Category Archives: Functions

Are you a fair weather fan?

This past weekend my husband and I went first home football game of the season for the Iowa Hawkeyes.  I was excited about the game until I saw the forecast for this past Saturday . . . every day on the news it seemed like the high temperature for the day kept creeping higher and higher.  Finally, on Thursday of last week the air temperature was forecast to reach 94 degrees and the University of Iowa athletic department began posting tips on now to start hydrating now for the game on Saturday.

I called my husband and work and our conversation went something like this:

Me: Did you see the forecast for Saturday?  I think its supposed to be dangerously hot . . .

Husband: Are you trying to bail?

Me: No!  I’m just worried about the heat . . . they said to start hydrating today.

Husband: You’re a fair weather fan!

Really?!? A fair weather fan?

We went.  We had a great time.  The Hawkeyes won.  I didn’t melt.  All in all it was a successful Saturday.

But my experience on Saturday got me thinking about a little thing called the heat index . . . I always thought it of it as the wind chill of really, really hot temperatures.  So, I decided to do a little digging to

  1. Find out about the heat index.
  2. Prove to my husband that I am not a fair weather fan.

According to the National Weather Service, the calculation of the heat index is a regression equation . . .which quite frankly seemed a little complicated for this blog (but if you’d like to see it, look here).

But, I did think that it was interesting that there was an important note when reading the heat index table . . . the NWS warns that the heat index can only be accurately calculated when the humidity and air temperature are represented on the chart.  In other words, this is a domain and range issue.

excessive heat events guidebook cover

There are many situations in mathematics when we’d like to model a particular phenomenon. . .  (heat index, racing times, time-lapse modeling) just to name a few.  And in those situations it does not make sense to have the domain and range be all real number.  Sometimes it doesn’t make sense because the situation represented doesn’t make sense (i.e. negative time) and sometimes it doesn’t make sense because the function will not fit the data as closely if we allow the domain to be all real numbers (as in the case of the racing times).

This past Saturday the temperature at game time was 90 degrees with about 60% humidity . . . we stayed until the end of the third quarter when the Hawkeyes were winning 31-0.  So, what say you . . . am I a fair weather fan?

P.S. If you’re new here, let me let you in on a little secret . . .I love to think about the weather.  Don’t all midwesterners?  Check out a few more weather related posts here and here and here.

What’d you do this summer?

Now that school’s back in session, I’m sure you’ve been answering the question “What’d you do this summer?”

We had lots of fun this summer, but one of the things I’m most proud of is my hike up Deer Mountain at Rocky Mountain National Park!

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My first experience with hiking anything other than flat land was this winter in Palm Springs, CA when my husband and I hiked through various canyons.  I must say I felt like quite the outdoors-man (or woman) on those hikes and the views were spectacular!

When we booked our flight to Denver for this summer I declared almost immediately that we would be hiking through Rocky Mountain National Park just like we had hiked the canyons.

After getting a recommendation to hike Deer Mountain we were off . . . and 15 minutes into the hike I thought I was dying!

“Can we slow down?” I’d huff while my husband trudged ahead.

“Wait . . . feel my heart, its racing!” I’d worry while trying to keep up with his strides.

and finally, “What is wrong with me!  This mountain is crazy!”

We hiked the mountain in a little under 2 hours and 15 minutes (not including our 30 minute lunch at the top where we enjoyed the views and chased ground squirrels away from our crackers).

When we finally got back to the car I pulled out the mountain statistics:

Starting Elevation: 8940 feet

Highest Elevation: 10013 feet

Round Trip Distance: 6.2 miles

Hello?!? No wonder I was out of breath.  I’m used to living at an elevation of 668 ft., so before we even took off up the mountain, I was already 8272 feet higher than I was used to!

Then, we took off like crazy people!  From my point of view there are two ways to measure the reason I thought this mountain climb was so hard . . . the first is the slope of that darn mountain trail must have been really high!  Or, the speed at which we were walking up the side of that mountain was much, much too fast to really enjoy the scenery.

What do you think?  Steep slope?  Fast walking?  Or just out of shape mathematician?

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:

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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

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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!

 

Thunderstorms!

It’s safe to say that thunderstorm season has officially arrived in Iowa!  The temperature and the humidity has been on a steady climb for the last couple of weeks (remember when we were making jokes about how cold it was?!?) and seasoned midwesterners can spot the ideal weather for a good thunderstorm from miles away!

I love thunderstorms!  For some reason, they always prompt me to bake a batch of chocolate chips cookies whenever they roll through!  (There’s nothing quite like watching the clouds roll in while you chow down on homemade cookie dough!)  Unfortunately, my children do not share my affinity for thunderstorms, not even the promise of warm chocolate chip cookies can calm their nerves when the thunder starts booming and the lightening flashes!

Last week a quick thunderstorm rolled up in the middle of dinner.  Instead of focusing on the scary booms and flashes I said to them “Did you know if you count the number of seconds between when you see the lightening and hear the thunder, you can estimate the distance the thunderstorm is from our house?”  (P.S. Did you know that?)

The speed of sound through the air is approximately 340 meters per second, and the speed of light is approximately 300 million meters per second.  Even though thunder claps and lightening  flashes are happening at the same time, the difference in speed makes it seem as though the lightening is flashing before the thunder.

Using the relationship between distance, rate, and time we know that D = R*t, where D is distance, R is rate, and t is time.  Since we have the rate of sound and light in meters and seconds, we’ll also report D and t in terms of meters and seconds.

Now, suppose you hear thunder approximately 5 seconds after you see a flash of lightening.  If we use the relationship between distance, rate, and time we can substitute known values into the equation, which gives us D = 340*5 = 1700 (remember this is meters).  1700 meters is approximately 1 mile.

The next time a thunderstorm rolls up in your neighborhood, see if you can track how quickly its  moving through the area.  Keep a record of the length of time between lightening flashes and thunder rumbles.  Can you tell when the storm is getting closer and farther away from you?

P.S. I got my facts and figures from two great sources: the National Weather Service and The Department of Physics at the University of Illinois Urbana Champaign.

 

 

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?

4.21.14

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?

Averagetime

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!

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.

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!).

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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:

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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 🙂