How Many Hot Dog Topping Combinations?

It was 6:12 PM EST.  We were eating dinner on our deck.  My sister messaged me.  She had a very important question.  Her and her colleagues were in a heated debate.  Just how many topping combinations were there at Cleveland’s fun hot dog restaurants Happy Dog?  I know, right?  This is a big deal.  Could I swoop in and save the day?  Yes.  Er, well, with the help of my trusty sidekick Google Sheets I could.  (Excel would have worked, but what if I need to access the calculations on the go?  or share them?  Yup, I made the right choice.  gSuite’s trusted cloud-based spreadsheet is the way to go here.)

So, I got the details.  There are 50 toppings possible.  No limits (you can do all 50, as my oldest son might choose) or minimums (0 toppings, as my youngest son prefers them, counts too).  Variations on the dog (veggie?  black bean!?) or bun (bleck, wheat?) were to be ignored.

I set right to it.  I picked a trusty Google Sheets formula – Combin – and got to work.  That formula deals with a common mathematics formula that finds the number of combinations of something.  You need only know two things – how many possible things and how many are to be chosen (i.e., 50 toppings choose 1, 50 toppings choose 2, etc.).  Now, don’t get this mixed up with permutations where order matters, because no one cares if you go peanut butter, sriracha, alien relish or alien relish, peanut butter, sriracha or … well … you get it.

COMBIN(nk) where n is the size of the pool of objects to choose from and k is the number of objects to choose.

The rest is history.  Check it out in the GIF below.

Oh yeah, I almost forgot to tell you the answer: 1,125,899,906,842,620 – one quadrillion, one hundred twenty-five trillion, eight hundred ninety-nine billion, nine hundred six million, eight hundred forty-two thousand, six hundred twenty combinations.

Side note to math teachers: I love how the numbers are symmetrical (i.e., there are 1,225 different 2-topping dogs and 1,225 different 48-topping dogs).  Could be a great discussion with math students.

Now, here’s how I did it:

Happy Dog Combinations Animations

The Problem with Fidget Spinners . . .

The Problem with Fidget Spinners . . . is not the distractions.  It’s not the noise.  It’s not even the obsessive collecting.  It ain’t the disruptions to classmates.  It’s not the who’s-got-the-best-spinner drama either.  It’s definitely not that they annoy some teachers.  And it’s not that they may cost parents a lot of money.

It’s that kids need them.  It’s that our youth – and our society in general – see school as an experience that is so mind-numbingly, torturously boring that we assume that kids need something to fidget with during it.  It’s that learning, in many classrooms, is seen as a passive behavior and that students need something active to do with their hands while it happens.

Make learning experiences that make your students want to put their spinners away.

STEM Practices

In a training webinar for the PEAR (Partnerships in Education and Resilience) Institute’s DoS (Dimensions of Success) Observation Tool, the facilitators discussed how the 3rd of their 4 domains – STEM Knowledge and Practices – was based on the STEM Practices outlined by the NGSS‘ (Next Generation Science Standards) “A Science Framework for K-12 Science Education.”  I think that these 8 practices are fantastic and that schools should place a focus on integrating into the curriculum maps for all content areas, not just science.  Here they are: Continue reading STEM Practices

Reflections on “Misconceptions about Progressive Education” Video

I’m not sure where I found this video – at some point I put it into my YouTube Watch Later playlist – but when I sat down with my lunch one day and watched it, I was blown away by how spot on it was.

After researching a bit, I discovered that this video is from Green Acres School in Maryland.  The gentleman in the center with the beard is Neal Brown, who appears to be their Head of School.  To his right, with the dark hair, is Dan Frank from the Francis W. Parker School.  To Brown’s left is Robert Shirley from Charleston Collegiate School.  There is a series of videos from this event that I intend to watch in the future – probably over a turkey sandwich, bowl of cottage cheese and some Doritos – but for now I’d like to reflect on my favorite parts of this one.

Check out the video and then meet me in the space below the video to see some of my thoughts. Continue reading Reflections on “Misconceptions about Progressive Education” Video

A New Acronym for PBL

PBL = Prohibited by Logistics

Often, when we are presented with a new, high-quality, research-based way to promote student learning, educators identify the obstacles.  The roadblocks.  The logistics.

My response to those logistical roadblocks?  One of my favorite quotes, which I’ve found credited to Ryan Blair:

“If it is important to you, you will find a way. If not, you’ll find an excuse.”

Continue reading A New Acronym for PBL