In mid-October, I attended the National WIDA Conference in Philadelphia, Pennsylvania. My colleagues and I took a long walk from the conference center to the "Rocky Steps" in front of the Philadelphia Museum of Art.
After walking for about an hour in the lovely fall weather, we stopped at the statue before the steps. Two of my colleagues checked their pedometers...and they showed completely different distances! How is it possible that two people could have walked different distances while walking side-by-side.
All 5 of us discussed this. "Well, maybe one of your fit-bits is broken, " was one suggestion. Another said, "And you ran to the store back there. Maybe that accounts for how much further you walked," but a friend interjected "She didn't take that many more steps to get there!"
A colleague of mine who loves solving puzzles chimed in: "Maybe it's the difference in your strides!" My two colleagues with pedometers looked interested. I suggested that we could use math (specifically multiplication) to see if stride length x steps could = distance. But how? Well, they could start at the same point on the sidewalk and count steps until their strides met again: the lowest common multiple of their stride length (we didn't have a tape measure or yardstick with us:)
Well, my coworker in purple, although it's hard to tell from the angle of this photograph, is about 4 inches shorter than my red-shirted friend. When they reunited in step, it was a ratio of 4:3. We all said or thought "Of course! Two people can walk the same distance together and it might seem like they've walked different distances if we consider their steps of equal distance. But since their strides are different, the number of steps taken by "purple" was much great than those taken by "red:" 4 steps for every 3 taken, to be exact.
From research, here's data that shows how their strides might compare:
A widely quoted estimate of stride length is 42 percent of height, although further research shows that ratio is only moderately accurate. Rough estimates of steps per mile based on a stride to height ratio are:
| Height | Steps per Mile |
| 4 feet 10 inches | 2,601 steps |
| 4 feet 11 inches | 2,557 steps |
| 5 feet even | 2,514 steps |
| 5 feet 1 inch | 2,473 steps |
| 5 feet 2 inches | 2,433 steps |
| 5 feet 3 inches | 2,395 steps |
| 5 feet 4 inches | 2,357 steps |
| 5 feet 5 inches | 2,321 steps |
| 5 feet 6 inches | 2,286 steps |
| 5 feet 7 inches | 2,252 steps |
| 5 feet 8 inches | 2,218 steps |
| 5 feet 9 inches | 2,186 steps |
| 5 feet 10 inches | 2,155 steps |
| 5 feet 11 inches | 2,125 steps |
| 6 feet even | 2,095 steps |
| 6 feet 1 inch | 2,067 steps |
| 6 feet 2 inches | 2,039 steps |
| 6 feet 3 inches | 2,011 steps |
| 6 feet 4 inches | 1,985 steps |
In the moment of asking and answering an "I wonder why...?" question out of the classroom and on vacation, I exclaimed "This is authentic math!" and wanted to document this one moment when math is used in real life.
I would love to try to go on a walk with some of my students (of varying heights) wearing pedometers (without mentioning the purpose), and have them lead their own mathematic inquiry about how the distances-walked afterward were so different! With hope, their dialogue around this could lead them to their own hypotheses and I, as facilitator, could guide them to the same test and reasoning that I came to with my colleagues. Math is understanding life, and multiplication fluency is an everyday tool are two mantras I want my students to take away from a year with me as their teacher.
Want to see an exemplary teacher explain how to draw students in with authentic math? Watch this!
