Week 5 Activities + Connections

This week we get to choose either a dance or art that embody various concepts of mathematics. I have chosen to explore Sarah Chase's dancing mathematics. 

In the video, Chase (2018) shows various ways of embodying multiplication, lowest common multiple and factors using concepts of relative prime numbers. She assigns various body parts a different number (which translates to a movement sequence of the same number), and then simultaneously runs through the sequence with each assigned body part. 

Chase demonstrates this three ways:

1. multiplying 3 (left arm) x 2 (right arm), producing 6 unique full body movements before returning to the beginning of the sequence. Chase extends this version by assigning a narrative quality to the values 2 (summer/winter) and 3 (mother/father/myself) to more easily engage with the sequencing of movements.
   
   Here's my version:
   
   
   
   
2. multiplying 7 (legs) x 11 (left arm) x 13 (right arm), producing 1001 unique movement combinations.
   
   
3. multiplying 4 (right arm) x 12 (left arm), this time as a measurement device for discovering which element is associated with each Chinese Zodiac animal by year.

Four ideas of extending this activity:

1. a sequence of notes could be performed by individuals on a monochord. Then, as they play their notes, we could listen for how when the cycle starts repeating again. It would be very interesting to have students silently choose a number (between 1-6 to start) without telling anyone and develop their number into a note sequence in the same key signature (let's imagine "C+"), then we all play together. A instrument-less student would keep a tally of how many notes were played before the sequence repeats itself. The music that would come about would be very interesting - especially if we started putting restrictions or extra criteria upon it (ie. Lydian mode only! or Blues scale notes only!).
   
   
2. Using hand-clapping games from childhood. It would be interesting to develop a two person sequence where one individual has a set of 15 movements (ie. Kit-Kat Bar hand clapping), and the partner has a 8 movement sequence (ie. Miss Mary Mack hand clapping) and see when these patterns would mesh. 
   
   
3. Instead of thinking about the numbers in which the number sets share common multiples, we could imagine each number set as a cycle: a toothed gear. Then we could talk about ratios in how many revolutions through a movement set until the other set is complete. When one small gear turns through its set, how far into the next number set have we gone (or what portion of the cyclical gear has turned)?
   
   
   Source: https://www.notesandsketches.co.uk/images/Wheel_and_pinion.jpg
   
   
4. As another cross-curricular extension, we could connect this idea with chemical interactions in developing how many of each atom are required for an ionic chemical formula.  Part 1: For a multi-party activity, each student is assigned a different charge based on a cation (ie. Ca 2+, Fe 3+, Pb 4+, Va 5+), and anion (ie. (Br 1-, O 2-, N 3-, Si 4-), then students would approach their ionic opposite, and they would perform their movement together until they're both done counting how many times they needed to complete the sequence while the other person was still moving. This number is how many of them are needed in the chemical formula. Part 2: this idea can further be extended by using only anions, and determining how many of each are needed in a covalent compound. In this situation, anions would interact with anions and complete their movement sequence.

Source: https://chemistry.mtsu.edu/wp-content/uploads/sites/57/2024/07/Chapter-3Ions-Ionic-Compounds-and-Nomenclature.pdf

The potential sequence of events in a classroom lesson for my Math 9 students on LCM: 

• Lesson hook: Chase's (2018) 3 x 2 arm set. Students would try. I would ask them:
  What do you notice? 
  What do you wonder about this sequence?
• I would extend the complexity to then involve a third number (4), by having them turn their bodies in the four cardinal directions (N, E, S, W) and ask them when do they end up back in their same spots facing "forward" or "North"?
  
  
• Exploration: I would ask my students to choose numbers between 1-5 to develop into movements for each body part or body direction/orientation. 
  
  
• Extension: Map a phrase to each position for the individual movements. Then, express verbally their movement while dancing. (This must be the equivalent to rub your head & pat your belly and will be very tricky for coordination). 
  
  
• Think-Pair-Share: In your partnerships, explain your attempt and what you noticed/experienced. 
  
  
• Class discussion: Share out to the rest of the class what you've rehearsed through explaining to your partner.
  
  
• Lesson: Lowest Common Multiple - a pen and paper lesson with various methods of determining the lowest multiple among a set of numbers. 
  
  
• Brain Break: 5 minutes at different physical stations around the classroom (2000 pushup challenge, plank hold, desk yoga, partner squat hold, hand-clapping games, competitive games of arm wrestling/thumb war/rock-paper-scissors-lizard-spock)
  
  
• Skill development: Practice worksheet - try questions that look challenging to you. Check your work. Ask questions of your partner and teacher to gain more understanding if confused. 20 minutes.
  
  
• Reflective Journal: Prompt...
• What was your big take-away from today? 
• Where have you experienced this concept of Lowest Common Multiple in everyday life? 

Videos referenced:

Sarah Chase: Dancing combinatorics, phases and tides (long version 13:35);

New teachers riff on Kandinsky in Binary (5:00)