~~NOTOC~~
{{:2018:mathematics:mathematical-thinking-banner-790x50.jpg |Mathematical Thinking Banner}}

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=== Each menu item links to one or more classroom activities: ===
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^  MENU - MATHEMATICAL THINKING 2019  ^^
| **[[https://goo.gl/forms/7zkoaAa27S8yD2lx1|Mathematical Thinking Quiz (DE 2019)*]]** | **[[https://flipster.tv/doku.php?id=2018:mathematics:home|Mathematical Thinking Home Page]]** |
| **[[https://flipster.tv/hanoi/|Towers of Hanoi Simulation - Simple]]** | **[[https://flipster.tv/hanoi/hanoi.html|Towers of Hanoi Simulation - Complex]]** |
| **[[https://flipster.tv/hanoi/brahma.html|Towers of Brahma - End of Universe]]** | **[[https://flipster.tv/hanoi/help.html|Towers of Brahma - Help]]** |
| **[[https://flipster.tv/hanoi/about.html|Towers of Brahma + Coding - About]]** | **[[https://flipster.tv/hanoi/learn.html|Towers of Brahma Activities - Learn]]** |
| **[[https://flipster.tv/doku.php?id=2018:mathematics:introduction:home|Teacher resources]]** | **[[https://goo.gl/forms/DWfqJZL3XVKOAZYU2|Belrose PD Feedback Survey]]** |

* [[https://docs.google.com/presentation/d/1qIQlr-NbMHjz8leRCiQCiR7C2Qt9sC8iIzPTDhtJB8c/edit?usp=sharing|Mathematical Thinking - Workshop Presentation]]
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=== Also see: ===
  * [[https://mathsnoproblem.com/maths-misconceptions-multiplication/|Multiplication misconceptions]]

  * [[https://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/Pages/misunderstandings.aspx|Assessment for common misunderstandings (VIC.GOV.AU)]]

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====== Random Coin Tossing Example Activity (Random.org) ======
  * **[[https://www.random.org/coins/?num=4&cur=60-aud.1dollar|AU$1 Coin toss randomiser (random.org)]]**

====== Tower of Hanoi/Brahma: (Wikipedia) ======
The puzzle was invented by the French mathematician Édouard Lucas in 1883.

There is a story about an Indian temple in Kashi Vishwanath which contains a large room with three time-worn posts in it surrounded by 64 golden disks. Brahmin priests, acting out the command of an ancient prophecy, have been moving these disks, in accordance with the immutable rules of the Brahma, since that time. The puzzle is therefore also known as the Tower of Brahma puzzle.

According to the legend, when the last move of the puzzle will be completed, the world will end.[2] It is not clear whether Lucas invented this legend or was inspired by it.

If the legend were true, and if the priests were able to move disks at a rate of one per second, using the smallest number of moves, it would take them 264−1 seconds or roughly 585 billion years[3] or 18,446,744,073,709,551,615 turns to finish, or about 127 times the current age of the sun.
  * https://www.scientificamerican.com/article/the-tower-of-hanoi/
  * Wikipedia https://en.wikipedia.org/wiki/Tower_of_Hanoi

=== Ian Parberry's Towers of Hanoi ===
  * [[http://larc.unt.edu/ian/TowersOfHanoi/help.html|Help documentation]]
  * [[http://larc.unt.edu/ian/TowersOfHanoi/index.html|Interactive simulation]]
  * [[http://larc.unt.edu/ian/TowersOfHanoi/index64.html|End Of The Universe simulation]]

=== Tower of Hanoi - Algorithm ===
  * https://stackoverflow.com/questions/6947653/how-does-recursive-algorithm-work-for-towers-of-hanoi
  * https://www.geeksforgeeks.org/iterative-tower-of-hanoi/


=== Here's an iterative solution that's succinct: ===
<code>
#!/bin/sh
/bin/echo -n "Towers of Hanoi. How many disks? "
read disk
for (( x=1; x < (1 << $disk ); x++ )) ; do
  i=$((($x & $x - 1 ) % 3))
  j=$(((($x | $x - 1 ) + 1 ) % 3))
  echo "Move from tower $i to tower $j"
done
</code>

When run, this delightfully short script produces the result I desire, a step-by-step solution to the Towers of Hanoi problem.
 
Mathematical Thinking Quiz links:
  * **[[https://goo.gl/forms/i2EKfmjGkU18N1Q03|Mathematical Thinking Quiz Copy V1]]**
  * **[[https://goo.gl/forms/5vbdfqrrnOI3aSof1|Mathematical Thinking Quiz DE 2019)]]**