It's only been 3 days, and I'm exhausted!

Students came back to school this week, but not until Wednesday.  That means that I only saw them for 3 days and the beginning of school generally means going through routines (pretty general), but I AM EXHAUSTED!  I got home last night after junior high volleyball practice and then working the football gate, and I was asleep by about 9:30pm. 

While I'm tired, it was a good week.  And, I'm happy to report that I think incorporating the mathematical reflections on the photographs is going to be a success!  Friday, while describing the assignment in class, we got into some good discussions about whether or not the columns in a photograph were truly parallel because of the shape of the columns.  They also debated what might be the best term to describe the columns.  They weren't cylinders because the diameter changed throughout the column, but they weren't "shape" that would be. 

In another class, I got great participation and a wide spectrum of ideas, all about the same photograph.  Needless to say, I'm excited!!!

Now it's on to less exciting things like taking recycling to the drop-off, scrubbing my floors, and trying to get my apartment super clean!  Because I know it won't happen again until the end of October when volleyball season is complete!  Hope you all have a good weekend!

MathFest 2011 Presentation

I know this won't share the whole experience with you since you won't hear the presentation that goes with it, but here are my presentation slides.

Outdoors with Math in the National Parks, MathFest 2011

There is much more to be developed and detailed with this project, but I've got a start!

MAA's MathFest 2011: as nerdy and wonderful as it sounds

Yesterday, I traveled to Lexington, Kentucky, to attend MAA's MathFest 2011.  MAA is the Mathematical Association of America in case that's an acronym with which you're not familiar.  Mathematicians from across the country (and some internationally), and mostly from colleges and universities, come together to talk math, all kinds of math.  Because I'm one of them, I can comfortably say that mathematicians have a style all of their own.  Actually, there are about 2-3 styles, but they all very much scream, "I live for math!"  Let's just say it wasn't difficult to spot which individuals in the airport were headed to MathFest.  And now I'm wondering how easy I am to spot.

Today, I went to a variety of presentations.  One professor used the popularity of zombies to grab his students' attention and practice using the SIR model (Susceptible-Infected-Recovered) which is typically used with infectious diseases.  Another discussed research on how teachers' mathematics content knowledge explains their teaching practices.  And, I have to say I experienced that "student" feeling today: when it came time for questions in some of the presentations, I wasn't even sure what I would need to ask to begin to understand!  A great reminder to put yourself in your students' shoes once in awhile.  My favorite way to do this in junior high is to ask for a volunteer to be the teacher for an example problem.  I take a seat and ask every single question I can think of to be sure they explain each step, especially the ones I know are out there but just aren't being asked.  The students think it's fun, maybe because I tend to play it up and be borderline ridiculous.

The very best part of my day was seeing my undergraduate college advisor, Dr. Lisa Townsley.  She's at the University of Georgia now, and I haven't had the chance to see her in person since shortly after graduation.  She continues to be an inspiration and mentor for me, and I'm hoping I'll have the chance to see her (or at least talk with her) much more frequently in the future.  I have her to thank for encouraging me to submit an abstract to speak at MathFest.  Thank you, Lisa!

After a few more presentations, I walked into "Thursday Night Live" in Lexington's Fifth Third Pavilion where I listened to some live music and grabbed crepes from a local restaurant for dinner.  And then back to the hotel to look up my students' MAP (standardized tests) scores from last year, and possibly start planning a new hair color if they did well....

Overview of the Trip

I am blessed.  The past month has been an experience about which most people only dream.  I feel invigorated about heading into my classroom and about my career as a teacher.  I am excited to begin work editing photographs, writing lesson plans, outlining a plan for the year, and putting together a presentation for the Mathematical Association of America’s 2011 MathFest.  Thank you to all of those have supported me and those I know will continue to do so.

I am going to continue to blog, though I’ll admit it may be more hit and miss than I’d like as the school year begins.  Maybe I’ll surprise myself and be regular!  In the meantime, keep an eye out for the math around you and don’t underestimate your math skills (or how much you’re using them and need them)!

