9oOgakfiaWXXIc3eSuP9Wug8zx6kllmg6rnV2h5AfvIiAzWPDmHxzmW6kWX0dAtHGPV2XmcZuE0q3cA" width="286px;" /></span><br /><span>This idea was about adding up groups of tens, nines, eights, and so on. The group noticed that each successive group of numbers was reduced by five, which was very cool, and they were able to use that to quickly get to multiplying their sums. </span><br /><span><br /></span><span id="docs-internal-guid-3dab26a9-d564-9f0d-e25c-09eeca2e2945"><img height="111px;" src="https://lh5.googleusercontent.com/Ccv3scSf4ew_uQWqa3Ot3Jkt08nnjpC-UF39W5vRp7wUMXjLLQI9TSWRUcNm_UJUaoDkUYw_tXDECTgm1QDHGp5yGALqli3HaCj0J3eCJElgceoR5CQ4W3qIb0uSxQ" width="194px;" /></span><br /><span>This idea was very impressive to me. This group was trying to find a formula to use to find the number of cans. They went through a few different ideas, tried them out to see if they worked, and they finally landed on this beauty for any pyramid with base B. </span><br /><span><br /></span><span>The other three groups came up with similar solutions, and this served as a great problem for the start of the year. They loved working in groups, they really enjoyed using the white boards, and I enjoyed being able to go to each group and help them make sure that each member of the group was on board and asking good questions. </span><br /><span><br /></span>I look forward to posting more of these fun activities throughout the year. I am very excited about the start of the new year.<br /><span><br /></span><span><br /></span>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-50360605266569036622013-08-18T19:27:00.002-07:002013-08-18T19:29:00.956-07:00Count Down to the First Day of School: 2 days and 9 hoursStudents arrive this Wednesday, and I am starting to get more and more excited about starting a new year with a new set of students. Tomorrow will serve as my day to finish getting my classroom ready, and Tuesday will be the day I get to meet students and parents for the first time. The summer has flown by, and I find myself reflecting on all that I have learned from last year and from this summer.<br /><br />My goals for this year include making better use of technology to help reduce the time it takes for me to give feedback to the students, being effective in challenging students to figure things out with tough questions while providing just enough supports to keep them from feeling discouraged, and I want to execute effective problem based learning this year.<br /><br />Some challenges I'm anticipating include the space limitations in my classroom, the time it will take me to plan and set up the technology, and my ability to manage my classes when they work with each other.<br /><br />Another goal is to journal at least every week on my progress, so we will see how that goes.<br /><br />Wish me luck, and tell me what your goals are?MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-56677931147132884372013-08-16T19:38:00.001-07:002013-08-16T19:40:07.281-07:00Bottle Holder Problem IdeaLast weekend I had the privilege of having dinner with my grandparents. While I was there, my grandma showed me a gift she received on the form of this wine bottle holder. Upon seeing it, I instantly thought of a number of questions. <div> <br><div class="separator" style="clear: both;"><a href="https://lh5.googleusercontent.com/-JfKYgM2ri-8/Ug7iOHIq7kI/AAAAAAAAARI/w-8aqvhB_pY/s640/blogger-image--96350408.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh5.googleusercontent.com/-JfKYgM2ri-8/Ug7iOHIq7kI/AAAAAAAAARI/w-8aqvhB_pY/s640/blogger-image--96350408.jpg"></a></div></div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">1) What is the angle of the base of the holder? </div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">2) At what angle is the bottle in relation to the holder? </div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">3) Are those angles the same? </div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">4) Is there a way to prove the angle congruence?</div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">5) If the bottle angle is equal to the angle of the base is that a requirement for the holder to work?</div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">6) At what level of liquid will the bottle fail to stay up? </div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">7) Would it be possible to dispense liquid from the bottle while it is in the holder? If so, for how long? </div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">These are all questions that my family and I brought up during dinner, and I think it would be interesting for students to think about these questions and formulate a way to answer them. </div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">What questions would you ask, and do you know the answers to any of the ones above? </div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;"><br></div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-75704443277168538682013-07-12T08:30:00.000-07:002013-07-12T08:30:34.995-07:00Trying to Improve this QuestionThis summer I have been working with a few other teachers to help shape the math curriculum for our county. Part of that process has involved compiling tasks for each unit that are meant to serve as representations of what students should be able to do within that unit of content.<br /><div><br /></div><div>I like that a lot of these tasks have a focus on student discovery, and all in all most of the tasks that we have put together have the potential to establish good learning opportunities. One, however, stood out as a candidate for fixing. </div><div><br /></div><div>In the spirit of Dan Meyer's Makeover Monday posts, I set out to improve the task below. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-d-Z0O_OqEl4/UeAak1RUm8I/AAAAAAAAAP4/zYFu6T3Mi4c/s1600/Triangle_Roofing_Problem.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="319" src="http://3.bp.blogspot.com/-d-Z0O_OqEl4/UeAak1RUm8I/AAAAAAAAAP4/zYFu6T3Mi4c/s320/Triangle_Roofing_Problem.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div>The main reason this problem stuck out as a candidate for fixing is it makes poor use of the cabin idea. My first inkling was that this could do much better in engaging the connection between triangles and roofs. From that motivation, my goal became getting at the same congruence content with something that got away from the step by step set up. