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Mathematics Statistics and Probability

Common Core Standards

Mathematics: Statistics and Probability

In Statistics and Probability, instructional time should focus on four major areas: (1) determining what methods to employ when collecting data and understanding if the data being collected is categorical or quantitative; (2) analyzing the data gathered to determine trends in the data, what the center of the data is, or the data spread and using this information to represent data in plots or tables; (3) calculating the probability of an event occurring and developing an understanding of independent and conditional probabilities; (4) performing inference analysis on data to determine the validity of data and making appropriate decisions based on that analysis.
Sophia and Common Core Standards
Our Many Ways to Learn method makes it easy to integrate the new standards into your teaching. By using multiple instructors and teaching styles for each tutorial, we make sure you're reaching your students, so they can reach their goals.
Note: Our Common Core-aligned content is middle and high school-focused. We're continually expanding our library, so stay tuned - more great content coming soon.

S.ID - Interpreting Categorical and Quantitative Data

Summarize, represent, and interpret data on a single count or measurement variable
Code
Standard
Concepts
S.ID.1
Represent data with plots on the real number line (dot plots, histograms, and box plots).
13
S.ID.2
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
6
S.ID.3
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
8
S.ID.4
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
10
S.ID.5
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
1
S.ID.6a
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
3
S.ID.6b
Informally assess the fit of a function by plotting and analyzing residuals.
1
S.ID.6c
Fit a linear function for a scatter plot that suggests a linear association.
4

S.CP - Conditional Probability and the Rules of Probability

S.MD - Using Probability to Make Decisions

Calculate expected values and use them to solve problems
Code
Standard
Concepts
S.MD.1
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
4
S.MD.2
(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
1
All five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.
Code
Standard
Concepts
Use probability to evaluate outcomes of decisions
Code
Standard
Concepts