Helping Nepal Through Learning About Logarithms

nepalA 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!

polyhedron2polyhedron 1polyhedron 3

Skype Updates (Thoughts That Keep Me Up Part 2)

Last week, I Skyped with an educator who works as the Director of Instruction and Technology for the Solon Community Schools, Matt Townsley. After reading his blog, I was intrigued to find out more about SBG and somehow he must have either found out that I linked him on my post (Thoughts That Keep Me Up At Night), or maybe the Gods of math just brought us together, because he asked me to Skype with him to further the conversation. The Skype chat we had is essentially why I created this blog…to get the conversation going about education, math, and positive adjustments/additions we can make in our classrooms to better student learning. I was so excited to get a message from Matt saying he wanted to Skype because I knew he had been successful with the SBG changes he made in his district and so there would be so much to learn and so much to discuss. Next on my list of people to meet and chat with…Dan Meyer…he’s like the Justin Timberlake of math blogging to me!

So, here are some big takeaways I got from our conversation:

1. Red, Yellow, Green: One quick addition I liked that he did is to have students write red, yellow, or green at the top of their quiz. The next day, a teacher can make pairs easily either by similar understandings or heterogeneously and set up a productive tutoring environment. This would just save time because “red, yellow, and green” are so easily identifiable.

2. Likert scale: Here is a sample Matt sent me. I like this added on to quizzes and tests. Likert Scale

3. No points for homework: I’m convinced…I will definitely be doing this next year after talking with him. I already provide my students the answer key during class which because I believe in his similar philosophy in which we should not make students wait until the next day to see if they are working problems correctly. Furthermore, as I said in my previous post, I don’t want to take off or inflate grades based on practice. So, I will keep track of the assignments/practice we have done and in order to retake, students must be able to prove they have completed all assignments/practice up to that assessment. The homework category, however, will be set to 0%. I think this will help remedy the motivation or accountability factor of 0% homework.

4. Teacher insurance policy: This was just an explanation of what students need to do in order to retake. Right now in my class, any student who got below an 80 on a quiz can retake before the test that covers that material. Under my SBG system, I will still allow students to retake because I know students learn at different rates and paces. I know some need second, or third chances to master material. However, right now students are simply coming in to tutoring, cram studying (or requesting to be retaught on all the concepts) and then right away while it’s “fresh in their minds” they are wanting to retake. Honestly, because I feel like I should capitalize on a student actually coming in to to tutoring, I let them retake right then and there. But, this does absolutely no good! Instead, I like how Matt had it set up…first, I will be sure students have completed all the assignments/practice before they can retake (I say this every year, but I have been too lenient on it throughout the year. That’s only making me work harder because they are coming in blind to the material…I will be better about it this year). So once that the assignments/practice are complete, students must correct the piece of the assessment they want to retake and go over it with the teacher (I do this too)…so here’s the new part: one more practice will be assigned…this could be something sample questions done at home, or telling the student to go home and record themselves teaching the material to their mom or sibling. THEN, they can retake. This ensures several things…students are not cramming, students are doing the learning, students are not retaking in the same day and then forgetting it the next.

5. Buffet-style final exam: Day 42 on this blog describes this concept. I really like this idea!

6. Grading rubric for SBG: I like the kid friendly language here.

rubric

Lots to think about! But luckily, I feel like these can be easily applied to the classroom I have already set up.

Thank you again, Matt, for taking the time to chat with me and giving me so many ideas to think about!

Sources: Solon Community School District

Math and March Madness

Now that the NCAA basketball tournament is over and sadly my pick of UK lost (my dad went to UK so don’t think that I just jumped on the bandwagon this year), I started thinking about how I could apply math to the tournament. To celebrate the beginning of March Madness, we played “trashketball” one day in class a review game (little did they know, this effectively helped me get them away from sneakily watching the games on the ESNP app from their phones). However, I am sure there are more complex things we could do for some hands on applications.

There’s so much hype around a perfect bracket, so we could definitely explore the odds of getting a perfect one. Thinking through the odds we can note that each team has 1 of 2 options in the game…winning or losing. There are 64 teams in the tournament and therefore, to create a perfect bracket you would have 2^63, or one in 9.2×10^18 (9.2 quintrillion), chances of getting a perfect one. Of course that’s if you predict like a coin flip…heads or tails…but we know there is a lot more that goes into basketball. Just calculating that is a good exponential application for students and might be a cool way to open the exponents unit that we do around this time of the year, but could we do more?

Students could watch the games and pick out any key vocabulary they see during the games…parabolas, circles/polygons/curves/lines on the court, spheres…but, hmm I’m already kind of bored by this simplicity for high schoolers…

Maybe we could look at statistics: Students could pick a player and follow their stats. They could watch for points, assists, rebounds, blocks, field goal %, and steals (I might have to have a coach come in or a kid on the team explain how to track stats like this to some students). Then students could compare what they find to ESPN’s calculations. Or, students could team up and find the stats of an entire team vs. another team. We could do this before the tournament and then using those predictions calculate which team they think would win. Granted a lot of other factors are involved in winning a game, but I think player’s individual stats could be a good start. I’d love to talk to a statistician and get some more ideas…! Maybe students could even write in to ESPN or our local news and give their own feedback on how their player/team did…they’re always looking for more commentators right?!

We could also use regressions with our statistical data: We could take a team’s win-loss history and run a linear regression to graph the data and find trends. We could compare the prediction to what happens in the tournament or even compare the seed rankings to our predictions.

Or maybe we could relate it all to quadratics: I am thinking students could take a picture of a shot attempt that did not go in and analyze the parabola. A few years ago, my dean and I used Logger Pro to analyze a thrown ball. The program will calculate the equation and from there you can find key points along the parabola (this is what I did for the “Saving the World with Math” project here). I bet we could do a similar thing with a video of a shot attempt, or maybe just with a printed out picture, to analyze why the shot did not go in. Students could put their video/picture on a graph, find the equation and certain points on the graph like the vertex and x-intercept. Then, by seeing if the point of the basket is along their parabola, they could calculate why the ball didn’t go in. From there, students could correct the equation for an accurate basket to be made.

Does anyone do anything in their classrooms related to March Madness?

I guess I have a whole year to think about this…in the mean time, go Spurs go!