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"></div><div style="margin-left: 1em; margin-right: 1em;"></div><br /><div>Below is<a href="https://docs.google.com/file/d/0B8hYicf5bKkaMlZLVHFYTzJHQWc/edit?usp=sharing"> what I came up with</a>. I did some searching about roof structure and trusses, and I found a visual that made use of triangles complete with all of the terminology.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-nIb0DlIRun4/UeAdQ19J-cI/AAAAAAAAAQI/NBCpDMOX6aw/s1600/Triangle_Congruence_Roofing_.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://1.bp.blogspot.com/-nIb0DlIRun4/UeAdQ19J-cI/AAAAAAAAAQI/NBCpDMOX6aw/s320/Triangle_Congruence_Roofing_.png" width="262" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>I'm happy with the facts about common trusses that the students will use to support their proof, but I'm struggling with the task portion. I think that it is a good problem that would require students to make a number of connections as they built their proof, and I like that it's to the point and the pictures can speak for themselves. My trouble comes in establishing a driving motive for why anyone would care that those two triangles are congruent.<br /><br />The fact that the triangles are congruent does appear to be obvious, and the main challenge is in structuring the reasoning for why that is true. But why does it matter that they are congruent? Why would anyone care that they are congruent? And if no one cares, then how could this problem be saved?<br /><br />As a bonus, I did find <a href="http://www.pole-barn.info/roof-pitch.html">an interesting resource related to the pitch</a> of a roof and how to calculate the angle measures for the truss cuts, but that didn't relate to congruence. It relates more to slope, and so I will save it for then.<br /><br />In the meantime, what would you do to improve this task? How would you have improved the original problem?<br /><div><br /></div><br /><br /><div style="text-align: center;"><br /></div><br /></div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-4692076513533698902013-07-06T16:35:00.001-07:002013-07-06T16:35:58.449-07:00Exploring Quento<div class="separator" style="clear: both;">I found this game a few months ago, and since playing it, I have been thinking of a lot of questions that I think would be fun for students to explore. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">If you're unfamiliar, <a href="http://www.quento.com/">Quento</a> is a math game that tests the user's ability to do basic arithmetic. As you can see from the image, there are varying levels of difficulty, and the objective of the game is to combine the numbers in such a way so as to get the desired number. The trick is that the user can only use the specified number of numbers to get the result.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><a href="https://lh5.googleusercontent.com/-WSgvNrMHC2k/UdihHgMmucI/AAAAAAAAAOs/cgs-ok6H9aY/s640/blogger-image-1964861913.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh5.googleusercontent.com/-WSgvNrMHC2k/UdihHgMmucI/AAAAAAAAAOs/cgs-ok6H9aY/s640/blogger-image-1964861913.jpg" /></a></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">I have had quite a bit of fun playing this game, and I was glad that I was able to show my students the game on the last day of this past school year. While playing it as much as I have, I have been thinking of some fun questions about the math around the game. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Aside from the obvious arithmetic component, Quento has some interesting design questions too. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><b>Question 1:</b></div><div class="separator" style="clear: both;">How many rounds could the game have? </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">I like this counting problem because it requires the distinction between having numbers repeating and not. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><b>Question 2: </b></div><div class="separator" style="clear: both;">How long will it take before I reach the final round? </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Having played through over 300 rounds, I wonder if I'll ever reach the end of the game. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"></div><div class="separator" style="clear: both;"><a href="https://lh5.googleusercontent.com/-BHy7XyvvBg8/UdihIU0nAcI/AAAAAAAAAO0/daE45uGPixs/s640/blogger-image--1519085430.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh5.googleusercontent.com/-BHy7XyvvBg8/UdihIU0nAcI/AAAAAAAAAO0/daE45uGPixs/s640/blogger-image--1519085430.jpg" /></a></div><br /><b>Question 3:</b><br />How many positive (and negative solutions) are there for each section of a round?<br /><br />The fun part of this question is finding multiple ways to get 5 (for example) using only two or three numbers. Also, while negative numbers can be used to get a result, there have not been any negative solutions in the entire game. What if there were? (I guess that's question 3b).<br /><br /><b>Question </b> <b>4:</b><br />By how much does the difficulty increase as more numbers need to be used to get a solution?<br /><br />This is interesting because, while Quento does not have a timer, difficult could be measured in how long it takes to reach a solution. It could also be measured in the number of possible arrangements that arrive at the solution, which is connected to question 3.<br /><br /><b>Question 5: </b><br />Could there be a level that requires using six numbers?<br /><br />Quento has a "Hard" setting that I have not yet tried, but it only goes up to requiring four and five numbers. Would a round of six fall into the "Easy" or "Hard" category? (5b)<br /><br /><b>What do you think? </b><br />I encourage you to try out the game, and ask your own questions. My dad and I are having a competition to see who can get further in the game, and it is a nice game for keeping your arithmetic skills sharp. I also encourage you to show your students the game, and ask them what questions they have about it. It comes on many platforms for free, so let me know what you come up with.