Tag Archives: Rates

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!




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?


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:

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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?


Last month my husband and I decided to take our kids to a local state park for a picnic and some fishing.  We had scouted the best places in the park to fish and took off for an afternoon adventure.

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For those of you who don’t have a lot of experience fishing with a 7, 5, and 1-year old time is of the essence.  You have a very important 15 minute window in which to have someone catch their first fish.  If you don’t get any action in about the first 15 minutes you can pretty much bet on the fact the the kiddos you brought fishing will be ready to put away the fishing poles and start to build a fire for the s’mores.

Well on that fateful day in the middle of August, that 15 minute window slipped right through our fingers.  And then, the 15 minutes turned into 30 without so much as a nibble.  My husband was able to entertain the kids a little while longer by letting each of them practice casting their own finishing line (while everyone else crouched in the bushes to avoid an accidental snag), but even the novelty of doing that wore off about an hour into the fishing expedition.

Soon, the excitement of going on a fishing trip turned in to:

“When can we make s’mores?” –My 5 year old

“How come that person is catching fish?!?”–My 7 year old

“Dad are you sure there are even fish in this lake?”–My 5 year old again

(Just as a side note we stayed at the park for 3 hours and did not catch ONE. SINGLE. FISH., but to make up for it we made s’mores and then stopped for ice cream on the way home.)

Anyway, this fishing trip reminded me of a method for estimating the fish population in rivers and streams called the Mark-Recapture method.

The Iowa DNR has a really nice explanation of the Mark-Recapture method, although the whole using real crickets thing creeps me out a little; but this is basically how it works:

1. Catch fish and tag them (or Mark them).  Record the number of fish you’ve caught and tagged.

2. Go fishing again.  Record the total number of fish you catch and the number of caught fish that you tagged previously (that’s the Recapture park).  Then set up the following proportion to estimate the population of fish in the the lake/river/stream you were fishing.

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Now that you know the basics of Mark-Recapture, lets think about a few things:

1. Taking a census of the fish in the lake is not practical in this case.  Why?

2. If I’d really like this to be an accurate picture of the population of fish in this lake, what are some things that I will have to consider when collecting the data (ie fishing, tagging, and counting)?  Think about things like location of the fisherman, time of day for fishing, weather conditions during the Mark-Recapture data collection.  What are other items that should be considered?

3. Why might the Iowa DNR or any naturalist for that matter be concerned with the fish population of a particular lake or stream?  How can the Mark-Recapture method help address those concerns?

P.S. If you’re an AP Statistics Teacher or Student, this is a great sampling example to consider.  Did you know sampling questions occur the most frequently on AP free response exams, and they are also the most often missed on the exam too?  Don’t believe me?  Check out this article.

Iowa Butter Cow

I’ve lived in Iowa for 27 of my 32 years, but until 2 days ago I had never been to the Iowa State Fair.  It’s true what they say, you can get everything on a stick and the fair is larger then anyone could imagine (well, until you’ve been there of course!)


(My children watching some sort of cow show.  You can tell the 2-year was enthralled; the other   2 were humoring their little sister)

The Iowa State Fair frequently shows up on National and Families with Kids Summer Bucket Lists.  In fact, this year Al Roker visited the fair!

One of the main attractions at the fair is the Butter Cow.  Its a sculpture of a cow made entirely of Iowa Sweet Cream Butter (with a little help from wood and wire forms underneath it all!).

I’d heard about the Butter Cow before.  I’m sure I’d even seen a picture or two of the cow, but as soon as we got through the gates and on to the fair grounds I told my family the first thing we must see is the Butter Cow!  So my family of 7 (my mom and dad were with us, also visiting the Iowa State Fair for the first time) walked right past the bacon wrapped ribs on the stick, and the hand-dipped corn dogs (OK, OK so we made an impromtu stop at the mini cinnamon roll stand . . . you would understand, if you could have smelled them) to see the famous Butter Cow.

We could tell where the cow was, before we even saw it because of the steady stream of people walking by the large window to catch a glimpse of the cow.  But, when we finally got there this is what we saw:


Pretty impressive, if you think about it.  The butter cow is about 5 feet 6 inches tall and 8 feet long.  It weighs approximately 600 pounds (a really dairy cow weighs about 1000 pounds)  According to the Iowa State Fair website the butter cow could butter about 19,200 slices of toast and would take the average person 2 lifetimes to eat.  These statistics got me thinking:

1. If this cow could butter 19,200 pieces of toast, how much butter is being put on each piece of toast?

2. If it would take the average person 2 lifetimes to eat the butter cow, how much butter per day is the “average person” eating?  And, what makes a person “average”?

3. In the video about the 2013 butter cow artist Sarah Pratt says that this year’s cow weighs between 450 and 50 pounds.  If one stick of butter weighs 4 ounces, approximately how many sticks of butter were used for this year’s butter cow?

Want to know more about the Butter Cow?  Check out this YouTube video produced by Iowa Public Television.

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