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

- Find out about the heat index.
- 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.

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.

Filed under: Algebra, Functions, High School, Middle School, Modeling, Uncategorized Tagged: Functions, Hawkeyes, Heat Index, Modeling, National Weather Service, University of Iowa ]]>

For example, if the random number generator produced the number 17 a winning answer could be

17 = (4)²+1+((3+5+6+7+8+9)0) = 16 + 1 + 0 = 17

The first team to figure out a way to represent the number got 5 points. If another team could represent the number in a different way they earned 2 points. If a team checked another answer and found an error, they earned a point also.

The game was exciting! It was loud! People were yelling about the order of operations and exponents! They were challenging each other about math! It was music to my ears!

Then, the random number generator displayed the number 147. It started off like any other round . . . whispering, writing, stopping, writing some more . . . and then something interesting happened–no one could figure out a way to combine the 10 digits to get the number 147.

I left that day thinking about the number 147 . . . was it impossible to generate the number using all 10 digits? If so, how many other numbers could not be generated using this method also? As I was driving back to my office I began thinking about the properties of 147. First, I wondered is 147 prime? But I quickly figured out that is was not prime (I used the test for divisibility by 3–1+4+7=12, which is divisible by 3, so 147 is divisible by 3). The prime factors of 147 were 7 and 3, in fact 147 = 7²(3).

Now I had a strategy! Was there a way I could combine 10 digits to equal 7, 7, and 3? If so I could represent 147 in the way that was so tricky! Guess what? I could! And now its your turn! Show me how you represented 147! Can you do this in a way that doesn’t build off of the prime factorization of the number? Good Luck!

Want to recreate this activity yourself? Here’s a random number generator. Want to learn more about divisibility tests? Look here. And you can find a related post here. Or here.

Filed under: Algebra, High School, Middle School Tagged: Counting, Divisibility Tests, Long Division, Math Games, Order of Operations, Random Number Generator ]]>

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!

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?

Filed under: Algebra, Functions, High School, Middle School Tagged: Deer Mountain, hiking, Math, Mathematics, Rocky Mountain National Park, Slope ]]>

Filed under: Uncategorized ]]>

For more Tau Day fun check out my Pi Day activities . . . just do them twice!

Filed under: Uncategorized ]]>

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!

Filed under: Algebra, Functions, High School, Middle School, Modeling, Statistics Tagged: 000 steps, 10, 5 miles, FitBit, HIgh School, Illuminations, length of stride, Math, Mathematics, Middle School, NCTM, Rates, Statistics, STEM, walking ]]>

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.

Filed under: Algebra, Functions, High School, Middle School, Modeling Tagged: Conversions, Data Collection, Distance, Lightening, Math, Mathematics, Meters per Second, National Weather Service, Patterns, Physics, Rate, Rates, Thunder, Thunderstorm, Time, University of Illinois ]]>

Well, if she’s kept up with her New Year’s Resolution, she should have made 19 deposits by now . . . for a total of

52+51+50+49+48+47+46+ . . . .

(Please tell me you’re not really adding these?!?–Remember, just ask yourself “What would Gauss do?)

$817!!! (Former student of mine, if you’re still on the Reverse Savings Plan Way to Go! $817 is a lot of money!)

Wow! In just 19 weeks time or 37% of the year), she’s been able to save nearly 60% of her total goal!

Maybe she should just give up on the rest of the plan? I mean, $817!

Let’s suppose she’s putting that money into her savings account. Last year, CNN Money reports that, on average, people made about 0.06% interest on the money in their account.

Let’s compare the two amounts:

If she stops today: $817 If she stops in 33 weeks: $1378 (her goal)

One year from now: $817.49 One year from now: $1378.83 (off to college)

Five years from now: $819.45 Five years from now: $1382.14 (graduates from college)

Ten years from now: $821.92 Ten years from now: $1386.29

20 years from now: $826.86 20 years from now: $1394.64

50 years from now: $841.88 50 years from now: $1419.97

Total Amount of Interest earned: $24.88 vs. $41.97

The moral of the story? Keep on keeping on (and throw an extra few bucks in each month if you can!)

Filed under: Algebra, Functions, High School, Middle School, Uncategorized Tagged: 52 week reverse savings plan, Calculus, CNN Money, Compound Interest, e, Exponential Growth, Gauss, HIgh School, Math, Mathematics, Middle School, Rates, savings account, series ]]>

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 . . .

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?

Filed under: Algebra, Geometry, High School, Middle School Tagged: geometry, Kite, Making a kite, Math, Mathematics ]]>

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!

Filed under: Algebra, Discrete Mathematics, Functions, High School, Middle School, Modeling Tagged: Boston Marathon, Couch-to-5k, Data Collection, Exponential Growth, HIgh School, Marathon Times, Math, Mathematics, Patterns, Rates, STEM ]]>