Grade Level and Grade Span Expectations

M.N&O.HS.2: Demonstrates understanding of the relative magnitude of real numbers by solving problems that involve ordering or comparing elements of any subset of the real numbers.

Comparing and Ordering Decimals

Rational Numbers, Opposites, and Absolute Values

M.N&O.10.2: Demonstrates understanding of the relative magnitude of real numbers by solving problems involving ordering or comparing rational numbers, common irrational numbers (e.g., square root of 2 , pi), rational bases with integer exponents, square roots, absolute values, integers, or numbers represented in scientific notation using number lines or equality and inequality symbols.

Comparing and Ordering Decimals

Rational Numbers, Opposites, and Absolute Values

Unit Conversions

Unit Conversions 2 - Scientific Notation and Significant Digits

M.N&O.HS4.b: Interprets and computes in scientific notation with and without a calculator.

M.N&O.10.4: Accurately solves problems involving rational numbers within mathematics, across content strands, disciplines or contexts (with emphasis on, but not limited to, proportions, percents, ratios, and rates).

Beam to Moon (Ratios and Proportions)

Estimating Population Size

Geometric Probability

Part-to-part and Part-to-whole Ratios

Percent of Change

M.N&O.HS.8: Applies properties of numbers and field properties (including determining whether a given subset of numbers is closed under a given arithmetic operation) to solve problems or to simplify computations; and compares and contrasts the properties of numbers and number systems; adds and multiplies numerical matrices with attention to the arithmetic properties of these operations.

Solving Algebraic Equations II

M.G&M.10.2: Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem).

Circles

Sine, Cosine, and Tangent Ratios

M.G&M.HS.4: Applies the concepts of congruency by using matrices to represent reflections, translations, and rotations.

M.G&M.10.4: Applies the concepts of congruency by solving problems on or off a coordinate plane involving reflections, translations, or rotations; or solves problems using congruency involving problems within mathematics or across disciplines or contexts.

M.G&M.HS.5: Applies concepts of similarity to define the trigonometric functions as ratios of sides of right triangles; uses the ratios of the sides of special right triangles (30¡ - 60¡ - 90¡ and 45¡ - 45¡ - 90¡) to determine the sine, cosine and tangent of 30¡ , 45¡ , and 60¡ ; and solves related problems.

Cosine Function

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

M.G&M.10.5: Applies concepts of similarity by solving problems within mathematics or across disciplines or contexts.

M.G&M.10.6: Solves problems involving perimeter, circumference, or area of two-dimensional figures (including composite figures) or surface area or volume of three-dimensional figures (including composite figures) within mathematics or across disciplines or contexts.

Area of Triangles

Surface and Lateral Areas of Prisms and Cylinders

M.G&M.10.7: Uses units of measure appropriately and consistently when solving problems across content strands; makes conversions within or across systems and makes decisions concerning an appropriate degree of accuracy in problem situations involving measurement in other GSEs.

M.G&M.10.9: Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope.

Constructing Congruent Segments and Angles

Parallel, Intersecting, and Skew Lines

Slope

Slope-Intercept Form of a Line

M.G&M.HS.10: Demonstrates conceptual understanding of spatial reasoning and visualization by sketching or using dynamic geometric software to generate three-dimensional objects from two-dimensional perspectives, or to generate two-dimensional perspectives from three-dimensional objects, and by solving related problems; perform and justify constructions with a compass and straightedge or dynamic geometric software.

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

Segment and Angle Bisectors

Surface and Lateral Areas of Prisms and Cylinders

M.F&A.10.1: Identifies, extends, and generalizes a variety of patterns (linear and nonlinear) represented by models, tables, sequences, or graphs in problem solving situations.

M.F&A.HS2.a: Analyzes characteristics of classes of functions (polynomial, rational, and exponential) to include domain, range, intercepts, increasing and decreasing intervals and rates of change.

