# Stripping Down the Stock Photo

Much of what impacts our memory of particular events as positive or negative is rooted in how the story ends.  I believe the same can be true for education.  My incurable optimism tells me that something else will work for these kids and I believe in them and in myself.  To end that class period on Friday, I called on a good friend, Nrich.

One hundred percent of them participated, 100% of them engaged and wanted to be the one closest to 1000.  It was a small victory, but was absolutely essential in ending the week pointed in the right direction again.  Mathematical curiosity ensued for a brief moment (Why did one person get 1008 and another 992?  Who is the winner?)  Now Monday won’t feel like more of the same for my students and me.  It’s a new chance to bring them together with mathematics and hopefully have some fun in the process.

# Alright, Mr. Stadel. We’ve Got Some Bacon Questions

Greetings, Mr. Stadel.  We know that you are very busy.  We appreciate your brief attention.  Rather than bombard you with tweets, we decided to bloggly address our questions and comments about your Bacon Estimates.

First of all, bravo.  You dedicated an entire section of your estimation180 blog to a culinary wonder some refer to as “meat candy.”  Even our vegan teacher felt compelled to engage us with these estimates.  (She says it is for the sake of the learning.)

Second, the time lapse videos of the cooking are pretty sweet.  Too bad the school internet wouldn’t stop buffering.  But nice touch, Mr. Stadel.  Nice touch.

A question:  Did you know that the percent decrease in length of bacon is 38% after cooking, but the percent decrease in width is only 23%?  We figured that out adapting your “percent error” formula to the uncooked/cooked bacon.  Do you have any initial thoughts about that discrepancy?  Is it bacon’s “fibrous” fat/meat striped makeup that allows it to shrink more in length than width, inch for inch?

Also, did you know that the percent decrease in time from the cold skillet to the pre-heated skillet is 29%?  That one was a little harder for us to calculate, because we figured out that we needed to convert the cooking times to seconds rather than minutes and seconds.

To summarize, we wanted to thank you, Mr. Stadel.  Our teacher tells us that you dedicate your time and energy to the estimation180 site so that WE don’t have to learn math out of a textbook.  We wanted to tell you that we appreciate it.  And the bacon.  We appreciate the homage paid to bacon.

Sincerely,

Mrs. Schmidt’s Math Class

St. Francis, MN

# When the Answer is E: He Falls Off the Roof and Breaks His Neck

Our annual state testing season is almost here. The juniors will partake in the Minnesota Comprehensive Assessments in Mathematics a week from Tuesday. Our department decided issuing a practice test to all of our juniors would help re-familiarize them with long lost skills. After distributing copies during our monthly staff meeting, I’m always curious if any teachers in other disciplines look at the practice materials. Much to my delight, the choir director approached me at lunch on Friday, test in hand.

Mr. Warren: Is this test just like the MCAs?
Me: Most likely similar. Why?
Mr. Warren: Ok, well look at this one.

Mr. Warren: I think the answer is E, Xai s going to fall and break his neck.

The conversation went on for another few minutes, with me agreeing  that what’s been called “math education” includes ignoring the context of situations and focusing on a procedure.  In fact, I was curious how many juniors who completed this practice test even noticed that the situation was outrageous.

Since we were running on a 2-hr delay schedule Friday, I thought it would be the perfect opportunity to present the problem to my algebra class. They are mostly juniors who have been continually frustrated with a mathematics curriculum that doesn’t make any sense in the real world.

Me: Read through this problem. Does it make sense?

Student: ok, it looks like 32.

I didn’t expect any of them to apply any trigonometry, so I thought we needed to approach the problem differently.  In fact, I wasn’t even concerned about the angle measure.  I wanted them to look at the scenario itself.

Me: Imagine this scenario. We’ve done a lot of estimating in here. We need to envision a 20-foot ladder, three feet away from a house. Does this seem reasonable?

Unfortunately, it did seem reasonable to most of them. I needed another approach.

Me: ok, how could we simulate this in classroom-scaled size?

Student: Get a ruler.

Me: Perfect. How close does it need to be to the wall?

After exploring multiple methods of calculating exactly how far, we arrived at 1.8 inches.  With as much drama as possible, I set the ruler against the wall, exactly 1.8 inches away.

Me:  Does this look like a ladder that any of you would want to stand on? (of course, a few did).  Keep in mind, this is a TWENTY foot ladder, not a 12 inch ruler.

Student:  Yea, I don’t think anyone is climbing up that ladder and coming down in one piece.

Another Student:  What if they had a spotter?

A spotter!  Now we’re talking.  To be honest, I have no idea if a spotter could hold a 20-foot ladder so that it could be placed three feet from the wall.  But now I’m interested to find out!

I know Mathalicious investigated a similar scenario using a claim from Governor Janet Napolitano.

In my mind, these are the questions that should be circulating Facebook and aggravating parents.  This is the kind of math that should rile up Glenn Beck and company.  Our state of Minnesota opted not to adopt the Common Core State Standards in Mathematics, but requiring this kind of math instead is what is actually dumbing down the curriculum.  It assumes that the real world doesn’t apply, only rote procedure does.  “Just figure out the answer, don’t question the situation,” is what kids read and do over and over when problems like this are solved without real context.  A richer classroom experience for both teachers and students comes when we ask students to assess the reasonableness of situations, create new scenarios that are more appropriate, and solve the new problems they develop.  The CCSS Standards for Mathematical Practice tell students that it’s vital that they “construct viable arguments and critique the reasoning of others.”  I don’t think “critique the reasoning of others” should be reserved for only reasoning created in the classroom.  I’d like my students to critique the reasoning of the creator of these types of problems and others like it that have been deemed a necessary component of high school math success.

Thank you, Mr. Warren for igniting the exciting conversation in my classroom.