Monday, June 29, 2015

100,000 Times

I saw a commercial in which someone said, "My heart beats one hundred thousand times a day." I thought that sounded a little high. So in a week and a half it would beat a million times. That seemed high as well. We should check that out.

Sometimes students just aren't sure how to get started. One thing that can help to look at the labels. For example ,if someone wants to find out miles per hour, the label mi/hr would imply one would divide miles by hours. If someone had traveled at 23 miles per hour for 1.3 hours, how far would they go? The labels work out if the miles per hour quantity is multiplied by the number of hours. The labels would be (mi/hr) x (hr/1). The hours cancel leaving us with miles, just like we want.

Suppose a student wants to see if the 100,000 value is plausible, but has no idea how to begin. One could start with just looking at the labels and see if that works out. The Mayo Clinic says normal is somewhere between 60 and 100 beats per minutes. That is a pretty broad range. I have heard 72 in the past, so let's go with that. We want to see a final answer that is in beats per day. So the student is starting with beats per minute and we want to end up with beats per day. How do we get there? Hopefully they can see that 60 beats per minute will bridge that gap.

                    72 beats/min x 60 min/hr x 24 hours/day
                         = 72 beats/min x 60 min/hr x 24 hours/day
                         = 103,680 beats per day

Nicely done.

What number of beats per minute would correspond to 100,000 beats per day? As in the last problem, we can examine labels. This is not the only way, and not even necessarily the best way, but for some students it might make the most sense.

So we start with 100,000 beats per day and want to end up with so many beats per minute. We have to find some linking labels to get from one to the other. We have to fill in the blanks for:  100,000 beats/day x ?????? = x beats/min

                   100,000 beats/day x ?????? = B beats/min
                   100,000 beats/day x day/24hr x hr/60 min = B beats/min          
                   100,000 beats/day x day/24hr x hr/60 min = B beats/min
                            B = 69.444... beats per minute