“Dr. Crocker, I don’t get it. Why’d you take a point off for my answer? I’m sure that all my calculations are right.” Samantha, a nursing student, was red-faced.
Mathematical Thinking
“Well, let’s forget the calculations for a minute and just think about your answer logically. You say there were 10-5 bacteria present on the Petri dish. Does that make sense?”
“Yes, we did the dilutions right and everything, and those are the results we got.”
“Tell me, what does 10-5 mean?”
“Umm….oh, I remember! You said that you put a “1.” and move the decimal point back five times.”
“Okay, but what does that mean?”
“I don’t know what you’re asking.”
“Well, how does 10-5 translate into a fraction?”
Samantha’s lab partner joined in, “I know! It’s 1/100,000.”
How Tiny?
“That’s right. Now, is it possible to have 1/100,000 bacteria on a plate?”
“I think so,” pondered Samantha, “They’re very small.”
Now, I had to think. How could I help these students visualize what numbers mean in real life? “Let’s go over to the blackboard.” I drew a circle on the board. “Okay, show me the circle cut in half (1/2).”
Samantha drew a line down the center of the circle.
“Good. Now make it in quarters (1/4).”
Samantha did this, as well.
“Now make it in 100,000 pieces (1/100,000).”
Samantha laughed. “I can’t. They would be too small, and it would take too long.”
“So, how about if we were to cut a person into 100,000 pieces? Would that be possible? They’re bigger than the circle.”
They’re Goners
Samantha’s partner chimed in, “No, it would kill them.” Suddenly, understanding dawned on their faces. “Oh, so that’s why you can’t have 10-5 bacteria on a plate.”
“Yes, if you were to do that, you would have way less than one. The only way to do it would be to explode a bacterium, and then it would no longer be a bacterium.”
The girls nodded their understanding, so I decided to go a step further. “So, would it be possible to have 10-5 bacteria/ml?”
Samantha’s brow furrowed in thought, and she scribbled numbers on a piece of paper. Then she smiled, “Yes, but unless you had more than 100 liters of media, the bacterium would be very lonely.”
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