Open Middle

After joining the Twitter Open Middle conversation last week by Michael Fenton, I was intrigued to try out some Open Middle problems in the last few weeks of school. To kick off our review for the final exam, I posed one problem to Algebra II and one to Geometry. My students reactions were great, starting with one kid saying, “nope, Mrs. Taplin, it’s impossible.” After explaining the concept of “Open Middle” and encouraging them to have some grit and resilience with the problems, my students really got into it. Some proudly held up their whiteboards for me to check when they got their answer, many requested just a bit more time so they could finish it, one excitedly jumped out of his seat when he got the answer, and another claimed, “this is my greatest accomplishment!” I would say that means Open Middle was a success!

Here are the problems I used and if you haven’t checked out Open Middle, it’s a great resource…here is the site for even more information on these types of problems: http://www.openmiddle.com/.

Algebra II: Create three equations that produce the exact same parabola by filling in the blanks with whole number 0 through 9, using each number at most once.

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Geometry: What is the longest chord in a circle that has an area of 25pi square units? 

What I like most about these problems is the conversation that unfolds with students. For the Algebra II problem, I started with vertex form, but several students started with factored and/or standard form. One student said she went from standard to vertex, but another argued that she did both factored and standard, then graphed to get vertex (something I didn’t even think of doing, but what a great well rounded way to review this concept). In geometry, I thought this problem might be too easy, but with the different way of thinking from more straight forward problems it created a challenge to students. I loved the conversation focused around vocabulary, the “good mistakes” (as I like to say) students made, and the corrections they did. Several students got 5 units for their answer, but forgot that the question was asking for a chord, not a radius. It forced students to reevaluate their answer and not stop too early.

I like to do Mental Math Monday’s (I got this idea from my mom…the teacher verbally says a string of arithmetic problems and students try to quickly get to the correct answer in their heads) for warm ups into class on Monday’s, so maybe I can add this to the week rotation next year and try Open Middle Wednesday’s (since it’s the middle of the week). Thanks again, Michael Fenton, for some great ideas!

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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 🙂

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!

3D Solids Lesson Using Jigsaw Cooperative Learning

Here is a quick lesson I put together using the Jigsaw Cooperative Learning technique for 3D solids. We learned the surface area and volume formulas for prisms in a direct instruction model and because we have such little time left in the year with testing and such, I decided Jigsaw-ing these concepts would be the best way. Overall, it went well…I did have to model how to have students teach each other and not simply copy, but after doing that, I was very pleased with how they communicated their understanding to each other.

I gave each expert group some cards of one of the solids I found here: http://math.about.com/od/formulas/ss/surfaceareavol_2.htm. With these cards, they had to talk through what the variables meant, what the lateral vs. total areas were, and how to use the volume formula. After each group finished completing their row of one assigned solid (writing the formulas, defining variables in their own words, solving a given example, and creating their own example), I mixed up the groups to have one solid represented in each new group. Then each expert taught the others how the formulas work and what they learned.

Here is front and back of the student worksheet I created, the rest can be found here: .

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