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The Genes of Gilgamesh

Age 14 to 16
Challenge Level

Why do this problem?

This is an interesting, quick question for use whilst studying genetics and will draw the learners in to the mathematical issues surround inheritance and fractions.

Possible approach

Discuss the question before attempting a detailed solution. Some students might see it as possible to make (GGM), others might see it as impossible. The challenge will be in explaining clearly why this is or is not the case. Do not allow students to get away with saying 'it is obvious' one way or the other. A full explanation will require clear reasoning, and this should be encouraged. Help by asking 'why is it obvious?' Part of the subtlety will be that the parents, grandparents and other generations could be made from a variety of mixes of (GM). Students will need to be clear that they have considered this point.

Key questions

  • Do you think that it is possible to make (GGM)?
  • What other ratios (e.g. GGGGMM) would be equivalent to (GGM)?
  • What possible fractions would be within 1% of (GGM)?

Possible extension

  • Generally speaking, starting from a stock of pure G and pure M, can you determine thestock of all possible descendants?
  • Can students invent a similar question of their own?

Possible support

Students struggling to get started could be asked directly to work out possible great-grandparents for (GM), (GGGM), (GGGGGGGM)