For an entire year, I’ve been anticipating our family’s return to Stade’s Shades of Autumn Festival.  My excitement has been building for one reason:  To estimate the amount of corn contained in their corn play area (or the Corn Sandbox as my 4 year-old has named it).

We went last Friday, armed with a measuring tape and a measuring cup.  The sign seemed to give away the answer of 800 bushels, but I wasn’t satisfied given that their was no mathematics to back up their claim.  We needed to attend to precision. Here are some of the photos I took:

My favorite is the bottom photo, my parents counting kernels of corn in 1 cup. (There are 579, by the way)

I love when I present a problem to my class, and it takes longer than I anticipate for them to solve. There was supposed to be time for solving inequalities for the group that worked with this, but that will just have to wait until tomorrow.  I’m sure they were crushed.

The essential question we wanted to answer was:  How many kernels of corn are there in this corn sandbox?

Initial estimates were very low.  I let them revise after I revealed that 1 cup contained 579 kernels.

One approach:  Use the number of bushels to calculate kernels.

After looking up on Wolfram Alpha that 1 bushel = 9.31 gal, we determined that a reasonable calculation of the number of kernels, based on our 1 cup count, was 69,000,000.

Second Approach:  Use the volume of the enclosure to calculate kernels.

This was a little trickier given the irregular shape of the sandbox.  Numerous calculations and conversions later, we arrived at 81,667,931 kernels of corn.

We were uncomfortable with the over 12 million kernel discrepancy between our two methods.  It remains unclear which is more accurate given the fact that one includes actual measurements and assumptions and the other is provided by the farm.  Perhaps Stade’s Farm should expect a call from Mrs. Schmidt’s 2nd hour Algebra 2 class in the near future to clear this up.

Steven Leinwand has a huge influence on how I approach a math lesson.  In my experience, one of the easiest ways math can be extrapolated from almost any task is by asking the questions:  How big? How far? and How Much?

This weekend, I came across this picture on social media, posted by David Roberts:

Of course the question I asked first was “How big is that tarp!?”

Luckily, David was willing to make an estimate and allowed me to share his reasoning:

I thought it might be interesting to present the photo to my first hour and see what questions they would ask about the photo.  Of course, the surface area of the tarp was on their list.

The original article including the photo added more depth to their questions.  As it turns out, the house is being fumigated after a spider infestation.  It seems as though their curiosity surrounded more the spiders than the tarp and legitimately so.  (The article estimates the house was infested with approximately 5,000 spiders)

I was pleased that my students used visual cues in the photo to make their estimates including the average height of a story of a house, the approximate height of the man in the photo, and the size of the window.  Luckily, we found another photo that gave us a better understanding of how much tarp was needed for the other side of the house.

I’m glad this man’s golf game was not disturbed by a spider problem in the distance.  (sarcasm)

Anyway, after making some calculations, my industrial-minded first hour realized that this type of tarp must have a somewhat standard size.  After doing some Google searching and actually calling one of the companies that manufactures these behemoth plastic coverings (authentic!  Yes!), they decided that there were four 84′ x 25′ tarps covering the house and the space surrounding it. (We were able to have a nice conversation about how multiplying each dimension by 4 was different that multiplying the area of the tarp by 4.)

In the end, their estimate was 8,500 square feet, approximately double of what David had estimated.  We then critiqued David’s argument and decided that based on the picture only, his calculations were reasonable.  Because we were able to dig for more information, my class believes that their estimate may be a tad more accurate.  Thanks, David for sparking our curiosity this morning.

I’ve heard this said a thousand different ways:  a task does not need to apply to the real world in order to be engaging.  Dan Meyer’s version seems to be thrown around most often:  The “real world” isn’t a guarantee of student engagement. Place your bet, instead, on cultivating a student’s capacity to puzzle and unpuzzle herself.

Today is Homecoming Friday.  It’s tough to get students engaged today, as their minds are on the game and the glitter (oh, the glitter).

Here’s a very short video clip of the noise level in my Algebra class.  Crickets.

No, I’m not giving a test.  I gave them a puzzle called Quadruple Sudoku:

In short, besides regular Sudoku rules applying, the four small numbers are clues as to what goes into the boxes touching them.

And both classes, all period, the brain sweat was palpable.  Why, on such a wild, exciting school day would these kids be so focused and so engaged?  The answer I come up with every time is puzzling and unpuzzling.  

By the way, Nrich has tons of these fun, puzzling, engaging variations on Sudoku.  Check them out.