Building
upon knowledge and skills gained in preceding
grades,
by the end of Grade 8, students will:
Standard 4.4
(Data
Analysis, Probability, and Discrete Mathematics)
All students will develop spatial sense and
the ability to use geometric properties, relationships,
and measurement to model, describe and analyze
phenomena.
Standard 4.4.8.A
Data
Analysis
Standard 4.4.8.A.1
Select
and use appropriate representations for sets of
data, and measures of central tendency (mean, median,
and mode).
· Type of display most appropriate for given
data
· Box-and-whisker plot, upper quartile, lower
quartile
· Scatter plot
· Calculators and computer used to record
and process information
· Finding the median and mean (weighted average)
using frequency data.
· Effect of additional data on measures of
central tendency
Standard 4.4.8.A.2
Make
inferences and formulate and evaluate arguments
based on displays and analysis of data.
Standard 4.4.8.A.3
Estimate
lines of best fit and use them to interpolate within
the range of the data.
Standard 4.4.8.A.4
Use
surveys and sampling techniques to generate data
and draw conclusions about large groups.
Standard 4.4.8.B
Probability
Standard 4.4.8.B.1
Interpret
probabilities as ratios, percents, and decimals.
Standard 4.4.8.B.2
Determine
probabilities of compound events.
Standard 4.4.8.B.3
Explore
the probabilities of conditional events (e.g., if
there are seven marbles in a bag, three red and
four green, what is the probability that two marbles
picked from the bag, without replacement, are both
red).
Standard 4.4.8.B.4
Model
situations involving probability with simulations
(using spinners, dice, calculators and computers)
and theoretical models.
· Frequency, relative frequency
Standard 4.4.8.B.5
Estimate
probabilities and make predictions based on experimental
and theoretical probabilities.
Standard 4.4.8.B.6
Play
and analyze probability-based games, and discuss
the concepts of fairness and expected value.
Standard 4.4.8.C
Discrete
Mathematics-Systematic Listing and Counting
Standard 4.4.8.C.1
Apply
the multiplication principle of counting.· Permutations:
ordered situations with replacement (e.g.,
number of possible license plates) vs. ordered
situations without replacement (e.g., number
of
possible slates of 3 class officers from a 23
student class)
· Factorial notation
· Concept of combinations (e.g., number of
possible delegations of 3 out of 23 students)
Standard 4.4.8.C.2
Explore
counting problems involving Venn diagrams with three
attributes (e.g., there are 15, 20, and 25 students
respectively in the chess club, the debating team,
and the engineering society; how many different
students belong to the three clubs if there are
6 students in chess and debating, 7 students in
chess and engineering, 8 students in debating and
engineering, and 2 students in all three?).
Standard 4.4.8.C.3
Apply
techniques of systematic listing, counting, and
reasoning in a variety of different contexts.
Standard 4.4.8.D
Discrete
Mathematics–Vertex-Edge Graphs and Algorithms
Standard 4.4.8.D.1
Use vertex-edge graphs and algorithmic thinking
to represent and find solutions to practical problems.
· Finding the shortest network connecting
specified sites
· Finding a minimal route that includes every
street (e.g., for trash pick-up)
· Finding the shortest route on a map from
one site to another
· Finding the shortest circuit on a map that
makes a tour of specified sites
· Limitations of computers (e.g., the number
of routes for a delivery truck visiting n sites
is n!, so finding the shortest circuit by examining
all circuits would overwhelm the capacity of
any computer, now or in the future, even if n is less
than 100)
