Parabolic Solar Cookers

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I am excited for our final project in Algebra II…parabolic solar cookers! After we did an in class investigation of the four different types of conics with play-doh, evaluated the standard equations, and explored the graphs of each, I wondered if there was one more way I could help my students deepen their understanding of conics. So, while sitting on the couch at home with my husband and searching online, I found this (http://www.education.com/science-fair/article/solar-hot-dog-cooker/) and excitedly told him, “I’m going to make this happen!!” The next day at school, I talked with my dean about the logistics of creating solar cookers and ways to help scaffold the lesson.

The summary of the project and the student materials that I revised from the website are below (some wording and pictures are directly from the website above…so please credit that source if using this.) The directions are quite lengthy, but very step-by-step, so I suggest breaking this up into at least 3-5 days with groups of 2-4 students.

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Summary: To begin the project, students spent a class day researching and answering questions about solar cookers. With the help of an actual solar energy engineer (see his website and work here: energyae.com) generating some ideas, the questions helped students buy in to the project (he also sent me some videos to show students real life parabolic solar panels…if you have Dropbox, check them out here: https://www.dropbox.com/home/SolarMrsTaplin). The next day, students found three points to create a parabolic curve based on the dimensions of their shoe box (two top corner points and one center origin point). From these, students calculated the equation and plotted other points to create a nice, accurate curve. Next, students calculated the focal point, which we talked about the reasoning as to why this is the spot they should place their food at to cook. Lastly, students covered their curves in poster board and foil for the reflective surface and fashioned holders for the focal point.

A few groups still need to finish, but they are coming along very nicely! It has been raining/cloudy for about a week straight now, so please do a little anti-rain dance for us and hope for some sun so we can test out these cookers before the school year ends!! I will post after we get to and show the results!solar 5

Student Materials: (link to word doc: solar cooker proj or click on thumbnails below for images)

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Update: We finally had some sunny weather and got to go out to cook. We left the solar cookers out for about 45 minutes. The marshmallows didn’t melt the way we predicted, but having thermometers out with us proved that it definitely got hotter at the focal point. Most had an initial temperature of 90-92 degrees F, and after about 20 minutes, the temperature rose to about 105. The final temperature recorded was about 120 degrees F at the focal point of most solar cookers. Although they were a little bummed that the marshmallows didn’t melt completely, we talked about the fact that if it were 120 degrees F outside, they would not want to be outside themselves. So, that helped put it in perspective and see that it worked. Next year, I think we should try cooking a darker food substance…maybe chocolate, and we could do fondue 🙂

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UbD Unit for Systems of Equations and English STAAR

I completely forgot about a UbD unit I created a few years ago which connects mathematical systems of equations to writing for the English STAAR (I wasn’t able to use it this year due to a calendaring scheduling conflict, so it slipped my mind). I was searching around for some English/Math connections and stumbled upon this unit published by Trinity University…turns out it’s mine! I figured my blog would be a good place to leave this link to the unit. I know it’s a bit late in the year to use for STAAR writing practice, but maybe it can be stored away for next year!

Thoughts That Keep Me Up at Night

I have been thinking a lot about grading, assessment, and the meaning behind these to both teachers and students. I have read Dan Meyer, Daniel Schneider, Educational Leadership, Matt Townsley, and Rick Wormeli while researching and talking with colleagues about mastery and standards based grading (SBG). I really like a lot of the ideas of SBG including more frequent and smaller assessments that allow one to know a student’s mastery on a standard. I also like the thought of a 1-4 scale and the language that is used to convey what each number means. One example I found that I really like is that the Solon School’s language in their rubric (1).  CaptureHowever, I am still struggling to wrap my head around SBG and mastery in the math classroom. I still have lingering questions that honestly keep me up at night. I want to do what is right for students and I want to push them to understand what they know and what they don’t. Even further, I want them to take charge of their learning and with my feedback, help them to know how to gain mastery on a concept.

Here is what I want to keep in my classroom regardless of grading…

Student communication and group work: I think when students talk out mathematical problems together, they cognitively grow a lot. A student’s ability to explain a topic further enriches their own understanding, and when they hear an explanation from another student, they relate to the language they’re using. So, regardless of how I grade and what I grade, I still want students to work together to solve problems.

Reasoning: I also want to be sure I am still allowing room for reasoning and processing skills beyond algebraic skills. I want to continue to provide opportunities for students to explain and justify their understanding of concepts through written and spoken dialogue. Whether this fits into a numerical grade or not, students still need to be pushed to think deeply and justify their reasoning.

