Tag Archives: Math

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?

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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.

 

 

Making a Kite

A few weekends ago I took my kids to a great kite festival in a near-by small town.  It was amazing!  There were huge kites, small kites, kite flying demonstrations, and even professional kite flyers!  Although the kite festival was really fun, there was one, small snag.

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The organizers of the event advertised that kids would be able to make their own kites.  This was the big draw for my kids, so as soon as we got out of the car, we made a beeline for the kite making station!  Imagine our excitement when we were the second family in line!

Then, imagine our frustration as we continued to stand in the line for the next 30 minutes.  The problem?  The kite builders were trying to have each of the children literally build. a. kite.  They had purchase dowel rods and parachute fabric. The idea was this . . . use a saw to cut the dowel rods.  Then, use a very teeny, tiny drill to drill holes at the ends of said dowel rods.  Next, tape the dowels together in a “+” and string tread through the holes to make the outline of the kite.  Finally, cut a piece of parachute fabric to cover the dowels and the edge of the kite and sew a hem around the entire perimeter of the kite with needle and thread.

Now, I have to say the up side of all of this?  The kites were legit kites . . . they probably would have actually flown!  The down side?  Every single child in line was under the age of 10 (interpretation–no one could do this on their own).  The station was set up so that only one child at a time could make the kites.

Finally, I leaned down to my kids and said . . . “Let’s go to a craft store, I’ll get the stuff to make the kites and we can do this at home!”

I made this offer numerous times, and about the 4th or 5th time I offered/begged them to get out of line, they finally agreed!

Now, we were going to make our own kites!  I headed to a craft store to get the supplies (which, by the way they don’t have parachute fabric!) and ended up with three, 36″ dowel rods, some fabric, and kite string.  We were ready to start making the kites!

Now, when you use the term “kite” it can mean many, many things.  There are kites like the kinds we saw flying that day, there are geometric shapes called kites, and there are kite graphs.  For this post I’m talking about kites that fly, but that are also in the shape of the geometric figure called a kite.

The definition of a kite is: a convex quadrilateral with two adjacent, congruent sides (length a) and two other congruent, adjacent sides (length b).  A rhombus is a special case of the kite.  The diagonals of a kite and perpendicular to each other, and one of the diagonals bisects the other diagonal.

I couldn’t make a rhombus kite, because I only had 3 dowels and two kids who wanted kites of their own.  And, it’d be really nice to only have to cut one of the dowels, instead of all 3 of them. Meaning, I’d like each of the kites to have one of the diagonals be length 36.”  The length of the other diagonal was up for debate, however . . .as long as it was at most 18″.  So, here’s what I knew . . .

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blue = dowel rods

red = string

So, I’m wondering . . . given these parameters what would you design the kite to look like?  How could you minimize the amount of string needed?  What about the amount of fabric needed to cover the entire kite?

 

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?

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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!

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?