Download Overview of CCSS Statistics and Probability

Overview of CCSS
Statistics and Probability
Math Alliance
September 2011
CCSS Focus
• Key ideas, understandings, and skills are
identified.
• Deep learning of concepts is emphasized.
– That is, adequate time is devoted to a topic to
counter the “mile wide, inch deep” criticism
leveled at most current U.S. standards.
CCSS Standards for
Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of
others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
NCTM Process Standards and the
CCSS Mathematical Practice Standards
NCTM Process Standards
CCSS Mathematical Practices
Problem Solving
Make sense of problems and persevere
in solving them.
Use appropriate tools strategically
Reasoning and Proof
Reason abstractly and quantitatively.
Critique the reasoning of others.
Look for and express regularity in
repeated reasoning
Communication
Construct viable arguments
Connections
Attend to precision.
Look for and make use of structure
Representations
Model with mathematics.
Common Core Organization
K-8
High School
Grade
Conceptual Category
Domain
Domain
Cluster
Cluster
Standards
(No pre-K Common Core Standards)
Standards
Common Core - Domain
• Overarching “big ideas” that connect
topics across the grades
• Descriptions of the mathematical content
to be learned, elaborated through clusters
and standards
Common Core - Clusters
• May appear in multiple grade levels with
increasing developmental standards as
the grade levels progress
• Indicate WHAT students should know and
be able to do at each grade level
• Reflect both mathematical understandings
and skills, which are equally important
Common Core - Standards
• Content statements
• Progressions of increasing complexity
from grade to grade
CCSSM Domains
CCSSM-Grade 6
1. Ratio and
proportional
Relationships
2. The Number
System
3. Expressions
& Equations
4. Geometry
5. Statistics and
Probability
CCSSM-Grade 7
CCSSM-Grade 8
1. Ratio and
proportional
Relationships
2. The Number
System
3. Expressions &
Equations
4. Geometry
5. Statistics and
Probability
1. Functions
2. The Number
System
3. Expressions &
Equations
4. Geometry
5. Statistics and
Probability
Grade 5 Measurement & Data
Represent and interpret data.
2. Make a line plot to display a data set of
measurements in fractions of a unit (1/2,
1/4, 1/8). Use operations on fractions for
this grade to solve problems involving
information presented in line plots.
Grade 6 Statistics & Probability
Develop understanding of statistical
variability.
•
•
•
1. Recognize a statistical question as one that anticipates variability in the
data related to the question and accounts for it in the answers. For example,
“How old am I?” is not a statistical question, but “How old are the students in
my school?” is a statistical question because one anticipates variability in
students’ ages.
2. Understand that a set of data collected to answer a statistical question
has a distribution which can be described by its center, spread, and overall
shape.
3. Recognize that a measure of center for a numerical data set summarizes
all of its values with a single number, while a measure of variation describes
how its values vary with a single number.
Grade 6 Statistics & Probability
Summarize and describe distributions.
4. Display numerical data in plots on a number line, including dot plots, histograms,
and box plots.
5. Summarize numerical data sets in relation to their context, such as by:
• Reporting the number of observations.
• Describing the nature of the attribute under investigation, including how it was
measured and its units of measurement.
• Giving quantitative measures of center (median and/or mean) and variability
(interquartile range and/or mean absolute deviation), as well as describing any
overall pattern and any striking deviations from the overall pattern with reference
to the context in which the data were gathered.
• Relating the choice of measures of center and variability to the shape of the
data distribution and the context in which the data were gathered.
Grade 7 Statistics & Probability
• Use random sampling to draw inferences about
a population.
• Draw informal comparative inferences about
two populations.
• Investigate chance processes and develop, use,
and evaluate probability models.
8th Grade Statistics Domain
Investigate patterns of association in
bivariate data.
1. Construct and interpret scatter plots for
bivariate measurement data to investigate
patterns of association between two
quantities. Describe patterns such as
clustering, outliers, positive or negative
association, linear association, and
nonlinear association.
8th Grade Statistics Domain
2. Know that straight lines are widely used to
model relationships between two
quantitative variables. For scatter plots
that suggest a linear association,
informally fit a straight line, and informally
assess the model fit by judging the
closeness of the data points to the line.
8th Grade Statistics Domain
3. Use the equation of a linear model to
solve problems in the context of bivariate
measurement data, interpreting the slope
and intercept.
8th Grade Statistics Domain
4. Understand that patterns of association
can also be seen in bivariate categorical
data by displaying frequencies and relative
frequencies in a two-way table. Construct
and interpret a two-way table summarizing
data on two categorical variables collected
from the same subjects. Use relative
frequencies calculated for rows or columns
to describe possible association between
the two variables.