Lake Levels: Variation from full
The table presented here is from the Angling column of the newspaper and refers to lake levels in central Tasmania. It is interesting because of the manner in which the data, the lake levels, are presented.
When presented with a data set, the first thing students must do is appreciate what it represents and how this is done. Notice that at the top of the table it says, "Water - Minus Metres". Glancing down the table, the only mathematical symbols used besides numbers and decimal points are plus signs. The convention in this table is that negative values appear with NO sign, while positive values appear with a "+" sign. This is the opposite convention to that which we are used to in mathematics. Hence students working out a way to graph the data, need to think carefully about how to go about the task. In fact, this is a very good exercise to set - it may be helpful for students to visualise lake levels in relation to a zero and plot values or draw bars above and below a horizontal axis.
This is also a good exercise when introducing negative numbers in the mathematics curriculum. Another interesting discussion point is related to our intuitive understanding of the word "full" which we would intuitively associate with the value zero since the headline indicates that the values in the table are "variations from full". People old enough to have studied comparative and superlative degrees for adjectives may recall being given the trick question to grade "full". The correct answer is, of course, "full, full, full", not "full, fuller, fullest". The assumption is that if something is full in the first place it cannot become any "fuller". But what about these lakes in Tasmania? There were seven lakes "fuller" than full with Lake Rowallan the "fullest" of all. It must be that authorities define a level of water to be "full" which is not the actual capacity of the lake. Hence it is possible to have these positive (+) values before lakes overflow. In this context, the scientific definition of full does not match the literary one.
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