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6 OnTRACK Algebra I: Properties and Attributes of Functions
Students will learn how to use the properties and attributes of functions.
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.
Solving Quadratic Equations Using Algebraic Methods
Given a quadratic equation, the student will solve the equation by factoring, completing the square, or by using the quadratic formula.
Quadratics: Connecting Roots, Zeros, and x-Intercepts
Given a quadratic equation, the student will make connections among the solutions (roots) of the quadratic equation, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.
Using the Laws of Exponents to Solve Problems
Given problem situations involving exponents, the student will use the laws of exponents to solve the problems.
Formulating Systems of Equations (Verbal → Symbolic)
Given verbal descriptions of situations involving systems of linear equations the student will analyze the situations and formulate systems of equations in two unknowns to solve problems.
Solving Quadratic Equations Using Graphs
Given a quadratic equation, the student will use graphical methods to solve the equation.
Writing Equations to Describe Functional Relationships (Verbal → Equation)
Given a problem situation represented in verbal form, students will write an equation that can be used to represent the situation.
Writing Inequalities to Describe Relationships (Verbal → Symbolic)
Given a problem situation represented in verbal form, students will write an inequality that can be used to represent the situation.
Determining the Meaning of Intercepts
Given algebraic, tabular, and graphical representations of linear functions, the student will determine the intercepts of the function and interpret the meaning of intercepts within the context of the situation.
Predicting the Effects of Changing y-Intercepts in Problem Situations
Given verbal, symbolic, numerical, or graphical representations of problem situations, the student will interpret and predict the effects of changing the y-intercept in the context of the situations.
Solving Linear Inequalities
The student will represent linear inequalities using equations, tables, and graphs. The student will solve linear inequalities using graphs or properties of equality, and determine whether or not a given point is a solution to a linear inequality.
Direct Variation and Proportional Change
The student will use a variety of methods inculding tables, equations and graphs to find the constant of variation and missing values when given a relationship that varies directly.
Given scatterplots that represent problem situations, the student will determine if the data has strong vs weak correlation as well as positive, negative, or no correlation.
Making Predictions and Critical Judgments (Table/Verbal)
Given verbal descriptions and tables that represent problem situations, the student will make predictions for real-world problems.
Collecting Data and Making Predictions
Given an experimental situation, the student will write linear functions that provide a reasonable fit to data to estimate the solutions and make predictions.
Writing Expressions to Model Patterns (Table/Pictorial → Symbolic)
Given a pictorial or tabular representation of a pattern and the value of several of their terms, the student will write a formula for the nth term of a sequences.
Analyzing the Effects of the Changes in m and b on the Graph of y = mx + b
Given algebraic, graphical, or verbal representations of linear functions, the student will determine the effects on the graph of the parent function f(x) = x.
Writing Equations of Lines
Given two points, the slope and a point, or the slope and the y-intercept, the student will write linear equations in two variables.
Predicting, Finding, and Justifying Data from an Equation
Given data in the form of an equation, the student will use the equation to interpret solutions to problems.