New Common Core Standards: Content Standard(s):
Quantities N -Q Reason quantitatively and use units to solve problems.
- Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
- Define appropriate quantities for the purpose of descriptive modeling.
- Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
- Modeling: When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data.
Interpreting Categorical and Quantitative Data S-ID Summarize, represent, and interpret data on two categorical and quantitative variables
- 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.
- Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
a. 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.
b. Informally assess the fit of a function by plotting and analyzing residuals.
c. Fit a linear function for a scatter plot that suggests a linear association.Interpret linear models
- Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- Compute (using technology) and interpret the correlation coefficient of a linear fit.
- Distinguish between correlation and causation.
NCTM Standards and Expectations:
- Use graphs to analyze the nature of changes in quantities in linear relationships.
- Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.Algebra 9-12Use symbolic algebra to represent and explain mathematical relationships.
- Approximate and interpret rates of change from graphical and numerical data.
Data Analysis & Probability 6-8
- Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.
- Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.
Data Analysis & Probability 9-12
- Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled.