September 22, 2008 Page 33 of 60
6
Data Analysis &
Probability
Use probabilities to solve real-world
and mathematical problems;
represent probabilities using
fractions, decimals and percents.
6.4.1.1
Determine the sample space (set of possible outcomes) for a given
experiment and determine which members of the sample space are
related to certain events. Sample space may be determined by the use of
tree diagrams, tables or pictorial representations.
For example: A 6 6 table with entries such as (1,1), (1,2), (1,3), …, (6,6)
can be used to represent the sample space for the experiment of
simultaneously rolling two number cubes.
6
Data Analysis &
Probability
Use probabilities to solve real-world
and mathematical problems;
represent probabilities using
fractions, decimals and percents.
6.4.1.2
Determine the probability of an event using the ratio between the size of
the event and the size of the sample space; represent probabilities as
percents, fractions and decimals between 0 and 1 inclusive. Understand
that probabilities measure likelihood.
For example: Each outcome for a balanced number cube has probability
, and the probability of rolling an even number is
.
6
Data Analysis &
Probability
Use probabilities to solve real-world
and mathematical problems;
represent probabilities using
fractions, decimals and percents.
6.4.1.3
Perform experiments for situations in which the probabilities are known,
compare the resulting relative frequencies with the known probabilities;
know that there may be differences.
For example: Heads and tails are equally likely when flipping a fair coin,
but if several different students flipped fair coins 10 times, it is likely that
they will find a variety of relative frequencies of heads and tails.
6
Data Analysis &
Probability
Use probabilities to solve real-world
and mathematical problems;
represent probabilities using
fractions, decimals and percents.
6.4.1.4
Calculate experimental probabilities from experiments; represent them as
percents, fractions and decimals between 0 and 1 inclusive. Use
experimental probabilities to make predictions when actual probabilities
are unknown.
For example: Repeatedly draw colored chips with replacement from a
bag with an unknown mixture of chips, record relative frequencies, and
use the results to make predictions about the contents of the bag.
7
Number &
Operation
Read, write, represent and compare
positive and negative rational
numbers, expressed as integers,
fractions and decimals.
7.1.1.1
Know that every rational number can be written as the ratio of two
integers or as a terminating or repeating decimal. Recognize that π is not
rational, but that it can be approximated by rational numbers such as
and 3.14.