Monday, July 11, 2011

Stats for the day:

·         Daily miles: 546.3

·         Total trip miles: 4629.2

·         Temperature on the side of the I-70 tollway: 102°F

·         Tow trucks needed: 1

·         Miles I was from making it home with no drama: 81

After saying goodbye to the Brooke and the kids, I started my trip across Colorado and the state of Kansas to make it back to Weston.  Most of the drive was uneventful.  Kansas raising the speed limit to 75 on I-70 helped a bit, and the weather was great (just super hot!).

And then, I reached the Kansas Tollway on I-70, just east of Topeka.  I grabbed my ticket, tried to accelerate, sawing my RPM needle drop to zero, and lost any engine power.  I pulled to the side of the road and had a car that wouldn’t start.  Seriously?!?!?!?

So, after talking with the rental company, there were a couple of options. 1) I could be towed to the closed location in Topeka and have a family member pick me up from there.  OR, 2) I could be towed to a location that was still open and be put in a new car, but it’d be a much longer tow.  Because I have a wonderful family, I voted for option 1.  I was supposed to turn in the car early tomorrow morning, anyway. 

I’m thankful the tow truck company arrived quickly and that overall it was the best scenario for a car breaking down that I could imagine.  I’d traveled 4,500 miles over 4 weeks and was only an hour and a half from home.  The best part is that when I arrived at the rental car location and the tow truck driver, Sam, tried to start the car (he said he always tries before and after towing), it started!!! He shrugged his shoulders and said I’d be surprised how often it happened.  But advised me to take the ride with my family and not risk it!

Math thoughts for today:

·         A higher speed limit (or even driving faster) always makes people think they’re going to get somewhere so much faster.  But, it’s impact, and whether or not it really makes one, really depends on how far you are traveling.  My students can do some simple calculations to determine the amount of impact. I happen to know of someone who got a speeding ticket when he first got his license – the faster speed would have saved him less than 5 minutes if he hadn’t been caught.  But, he was.  And it therefore took him longer, and cost him more!

Shout-outs:

·         Happy Birthday, Alexia Norris!!!

Sunday, July 10, 2011

Matt flew back to Boston today.  After getting to spend 3 weeks with him, it’s going to take me a little bit to adjust to not being in the same state as him.  He seemed to think that driving across the state of Kansas wouldn’t be all that interesting.

I headed to the home of a childhood friend, Brooke, and spent the evening meeting her husband, Frank, and their wonderful children (Blase, Caroline, Michael).  I haven’t seen Brooke in well over a decade, but our moms get together once a year with two other “babes.”  I’ve stayed updated on what she’s doing because of our moms, and it was such a blessing to get to spend time with her.  And to eat the wonderful meal Frank prepared.  And to play with the kids!  They all made me feel so at home, and I’m hoping I don’t have to wait a decade to see them again!  Thanks for welcoming me!

After our walk home from the park in the rain.

And then the silly pictures began!

Saturday, July 9, 2011

The drive to Denver included a quick stop at a casino so Matt could play a few hands of Blackjack.  After grabbing a meal in the late afternoon with a restaurant full of 70 year-olds, we headed to Red Rocks Amphitheatre for The Avett Brothers concert.  I’ve not been to Red Rocks, but I’ve heard wonderful things about the venue, AND it’s an amazing band.  The thunderstorms rolled in and out before the show was in full swing, and it was a perfect evening to listen to a band I love with the man I’m going to marry.

Math thoughts for today:

·         I’m determined to write some lessons that connect music notes and fractions.  I know a lot of students who are great with music but struggle with fractions.  It’s a natural connection, and one I can hopefully work with my fine art colleagues to reinforce!

·         It may be a bit beyond my junior high students, but how matrix work can be used for traffic flow (input and output) is a very real application.

