| Modeling Growth over periods |
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To introduce the concept of doubling as a function of time.
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| Overview of lesson |
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Bacteria and yeast double by the process of binary fission, but not all microbes double at the same period of time. We prompted students to think about how different periods of time between doublings affect the results of the basic doubling model. If one population of cells doubles every 30 minutes and another population of cells doubles every hour, how would the two populations differ at the end of a given period of time? Using drawings, tables, graphs, and equations, students discussed the effect of doubling time on the model. Before beginning their investigation, students were asked to predict the effect of time on doubling.
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| Children's thinking during lessons |
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| Modeling growth over periods with tables |
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The students were split into groups. Group #1 was assigned to see how many cells there would be after 4 hours, if doubling occurs every 30 minutes. Group #2: every 60 minutes. Group #3: every 120 minutes Group #4: every 180 minutes. Some of the students in group #4 (every 180 minutes) decided to extend their time course to >240 minutes.
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Number of cells |
Time(minutes) |
Dubling every 30 minutes |
Dubling every 60 minutes |
Dubling every 120 minutes |
Dubling every 180 minutes |
0 |
1 |
1 |
1 |
1 |
30 |
2 |
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60 |
4 |
2 |
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90 |
8 |
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120 |
16 |
4 |
2 |
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150 |
32 |
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180 |
64 |
8 |
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2 |
210 |
128 |
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240 |
256 |
16 |
4 |
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Most students were surprised at how small changes in doubling period(30 min. differences) had great effects on population growth. Students used the data in the tables to compare the effect of different doubling times on population growth. Students concluded that populations of cells that had faster doubling periods increased their population faster.
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| Modeling growth over periods with graphs |
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Students graphically represented the doubling model over time. By graphing population size at each interval, students understood that the shape of the line generally remains the same, but the rate at which the populations grow is different. Students' concluded that their initial predictions about time and doubling were on target.
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| Go to the related big ideas |
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