Inside the facility there is a lot of repetition: white
walls, red trim, locked doors, and many ceiling vents. The monotony can be a
bit tiresome when you spend all day inside. This summer I invited a few classes
to explore this monotony with me. Equipped with iPads we walked up and down the halls,
into units, pods, classrooms, and staircases in search of the extraordinary.
Our goal was simple, to take interesting photographs and transform them into
mathematics problems.
One student’s photo was a bit less than extraordinary. Actually
it was really ordinary. I want to share that one today to illustrate how a simple concept can be explored.
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| The Ceiling Vent |
The student was interested in knowing how many tiny squares precisely comprised this ceiling vent. 100? 500? 1000? More? Now this type of question might seem quite elementary. Just
count the amount of squares in the width and height, then multiply, but that’s
not how we roll.
Instead we came up with a rule for this problem. No counting!
Since the student had been studying ratios, we thought it would be interesting to measure the width of one cell, and then measure the width of the entire vent and divide. We accomplished this task using the GeoGebra software on our Macbooks. We then applied the same strategy to the height. Given these two numbers, we could finally multiply them to discover how many squares comprise this vent.
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| Geogebra Analysis |
In addition to determining the amount of squares, we were also able to determine whether this vent is actually a square by our measurements.
Now if we had just stopped here it probably would have been a good day's math class, but again we are always looking to go the extra mile. Answer in hand, we took to the halls and surveyed staff and residents alike for an estimate of how many squares are actually in the ceiling vent. We developed averages, ranges, and medians to analyze how good our local population is at estimation.
It's amazing how such a simple photograph led to another interesting day in mathematics class.
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