Shout-outs:

·         The first time I saw The Avett Brothers was with Brian and Angie (both siblings). My mom was out of town for the weekend with her “babes,” and I thought I could talk my dad (a former sound and lighting guy for a band now in the Iowa Rock ‘n Roll Hall of Fame) into coming, too.  He loved it.  And we had such a great time bringing him out with us!

·         Brother Simon Baker (aka Carl Baker): I love that you told me about The Avett Brothers so long ago when we were in grad school. 

Friday, July 8, 2011

Stats for the day:

·         Daily miles: 70.6

·         Number of cyclists on the road: too many to count!

Today, we headed to Boulder.  After spotting The Avett Brothers (specifically Joe Kwon) and making an additional walk-by to see if we could run into them again, we continued to explore downtown Boulder.  At this point, I think we’re both a bit worn.  I haven’t totaled the miles hiked in the past month, but I’d estimate it to be 75-100  miles.  And it’s been hot.  And it’s been wonderful.  And I’ve collected more photographs and data than I’d even dreamed.  And we’re now headed into a few days of vacation.

Our exploration of Boulder continued outside of downtown, where we drove on a road that had a 16% gradient.  Crazy steep!  I’m still trying to figure out exactly how people who live on this road are able to travel to work in the winter.  But, boy, do they have a view!  We’re also not convinced that people work in Denver.  There are always too many cyclists on the road to think they have time to work!  I wish more places had bike lanes.

The evening was an early one as we settled into the comfort of a hotel room, watched Inception, and tried to catch up with family and friends.

Math thoughts for today:

·         The steepness (slope) of roads is communicated with different verbiage than what is typically used in math classrooms.  Slope goes by lots of different names and formulas.  This adds just one more to share with the students!

Thursday, July 7, 2011

Stats for the day:

·          65°F at 9am at 7600 feet (Mary’s Lake Campground, Estes Park, CO)

·         Total trip miles to date: 3836.3

·         Mid-afternoon thunderstorms avoided: 1

·         Giant holes ripped in shorts without knowing: 1

When my mom speaks of Estes Park there is one story that sticks out in my mind: the Coleman campstove blowing off of the table because the wind was so strong.  I now know what she meant.  so strong it sounded like a train (just like how people describe the approach of tornados)!

Our campsite in Estes was just outside of the park (our late arrival the evening before made us make a conjecture that all of the first come, first serve campsites in the park would be taken), and we really liked it (right next to Mary’s Lake), so we decided to stay at the same campsite and simply drive into the park for the day. 

We drove to the Continental Divide and on the way down from the Divide stopped to hike the Tundra Trail.  Upon getting out of the car, Matt immediately laughing, trying to get my attention, and calling me to stop and come back to the car.  I thought he was just trying to give me a hard time and make me paranoid, but then I reached down to touch my behind and realized the entire back of my shorts had ripped!  There was no sudden movement to cause it, no loud rip to alert me, not anything!  After a quick wardrobe change, we headed to the tundra.  If I wanted to give him an excuse to not ever have to do it again, I’d say that Matt’s laundering skills must have caused the rip. BUT, I like that he helps, so I’ll blame the rip on the fact that I’ve been doing so much rock climbing and hard hiking that it just wore out the fabric.

Note my navy shorts.

And now they're khaki.

The Tundra Trail had lots of fun facts along the way and on top of the rocks at the summit (I use that word loosely), there was a cool compass rose that included info on various features in each direction, many of them beyond the state of Colorado. 

After some elk watching, we headed to do the hike from Bear Lake to Emerald Lake, passing through Nymph Lake and then Dream Lake.  There was a small delay because of Matt’s feet.  He’s been quite the trooper dealing with some extreme blisters and cracked heels.  (We’ve been through quite a bit of moleskin and liquid bandage.) But I love him so much, I hiked back to the vehicle to get some medicine and then back to where he was (it was only an extra mile, but a mile with quite the elevation change), and he powered through the hike.  And I’m glad he made it because we saw some beautiful lakes and hiked the last mile on snow!  Quite the change from the sand and dust of the desert!  Emerald Lake was still pretty full because of the late snow melt, and you could still see snowboarding tracks on the mountain beside the lake.

