Teaching & Learning Plans - Project Maths

Teaching & Learning Plan 2: Probability and Relative Frequency
Student Learning Tasks: Teacher Input
»» What is different about this and the
outcomes for the fair die?
»» How might we find out the
probability?
Student Activities: Possible
and Expected Responses
• They are not all equally
likely.
• We might do a survey but
could only get estimated
values of the probability
as outcomes are not
equally likely.
Teacher’s Support and
Actions
»» Give students a minute
to discuss this in their
group and then ask
different groups. If
someone answers ‘yes’,
ask if anyone else has a
suggestion.
Checking
Understanding
»» Can students
distinguish between
‘equally likely ‘and
‘not equally likely’?
»» Can you think of other examples of
situations where the outcomes are
not equally likely?
• In horse racing – depends
on form, jockey, etc.
• 5 people going for an
interview do not all
have an equal chance of
getting the job.
»» Pose the question to
the class and take
answers as students put
up their hands.
»» Did students actively
participate in the
discussion, giving lots
of ideas and showing
understanding?
»» The last approach is known as
the ‘experimental ‘or ‘empirical
approach’ to calculating probabilities.
However, we did not calculate
probabilities but instead calculated
the relative frequencies – so what is
the connection with probability? Has
anyone got any ideas on this?
Note: (Students who may see the
connection need to be allowed say so).
»» What do you think would be the
value of the relative frequencies if we
did more and more trials?
• Loaded die , die with, say,
two 1’s and two 2’s, etc.
• Experiments give
estimates of theoretical
probability based on the
relative frequency of
each outcome. Relative
frequency tends towards
the probability as the
number of trials gets very
large.
• They would get closer and
closer to 1/6 and hence
would all be the same.
© Project Maths Development Team 2009 www.projectmaths.ie KEY: » next step and apply to all • student answer/response 10