3.5.9 Students are able to understand the concepts of parallel and perpendicular line and how their slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. 3.5.10 Students are able to graph quadratic functions and know how its roots determine x-intercepts. 3.6.1 Students use properties of number to demonstrate that assertions are true or false. Students explain the differences between inductive and deductive reasoning, and identify and provide examples of each.
Students identify the hypothesis and conclusion in logical deduction.
Students use counter examples to show that an assertion is false and recognize that a single counter example is sufficient to refute the assertion. Students judge the validity of an argument based on whether the properties of the real number system, and order of operations have been applied correctly at each step. Students prove general algebraic statements for all real numbers by justification of steps until an obvious identity is achieved, or disprove by specific counter example or contradiction. Given a specific algebraic statement involving linear, quadratic or absolute value expressions, equations or inequalities, students determine if the statement is true sometimes, always or never, and justify reasoning. Statistics, Data Analysis and Probability 4.3.1 Summarize trends in bi-variate data by informally fitting lines to data that appears to have a linear trend.