Grade Level Expectations
M(N&O).12.2: Demonstrates understanding of the relative magnitude of real numbers by solving problems that involve ordering or comparing any subset of the real numbers.
Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values
M(N&O).12.4: Accurately solves problems involving scientific notation or uses significant digits to assess the precision of an answer. Interprets rational exponents and their relation to radicals; computes by hand in simple cases (e.g. "4 to the 3/2 power"), and using a calculator when appropriate. Interprets numbers given in scientific notation and carries out computations of them with and without a calculator. Solves problems involving compound interest.
M(G&M).12.4: Applies the concepts of congruency by using matrices to represent reflections, translations, and rotations.
M(G&M).12.9: Solves problems involving circles as loci of points in the plane satisfying certain distance requirements, and uses the distance formula to obtain equations for circles.
M(F&A).12.2: Demonstrates conceptual understanding of linear and nonlinear functions and relations by representing and analyzing functions in several ways; recognizing properties of functions and characteristics properties of families of functions; applying knowledge of functions to interpret, model, and solve problems; analyzing characteristics of classes of functions (polynomial, rational, and exponential) to include domain, range, intercepts, increasing and decreasing intervals and rates of change; representing functions numerically, algebraically, graphically, and verbally (i.e. in written words), recognizing properties of a function from these representations, and transfers information from one representation to another; graphing polynomial, rational and exponential functions, including vertical and horizontal shifts, stretches, and compressions as well as reflections across vertical and horizontal axes; applying knowledge of functions to interpret and understand situations, design mathematical models, and solve problems in mathematics as well as in natural and social sciences.
Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Graphs of Polynomial Functions
Linear Functions
Quadratics in Vertex Form
Slope-Intercept Form of a Line
M(F&A).12.3: Demonstrates conceptual understanding of algebraic expressions by manipulating, evaluating, and simplifying algebraic and numerical expressions; adding, subtracting, multiplying and dividing polynomials; adding, subtracting, multiplying and dividing rational expressions; simplifying complex fractions; factoring quadratic and higher degree polynomials, including difference of squares; applying properties of logarithms (e.g.,log base a of (b to the nth power) = n times log base a of b, a to the power (log base a of b) = b) and converting between logarithmic and exponential forms; manipulating, evaluating, and simplifying expressions involving rational exponents and radicals and converting between expressions with rational exponents and expressions with radicals.
Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Factoring Special Products
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Radical Expressions
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
M(F&A).12.4: Demonstrates conceptual understanding of equality by solving equations and systems of equations or inequalities and interpreting the solutions algebraically and graphically; by factoring, completing the square, using the quadratic formula, and graphing quadratic functions to solve quadratic equations; solving and interpreting solutions of equations involving polynomial, rational, and radical expressions; analyzing the effect of simplifying radical or rational expressions on the solution set of equations involving such expressions. (e.g. x^2/x =x for x "not equal to" 0); finding approximate solutions to equations by graphing each side as a function using technology. [Understand that any equation in x can be interpreted as the equation f(x) = g(x) and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).]; solving 2x2 and 3x3 systems of linear equations and graphically interprets the solutions; solving systems of linear and quadratic inequalities; solving and graphically interpreting solutions systems of equations involving nonlinear expressions.
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations on the Number Line
Solving Two-Step Equations
M(DSP).12.1: Interprets a given representation(s) (e.g., regression function including linear, quadratic, and exponential) to analyze the data to make inferences and to formulate, justify, and critique conclusions.
M(DSP).12.2: Analyzes patterns, trends, or distributions in data in a variety of contexts by calculating and analyzing measures of dispersion (standard deviation, variance, and percentiles).
Polling: City
Real-Time Histogram
M(DSP).12.3: Organizes and displays one- and two- variable data using a variety of representations (e.g., box-and-whisker plots, scatter plots, bar graphs, line graphs, circle graphs, histograms, frequency charts, linear, quadratic, and exponential regression functions) to analyze the data to formulate or justify conclusions, make predictions, or to solve problems with or without using technology.
Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Histograms
Least-Squares Best Fit Lines
Polling: City
Real-Time Histogram
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots
M(DSP).12.4: Uses counting techniques to solve problems in context involving combination or permutations using a variety of strategies (e.g., nCr, nPr, or n!); and finds unions, intersections, and complements of sets.
Binomial Probabilities
Compound Inequalities
Permutations and Combinations
M(DSP).12.5: For a probability event in which the sample space may or may not contain equally likely outcomes, predicts the theoretical probability of an event and tests the prediction through experiments and simulations; compares and contrasts theoretical and experimental probabilities; finds the odds of an event and understands the relationship between probability and odds.
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability
M(DSP).12.6: In response to a teacher or student generated question or hypothesis decides the most effective method (e.g., survey, observation, research, experimentation) and sampling techniques (e.g., random sample, stratified random sample) to collect the data necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the questions or hypotheses being tested while considering the limitations of the data that could effect interpretations; and when appropriate makes predications, asks new questions, or makes connections to real-world situations.
Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Geometric Probability
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots
M(DSP).10.6: In response to a teacher or student generated question or hypothesis decides the most effective method (e.g., survey, observation, research, experimentation) and sampling techniques (e.g., random sample, stratified random sample) to collect the data necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the questions or hypotheses being tested while considering the limitations of the data that could effect interpretations; and when appropriate makes predications, asks new questions, or makes connections to real-world situations.
Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Geometric Probability
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots
Correlation last revised: 5/23/2018