Functions and their Inverses
Given a functional relationship in a variety of representations (table, graph, mapping diagram, equation, or verbal form), the student will determine the inverse of the function.
Rational Functions: Predicting the Effects of Parameter Changes
Given parameter changes for rational functions, students will be able to predict the resulting changes on important attributes of the function, including domain and range and asymptotic behavior.
Finding the Probabilities of Dependent and Independent Events
Given problem situations, the student will find the probability of the dependent and independent events.
Recognizing Misuses of Graphical or Numerical Information
Given a problem situation, the student will analyze data presented in graphical or tabular form by evaluating the predictions and conclusions based on the information given.
Evaluating Methods of Sampling from a Set of Data
Given a problem situation, the student will evaluate a method of sampling to determine the validity of an inference made from the set of data.
Domain and Range: Graphs
Given a function in graph form, identify the domain and range using set notation, interval notation, or a verbal description as appropriate.
Domain and Range: Function Notation
Given a function in function notation form, identify the domain and range using set notation, interval notation, or a verbal description as appropriate.
Domain and Range: Verbal Description
The student will be able to identify and determine reasonable values for the domain and range from any given verbal description.
Domain and Range: Contextual Situations
The student will be able to identify and determine reasonable values for the domain and range from any given contextual situation.
Modeling Data with Linear Functions
Given a scatterplot where a linear function is the best fit, the student will interpret the slope and intercepts, determine an equation using two data points, identify the conditions under which the function is valid, and use the linear model to predict data points.
Formulating Systems of Inequalities
Given a contextual situation, the student will formulate a system of two linear inequalities with two unknowns to model the situation.
Solving Systems of Equations Using Substitution
Given a system of two equations where at least one of the equations is linear, the student will solve the system using the algebraic method of substitution.
Solving Systems of Equations Using Elimination
Given a system of two equations where at least one of the equations is linear, the student will solve the system using the algebraic method of elimination.
Solving Systems of Equations with Three Variables
Given a system of three linear equations, the student will solve the system with a unique solution.
Solving Systems of Equations Using Matrices
Given a system of up to three linear equations, the student will solve the system using matrices with technology.
Using Properties of Transformations
Given examples of mathematics in the real world, the student will use properties of transformations and their composites to describe and perform transformations of figures in a plane.
Developing Algebraic Expressions to Represent Geometric Properties
The student will investigate patterns to make conjectures.
Developing Algebraic Expressions to Represent Geometric Properties of Polygons
Given numerical and/or geometric patterns that represent geometric properties of polygons, the student will develop algebraic expressions that represent the geometric properties.
Developing Algebraic Expressions to Represent Geometric Properties of Angle Relationships in Polygons
Given numerical and/or geometric patterns that represent geometric properties of angle relationships in polygons, the student will investigate patterns to make conjectures about interior and exterior angles of polygons.
Applying Pythagorean Triples to Solve Problems
Given verbal and pictorial representations of problem situations, the student will apply patterns from right triangles whose sides are Pythagorean Triples to solve the problems.