M.O.A1.2: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contexts.

M.O.A1.2.1: formulate algebraic expressions for use in equations and inequalities that require planning to accurately model real-world problems.

Linear Inequalities in Two Variables

M.O.A1.2.2: create and solve multi-step linear equations, absolute value equations, and linear inequalities in one variable, (with and without technology); apply skills toward solving practical problems such as distance, mixtures or motion and judge the reasonableness of solutions.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form)

M.O.A1.2.3: evaluate data provided, given a real-world situation, select an appropriate literal equation and solve for a needed variable.

Box-and-Whisker Plots
Estimating Population Size

M.O.A1.2.4: develop and test hypotheses to derive the laws of exponents and use them to perform operations on expressions with integral exponents.

Dividing Exponential Expressions
Multiplying Exponential Expressions

M.O.A1.2.5: analyze a given set of data and prove the existence of a pattern numerically, algebraically and graphically, write equations from the patterns and make inferences and predictions based on observing the pattern.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

M.O.A1.2.7: analyze situations and solve problems by determining the equation of a line given a graph of a line, two points on the line, the slope and a point, or the slope and y intercept.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

M.O.A1.2.8: identify a real life situation that involves a constant rate of change; pose a question; make a hypothesis as to the answer; develop, justify, and implement a method to collect, organize, and analyze related data; extend the nature of collected, discrete data to that of a continuous linear function that describes the known data set; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using the predictive and analytic tools of algebra (with and without technology).

Compound Interest
Dilations
Direct and Inverse Variation
Trends in Scatter Plots

M.O.A1.2.9: create and solve systems of linear equations graphically and numerically using the elimination method and the substitution method, given a real-world situation.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

M.O.A1.2.10: simplify and evaluate algebraic expressions

M.O.A1.2.10.a: add and subtract polynomials

Addition and Subtraction of Functions
Addition of Polynomials

M.O.A1.2.10.b: multiply and divide binomials by binomials or monomials

Dividing Polynomials Using Synthetic Division

M.O.A1.2.12: use area models and graphical representations to develop and explain appropriate methods of factoring.

Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

M.O.A1.2.13: simplify radical expressions

M.O.A1.2.13.a: through adding, subtracting, multiplying and dividing

Operations with Radical Expressions
Simplifying Radical Expressions

M.O.A1.2.14: choose the most efficient method to solve quadratic equations by graphing (with and without technology), factoring quadratic formula and draw reasonable conclusions about a situation being modeled.

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

M.O.A1.2.15: describe real life situations involving exponential growth and decay equations including y=2 to the x power and y=(½) to the x power; compare the equation with attributes of an associated table and graph to demonstrate an understanding of their interrelationship.

Compound Interest

M.O.A1.2.17: perform a linear regression (with and without technology),

M.O.A1.2.17.a: compare and evaluate methods of fitting lines to data.

Correlation

M.O.A1.2.17.b: identify the equation for the line of regression,

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

M.O.A1.2.17.c: examine the correlation coefficient to determine how well the line fits the data

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

M.O.A1.2.17.d: use the equation to predict specific values of a variable.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

M.O.A1.2.19: gather data to create histograms, box plots, scatter plots and normal distribution curves and use them to draw and support conclusions about the data.

Correlation
Describing Data Using Statistics
Histograms
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

M.O.A1.2.20: design experiments to model and solve problems using the concepts of sample space and probability distribution.

Polling: City