Why do this problem?
This problem is about flow charts, factors and prime
Teachers can present the flow chart to
students and ask
them to try to figure out what to do with it. A table of values can
be drawn on the board to collect results.
There won't be an obvious algebraic relationship emerging but this
might be a good opportunity to emphasise the need to look at the
underlying mathematics rather than just the values. Discussion with
the group can draw out comments and observations about what the
flow chart is doing.
Students can then be directed to the questions in the problem.
If the group hasn't had much experience of using flow charts, some
time could be set aside to discuss the merits of flow charts
(efficient, clear, unambiguous) and some of their drawbacks
(repetitive, tedious - try starting with a large prime number!).
Students can be asked to produce a flow chart that finds the
Highest Common Factor or Lowest Common Multiple of two inputs. Half
the class could work on the HCF while the other half works on the
LCM. They could then swap and test each other's flow charts.
Suggest to students that they use a table of values to keep
track of M, D and N as they change.