20771_Problem_solving_Year_6_Background_information_resources

INTRODUCTION
A farmer had emus and alpacas in one paddock.
When she counted, there were 38 heads and 100
legs. How many emus and how many alpacas are
in the paddock?
There are 38 emus and alpacas. Emus have 2 legs.
Alpacas have 4 legs.
Number of
alpacas
Number of
emus
There are 12 alpacas and 26 emus.
Number of legs
4 34 84 – too few
8 30 92 – too few
10 28 96 – too few
12 26 100
As more experience in solving problems is gained, an
ability to see patterns in what is occurring will also
allow solutions to be obtained more directly and help
in seeing the relationship between a new problem
and one that has been solved previously. It is this
ability to relate problem types, even when the context
appears to be quite different, that often distinguishes
a good problem-solver from one who is more hesitant.
Building a problem-solving process
While the teaching of problem-solving has often
centred on the use of particular strategies that could
apply to various classes of problems, many students
are unable to access and use these strategies to solve
problems outside of the teaching situations in which
they were introduced. Rather than acquire a process
for solving problems, they may attempt to memorise
a set of procedures and view mathematics as a set of
learned rules where success follows the use of the
right procedure to the numbers given in the problem.
Any use of strategies may be based on familiarity,
personal preference or recent exposure rather than
through a consideration of the problem to be solved.
A student may even feel it is sufficient to have only
one strategy and that the strategy should work all of
the time; and if it doesn’t, then the problem ‘can’t be
done’.
In contrast, observation of successful problem-solvers
shows that their success depends more on an analysis
of the problem itself—what is being asked, what
information might be used, what answer might be
likely and so on—so that a particular approach is used
only after the intent of the problem is determined.
Establishing the meaning of the problem before any
plan is drawn up or work on a solution begins is
critical. Students need to see that discussion about
the problem’s meaning, and the ways of obtaining a
solution, must take precedence over a focus on ‘the
answer’. Using collaborative groups when problemsolving,
rather than tasks assigned individually, is an
approach that helps to develop this disposition.
Looking at a problem and working through what is
needed to solve it will shed light on the problemsolving
process.
Great Grandma
Jean left $93 000 in
her will. She asked
that it be shared
out so that each
of her three great
grandchildren
received the same
amount, their
father (her grandson) twice as much as the three
grandchildren together, and to her daughter (the
children’s grandmother) $3000 more than the
father and great grandchildren together. How
much does each get?
Reading the problem carefully shows that Great
Grandma left her money to her daughter, grandson
and three great grandchildren. She arranged her
will so that her daughter was given $3000 before
the remaining $90 000 was distributed so that the
amounts given to the grandson is twice that given to
her great grandchildren, while the amount she gets
is equal to the sum given to all the others. All of the
information to solve the problem is available and no
further information is needed. The question at the
end asks how much money each gets, but really the
problem is how the money was distributed among all
the beneficiaries of her will.
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Problem-solving in mathematics www.ricpublications.com.au R.I.C. Publications ®