Week 5 - Activity - Piano, Movement, Sketching, Curriculum Idea

    I couldn’t resist playing around with both activities but settled on Sarah Chase’s movements to do the required activities.

    But first – let me quickly tell you how I explored the New Teachers’ Riff on Kandinsky in Binary…

    I jumped right into extending the activities in the video. Ali commented that he wasn’t much of a musician but still came up with a way using 3 notes to add sound to the animation. I wondered if there was a way to play around with some notes and a different base. I chose Base 5 because I could work with a pentatonic scale – one without semitones that is supposed to eliminate discordant sounds but the one I chose has a major 2^nd in it (C D E G A) which I find discordant. Anyway, I did play around with circles and colours on PowerPoint slides but I didn’t save my work and it disappeared…not even a “do you want to recover this file?” notification next time I went into PPT. Sigh. What I did on my iPad keyboard was zoom out so I could get 2 full octaves and another 6^th. I set C as 0, D as 1, E as 2, G as 3, and A as 4. I used the upper most octave as the ones place, the middle octave (starting at middle C) as the 5s place, and the lower octave as the 25s place (is my elementary teacher terminology making people cringe?). I assumed a 0 in the 5s and 25s from the beginning – I wrestled with that and went with that...having a sound for 0. I played up to (255)₅ .  Here is the result with a few slips (wish I had a real piano to play on):

    I had to pause that to go do life things and came back to find my PowerPoint gone so didn’t pursue this further.  I wanted to put the music to the PowerPoint slides of coloured concentric circles that were like Ali and Colin’s template.

    So I moved onto Sarah Chases’ movement.

    I have a physical memory of her 2 and 3 movement – my jazz dance teacher when I was a teenager used to make us do that as part of our warm up. It was interesting to see it used it for combinatorics.

    I did 3 and 4 and 4 and 5.  My introvert didn’t want to be filmed or photographed today so after doing some choreography in my living room (many tries to get through the 4 and 5 but practicing each separately helped), I notated them on paper.

 

Notation of movements for 3 and 4 - common multiples circled

Notation of movements for 4 and 5

I thought this is another way of extending the activity – 3D movement into a 2D representation.

    I took exception to Chase saying that numbers like 6 and 8 together would be wrong but she might let people try it and see that they were wrong. It seemed they were “wrong” because they have a common multiple that is less than their product. I’ll expand on this more in my reflection.

I wondered if 6 and 8 could be notated in a circle some how to find common multiples, lowest or not.  This is what I came up with:

 

The blue lines divide the circle in 8ths and the orange lines 6ths. Then I used 2 colours (green and pink) to ‘count’ around the circle, noting when I wrote the same number on the last 6^th and 8^th number which would be a common multiple – they would start again together on the vertical radius.

I also tried some combinatorics on PowerPoint – 5 shirts, 3 pants, 2 hats. I’m having trouble recording it as an animation.  I might come back to it…I remembered to save!

 

Curriculum Idea Sketch

Issues – common multiples, combinatorics

Guiding Questions – How can you use body movements representing two (or more numbers) to understand how their cycles coincide? How can you notate this? How does this relate to common multiples? How is using strictly prime numbers different than including composite numbers? What kind of problems can we solve with these movements?

The Story – watch part of Sarah Chase’s video (opening and 2 and 3 movements); students try 2 and 3 and then explore other combinations of two or more numbers; explore ways of notating; how can pare down (e.g., write down only the numbers that end the cycle for each number – leads to listing multiples and finding least common); apply to combinatorics – e.g., clothing combinations, lunch combinations, etc;

Integrating embodied learning and other learning – move from 3D to 2D with notation, problem solving

Possible extensions - find another way of notating (e.g, on circle); coding, shuffling on PPT slides, stop motion videos