Sunday, July 1, 2018

Math Teachers at Play #118


In two more months, we'll hit MTAP #120, which should be the ten-year anniversary mark. Is it?



The number 118 ...
... factors to 59*2.
... is 1110110 in base two, 11101 in base three, 1312 in base four, 433 in base five, and 226 in base 7.
Not particularly exciting...



Aha! Can you make 118 using four 4's? (I did.) I wonder if you can make it using five 5s, or ...?








Summertime Learning
Summer Math Resources from Math Mammoth's Maria Miller. 

Denise Gaskins offers us one of her FAQs, on forgetting what they learned. My favorite of all her suggestions? Play games!

On Routines and Lessons
I like Geoff's perspective: "What’s the shortest amount of time you could possibly do the talking? Go with that. And maybe subtract a few more minutes." After 30 years of teaching, I am still learning, and I still get excited when I see something that might make a difference for my students. This looks helpful, and perfect for my summer meditations on teaching.



Young Math
Can you imagine doing a college math lesson with 2nd graders, and having it work out well? Manan Shah did it! His lesson was on set theory.

Ahh... A whole blog on magical math books. And she wrote about Christopher Danielson's new book, How Many? If you like this, she also has a list of every book she has posted about. Thank you, Kelly Darke!

Remember playing the card game War? If you're a parent, those memories may not be so fond. Kids love it and parents can get sooo bored. Kent wrote a great post about his interactions with his son around Addition, Subtraction, and Multiplication War. (If you want a good summary of even more mathy variations on war, check out Denise Gaskins' classic post.)

The first ever Global Math Week went well, with its exploding dots exploding around the world. Thank you, James Tanton, for getting people all over the globe into math.

How do you talk about numbers with young children? There are so many ways! Here's another: Counting with Dice, from Dave Martin.




Calculus
Which is bigger, eπ or πe? Sure, you can check it on a calculator. Or you can use areas to see why it's true. Lovely! (from Glenn Waddell)

The Fundamental Theorem of calculus says that you can figure out areas by using anti-derivatives. I do a project to help students understand it. Sam Shah does even more. This is Part III of his lessons for this topic. I recommend clicking on the links to Parts I and II first.





A Few More Goodies...
Dan McKinnon shares his notes from his Origami Workshop. For those who enjoy doing origami, can you find something new here?

Logic and Math go together so well. Check out this blog full of Venn Diagrams to fill in.

In his post From Surds to Ab-surds, Pat Bellew looks at an interesting relationship, which looks like bad simplifying but is still correct. He suggests it as a challenge in an algebra course to produce more correct 'bad simplifying' equations. Hmm, I want to think about how to do that.




Until Next Month...
Our sister blog carnival, The Carnival of Mathematics, often includes posts that are above my head. This month, our big sister is quite approachable. Enjoy!

If you have suggestions for next month's MTAP, share via the form at the Carnival home page.  Sharing in the carnival, or hosting, is a great way to increase connections in the #mtbos/#iteachmath community.

Sunday, January 7, 2018

Logic Puzzle - What Does Your Friend See?

I love logic puzzles, and was drawn by the title saying this was a hard one. Usually Nautilus is well-written, but their version of this puzzle isn't as good (in my opinion) as the original, blogged about by Presh Talwalkar.
 
The Nautilus version of the puzzle says to imagine your brightest friend. I imagined a friend I know likes logic puzzles (Sharon), but since I wanted a different initial than mine for notation purposes, I imagined another smart friend who might like logic puzzles (Linda). And I began scribbling away with S's (for Sue) and L's.
The answer I got is different than the answer the author got because we made different assumptions. Mine were based on his wording, his were based on Presh's wording.

Puzzle #1 (with Sue's interpretation):
You’ve been caught snooping around a spooky graveyard with your best friend. The caretaker, a bored old man fond of riddles (and not so fond of trespassers), imprisons each of you in a different room inside the storage shed, and, taking your phones, says, “Only your mind can set you free.”

To you, he gestures toward a barred window. Through it, you can see 12 statues. Out of your friend’s window, which overlooks the opposite side of the graveyard, she can see eight. Neither of you know the other’s count.The caretaker tells you each, individually, that together you can see either 18 or 20 statues. Unfortunately, there’s no way to tell your friend how many you can spot.

The only way for you both to escape is for one of you to give the total number of visible statues. Get it wrong, and neither of you ever leave. The caretaker asks you each once a day [Sue assumed neither person knew who was asked first], and you can choose to answer or to pass. If you both pass on a given day, the question—are there 18 or 20?—is posed to each of you again the next day, and the next, and so on, until you get it right or wrong.
Puzzle #2 is at Presh's blog. (No way to copy-paste that one.) It's now Alice and Bob, and they know that Alice gets asked first, so they'd both be released before Bob is asked if she has it right.
I think I have found a solution to (my version of) Puzzle #1. I would love to hear other folks reasoning before posting anything.
 
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