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

Screencasts in Math Class

Years ago, as a middle school math teacher, I had a dilemma.  My 51 minute math classes had been shortened to 43 minutes.  As any teacher knows, this is a big deal.  After wrestling with a lot of ideas for how to handle here’s what I landed on:

Each day, during my planning period, I pressed record in a screencasting program called Jing, stepped up to the SmartBoard and went over the day’s homework as if my class was there.  (I’m sure I looked like I had lost my marbles to any passerby) I did it quickly, forcing myself to keep it under 5 minutes.  Any longer would mean 2 things: my assignment was too long and I was using to much class time to explain content that my students had already done.

The next day, I would play that video while taking attendance, checking to see who did their homework and meeting with any students who had been absent.  This allowed me to combine two sets of things that I had previously done–going over the homework and doing the beginning of class teacher stuff–at once.  It made up for those 8 lost minutes, and then some.

Nowadays, my philosophies about homework and classrooms where all students are doing the same thing at the same time has changed, so I wouldn’t repeat this format.  However, I think these recordings would still be valuable in a blended learning setting.  When students finish certain assignments, they could view the videos to self-assess and learn more.  Learning Management Systems and websites really open up the possibilities on this.

Here’s a sample of one of these videos:

Exploring the Number pi with Google Sheets & Forms

What better way to celebrate Pi Day than with a hands-on, tech-on exploration activity that helps students build their own understanding of what pi really is?  Well, probably a good piece of pie, but this is awesome nonetheless.

Here’s what you do:

  1. Get a bunch of fabric tape measures (using string and then measuring lengths on the string works too).
  2. Get a bunch of circular objects.
  3. Have kids measure the circumference and diameter of different circular objects.
  4. Instruct the kids to submit their measurements to a Google Form
    (note: my form doesn’t collect names, but it would be best to collect them so you can help kids who have measurement errors).
  5. Setup a QUERY formula to find the circumference/diameter for each entry.
    =QUERY(B2:C1000, “select B/C”)
  6. Fix that pesky 2 in the Query formula after the first submission – when the first entry inserts a row, it changes B2 to B3.  Change it after the first entry and you’re good to go.
  7. Setup an AVERAGE formula to find the mean of the circumference/diameter calculations.
  8. Project the spreadsheet as entries are recorded.  See what your kiddos notice about the numbers they see on their screen!

Exploring Measures of Center with Google Sheets

My obsession with Google Sheets is no secret. I loooove spreadsheets.  And I think that they have a big place in education, especially in math (but elsewhere as well).

Recently, I posted about how you can prove the mean (or average) formula using Google Sheets.  In this post, I’d like to share with you how you can find all 3 measures of center (or measures of central tendency) and explore them in Google Sheets.  I love to change or add numbers in the data set and ask students to make predictions about what will happen.  It really is a great–and relevant–way for students to become more familiar with these statistical measures.

Proving the Algorithm for Mean (Average) in Google Sheets

I am a huge spreadsheets nerd and a huge advocate of the use of spreadsheets in mathematics instruction.  If you keep an eye on my site (or Twitter feed or YouTube Channel) you’ll see plenty of my reasons why I feel this way.  Here’s one:

Spreadsheets are a great tool for proving mathematical algorithms and formulas.  In this post . . . how we can use a Google Sheet to prove the formula for the mean (which, in spreadsheet land, is known as the average).

Check out this post about finding and exploring all 3 measures of central tendency with Google Sheets.