Tuesday, November 11, 2014

#PuzzleMath ideas

Tonight, my son wanted me to work with him on his new puzzle.

I don't know your strategy for doing puzzles, but I find all the corners first and then start putting the border together before I start working on the inside. Look at that box again. Would you be able to determine the dimensions (in puzzle pieces) of this puzzle by knowing the total number of pieces?

That was my first question:
A) If you know the total number of puzzle pieces, could you think of the all the possible dimensions (in puzzle pieces) of the puzzle?

This puzzle will either be a 1x35 or 5x7.

Then came the next question:
B) Estimate the actual dimensions (in puzzle pieces) given the picture on the box?

I'm going to go with 5x7 because five and seven are the only factors of 35 that would reasonably make the rectangular picture on the front of the box. The puzzle should be 5 pieces high and 7 pieces across from left to right.

With a box of 35 pieces, these questions aren't too ridiculously challenging. However, I know there are crazier puzzles out there in the world; puzzle with 500, 750, 1000 pieces, etc. That's where I called on Twitter to help out. Like a champ, the #MTBoS came through and hopefully will continue to come through with #puzzlemath.

Below are some of the tweets I received followed by additional math questions I'm curious about.

Additional Questions:
C) If you think you know the dimensions, could you determine:
  • The number of corner pieces
  • The number of border (non-corner) pieces
  • The number of inside pieces
If so, could you write a rule for any of these?

D) Knowing these quantities, say you randomly choose a puzzle piece, what are the chances it's:
  • A corner piece
  • A border (non-corner piece)
  • An inside piece
  • The exact center (if possible) piece
Please add to the collection of puzzles and questions by tweeting with the hashtag #puzzlemath.


Roofs Are Expensive!

Today is Veteran's Day. If you personally know a veteran, say "thank you" to them somehow: call, email, text, or in person. If you don't know a veteran, then ask a friend if they know a veteran and if they do, ask them to say "thank you" on your behalf.

Because today is Veteran's day, my district isn't in service today. Therefore, I was able to sleep in a few minutes longer today. I woke up to the sound of this pitter-pattering on the roof of our house. Not five minutes later, my 4.5 year-old son walks into the room and says he hears something that woke him up. I wonder what? Ha.

He climbs in bed with me and I ask him if he knows what the sound is. I proceed to tell him the sounds he hears are birds walking around on the roof hitting the roof with their beaks. When we moved into our house, there was a fake owl tied to our roof. Supposedly it keeps birds away. Not too sure it's all that effective, but we keep it up to have an occasional laugh.

My son thinks that the birds might start to ruin the roof and that we'll have to replace it.
Son: That will probably cost more than $100 to fix.
Me: How much more?
Son: Probably like one-hundred, one thousand dollars.
If you read my Pumpkin Seeds post, you know that his vocabulary includes a thousand now which is the biggest number he currently "knows". I use "knows" very loosely.
Me: Oh, I see. Well, which number is bigger? One hundred or one thousand?
Son: One thousand!
Me: Right. So we say the bigger number first, like this, "One thousand, one hundred."
Son (whispering to himself): One thousand. One hundred.
Me: That's a lot of money.
Son: Maybe one hundred twenty?
Me: Oh, so that's smaller than one thousand, one hundred.
Me: How do you know?
Son: Well, we have a big roof. We would need a lot of wood. We'd have to go to Home Depot and get all the things. 
Me: So we can buy all the things from Home Depot?
Son: Yes.
Me: And then would we put the roof on by ourselves or have some worker-men do it for us.
Son: You and I can do it Dad.
It dawns on me. Geez, I hope it's not $10,000. That's a lot of money. At the same time, I'm glad my son doesn't know the concept/magnitude of "A million" yet. Regardless, I have no idea what a new roof might cost, let alone how to put a new roof on. But maybe I'll save a lot of money on the labor because I have a 4.5 year-old son extremely willing to climb on top of our house and help install a new roof.


P.S. I'm enjoying these conversations and posting about them.
Today felt like Mathematical Practice 4 with my son.

Monday, November 10, 2014

An Amusing Context for Zero

From the mouths of babes:

Tonight, my 4.5 year old son was getting ready for bed. Getting ready for bed means he needs to shower. And as any parent can relate, there's the usual banter of "get your jammies out" to "let's brush your teeth." Tonight went in this direction:
Me: C'mon. Let's get ready for your shower. I have three clothes on still.
He comes around the corner.
Son: Dad, I have zero clothes on still. 
Yes. Yes, he did. He was, indeed, ready for shower. Bahahahaha.

Like I said, from the mouths of babes: an amusing context for zero.