Standards for Teaching and Learning
AI.N.1: Use the properties of operations on real numbers, including the associative, commutative, identity, and distributive properties, and use them to simplify calculations.
Solving Algebraic Equations II
AI.N.3: Calculate and apply ratios, proportions, rates, and percentages to solve a range of consumer and practical problems.
Beam to Moon (Ratios and Proportions)
Household Energy Usage
Percent of Change
AI.N.4: Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers, including approximate error in measurement and the approximate value of square roots. (Reminder: This is without the use of calculators.)
AI.N.6: Apply the set operations of union and intersection and the concept of complement, universal set, and disjoint sets, and use them to solve problems, including those involving Venn diagrams.
AI.P.1: Recognize, describe, and extend patterns governed by a linear, quadratic, or exponential functional relationship or by a simple iterative process (e.g., the Fibonacci sequence).
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
AI.P.3: Demonstrate an understanding of relations and functions. Identify the domain, range, and dependent and independent variables of functions.
AI.P.4: Translate between different representations of functions and relations: graphs, equations, sets of ordered pairs (scatter plots), verbal, and tabular.
Introduction to Functions
Linear Functions
Points, Lines, and Equations
AI.P.5: Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line.
Cat and Mouse (Modeling with Linear Systems)
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line
AI.P.6: Find a linear function describing a line from a graph or a geometric description of the line (e.g., by using the point-slope or slope y-intercept formulas). Explain the significance of a positive, negative, zero, or undefined slope.
Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line
AI.P.8: Add, subtract, and multiply polynomials with emphasis on 1st- and 2nd-degree polynomials.
Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x2+bx+c
AI.P.9: Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms, factoring [e.g., a² - b² = (a + b)(a - b), x² + 10x + 21 = (x + 3) (x + 7), 5x the the 4th power + 10x³ - 5x² = 5x² (x² + 2x - 1)], identifying and canceling common factors in rational expressions, and applying the properties of positive integer exponents.
Simplifying Algebraic Expressions II
AI.P.10: Divide polynomials by monomials with emphasis on 1st- and 2nd-degree polynomials.
Dividing Polynomials Using Synthetic Division
AI.P.12: Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods.
Modeling the Factorization of x2+bx+c
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic
AI.P.14: Solve everyday problems (e.g., compound interest and direct and inverse variation problems) that can be modeled using linear or quadratic functions. Apply appropriate graphical or symbolic methods to the solution.
Compound Interest
Determining a Spring Constant
Direct and Inverse Variation
Estimating Population Size
AI.P.15: Solve everyday problems (e.g., mixture, rate, and work problems) that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution.
Cat and Mouse (Modeling with Linear Systems)
Linear Programming
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)
AI.D.1: Select, create, and interpret an appropriate graphical representation (e.g., scatter plot, table, stem-and-leaf plots, circle graph, line graph, and line plot) for a set of data, and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data.
Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Distance-Time Graphs
Least-Squares Best Fit Lines
Mean, Median, and Mode
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Sight vs. Sound Reactions
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots
Correlation last revised: 5/9/2018