Students will:

• Formulate investigative questions that require the collection or acquisition of bivariate data, where exactly two of the variables are quantitative.
• Collect or acquire bivariate data from a representative sample to answer an investigative question. 
• Represent bivariate data with a scatterplot using technology and describe how the variables are related in terms of the given context. 
• Make predictions, decisions, and critical judgments using data, scatterplots, or the equation(s) of the mathematical model.
• Formulate questions that can be addressed with data and assess the type of data relevant to the question (e.g., quantitative versus categorical).
• Investigate, describe, and determine best sampling techniques, such as simple random sampling, stratified sampling, and cluster sampling. 
• Plan and conduct an experiment and/or observational study. The experimental design should address control, randomization, and minimization of experimental error. 
• Collect or acquire data to answer a statistical question. 
• Recognize that data may contain errors, have missing values, or may be biased, and make decisions about how to account for these issues. 
• Identify biased sampling methods. 
• Given a plan for an observational study, identify possible sources of bias, and describe ways to reduce bias.
• Select, create, and use appropriate visual representations of data to brainstorm solutions. 
• Use appropriate statistical methods to analyze data.
• Communicate the description of an experiment and/or observational study, the resulting data, analysis, and the validity of the conclusions.

Students will:

• Determine the domain and range of a function given a graphical representation, including those limited by contexts. 
• Identify intervals on a graph for which a function is increasing, decreasing, or constant.
• Given a graph, identify the location and value of the absolute maximum and absolute minimum of a function over the domain of a function. 
• Given a graph, determine the zeros and intercepts of a function. 
• Describe and recognize the connection between points on the graph and the value of a function. 
• Describe the end behavior of a function given its graph. 
• Identify horizontal and/or vertical asymptotes from the graph of a function, if they exist. 
• Describe and relate the characteristics of the graphs of linear, quadratic, exponential, and piecewise-defined functions, including those in contextual situations.

Students will:

• Represent and interpret contextual problems requiring optimization with systems of linear equations or inequalities. 
• Solve systems of no more than four equations or inequalities graphically and when appropriate, algebraically. 
• Identify the feasible region of a system of linear inequalities. 
• Identify the coordinates of the vertices of a feasible region. 
• Determine and describe the maximum or minimum value for the function defined over a feasible region. 
• Interpret the validity of possible solution(s) algebraically, graphically, using technology, and in context and justify the reasonableness of the answer(s) or the solution method in context.

Students will:

• Determine the domain and range of a function given a graphical representation, including those limited by contexts. 
• Identify intervals on a graph for which a function is increasing, decreasing, or constant. 
• Given a graph, identify the location and value of the absolute maximum and absolute minimum of a function over the domain of a function. 
• Given a graph, determine the zeros and intercepts of a function. 
• Describe and recognize the connection between points on the graph and the value of a function.
• Describe the end behavior of a function given its graph. 
• Identify horizontal and/or vertical asymptotes from the graph of a function, if they exist. 
• Describe and relate the characteristics of the graphs of linear, quadratic, exponential, and piecewise-defined functions, including those in contextual situations.

Students will:

• Determine the domain and range of a function given a graphical representation, including those limited by contexts. 
• Identify intervals on a graph for which a function is increasing, decreasing, or constant. 
• Given a graph, identify the location and value of the absolute maximum and absolute minimum of a function over the domain of a function. 
• Given a graph, determine the zeros and intercepts of a function. 
• Describe and recognize the connection between points on the graph and the value of a function.
• Describe the end behavior of a function given its graph. 
• Identify horizontal and/or vertical asymptotes from the graph of a function, if they exist. 
• Describe and relate the characteristics of the graphs of linear, quadratic, exponential, and piecewise-defined functions, including those in contextual situations.

Students will:

• Identify graphs and equations of parent functions for linear, quadratic, and exponential function families. 
• Describe the transformation from the parent function given the equation or the graph of the function. 
• Determine and analyze whether a linear, quadratic, or exponential function best models a given representation, including those in context. 
• Write the equation of a linear, quadratic, or exponential function, given a graph, using transformations of the parent function. 
• Use a graphical or algebraic representation of a function to solve problems within a context, graphically and algebraically, when appropriate. 
• Graph a function given the equation of a function, using transformations of the parent function. Use technology to verify transformations of functions. 
• Compare and contrast linear, quadratic, and exponential functions using multiple representations (e.g., graphs, tables, equations, verbal descriptions)

Students will:

• Analyze, interpret, and make predictions based on theoretical probability. 
• Calculate conditional probabilities for dependent, independent, and mutually exclusive events. 
• Represent and calculate probabilities using Venn diagrams, probability trees, organized lists, two-way tables, simulations, or other probability models. 
• Interpret probabilities from simulations or experiments to make informed decisions and justify the rationale. 
• Define and give contextual examples of complementary, dependent, independent, and mutually exclusive events. 
• Given two or more events in a problem setting, determine whether the events are complementary, dependent, independent, and/or mutually exclusive. 
• Compare and contrast permutations and combinations, including those in contextual situations. 
• Calculate the number of permutations of n objects taken r at a time, without repetition. 
• Calculate the number of combinations of n objects taken r at a time, without repetition. 

Students will:

• Identify and describe the properties of a normal distribution. 
• Determine when the normal distribution is a reasonable representation of the data. 
• Describe how the mean and the standard deviation affect the graph of the normal distribution. 
• Calculate and interpret the z-score for a data point, given the mean and the standard deviation.
• Compare two sets of normally distributed data using a standard normal distribution and zscores, given the mean and the standard deviation. 
• Represent probability as the area under the curve of a standard normal distribution. 
• Determine probabilities associated with areas under the standard normal curve, using technology or a table of Standard Normal Probabilities. 
• Investigate, represent, and determine relationships between a normally distributed data set and its descriptive statistics.

In this unit, teachers will provide differentiated opportunities for students to review previous content and/or explore content at a deeper level.