Fatal sheep disease

This article offers several opportunities for assessing numeracy skills in an applied setting. The example may be particularly interesting to students in rural schools, although it could be used in conjunction with some social science topics anywhere.

An interesting exercise would be to let students devise their own problems (with answers) and then let other member of the class solve them. Calculators are an obvious resource to use with such exercises so that a focus can be on meaning rather than operations such as long division. Examples of questions range from very straight forward to quite complex.

  1. From paragraph one, what is the average number of sheep destroyed by each of the 24 farmers? [Discuss the rounding necessary to get a reasonable estimate.]
  2. From paragraphs two and three, what is the minimum number of sheep which could be destroyed with the compensation money? What assumptions have to be made? [If all are rams, then $1,000,000 / $100 = 10,000 rams.]
  3. From the same information, what is the maximum number of sheep which could be destroyed with the compensation money? Again what assumptions are needed? [If all are wethers or lambs, $1,000,000 / $15 = 66,667 wethers and lambs.]
  4. Within the range of values, what are reasonable numbers of sheep which could be destroyed with the compensation money? [The assumptions to be made here relate to the proportion or fraction of the sheep which are in the four categories. This is a more complex but more interesting modelling problem which may lead to a rudimentary algebra problem. For example, if X represents all of the sheep, what are reasonable fractions in each category? Maybe [guess by city dweller!]:
  • 1/3 X = ewes,
  • 1/3 X = lambs (one each),
  • 1/3 X = wethers and rams, with 1/4 X wethers and 1/12 X = rams.

    • This would produce an equation:

  • $25 (1/3 X) + $100 (1/12 X) + $15 (1/3 X + 1/4 X) = $1,00,000 OR
  • X = 39344.26 or 39344 sheep.

    • Obviously many variations are possible!]

    Another interesting point for discussion for this article after some of the considerations above: return to the first paragraph's claim that 62,000 sheep had already been destroyed.

    1. What conclusions can be drawn about the likelihood of the government being able to pay compensation for those already destroyed?
    2. What questions might be asked?

    Where to next?

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