Days 157, 158, 159, 160: Rolling Cups

I assigned this as a final project for my geometry classes. I wanted to see (and I wanted students to see) how well they could apply their mathematical skills to real world applications. I struggle with being less helpful, while keeping students from giving up, so i really studied all of the suggested questions that go with this lesson described by the Mathematics Assessment Project. I did not follow the lesson exactly as designed, but instead adapted it for my students. I broke the project down over four 50 minute class periods:

Day 1: Introduce activity, students work in pairs: turn in all thoughts & notes for feedback at end of class. This evening I replied with next steps / questions to keep students making progress the next day.

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Day 2: Time to work, select students to informally present their noticing’s so far. Introduce the cup calculator for students to study patterns and test hypotheses.

Day 3: Students analyze sample solutions, then begin revising their own work.

Day 4: Final work day & reflections, discussions, presentations

Next year I’d like to add time at the beginning for noticing & wondering & individual student work before they begin working in pairs. My fear is that many students will not even try just because they are not sure where or how to start.

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Day 155 & 156: The Triplets of Cellville

I chose this Mathalicious lesson because we have not used circles enough in my geometry classes. We stared the school year with constructions, but haven’t used them much this semester and I wanted them to recall and extend prior learning. I also wanted students to gain more experience modeling real world scenario’s with mathematics & I thought this task would be engaging do to it’s relevance to students lives.  I started off showing the introductory video clip which is a news story of a woman explaining how photos taken with a cell phone include GPS data and how your cell phone records your location. I was surprised that ALL of my geometry students were furious at this video. They thought this lady was dumb for being surprised because “…everybody knows that you can turn on and off the location settings on your phone!” one student argued that if this woman in this video was her mother, she would be furious at her for being so clueless. It was great because it got very intense, and I had no idea how savvy students are with their cell phones. After this discussion died down students inevitably asked: “Wait, what are we doing today? Are we learning how to stalk people with their phones?” and “Mrs B, you are so weird.” Also “This is going to be awesome!” They were hooked.

I don’t want to describe the entire lesson in too much detail because I want you to support Mathalicious and their quality activities, but students constructed circles on a map to determine possible locations of a person in relation to a few cell towers. The lesson also discussed coverage vs locate-ability and students had to use estimation & area formulas in order to draw conclusions and also to determine and justify where they would add a cell tower in a city if they were in charge of making the decision. The only thing I would change for next school year is that I would modify the lesson to use our town and cell tower locations locally to make this more relevant and less hypothetical. Students were engaged and it was a good way to use student interest and incorporate modeling at the end of a school year when motivation is typically pretty low.

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Day 151 & 152: Similarity transformation proofs

I waited until the end of the school year for this because I wanted to encourage retention by requiring students to remember basic transformations in addition to applying dilatation which we just worked on. I searched for a good way to help students develop understanding of this. The best description of this standard that I found was Kate Nowak here. In this post she included a link to Khan Academy’s interactive modules. I am not a fan, but these really helped students to see how to prove similarity. I searched for other options and even asked Desmos, but I found this Khan Academy module to be my best option. I set up a “coach” account, then on the first day my students set up accounts, made me their coach, and accessed the module. It took a while for them to get the hang of how it worked. On the second day they will try to get 5 correct in a row, really I just want them to experiment with this some more and develop mastery.

Day 148 & 149: Four fours

I’m surprised how much students struggle with four fours. I think I should do this earlier in the school year next year so that they can practice many the standards of math practice in an environment where they are more familiar with the basic math skills required. Additionally, I should add a part 2 where students use their work to prove whether or not all numbers can be constructed using 4 fours.

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Day 147: Practice similarity with Area & Volume

I had a sub. Students used their interactive notes to practice applying similarity to area and volume. I’m not sure why, but students really struggle with this concept. I need to find a better way for them to SEE the impact of a scale factor on area & volume next year.

This was the highlight. Look at number 8! IT is very fun to see our math talk warm ups reducing calculator dependency:

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