Can you make 147?

Last week I was in a high school algebra classroom and the teacher was helping students get back into the swing of the school year and doing mathematics.  He was playing a game with the students in which he would display a number using a random number generator and the students would have to use all of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 as well as operations and grouping symbols to equal the number displayed on the screen.

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.

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?

Moving right along . . .

I’m two weeks in to my new job at St. Ambrose University in Davenport, IA.  I’m the newest tenure-track faculty member in the School of Education.  This semester I’m teaching the Theory of Arithmetic (Elementary Mathematics Methods/Content course) and Pre-Calculus.  It seems as though the last few weeks many people in my life have been talking about money . . . my husband talking about the lack of my paycheck (a slight annoyance when starting a new job . . . the one month lag in pay!), my students talking about the cost of textbooks, and everyone else at the University talking about the rising cost of tuition and the shrinking amount of state aid/student scholarships.  With money on the mind, I thought it’d be nice to check in with my stellar mathematics student from a few years ago who started a reverse savings plan during the first week of 2014.  (Remember her?)  If not, check out the posts here and here.  I’m checking in to see how she’s been doing and I’ll update you soon!

Two times Pi = Tau

2π = τ, which means that tomorrow is Tau Day! (Remember 3/14 is Pi Day, since Pi ≈ 3.14).  Since tomorrow is 6/28 (or 2(3.14)) tomorrow, June 28 is Tau Day!  How will  you celebrate?  Might I suggest you celebrate with 2 pies?

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

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.