20771_Problem_solving_Year_6_Background_information_resources

INTRODUCTION
Each of the 9 equal parts represents $45 000, so each
great grandchild receives $5000.
Having tried an idea, the answer(s) and solution
need to be analysed in light of the problem in case
another solution or answer is needed. It is essential to
compare an answer back to the original analysis of the
problem to determine whether the solution obtained
is reasonable and answers the problem. It will also
raise the question as to whether other answers exist,
and if there may be other solution strategies. In this
way, the process is cyclic and should the answer be
unreasonable, then the process would need to begin
again.
If each great grandchild received $5000, then the
grandson received twice as much as the 3 great
grandchildren ($30 000). The grandmother received the
same as the grandson and three great grandchildren
(or $45 000 and another $3000). The total distributed
is $93 000. Looking back at the problem we see that
this is correct and that the diagram has provided a
direct means to the solution that has minimised and
simplified the calculations.
Having tried an idea, an answer needs to be analysed
in the light of the problem in case another solution is
required. It is essential to compare an answer back
to the original analysis of the problem to determine
whether the solution obtained is reasonable and
answers the problem. It will also raise the question
as to whether other answers exist, and even whether
there might be other solution strategies. In this
way the process is cyclic and should the answer be
unreasonable, then the process would need to begin
again.
We believe that Peta took $180 to shop with. She
spent half (or $90) on a dress, leaving $90. She spent
one-third of the $90 on sandals ($30), leaving $60.
Looking again at the problem, we see that this is
correct and the diagram has provided a direct means
to the solution that has minimised and simplified the
calculations.
Thinking about how the various ways this problem
was solved highlights the key elements within the
problem-solving process. When starting the process,
it is necessary to analyse the problem to unfold its
layers, discover its structure and what the problem
was really asking. Next, all possible ways to solve the
problem were explored before one, or a combination
of ways, was/were selected to try. Finally, once
something was tried, it was important to check
the solution in relation to the problem to see if the
solution was reasonable. This process highlights the
cyclic nature of problem-solving and brings to the fore
the importance of understanding the problem (and
its structure) before proceeding. This process can be
summarised as:
A plan to manage problem-solving
This model for problem-solving provides students with
a means of talking about the steps they engage with
whenever they have a problem to solve: Discussing
how they initially analysed the problem, explored
various ways that might provide a solution, and then
tried one or more possible solution paths to obtain
a solution—that they analysed for completeness and
sense making—reinforces the very methods that will
give them success on future problems. This process
brings to the fore the importance of understanding the
problem and its structure before proceeding.
Further, returning to an analysis of any answers
and solution strategies highlights the importance
of reflecting on what has been done. Taking time to
reflect on any plans drawn up, processes followed and
strategies used brings out
the significance of coming
to terms with the nature
of the problem, as well as
the value and applicability
of particular approaches
that might be used with
other problems. Thinking
of how a related problem
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