# Chicken Wings and Math

This hilarious Twitter post just went viral and shows kids (and adults) why we need math. After seeing the post, I started thinking how could we incorporate this into a math lesson, because clearly we need some simplifying or justification on what is going on here. If you read this article in Today, you can see several other mathematicians are thinking the same thing. What’s the deal with the 25th wing? According to the menu, each wing costs either \$1.10 or \$1.15 (why is it sometimes more?) until the 25th wing, and that one is only \$0.55…but the 26th is back to \$1.15…?! The internet reacted and “there’s gotta be a better way to convey this information!”

So, teachers, we could use this as a lesson to talk about so many standards!! I’m thinking in just Algebra I there are several. For example, TEKS A.3B, rate of change. Is it constant? Should it be if I’m buying multiple wings? When does it change? TEKS A.2A, domain and range. Is the information discrete or continuous? Why? What’s the least amount of wings and most? And that scale…it was going up by 1’s, then 5’s, then 10’s, then what? Can I even a certain amount like 55 wings? A.2C, writing linear equations from a verbal description. But it’s not linear, so maybe we need A.4A and A.4c to look at correlation coefficient and writing equations from data. Whew. I think this could definitely apply to all levels of math-elementary, middle, high, college! Let me know if try it out and what your kids think.

# Parabolic Solar Cookers

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.

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!

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

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 🙂

# Helping Nepal Through Learning About Logarithms

A few months ago I created an application investigation for my students involving logarithms in which one of the areas focused on earthquakes and the Richter scale. Students researched several earthquakes and saw the effects that differing sizes made on an area. Recently, my principal sent me this article about Nepal’s earthquake and again highlighted how much bigger one earthquake is versus another, even when the Richter scale values are only a small difference. I decided I was going to show this to my students as a great visual and reminder of mathematics in our own world, but didn’t want to just leave it at that. I thought we could do something for Nepal. I sought out one of my student’s who is the sophomore board president and asked her if she had any ideas (kids are always more creative!) She came up with the great idea to sell t-shirts around the school as a way to raise funds for a charity in Nepal. Two students then designed the tshirt and we decided to go with this local post-graduate student’s efforts who has been working directly in Nepal (see the article here and here). We loved the description of all they were doing there and that we could see exactly where the funds would go. After selling 100 shirts and paying back the funds we purchased the shirts with, we will be donating \$195 to their organization!

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If you are interested in the investigation, here is the student worksheet: Applications of Logs. I had students choose 3 areas they were interested in studying between population growth, earthquakes, sound/decibels, pH scale/chemistry, and risk. The population growth was an online investigation to understand the population growth equation, the rate, and predict future models. The earthquake investigation asked students to research different earthquakes that have happened around the world and see the impact of different Richter scale sizes. In the sound/decibels investigation, students used an iPad to record different sounds and then use logarithms to calculate the decibels. The pH scale investigation began by having students watch a video on pH and then analyze the pH value of certain foods that we eat. Finally, the risk investigation helped students to understand the role of an actuary and how logarithms are use to assess risk.

# Introduction to 3-D with Polyhedron Nets and Islamic Design

A couple weeks ago, I was planning for our last unit in geometry which is 3 dimensional solids, and as I was measuring nets and counting vertices, edges, and faces, I suddenly realized I was really bored. If I was bored, my students definitely would be! I knew I needed to amp up my curriculum to still teach nets, relationships between 2-D and 3-D, and constructions (TEKS G.6B and G.2A), but somehow make it more engaging.  What eventually fell out of my plans was a new connection between math and World History.

I started thinking that students could choose a 2-D net, decorate it, and then fold it into the 3-D polyhedron. However, this was not very exciting and required little critical thinking. Also, I knew I wanted students to decorate their models, but I didn’t want them to just draw flowers or smiley faces or simplistic designs with no reason behind it. So, I asked the World History teacher if there were any connections he thought I could make between our two classes. He told me they were about to start Islamic culture and history which was perfect because Islamic art incorporates a lot of geometric design. We talked about some questions to prompt some thinking for his class. By asking students to pre-think, my geometry students were able to be the experts the next day in World History.

Here’s the basic outline of the lesson plan.

1. Pass out the Islamic Art and Polyhedron student worksheet and talk with the students about the fact that we are going to make a connection between World History and geometry…yet again!! 🙂

2. Show this video (or any other video you find) and ask students to jot down anything they see that answers #1 (What patterns do you see in Islamic art?).

3. After the video, have students pair up and talk about what they saw. Then call on students to share out whole class. (Think, Pair, Share model)

4. Then, we went on to the questions #2-4 which talks about the history of the region and asks students to compare Islamic design to Chinese, Eurasian, and African Art, but you can add or take out any other questions that would be relevant to their World History class.

5. Show students the net templates they can choose from. Some chose simple nets like cubes, rectangular prisms, while others chose more complex such as octahedrons and stellated dodecahedrons. (There are many templates online…I decided to use this website. Warning: Some models are very tricky, but I think if students get to pick, they will have the buy in and motivation to complete it.)

6. After they have chosen their template, found the number of vertices, edges, and faces, we used the rest of the class to design their Islamic artwork. Remind students that they must use rules and compasses when drawing lines, circles, and arcs, because Islamic art focuses on very precise designs.

7. The next day, we came back and started class by having a chalk talk with this question: “What is the main focus of Islamic art…what does it include/not include?”

8. Then after a 3-5 minute chalk talk, I let them work on their design and fold their 3-D nets.

Overall, students enjoyed this hands on activity. One change I would make is to print out the larger nets rather than the single page nets, especially for the more complex types (anything larger than an octahedron) because folding and taping those got quite tricky! My plan is to hang these up with fishing wire between my room and the World History room as a visual connection between the two classes. Thanks, Mr. Sprott, for helping me dream up this mini-project!