# Ely, Nevada and its surrounding area

I discovered Ely, Nevada’s homepage recently and particularly enjoyed it: Ely, Nevada Home Page., but especially for the sentence (near the bottom of the page): “Centrally located in the intermountain west, Ely and the surrounding area contains a population of over 6 million people within a 500 mile radius.”

I loved the humor and creativity evident in that sentence. And then I thought, “What questions could I ask to make sense of this statement? How could I share this statement with a math class?” I considered the questions:

• In order to engage in answering any of the questions below, what tools can I use?
• Is there an online tool that, given a map, would create the circle for me? Is there a tool that would add up the populations for me?
• Creating the circle (if using the map, figuring out scales, etc. is important):
• Get a map of US (either a folded map or print out a map from Google Maps) and a compass, measure the size of “500 miles” and use the compass to create a circle
• Get a digital map of US and use GeoGebra to draw a circle (depending on how precise I want)
• Finding populations:
• How precise should I be?
• Should I choose the largest cities, and look up the metro populations? What is my “cut-off point” for city size?
• How far would I be under-estimating, if I don’t count all of the smaller towns and cities?
• What does “surrounding area” really mean?
• If I draw my intuitive sense of what “surrounding area” means on a map, how big of an area does it include? Do my classmates have similar or different ideas about the size of “surrounding area”?
• How big of a radius should I use to include the whole US? Where would I center it? How much of Canada, Mexico, or other countries would be included?
• How big is a region with a 500-mile radius?
• What cities / metro areas are included in the 500-mile radius circle centered at Ely?
• Could they have chosen a smaller radius and still included an impressive population?
• Are there particular cities they wanted to include that inspired their choice of 500 miles?
• Where I am now (in East Lansing, MI):
• If I created a circular region of radius 500 miles centered on East Lansing
• How many people would be contained in that region?
• What cities would be contained in that region?
• If I wanted to include a population of 6 million people, how large should the radius be, if I centered the circle on East Lansing?

I will try to engage in this task when I have more time…

In order to engage in answering any of the questions below, what tools can I use?

• Is there an online tool that, given a map, would create the circle for me?
• Is there a tool that would add up the populations for me?
• Finding populations:
• How precise should I be?
• Should I choose the largest cities, and look up the metro populations? What is my “cut-off point” for city size?
• How far would I be under-estimating, if I don’t count all of the smaller towns and cities?

How big is a region with a 500-mile radius?

• What cities / metro areas are included in the 500-mile radius circle centered at Ely? The map shows some large cities are: Salt Lake, Ogden, Provo, Las Vegas, Reno, Phoenix, Los Angeles, San Jose, San Francisco, Fresno, Sacramento, San Diego, Tijuana (Mexico), Boise, Idaho Falls
• I’m going to estimate the population. I notice that all of Nevada (2.839 million) and Utah (2.943 million) are contained. So that’s already about 6 million people! Most of California is contained, except for a tiny piece in the northwest that includes Crescent and Eureka, and California has population 38.8 million – let’s be conservative and knock off about 8.8 million for that tiny corner and we still have 36 million contained. The Phoenix metro area adds about 3 million. Tijuana adds about 1.483 million. Boise (0.616) and Idaho Falls (0.130) add a little less than a million. I could keep adding on, but a low estimate is still over 40 million.
• I found that the same site I used to create the circle also will estimate population within the radius, and it says “The estimated population in the defined area is 49,997,320.”
• Could they have chosen a smaller radius and still included an impressive population?
• I’m going to guesstimate and say 250-300 mile radius would probably still include 6 million people.
• Let me test my conjecture. (Note that I needed to reset the site before changing the radius, or it told me the same population as above.)  I entered 250 miles and was told “The estimated population in the defined area is 4,331,681.”  300 miles was closer with 5,438,487, and 315 was slightly more than 6 million with 6,396,013.
• Are there particular cities they wanted to include that inspired their choice of 500 miles?
• I’m guessing it is cool to say that San Fran and other California cities are “in the surrounding area.”

Where I am now (in East Lansing, MI):

If I created a circular region of radius 500 miles centered on East Lansing

• How many people would be contained in that region? Well, it includes all of Michigan (9.91), Wisconsin (5.758), Illinois (12.88), Indiana (6.597), Ohio (11.59), West Virginia (1.85), Washington, D.C. (0.658), and Kentucky (4.413). So, as a low estimate, a 500-mile region would include a population of at least 53.656 million.
• I was much, much too low! With the population finder, I found  the estimated population in the defined area is 101,594,400
• If I wanted to include a population of 6 million people, how large should the radius be, if I centered the circle on East Lansing? I conjecture 90 miles. Metro areas for Detroit (3.734), Lansing (0.464), Grand Rapids-Muskegon-Holland (1.321), Kalamazoo (0.326), and Flint (0.425) would be just over 6 million.

