# 10,000 step challenge

This year I asked for a FitBit for my birthday.  (For those of you that don’t know a FitBit is a pedometer, counting your steps, flights of stairs, daily active minutes, and approximate number of calories burned).  I was excited and curious to clip on my FitBit and see just how far I was walking every day!

But, after a few, short days I was a little confused.  I thought that about 2,000 walking steps = 1 mile, but I was getting FitBit read-outs on my phone that looked like this:

So, if you’ve been reading this blog for any amount of time, you can probably guess what I did next . . .Yep, I Googled the length of a walking step and discovered that this website (which seems legit to me) estimates that the average length of a person’s walking step is about 2.5 ft, which means that in order for a person with average walking steps to walk 5 miles, they’d have to take 10,560 steps . . . not 10,000.

Then, I started wondering how long my steps were (on average of course); compared to the published average of 2.5 feet/step.  I used my FitBit output for 3 different days

and discovered that, despite my relatively short legs my walking stride length was pretty average!

Then, I started thinking about a project I used to have some of my students work one, which is now an activity on the NCTM Illuminations Site, called Walking to Class.

This summer, make a walking strides chart of your day (or a trip to and from the park, pool, etc.) but instead of measuring distance in steps, change the units from steps to miles using the average 2.5 foot length, or you could dust off a pedometer and calculate the length of your actual stride!

# Boston Marathon Times

This morning thousands and thousands of people did something I can not even imagine doing . . . they ran the Boston Marathon (It was actually 35,671 entrants to be exact)!

This year the winning men’s time was 2:08:37 (Meb Keflezighi from California) . . . that’s an average speed of about 1 mile every 4.88 minutes.  (As a comparison I re-started Couch-to-5K last night . . . and I ran about 1 mile every 11 minutes).

Anyway, the whole Boston Marathon thing got me thinking . . . I wonder how Meb’s time compares to other people who have won the Boston Marathon?

The first Boston Marathon was run in 1917.  John J. McDermott (NY) won that race with a time of 2:55:10.  He was still averaging about 1 mile every almost 7 minutes.  So, is Meb just exceptionally fast?  Was John just exceptionally slow?

The graph above represents all of the Boston Marathon times–from John to Meb and all of the marathoners in between.  What do the data seem to tell you?  Was John exceptionally slow?  What about Meb?

This shows the average time for 10 year time spans of Boston Marathon winners.  What seems to be happening to marathon times-over time?

If you had to model Boston Marathon winning times, based on the number of years since the first marathon what type of model would you use?  Exponential Growth/Decay?  Linear Increase/Decrease?  Quadratic model?  Why?  Do you think there might be anything noteworthy about the graph as people continue running the marathon?  Will anyone ever run the marathon in under 2 hours?  1 hour? (if someone ran a marathon in under an hour they would be averaging 1 mile approximately every 2.25 minutes)

I’d love to know what you think!  In the meantime . . . I’ll be trying to get under the 10 minute mile mark with my Couch-to-5k app!

# In like a Lion; Out like a Lamb?

This morning as I was walking to work through whipping wind and freezing cold temps, I thought to myself “March, you’re supposed to be going out like a lamb.”  Goodness knows it sure came in like a lion!  Then, I started thinking about Groundhog’s Day and how unreliable that good old Phil actually is!  That made me wonder . . . is there really any truth to this whole lion/lamb thing?

I spent the better part of my morning trying to track down an answer!

This is what I did:

I’m only concerned with how March comes in and out, and not what happens in the middle of the month, so I thought I’d look at the first 7 days of March and the last 7 days of March.  Then, I did a quick search and found that the average March temperature in Iowa for the past 150 years is 34.5 degrees Fahrenheit.

Given this information I decided I would define “Lion” to be a 7-day span in which 4 or more of the days had an average temperature that was less than the average monthly temperature.  Then, a “Lamb” was a 7-day span in which 4 or more of the days had an average temperature that was greater than or equal to the average monthly temperature.