Dream Lake

On the way back to our campsite.

We finished the hike just in time for the raindrops to start falling.  So, the evening consisted of hunkering down in the tent with wedding magazines and notepads to start brainstorming! 

Math thoughts for today:

·         The tundra and its specimens really impressed me.  There were lots of facts about how long it takes for organisms (and maybe even micro organisms) to grow.  I think growth/decay models about populations for these organisms would be great to compare to those of organisms that grow a bit more quickly.

·         The reflections in the lakes were just what I had been hoping to find!

Shout-outs:

·         I took a picture of a great family from Des Moines (Iowa shout-out!!!), AND they had family who’d graduated from Briar Cliff in Sioux City.  Briar Cliff is where my parents (and LOTS of my aunts, uncles, pseudo-aunts and uncles) went and have worked. 

Wednesday, July 6, 2011

Stats for the day:

·          9370 steps (on pedometer)

·         Daily miles driven: 455

·         88°F at 12noon in Arches National Park and 94°F by 1pm

·         57°F at 9pm in Estes Park, CO

·         Complicated, windy roads taken: 1 (beautiful, but made it a long evening)

After packing up camp at the Moab KOA, Matt and I headed into Arches to hike to Landscape Arch.  This is the arch that had a large section suddenly fall in 1991 (and it’s not far from the rumbles of Wall Arch which collapsed in 2008).  Because of this, you can’t get very close to the arch anymore, but it’s still a pretty commanding view.  And, it’s in an area that’s filled with a number of arches.  It was amazing to me how many people were on these trails.  I think some of it is because it was a pretty easy trail, but also I can tell we’re getting further into the summer and vacations are in full swing!

Landscape Arch ~ Look to the right part of the arch and notice how thin it is.

Before the true heat of the day came, we started the drive to Colorado.  We’re headed to Rocky Mountain National Park which will be a quite a contrast to the parks in Arizona and Utah!  It was a long drive, ending with us taking the scenic (and therefore most complicated) way to Estes Park.  By the time we got to our campsite, we were ready to relax and head to bed!

The Ring and the Road ~ Don't worry, Matt took this picture.  My focus was on the road.  You can see how busy and curvy it was; but in all seriousness, it was insanely windy!

Math thoughts for today:

·         Landscape Arch is 306 feet from base to base, which will be fun to use to do some comparisons with distances and estimating (what would fit between the bases).

·         We experienced quite the change in temperatures today – perfect examples for working percent change problems in class.

·         There are a number of ways to get into Rocky Mountain National Park.  I think this could be an excellent park to have students do map work (routes, distances, rates, scale factors).

Shout-outs:

·         Estes Park makes me think of some specific people.  I remember Cindy Bond (my high school coach, mentor, and now, colleague) spending lots of her summers traveling here. 

·         Also, Kim and Edie Hays are huge fans of Rocky Mountain National Park, and my mom has made multiple trips with one or both of them.  I hope I can bring back some fun memories to share with them!

Tuesday, July 5, 2011

Stats for the day:

·         Loads of laundry: 3

·         Hours of typing and uploading: approximately 5

·         Times I started crying: 5-6

·         Wedding magazines purchased: 2

The plan for today had always been to work and catch up on laundry, cleaning out the car, and so on.  With last night’s events, it was a serendipitous plan.  I’ve spent much of today making phone calls, but also taking advantage of having electricity and internet to get blog updates typed and posted.  Matt has graciously washed dishes from last night’s feast, and he’s even off doing laundry as I type this.  (So the 3 loads of laundry is an estimate based on what I saw him carry out of the cabin.)

The day has been filled with interruptions of wedding brainstorming and lots of lovey-dovey comments and kisses. 

