Data Analysis & Probability
National Council of Teachers
of Mathematics
Standards 2000
URL: http://standards.nctm.org/document/chapter6/data.htm
For all grades, NCTM standards focus
on students being able to: "Formulate questions
that can be addressed with data and collect, organize,
and display relevant data to answer them; select
and use appropriate statistical methods to analyze
data; develop and evaluate inferences and predictions
that are based on data; understand and apply basic
concepts of probability ."
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In grades 6–8 all students should— |
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formulate questions, design studies,
and collect data about a characteristic
shared by two populations or different
characteristics within one population;
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select, create, and use appropriate
graphical representations of data, including
histograms, box plots, and scatterplots; |
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discuss and understand the correspondence
between data sets and their graphical
representations, especially histograms,
stem-and-leaf plots, box plots, and
scatterplots; |
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use proportionality and a basic understanding
of probability to make and test conjectures
about the results of experiments and
simulations.
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Rock, Paper, Scissors I-IV
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The Problem: Students predict the
"fairness" of a rock, paper, scissors
game given increasingly complex constraints.
Where's the Math: Students develop
an understanding of probability through
dynamic simulation, graphing and ratio calculation.Students
make predictions and generalizations and
offer explainations for a variety of conditions.
NCTM Standards: Data analysis and probability,
number & operations
Components: AgentSheets, simple
graph, text entry, button panel, ESCOT labels,
number entry
Rock, Paper, Scissors
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Click on the links above to learn more about
the problem series, the math involved, sample
solutions, and developers' assessment
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Fish Farm II
(click on image for larger view)
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The Problem: Students collect data
on randomly chosen fish from a pond. Using
this data, they try to determine the ratio
of male fish to female fish in the pond.
Where's the Math: By using this
problem, students can experiment with different
data collection methods (large sample size
with few trials, small sample size with
many trials, etc.) and investigate the accuracy
of these methods. The bonus question also
deals with the concept of expected value.
NCTM Standards: Number
& operations, data
analysis & probability
Components: AgentSheets, number
entry field, swing slider, button panel,
Pie Chart, data recorder, table, Evaluator, Guarded Action
Learn
more about the problem, the math
involved, sample solutions, and developers'
assessment
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