I obtained daily average temperature data for Des Moines from The University of Dayton Average Daily Temperature Archive dating back to 1995.  Because the month of March isn’t over yet for 2014, I didn’t use the temperature data for any of the days in March 2014.  This is what I came up with:

In the past 19 years March has followed the “In like a Lion; Out like a Lamb,” pattern in 13 different years (or 68% of the time).  It has followed an “In like a Lamb; Out like a Lamb” pattern 5 different years (or 26% of the time).  And once in the last 19 years March has come in like a Lion and gone out like a Lion . . . according to the average daily temperature in Des Moines.

This got me thinking about a few things:

1. This saying seems to be a little more accurate then the Groundhog shadow thing.

2. There weren’t any “In like a Lamb; Out like a Lion” years . . . I wonder how many times that has happened in the past 150 years (if at all)?

3. What do you think of my definition for Lion-like weather and Lamb-like weather?  Would you define it another way?  If so, how?

# Happy Pi Day!

How could a blog devoted to all things math not have a post on Pi Day?  Truthfully, I had big plans for today . . . starting with the Pi Day cookies I wanted to bake and bring to work:

This is as far as I got making Pi cookies for today.

#pidayfail

Honestly though, I’ve been running around like a crazy woman these last few weeks and just didn’t have enough time to get my self together to have a meaningful Pi Post today!  It seems as though the day as been jinxed.  You saw how well my Pi cookies turned out, then I went to the store to buy a pie to bring to work and they didn’t have any!  My husband did come through for me though and snagged this awesome Pi shirt from his junior high school (Thanks awesome junior high teacher!).

Since I don’t have a great Pi Day post for you today, I thought I’d round up some of my favorite Pi activities from around the web . . . former students of mine will know some of these activities well 🙂

A great Pi Day cartoon:

Pi set to music.  ( know there are lots of these around the web, but I have found this one to be the best!)

The argument for Tau Day (with two pies . . . I’m in!)

My favorite activity to do with students on Pi Day . . . although I’ve heavily adapted it!

Happy Pi Day one and all!  I’m off to round up some pie for lunch 🙂

# Happy Valentine’s Day 143

1 4 5 11

Do you?

It just makes me think of Valentine’s Day.  As a little kid I remember getting them from my parents, in their little cardboard box.  In high school, I used to tell my sweetheart of the month that all I wanted for Valentine’s Day was one of those little boxes . . . forget the flowers and stuffed bears!

What’s that you say?  You don’t know what 1 4 5 11 means?  It’s code.  1 4 5 11 is code for I love Necco Sweethearts.  You know those chalky little hearts with the Valentine sayings on them?  I didn’t make up this code, Necco did.  Have you seen these hearts?

Do you know what 143 stands for?  I (1) love (4) you (3).  Get?  If not don’t feel bad.  This person Facebooked Necco to find out why in the world she ate a heart with 143 on it!

Anyway, I think its cute and all but as far as codes go . . . its really not that great.  I mean 143 could stand for lots of things couldn’t it?

But here’s the thing, Necco’s touching on something that mathematicians have used for a long time.  That is, numbers as code for something else.  Try this one:

91215225251521.

OK, OK.  So its not that hard, right?

Its either:

IABAEBBEBEAEBA or ILOVEYOU.  I’m not sure that I would want to send some sort of top secret code through cyberspace if my coding technique was A=1, B=2, C=3, etc.  But what about this code?

4560776126257605

Do you want a hint?  OK.  It looks like that number might be divisible by 5.  Oh!  It is divisible by 5.  I wonder what you get when you divide the number by 5?

Hmm.  We might be on to something.  It seems to me that a great way to code something might be to do the whole A=1, B=2, C=3 thing and then to multiply it by another number.  If the person I’m sending the code to knows the number to divide my code by, the code is pretty darn easy for the receiver to crack and its fairly difficult for a spy to intercept and figure out what it says, don’t you think?

So, find a sweetheart and send them something in code for tomorrow.  My sweetheart is getting this message.  Can you crack it?

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