Here are my questions that linger…

How do I keep students motivated to practice mathematical concepts they are struggling with? How do I motivate beyond grades in practice settings? Ultimately, how do you stop students from asking, “is this for a grade?” A lot of SBG research shows that you should not grade homework because you should not penalize a student when they are practicing their mastery. I agree with that to an extent. As a basketball coach’s wife, I know that practice is important, but that my husband should not grade his students in their practice sessions. It all comes down to the game. The game is where they will be graded based on if their shots fell, if they played zone defense instead of man to man or vice versa, if they passed the ball smart, if they turned the ball over, if they made their free throws, etc. If he included practice in their final grade, the score at the end of the game would be quite skewed. Similarly, homework practice should not be a penalty or a reward to a student’s average…it should be a check for understanding and an identifier of strengths and weaknesses on the road to understanding. Overall, I don’t want to penalize my students for practice they get wrong. However, most students are much more motivated by sports than math practice. So, how do I keep my students motivated if I don’t grade practice? Naturally, you would think that they should make the connection that when you practice, you get better. So, when you do more math practice you should do better on your quiz/test…but students don’t always think in advance and the most common thing I hear in the classroom is, “is this for a grade?” I think I need to hold them accountable to doing practice and/or homework by counting it for a portion of their grade, but it should not inflate or penalize their average. Additionally, I think the word “homework” needs to change. It has such a negative and dreadful connotation, but I am still thinking about what it should be called.

How do I create a balance between group practice and independent practice? How do I convince students that individual work time is just as, if not sometimes more, beneficial than group work? And finally, how do I convince students that individual assessments are meant to be informative not punitive, especially when we take points off for wrong answers rather than give points for correct attempts? Right now I give a lot of time for group practice. Again, I love the learning that happens when students talk through math. But I am realizing as I read more about SBG, I need to create more opportunities to show what they know individually. In that, I need to create time to give my feedback to them on an individual level beyond tests. I think by adding in more frequent assessments, this will do that and give students the opportunity to analyze what they know. These could just look like short quizzes done on note cards at the beginning of class. They could be graded on a 1-4 scale with more feedback than a regular assignment as it leads up to a cumulative summative assessment. The question then becomes, do I have the time myself to dedicate rich feedback more often to every individual student? How do I create that time, especially as a math teacher, when so many of my days are dedicated to teaching new material rather than refining knowledge students already know? Ultimately, can someone find me some more hours in the day? 🙂

Feel free to respond to any or all of my questions, share this with every educator you know, and continue the conversation of grading and assessment!

(1). http://www.solon.k12.ia.us/vimages/shared/vnews/stories/52e8843978db1/scsd_sbg_update_powerschool_march_2014.pdf

MatHistory Part 2

This post has taken me a while to write with several revisions because I just haven’t known how to write it in a way that gives justice to everything I have loved about this assessment. Every time I sit down to write it, a new way to introduce the post races through my head. However, I think the best way to start out is simply thanking the AP World History teachers who had the vision and the enthusiasm for working with me to create this complex, unique, and highly successful interdisciplinary assessment. So, thank you, Mr. Freeman and Mr. Sprott! I hope this leads to many more mathistory and mathenglishistry (math-English-history-chemistry) ideas!

So, here’s how the project unfolded…

Last Tuesday, the World History teacher presented our students with the idea of a power scale timeline and explained how to create one. Each group of four students were given 16+ maps of various European empires that showed the time at which each empire owned land. After identifying the region, they transferred the area onto a larger scaled timeline. Then, when all the empires were on one map, students used their mathematical knowledge to identify key points and explain why they are important relevant to time and land area (we presented this part on the second day). At this point you may be thinking whhhat theee hecckkk is this lady talking about…don’t worry, our students were also a bit perplexed by the task at the beginning and in first period, we did have a brief time when we felt as if our students might revolt against us. However, after encouraging our students to just try it out, much to their surprise with a little patient problem solving (as referenced by Dan Meyer) they excelled at the task. After they got the hang of it, I asked one student to explain the process and here is his recording. I liked getting to be in the history classroom this day because I was a second person who could help facilitate and answer questions as students created their timelines. They also started to make the connection with me being in the room that this might have some math involved in it.

On the second day, as the students were finishing their timelines, we presented them with the math portion. As they identified key points historically, we heard them using mathematical language and vocabulary terms as they talked about undecagons, parallel slopes, parabolas, intersecting lines, exponential growth, etc. It was really cool to see students make connections and hypothesize using their knowledge from both classes. We encouraged students to work together because the questions we gave them ranged in topics from both Algebra II and geometry. Each group had students from both classes and therefore they were able to be experts in the subject they were taking. Walking around helping students work through the assignment, I overheard two students talking about interdisciplinary learning and caught the end of their conversation on tape. Hearing them voice their appreciation for interdisciplinary learning really made it all worth it!

