Today a friend emailed this math problem to me.
What *is* the “right” way for math anyway? Is technology inherently less “right” than algebra? Solving it graphically by Desmos (or by TI-84) still solves the problem, but maybe that doesn’t feel as elegant or satisfying. I did want to share the joy of Desmos (since my non-math teacher peers aged mid- to late-thirties did not grow up with it), so I sent the following screenshot (before I eventually solved it algebraically).
“Ha ha, neat toy.
Since I forgot all the tricks to resolve mixes of square roots and variables, I looked at it as, it must be an integer since what awful brain teaser would have 4.87645372 as an answer, and it had to be a number with an integer square root, and that square root had to be less than half of 15, and the square of that number is 15 less than the square of (15 – that number). So I tried 7 first, 7 + 8 = 15, square of 7 is 49 which is 15 less than square of 8 (64) so that was it. 7 squared, 49. Had that not worked I would have tried 6, 5, 4 etc.
In the meantime, I’ve filled the backs of two envelopes with desperate attempts to solve it algebraically, going nowhere.”
Poor friend! Sent this to him:
I then sent it to my math colleagues (and my boss, who is a former math teacher).
Boss’ response, which I will ask to see in its original form, since email apparently translated it into gibberish.
Alternate Hint: Try putting the square roots on different sides of the equation and canceling 🙂
I took a pic of my work but don’t want to spoil it… email me if you want a look-y-loo. Thanks for the Thursday PM pick-me-up!
I emailed her to trade answers and she solved it this way. It made us both happy to solve it algebraically, but differently!
So there you have it:
1) logical way
2) graphical way
3) algebraic way #1
4) algebraic way #2
…how many more ways?
As much as I dislike Facebook, I do find value in the “On this Day” feature. From April 21, 2011, I wrote this note. Six years later, 3) through 6) are still so important for teaching (and now parenting). Six years later, we have Google Classroom, SeeSaw, Workplace, ClassDojo, Khan Academy and countless other technologies that increase our ability to access content or transmit content to our colleagues or students. Six years later, we have Amazon PrimeNow to get whatever baby product we need within two hours. We have similar access to “wisdom” via countless online mommy/baby forums, sleep consultants, and ScaryMommy/Pregnant Chicken-esque blogs. We can also transmit our content in those forums, in mommy Facebook groups, or on group iMessage threads during late-night feeding sessions.
Increasing access to or ability to transmit content doesn’t make teaching or parenting any easier if the emotional aspects aren’t addressed.
“From my roommate, who attended a talk about happiness by an HBS negotiation professor tonight. The HBS students voted for the three professors who they wanted to hear from, and these are the main points of the first talk.”
1) Quit early and often. Save up enough to make it monetarily possible for you to do so, and make your own choices.
2) Create value and worry about monetizing it later. The opposite is thievery (going where the money is and trying to create value).
3) Cultivate empathy. See the world through gentler eyes, because you will be better for it.
4) Learn humility. Either humility or arrogance is not enough; you must have a combination to succeed.
5) Learn from unlikely sources and don’t judge your teachers. Everyone around you can teach you something. Even if it’s harsh, if you are willing to take it, you can’t go wrong.
6) Make time for reflection. Ask questions about who you’ve become and who you were. Build in this time to keep reevaluating. You don’t need to aim for being stagnant and stable. Inevitably, things will change about you.