Recently, during a walk I was playing The Walking Dead: The Zombies, and an awesome mathematical experience occurred.
I noticed that my team had slaughtered 497 zombies out of the 800 required to complete a challenge. Sadly, I commented to my friend, after killing 3 zombies, "Well at least we have 500....out of 800!", to which she asked "What percentage is that?"
I smiled, and replied "How would we do that?"
As she grabbed for her phone, I asked her to humor me and try it mentally....and as such began a wonderful minute of beautiful number play:
"Well I would make it 5 divided by 8.....then...."
At this moment she begins to draw out 5 under a divisor sign and an imaginary 8 to the left of it, and continues with...
"Ok 8 goes into 5....oh...this doesn't work....Why can't I just use my phone?"
After smiling, I asked her, "And how else might you say '5 divided by 8'?"
Revisiting middle school in her head, she exclaimed, "5 eighths. but that does not help"
"Yeah eights are a pain, is there an easier grouping we could from eighths?"
Seconds pass, and she admits she does not understand my question. I offer assistance with,
"Ok, eights is the denomination we are working with, but are tricky, so think about this....If I gave you unlimited eighths....what other fractions could you make?"
Eyebrow touch for a moment, and then she replies with "I could make quarters with 2 of them...."
At this point, I could not help from smiling as I knew to continue the journey of numerical delight all I had to do was ask, "So how many quarters is 5 eighths?" and so I did.
Tilting her head to the side, I could almost see the imaginary manipulatives going through her mind as she talked aloud, "Well 2 eighths is 1 quarter, and so 4 eighths is 2 quarters, and then 6...oh....2 and half eighths?"
I decided to ignore my Grade 6 teacher's rule of "NO DECIMALS IN FRACTIONS" (Which has never made sense!), and simply say "Hmmm...Interesting so what percentage would be 2 and half quarters?"
She had already started.."2 quarters is 50...half a quarter is... 12....no 12.5.....and so 50 plus 12.5 is 60....62.5 percent?"
I cheered, awarded her with a high 5, and asked "If it took us 2 days to do 5 eights and we have only 1 day left, are we going to make it?", to which he exclaimed "I don't love zombies enough..."
As I reflect on this experience, this is what I want my math classes to feel like for my own daughters. Moments of exploration, followed with choices from different mathematical tools, and ended with delight as they solve problems that make sense.
PS: This would have lost all of its joy if I simply entertained the idea that dividing 5 by 8 mentally, is best done with the traditional algorithm