Yesterday I finished grading the math portion of the timelines and was sitting with the English teacher during our monthly Saturday school when she asked me, “so, would you do it again?” My immediate answer was, “YES!!” I think that asking students to use mathematical evidence in their explanations of what was happening historically made them think deeper. I also think they were able to synthesize better by using logical mathematical thinking. Additionally the featured image at the top of this post is one that we were very impressed by. She spent time finding key images and icons from each empire and finished her timeline with detailed watercolors. It made us think of the possibilities…perhaps students could design a timeline based on different aspects of each empire (religion, architecture, art, etc.) I think there is so much more we can do and definitely lots to think about. Over the next few weeks students will continue to learn in their World History classes about each empire and add to their timelines in order to create a large final timeline in groups…so more to come!!

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Here is the link to the math student materials: MatHistory

Two More Review Games to Try Out

We played two different review games this week in Algebra II and Geometry. I gladly give credit to the two blogs hyperlinked throughout this post after seeing my students highly engaged and excited to do math practice with the addition of these two games.

Featured imageThe first game is one I call “The Laundry Game” and we played it before a geometry quiz. This game can be applied to any content and any grade level even though I actually found it on a 3rd grade blog. I love this game because it takes a normal review and adds movement, competition, and immediate feedback. My intern and I were talking about how changing the format of a routine review into this game makes students do so many more problems than they normally would. I changed it up a bit by providing the answers at each station rather than having students come to me to check. That way they could check their own work and then the teacher could be facilitating and answering questions. At the end, we drew their names from the buckets, awarded prizes, and then explained the reasoning behind the name, “The Laundry Game.” We told them when they go home that night, they will find the problems they need to review again in their pockets with their laundry! Featured image

The second game we played is a BINGO game that I found here. We played this as addition to a normal practice day. I have seen and played BINGO before in the classroom, but I love how this one gives choice to students and the downloadable file is already made for you to give to students…so easy! My students LOVED this…after the first student won, several kids shouted out, “can we keep playing?!” Little did they know, they were implying, can we keep practicing logs!! FullSizeRender (3)

Teams-Games-Tournament

I am always looking for new review games to use before a quiz or a test. This year, we have played Team-Games-Tournament (TGT) several times and have had great success with student mastery and engagement. This game is a cooperative learning strategy that is discussed further in “The Strategic Teacher” by Silver, Strong, and Perini. In their book, they explain the reasons why this strategy works with the number one reason being that “TGT incorporates the best of cooperation and competition.” Furthermore, it “highlights interdependence among group members, holds students individually accountable…promotes positive face-to-face interaction, builds small-group skills such as communication and conflict resolution, and encourages group processing so that students use their reflections to become better team members.” There is a bit of prep work on the teacher before hand to possibly reformat your review, create the playing cards, and make color-coded copies (my interns wonderful suggestion) for each role, but it proves very worthwhile. As compared to other review games that require the teacher to reteach or be the leader, this game is student centered and the teacher can now simply be a facilitator while students take ownership in playing, coaching, and teaching each other.

I typically give students a review sheet for the test the day before we are going to play the tournament. I give them some class time and/or assign the evens for homework. By only doing half, students are familiar with the material, but still need to review more the next day. The following day during the tournament, they will complete all the review questions. When they draw one they have already done they are instructed to do it again on a whiteboard (or a scratch piece of paper), whereas when they draw an odd question they should do it on the actual review. This gives them repetition of review and complete mastery of the content. The first time using this strategy, students will need the directions read to them and seen posted on the board. However, after a few rounds, the game becomes very clear and natural. I have loved watching students coach each other through the work while also competing with positive interactions.

Here are some directions that you can display for students as well as teacher notes to further clarify. Let me know if you play and what you thought!

Teams Games Tournament

Reference: Silver, Harvey F., Richard W. Strong, and Matthew J. Perini. The Strategic Teacher. Alexandria: ASCD, 2007. Print.

MatHistory

Featured imageI’m getting really excited for a new idea the world history teacher and I have been brainstorming for a few weeks. We are working to intertwine some math content when he teaches Eurasian Empire power scale timelines. He came to me with this thought that math could somehow be modeled in the drawings and as soon as I saw the previous year’s final products, my math brain started running! We started drafting the actual questions today and we are going to continue to formulate our ideas until we present it to our students next week (I’m sure there will be revisions even as we are presenting it to the students…forever in reflection of our craft). Here is the link to our questions and above is the image of our thought process…but stay tuned for the final student materials and some finished products!

Nuclear Culture

We just finished a 3 week long interdisciplinary unit on nuclear energy. I am very grateful to have the opportunity to work with the same core sophomore teachers for the past three years. We have grown together personally which I think in turn has had a positive effect on our students learning (supported by The Washington Post here), and we have also accomplished a lot professionally together. We started out three years ago trying to become more unified in our teaching approaches with simple ideas like wearing the same t-shirt on the same day. Needless to say, that wasn’t quite an authentic learning opportunity for students. Our approach evolved into us using the same vocabulary word somewhere in our dialogue throughout the week in hopes that our students would catch on and use it for their “personal dictionary” assignment in English. I definitely learned a lot of new words, but again, this was such a simple daily act and we knew we could do more!