I’m really under-estimating though, because I choose to balance time over precision (time of looking up populations), but the radius around East Lansing of 90 miles would definitely include 6 million people. Using the population tool, I found that 75 miles radius would include 6,795,008 people.

# Gambling with Woot

A few weeks ago, Woot.com advertised a “Mystery Box of Electronics.” One box cost \$50. Woot said: “Not knowing is half the fun!” Each box would include:

• Random consumer electronics items
• You get 3 items per order in a brown box (nothing special about the box!)
• Condition will be refurbished on most items. Some could be new

So, I decided, why not? And I gambled on Woot – I bought three mystery boxes of electronics! (Because not knowing really is kind of fun…)

Box 1:

• A very pink “beat mixr” headset. Other listings on Amazon.com show prices for new/used (for some reason some new are cheaper than the used!), starting as low as: \$110.
• A small Acesori PowerStick. Other listings on Amazon.com show prices for new/used, starting as low as: \$4.
• An Acesori Glass Vault screen protector for an iPhone 5. Other listings on Amazon.com show prices for new/used, starting as low as:  \$7.

Box 2:

In the box, I found:

• ifocus “Deluxe edition” educational system for kids (a set of CDs: one is an educational game and the other is a fitness program). The company that sells these says they are \$199.95, but it doesn’t look like I could resell them
• An Acesori Glass Vault screen protector for an iPhone 5. Other listings on Amazon.com show prices for new/used, starting as low as: \$7.
• Acesori Bluetooth Noise-canceling Neckband Headset with Built-in Microphone. Other listings on Amazon.com show prices for new/used, starting as low as: \$30.
• LG Electronics Gruve Bluetooth Stereo Headset. Other listings on Amazon.com show prices for new/used, starting as low as: \$30.

Box 3:

• BlueAnt Pump – Wireless HD Sportbuds – Black. Other listings on Amazon.com show prices for new/used, starting as low as: \$26.
• Turtle Beach Ear Force Z11 Amplified Gaming Headset. Other listings on Amazon.com show prices for new/used, starting as low as: \$24.
• TruGuard Tempered Glass Screen Protector for iPhone 5/iPhone 5S & iPhone 5C. Other listings on Amazon.com show prices for new/used, starting as low as: \$6.

So the big mathematics question is: Did I get my money’s worth?

In the Woot discussion (http://electronics.woot.com/forums/viewpost.aspx?postid=6481553&pageindex=60), many customers say, “No!” Others say, “Yes!” I’ll give several comments here, and let you decide!

• The value is there for at least what everyone paid for when they ordered it. The problem is people discount the value simply because it’s something they don’t want or can’t use, or they deem to be useless. That’s on them, not Woot.
• This sale rather was marked as getting mystery items that were either new or refurbished worth at least \$200. So for \$50 bucks, if thats the case, how could we go wrong. We should all consider that that this \$200 value should not by any means be gauged on our perception of value, but rather fair market value, which is really the point of taking up a mystery box. It may be worth it to you, but it may not. If its not, you can go through the legwork of selling it off and making back your money.
• (received my box 3 above) I am not satisfied because I don’t feel this box is worth the 50 bucks I paid. But still I will get use out of some of it. I understand that with these boxes you run the risk of getting items you don’t want or won’t use but you expect the value to still be there.
• As to “value”, that is in the eye of the beholder. The great marketing dilemma. Do we want to talk about MSRP, street price at release, current street price, or the best deal available? Naturally, very few items ever sell at MSRP, but it is still used everywhere to convince everyone how much money they are saving at the current street price.
• Overall – the value of the boxes I received is total crap – at least for me.
IMHO no quality items. Protectors for outdated devices. MSRP that are years old and cannot really count against today’s value. Overall inflated MSRP assumptions of products that cost cents to make (like cases and protectors)… no value there.

So…. what do you think? Was it a good decision or bad?

Preservice elementary teachers, both when they are seniors and interns, have opportunities to read about, discuss, and create high-level tasks. Even though we have several readings, and discuss ways to create high-level tasks or to adapt curriculum in high-level tasks, our preservice teachers are not always able to answer the question “What is a high-level task?”

This Fall, my co-instructor and I decided to have our interns come up with a list of what they see as the most important features of high-level tasks. I think it went well! What are other features that should be included? (acknowledging, of course, that it isn’t only the task itself that makes the activity high-level but also the discussion after and the teacher interaction with students as they explore)

When you create high-level tasks, consider whether they have the following features:

• Leads to a deeper mathematical understanding
• Authentic – should connect to students’ real-world (which may be very different than your real world
• Open-ended
• Collaborative
• Open to / requires multiple smartnesses (so that students are all valuable members of the team)
• Multiple entry points
• Multiple strategies and valid solutions
• Not just knowing strategies, but applying strategies as needed
• Allows for students to see why some strategies don’t work (sometimes or all the time), others work but might be easier / faster / make more sense
• Multiple possible representations (manipulatives, diagrams, numbers, words, pictures, etc.)
• Integrates multiple topics, strategies, and mathematical understandings