Monday, July 4, 2011

Stats for the day:

·          15741 steps (on pedometer)

·         85°F at 8am at Squaw Flat Campground

·         Sleepless/restless nights due to heat and no breeze: 2

·         Campers who were ready to get away from the incessantly present bugs: 2

·         Number of arches on which Matt climbed on top: 1

·         Number of hikes to complete today to finish the top 5 premier Colorado Plateau hikes:1

·         Hikers led astray by Matt: 1

·         Number of proposals: 1

Matt and I enjoyed Canyonlands, but couldn’t pack up quickly enough on Monday morning to move on to the next park.  It was probably mostly due to not getting much sleep the last few nights because it was hot.  And there was no breeze.  You could hear the breeze a hundred feet above (and we felt it when we were up on the rocks), but somehow it eluded ground level.  Plus, there were a few ravens whose nest was close and who liked to start talking early in the morning (once we’d finally fallen asleep).  And then there were the bugs!  Bugs don’t bother me as far as making me freak out, but these flies did nothing but stay right on you, buzzing and buzzing and buzzing.  There were also little gnat-like bugs that bite.  And insect repellant doesn’t work. The park literature tells you this and confirms the annoying nature of the bugs.  So, we were ready to go.

We drove to the Island in the Sky section of Canyonlands, the northern section.  I wanted to see Mesa Arch, which rather than looking up at as you do with most arches, you look at from eye level and look down through the arch.  It sits on the edge of an 800 foot drop off.  Matt decided to saunter across the bridge (rule-follower me saw no signs saying this wasn’t allowed).  After coming down from the bridge, he said not ever again.  I think between how easily it seemed like it could break away from the wall and the drop, it didn’t seem worth it.  This section of Canyonlands is much more prairie-like than the southern part.  Again, the diversity of landscapes within the area is amazing.  (And the video we watched later at Arches talked about how water is responsible for all of it.)

After Island in the Sky, it was on to the grocery store.  It is a holiday after all (Happy 4^th of July), and it’s also the anniversary of the day I met Matt 3 years ago.  So, we splurged and got some good grilling food.  We also splurged when we got to the KOA campground and upgraded to a “KOA Kabin,” complete with cool air.  We spent our afternoon prepping for our dinner, showering (it’s been a few days and it’s been hot), and then heading to Arches. 

We hiked to Delicate Arch for sunset.  Delicate Arch completes our 5 premier hikes on the Colorado Plateau, and it’s the famous arch that you see everywhere (Utah license plates, calendars you get from the pharmacy or grocery store with images from the US, etc).  It’s a little bit of a hike, but not bad, and one that is again marked by cairns (those small piles of stones).  I apologize on behalf of Matt to the hiker who took the turn we started to but then was gone from sight before we realized there were no cairns in the area.  His hike to the Delicate Arch was much more difficult than it should have been.

Balanced Rock in Arches National Park.  If you look to the lower left of the Balanced Rock, there is a smaller rock that looks similar (in math terms -- a dilation).

Delicate Arch, Arches National Park; Moab, UT

Delicate Arch sits in a natural amphitheatre.  Most people sit across from it (it’s “onstage”), with the occasional quick hike to go under the arch.  Matt asked the gentleman next to us to watch our bags and to take a picture of us under the arch.  Once we got under the arch, I asked, “Shouldn’t we turn to look at the camera?”  Matt said, “No,” and turned me to face him, to which I responded with the not-so-classiest of phrases.  I was putting together what was happening.  It wasn’t a strange request of a stranger to take our picture all the way across the basin of the theatre; it was a request to take a picture of our proposal.  Once I was facing him, Matt got on one knee, and said, “Kristi Hoffman, will you marry me?”  I was already bawling and simply put my hand out once I was able to move it away from covering my face.  I don’t think I said, “yes,” until we were hiking back to the car.  The sunset didn’t happen as famously as it typically does at Delicate Arch, but needless to say it was an unforgettable night there.  There were a few gasps when he got down on bended knee, a chorus of congratulations when we reached our seats again, and a number of unbelievable pictures thanks to the gentleman next to us.  I wish I had your name; thank you!