Featured imageWith the help of our Trinity University interns a couple years ago, our most unified approach was created- a UbD unit centered around nuclear chemistry with lesson plans in English, world history, geometry, and Algebra II. (I have to plug an incredible master’s program here that prepares student teachers with a high level of understanding about teaching pedagogy and practice). This unit has gone through three years of revision and I have to say, the way in which everything came together this year, I think it was the our best year yet!

The first year we did the project we were not able to incorporate math because it did not fit with the scope and sequence. I still remember hearing one student mumble, “you know, we’re studying nuclear energy n every subject except math.” My heart sank and I knew I was going to find a way to make it happen! The next year, I decided to switch the sequence of our curriculum and teach exponents at the beginning of the spring semester when the nuclear culture unit started. Working with my Trinity intern that year, we created investigative lesson plans where students discovered how radioactive elements decay. Understanding asymptotes also helped students see that nuclear waste will never reach 0. We then discussed the implications for using nuclear energy based on exponential growth and decay and exponential properties. This year, I added the geometry component and solidified the inclusion of math in the unit. After my students learned about proving congruent triangles, I went into the English/World History combined classes and introduced their persuasive essay by asking students to write an outline in a mathematical proof format (I was lucky to have another intern this year and she taught a great lesson on truss strength involving triangle properties this day while I was teaching in the other room…I’ll save that post for another day). I loved how the proof writing gave my geometry students the chance to be experts on the topic they just learned and were able to refresh the Algebra II students how to write proofs. Also, the English teacher loved the way they provided evidence for their essays and did some formulaic pre-writing before jumping on a computer to type their essays. Finally, after the culminating day of the project (a “town council meeting” to debate whether we should pursue nuclear energy in San Antonio), the World History teacher created a graph where the x-axis was labeled as a continuum from “San Antonio should not pursue nuclear energy” to “San Antonio should pursue nuclear energy” and the y-axis was a continuum with “the US should not pursue nuclear energy” to “the US should pursue nuclear energy”. Students then plotted their personal opinion as a visual representation for further dialogue.

My heart is full after this unit and I loved hearing quotes like this: “I like the way every class was included in this unit because we understood all perspectives.”Featured image

One of My Favorite Projects

Featured imageI am starting off blogging by sharing one of my favorite projects that I created with my dean a few years ago. After attending a conference at Southwest Research Institute, I got inspired to do a project that would help students connect their learning of quadratics to the real world. I decided to make it about projectiles. I dreamed of getting to launch projectiles across the math classroom, but had no idea how to make this possible. After talking with my dean who is essentially a physics guru, he helped my dream become a reality. Below you will find the process and some reflections on the project.

First, we modeled a projectile using LoggerPro software and found the quadratic equation. This equation became the central focus for our students to manipulate. We asked them to find the vertex form, x-intercepts, y-intercept, and the domain and range. The fun part came on the second day of the project. We hung tennis balls in the back of the room and gave each group (groups of 3-4 students) a different height at which they would set their equation to. Using the quadratic formula, they solved their equation for the x-distance at which to launch the projectile. If their calculations were correct, they would successfully hit the tennis ball. With safety goggles on, measuring sticks in hand, and genuinely excited emotions, each group stepped up to the projectile launcher to try out their solutions. Some chose to set the launcher at the farthest distance for more fun, and some chose to go the safe route and try the closer distance. Several groups hit the target on the first try which was so fun to to watch the teamwork of their groups as they high-fived and congratulated each other. The groups that didn’t hit the target on the first try realized they needed to watch for the human error of lining the projectile launcher up straight. By the end of each class period, each group had successfully hit the target and proved their math calculations correct.

I love this project because it’s an authentic way to check their work. Also, my first couple years of doing this, I connected it to space science by having a hook that the students were trying to blast a near earth object out of our orbit (Armageddon style). Two years ago, my sophomore team and I designed a full interdisciplinary unit on Nuclear Culture. So to connect it to this, I changed the theme up a bit and had students watch a video about NATO’s ballistic missile defense program and then act as if they were helping NATO use projectiles to intercept incoming harmful missiles. Students were able to communicate their reasoning behind advantages and disadvantages of using technology like this and what might happen if we were successful or unsuccessful in hitting their target. I loved that students made connections, communicated coherently, problem solved, and found reasoning and proof (all performance outcomes that the math department at my school tries to achieve) in one single project!

Here’s the link to the student materials: Saving the World with Math