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.
Transformations of Absolute Value Functions
Given an absolute value function, the student will analyze the effect on the graph when f(x) is replaced by af(x), f(bx), f(x – c), and f(x) + d for specific positive and negative real values.
Using Logical Reasoning to Prove Conjectures About Quadrilaterals
Given conjectures about quadrilaterals, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.
Making and Verifying Conjectures about Lines
Students will investigate patterns and make conjectures about geometric relationships.
Making and Verifying Conjectures about Polygons
Students will investigate patterns and make conjectures about geometric relationships, including interior angles of polygons.
Making and Verifying Conjectures About Circles
Given information about the relationship(s) witnin one circle or a set of circles, the student will explore special segments and angles of circles.
Writing the Converse, Inverse, and Contrapositive
Given a conditional statement, the student will write its converse, inverse, and contrapositive.
Making and Verifying Conjectures about Three-Dimensional Figures
Students will explore volume conjectures and solve problems by applying the volume formulas to composite figures.
Constructing and Justifying Statements about Geometric Figures
Students will distinguish between undefined terms, definitions, postulates, conjectures, and theorems and investigate patterns to make conjectures about geometric relationships.
Using Counter Examples to Disprove Statements That Are False
Given statements about a geometric relationship, the student will use counter examples to disprove statements that are false.
Using Inductive Reasoning to Formulate Conjectures
Students will practice identifying the converse, inverse, and contrapositive of conditional statements.
Using Logical Reasoning to Prove Statements are True
Given statements about a geometric relationship, the student will distinguish between the undefined terms, definitions, postulates, conjectures, and theorems to prove the statements are true.
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.