The Proposal



When I'd finally stopped sobbing enough (keyword, enough -- I hadn't stopped crying) that he could put the ring on and hug me.

Back at the cabin.

We headed back to camp watching fireworks all around us, making phone calls to family, and smiling nonstop.

We’re getting married!

Math thoughts for today:

·         I added a few arches to the archive for comparisons.

·         Let’s be honest; I was proposed to tonight.  My mind wasn’t thinking math.

Shout-outs:

·         Lauren Gebhardt and Ross Short – Congratulations on your first anniversary!

·         To all those couples I know – I can’t wait to join the ranks of marriage with you!

·         To James Matthew Pessarra, Jr. – I love you, and I can’t wait to be your wife.  I promise when the time comes, I’ll say, “I do,” and not the same phrase I said at our proposal.

Sunday, July 3, 2011

Stats for the day:

·          20231 steps (on pedometer)

·         77°F at 6am at about 6:12am

·         Miles hiked by noon: 6

·         Times today we scurried up onto the rock wall behind our campsite:2

·         Number of flies Matt killed on our morning hike: 6

We got up early to watch the sunrise from up on our rocks.  It was neat to see it hit various parts of the park, and then it quickly became warm.  We’d decided to head out as soon as possible after the sunrise for our hike, since it was going to get hot fast. 

This morning we were tackling the Chesler Park Trail and a beginning portion of the Joint Trail.  Our trailhead left from Elephant’s Hill, which also has a pretty cool looking off-road trail for 4x4 vehicles and adventurous mountain bikers.  The trail was marked by cairns (small piles of rocks) and this is the first trail I’ve done where I had to follow cairns.  It definitely makes you even more present than you are when you’re just watching for snakes and scorpions.  The hike takes you through sandstone rock paths and very desert-like scenery to an open field (Chesler Park).  There’s a 5-mile loop around the park, but we opted to do only part of it, as our hike was already going to be 6 miles, and we thought we’d avoid the mid-day sun beating down on you hiking. 

The Needles

 

We spent the afternoon seeking shade and doing some catching up on chronicling adventures until my battery died.  We looked at some books and maps and made more specific plans for the next few days, and ended the day with a hike back up onto the rock wall to watch the sunset.  It wasn’t as impressive as the day before, but there were thunderstorms moving in and it was fun to watch those clouds.

Math thoughts for today:

·         How many species can survive in this heat?

·         Of the established National Park Service trails, what percentages are dirt paths, paved paths, gravel paths, primitive paths, cairn marked paths, etc.?  And the question for my students: what would be the most appropriate graph to use to represent this data?

Shout-outs:

·         Michael – You would love some of the hikes I’ve done in the past week.  Plus, you’d love the scampering over the rocks we’ve been doing.  No real path – just see how high you can make it.  Safely.  You do have to come back down eventually!

Saturday, July 2, 2011

Stats for the day:

·          7215 steps (on pedometer)

·         83°F at 8am at 3620 feet at Wahweap Campground

·         97°F at 8pm at 5060 feet at Canyonlands Squaw Flat Campground

·         Total trip miles: 2921.7

·         Miles traveled today: 327.2 mi

·         Breathtaking sunsets from the top of a huge rock wall: 1

·         Cars decaying in a canyon from an apparent drive gone wrong: 1

Matt and I traveled to Natural Bridges National Monument on our way to Canyonlands.  Natural Bridges is out there, as in the path rarely ever traveled.  The road we took there was a winding, unpaved road, and at one point we looked into the canyon-type area and saw a car that’d been there for some time.  And the only way it was getting there was by accident.  Natural Bridges highlights three natural bridges, and they all provided some good contrast to Rainbow Bridge.  It was a quick trip through the monument area, and then on to Canyonlands. 

Canyonlands National Park is huge and is split into various sections.  We started in The Needles district, the southernmost part of the part.  Off of the interstate, it’s a good 40 minute drive to get to the park entrance.  Thankfully, there were campsites open and all of the campsites had good shade.  We set up camp, and then did the quick Cave Spring Hike.  It didn’t take a lot of energy, but featured an old cowboy camp, a few ladders to climb, some overhangs, and an intro to what hiking in this park would be like.

