h
Statistics and Probability Concepts: The
student creates and uses models of probability and understands the
role of assumptions.
i
Statistics and Probability Concepts: The
student uses concepts such as equally likely, sample space, outcome,
and event in analyzing situations involving chance.
j
Statistics and Probability Concepts: The
student constructs appropriate sample spaces, and applies the addition
and multiplication principles for probabilities.
The student
listed the faces of the dice in the experiment and constructed a
6x6 model, which the student referred to as a rug, to generate the
sample space, i.e., the 36 possible outcomes for the rolling of
the dice.
l
Statistics and Probability Concepts: The student chooses an appropriate
probability model and uses it to arrive at a theoretical probability
for a chance event.
From
the model, the student counted the number of ways each possible
sum could occur, then listed the probability for each sum.
Next, the
student used the probability for rolling a sum of “8”
(),
to answer part (a) of the task. The explanation is not completely
explicit; the student explains the meaning of the 36 in the denominator
but not the 4 in the numerator. However, knowledge of the concept
is evident in the model of the sample space and the listing of the
probabilities for each sum.
The student
went on to answer part (b) of the task by comparing the probabilities
for each sum and found that the probabilities for rolling a “5”
or a “6” were equal ()
and the chances were greater for rolling those sums than other sums
with smaller probability ratios.
b
Problem Solving and Mathematical Reasoning:
Implementation. The student selects appropriate mathematical concepts
and techniques from different areas of mathematics and applies them
to the solution of the problem.
The student
had to formulate an approach that worked. The student modeled the
complete sample
space using a clearly labeled and accurate table, then used the
sample space to calculate the probability of each event occurring
c
Mathematical Communication: The student
organizes work and presents mathematical procedures and results
clearly, systematically, succinctly, and correctly.
The student presented an orderly approach to the problem, explained
the steps of the solution process clearly and concisely, and arrived
at a result that is correct.