<br /><br /><br />MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-75917448634114446842013-07-05T15:50:00.000-07:002013-07-05T15:50:09.641-07:00Ordering PizzaOnce again, a problem idea comes from West Virginia. While I was waiting in line at a general store, I noticed the store's menu for pizza. Unfortunately, I forgot to snap a picture, but I did write the prices down.<br /><br /><b>Pepperoni and Cheese is $10.99</b><br /><b><br /></b><b>Each additional topping is $1.59</b><br /><b><br /></b><b>Toppings</b><br />Sausage, Onions, Green Peppers, Ham, Mushrooms, Bacon, Banana Peppers, Olives, Sardines.<br /><br /><b>A pizza with everything is ???</b><br /><br />The problem is straightforward for a student. Multiply 1.59 by nine, and add that to 10.99. However, the resulting price is not what the store advertised. Once students found the obvious answer, I plan on showing them that the store is selling an everything pizza for $17.99.<br /><br />Now the question is, why would they sell an everything pizza for $17.99, when it would make sense to sell it for $25.30?<br /><br />Why they would charge $1.59 for each topping when their everything price indicates that they can afford to only charge about $0.78 cents for each topping?<br /><br />I am glad that I found this problem because I'm not sure of the answer, and it would be interesting to see what students came up with with regards to the possible reasons for the stores pricing. I would be interested to find out what they would charge for an everything pizza, and it would be interesting to see how they support their decisions.<br /><br />This would also be extended to other businesses and how they go about deciding on their prices, and I could see a connection to systems of equations and tall about weighing cost versus revenue.<br /><br />What do you think about this problem? Have you seen stores price items in perplexing ways?<br /><br /><br />MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-67754494569900808302013-07-03T11:07:00.003-07:002013-07-03T17:19:12.606-07:00Train SpeedWhile working next to the train tracks in West Virginia, I was lucky enough to see three trains go by. It's possible that it was the same train going by three times.<br><div><br></div><div>At any rate, I was wondering, how fast was the train moving, so I took a video as it went down the tracks. </div><div><br></div><div><iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/hnxrZpMSLBE" width="420"></iframe></div><div><br></div><div>That would be my Act 1, and from here the students would go about figuring out how fast the train was moving.</div><div><br></div><div>I could see this problem being used in a unit about rates and unit co versions. I think it could seve as a nice quick activity to get students thinking and working. <br><br>There are a lot of angles to solving this problem. They could find the carts per second and convert to miles per hour, or they could see how long the driveway is and find out how long it takes a cart to travel that distance.<br><br>I might try to give them the original video file and let them manipulate to find the time from there. </div><div><br></div><div>What would you do with this video, and what else have you done that's similar? </div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-86291479011868456482013-06-28T14:05:00.001-07:002013-06-28T14:51:46.983-07:00Giving this blogging stuff a shotI'm about to enter my second year of teaching, and recently I have found an immense amount of fellow math teachers who have a plethora of great stuff online. As my goal is to make what I teach more relevant and thoughtful, I have spent the past month consuming a lot of great ideas from all over the math blogging and twitter community. I enjoy thinking about interesting new ways to create thought provoking learning experiences, and I'd like to start contributing some of my thoughts and ideas. <div><br></div><div>This year I'll be teaching Geometry, Algebra, and 7th grade math at a middle school close to home, and I'm excited to use some engaging projects and problems to get my future students thinking and and working with math in a way that will stick with them. </div><div><br></div><div>The planning starts now, as I try to answer a ton of questions ranging from the logistics of setting up the problems, how am I goi g to asses student work in a meaningful way, and how am I going to make sure that the projects they work on uncover the content that they need to know. </div><div><br></div><div>I welcome all of the feedback that you have to offer, and I look forward to building my toolbox as my career moves on. </div><div><br></div><div><br><div><br></div><div><br></div></div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0tag:blogger.com,1999:blog-274694369827286189.post-73129742101321796472013-06-28T12:02:00.001-07:002013-06-28T17:40:24.521-07:00Octagon TableWhile visiting family in West Virginia, I came across this table at their river lot. I'm wondering the angle at which the wood was cut. <div><br><div class="separator" style="clear: both;"><a href="https://lh5.googleusercontent.com/-I_gRxM0jiYw/Uc3dyXZOjvI/AAAAAAAAAMk/-M1oMtIuz14/s640/blogger-image--820649411.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://lh5.googleusercontent.com/-I_gRxM0jiYw/Uc3dyXZOjvI/AAAAAAAAAMk/-M1oMtIuz14/s640/blogger-image--820649411.jpg"></a></div></div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">I can see this as being a good problem for getting into polygons and how they're built from triangles, and I like the link to carpentry. </div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">I can see having the students build their own table top with a varying number of sides, and figuring out what angle to cut the wood cross sections.</div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;">I'm thinking that this would fall under common core standard G-MG-A.1 or G-SRT-B.5. What do you think, and what would do with this problem?</div><div class="separator" style="clear: both;"><br></div><div class="separator" style="clear: both;"><br></div>MrAdamsProblemshttp://www.blogger.com/profile/07066167741060820768noreply@blogger.com0