The second Newspaper Rock we've encountered.  This one is just outside of the Canyonlands, The Needles District.

Just before sunset, we climbed the huge rock walls behind our campsite and sat and watched the sunset.  It was fun scurrying up the rocks, and we had a great view.  At that point, we decided we’d get up and watch sunset from up there, too!

Math thoughts for today:

·         The natural bridges provide dimensions to work with to do comparisons with each other, as well as comparing the dimensions of these to other typical shapes.  This could be a good compare/contrast writing exercise to describe how the description of dimensions of an arch (or half circle if we make it simple) compare and contrast to those of a rectangle, for instance.

·         I’m curious about the number of visitors the various parks receive.  There is some data collection and graphing involved here.  Then, we could do some analyzing and make some conjectures (state testing loves the word conjecture) about why attendances are what they are.

Friday, July 1, 2011

Stats for the day:

·          11019 steps (on pedometer)

·         87°F at 8:30am at 3640 feet at Wahweap Campground

·         Hours on a boat: 4

·         Sympathetic looks due to a KC Royals Hat: 1

Today was a break from the extreme hikes and a day to recover a bit.  We had a lazy morning, with a short drive and then hike to Horseshoe Bend. 

Then, we boarded the Canyon Odyssey and headed to Rainbow Bridge National Monument.  It was great to spend the day on the water (Lake Powell is beautiful), and the scenery along the way was impressive.  Upon reaching the floating dock, there was a quick 1/3 mile hike to the bridge.  Now, some of you may not realize, but there is a difference between a bridge and an arch.  A bridge is formed above an established waterway, while an arch is formed from a combination of things (wind, water, etc), but isn’t over an established waterway.  Rainbow Bridge is nearly unchanged since its first documentation.  The ranger at the bridge was someone who loved his job, and it was neat to see all of the original photos he had.

Rainbow Bridge National Monument.  If you look very closely at the bottom left of the rainbow, there are people.  They're tiny, tiny, tiny, but provides some perspective.

After showering (something we all take for granted), we headed to dinner at the Wahweap Marina as a farewell to Brian.  It was nice to sit down, out of the sun, and once again to enjoy cold, cold water.  We treated ourselves to dessert, too.  Matt had crepes, Brian had cheesecake, and I had crème brulee.  I think we helped sell dessert to a few tables around us, too.  The end of dinner brought Brian’s departure.  It was great having him spend the week – thank you!!! 

Math thoughts for today:

·         Horseshoe Bend is where the Colorado River takes a 270° bend, or curve. 

·         Rainbow Bridge is a natural parabola, quadratic function, etc.  It’s also pretty massive.  This would be a perfect monument to have students come up with comparisons for the height and width (how many students standing on top of each other for the height, or standing next to each other for the width, how many school buses, etc).  I think it’s important for them to make comparisons to items around them that they know in order to truly understand (or at least grasp a bit better) dimensions.

Shout-outs:

·         Sherry McGhay – There was a McGhay (not sure how they spelled it as it as an auditory reference) who was involved in the exploration of the Glen Canyon area.  I was curious if you might be related through your in-laws.

·         Tim and Hilary from Houston – It was great to run into you tonight!!!  Tim and Hilary are a British couple who now live in Houston that we met while hiking Angels Landing in Zion.  We saw them again the next day in Zion on the shuttle and then happened to run into them after dinner in Page.  Much of our week had included similar excursions, and they were just a great couple.  I wish I had exchanged a phone number or email, but I’m hoping someday they might come across this blog and get in touch! Especially since I know I’ll be in the Houston area throughout my life (that’s where my boyfriend’s family lives)!

·         Mom – Brian’s dessert had this little strip of “fruit leather.”  Brought back memories of baking applesauce to make our own fruit roll-ups.