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Polynomials and Linear Factors

Quadratics in Factored Form

Radical Functions

Rational Functions

M.F&A.HS2.b: Understands one-to-one (injective) functions and that a function that is one-to-one has a converse that is also a function; and finds inverses algebraically and graphically.

Function Machines 3 (Functions and Problem Solving)

Logarithmic Functions

M.F&A.HS2.c: Graphs polynomial, rational and exponential functions, including vertical and horizontal shifts, stretches, and compressions as well as reflections across vertical and horizontal axes.

Compound Interest

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Polynomials and Linear Factors

Quadratics in Factored Form

Rational Functions

M.F&A.HS2.d: Applies knowledge of functions to interpret and understand situations, design mathematical models, and solve problems in mathematics as well as in the natural and social sciences.

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

Linear Functions

Points, Lines, and Equations

M.F&A.10.2: Demonstrates conceptual understanding of linear and nonlinear functions and relations (including characteristics of classes of functions) through an analysis of constant, variable, or average rates of change, intercepts, domain, range, maximum and minimum values, increasing and decreasing intervals and rates of change (e.g., the height is increasing at a decreasing rate); describes how change in the value of one variable relates to change in the value of a second variable; or works between and among different representations of functions and relations (e.g., graphs, tables, equations, function notation).

Compound Interest

Direct and Inverse Variation

Exponential Functions

Function Machines 1 (Functions and Tables)

Function Machines 3 (Functions and Problem Solving)

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Introduction to Functions

Linear Functions

Logarithmic Functions

Points, Lines, and Equations

Radical Functions

Translating and Scaling Functions

M.F&A.HS3.a: Manipulates, evaluates, and simplifies algebraic and numerical expressions.

Compound Interest

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Multiplying Exponential Expressions

Operations with Radical Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

M.F&A.HS3.b: Adds, subtracts, multiplies and divides polynomials and rational expressions.

Addition and Subtraction of Functions

Addition of Polynomials

Dividing Polynomials Using Synthetic Division

Modeling the Factorization of *x*^{2}+*bx*+*c*

M.F&A.HS3.c: Factors quadratic and higher degree polynomials.

Dividing Polynomials Using Synthetic Division

Factoring Special Products

M.F&A.HS3.d: Understands properties of logarithms and converts between logarithmic and exponential forms.

M.F&A.HS3.e: Manipulates, evaluates, and simplifies expressions involving rational exponents and radicals and converts between expressions with rational exponents and expressions with radicals.

Operations with Radical Expressions

M.F&A.10.3: Demonstrates conceptual understanding of algebraic expressions by solving problems involving algebraic expressions, by simplifying expressions (e.g., simplifying polynomial or rational expressions, or expressions involving integer exponents, square roots, or absolute values), by evaluating expressions, or by translating problem situations into algebraic expressions.

Compound Interest

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

Modeling the Factorization of *ax*^{2}+*bx*+*c*

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

Using Algebraic Equations

Using Algebraic Expressions

M.F&A.HS4.a: Factors, completes the square, uses the quadratic formula, and graphs quadratic functions to solve quadratic equations.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

Quadratics in Polynomial Form

Roots of a Quadratic

M.F&A.HS4.b: Solves equations involving polynomial, rational, and radical expressions. Graphs and interprets the solutions.

M.F&A.HS4.e: Solves 2x2 and 3x3 systems of linear equations and graphically interprets the solutions.

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

M.F&A.HS4.f: Solves systems of linear and quadratic inequalities.

Linear Programming

Systems of Linear Inequalities (Slope-intercept form)

M.F&A.HS4.h: Translates problem situations into inequalities; and solves linear and non-linear inequalities (symbolically and graphically).

Compound Inequalities

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Solving Linear Inequalities in One Variable

Systems of Linear Inequalities (Slope-intercept form)

M.F&A.10.4: Demonstrates conceptual understanding of equality by solving problems involving algebraic reasoning about equality; by translating problem situations into equations; by solving linear equations (symbolically and graphically) and expressing the solution set symbolically or graphically, or provides the meaning of the graphical interpretations of solution(s) in problem-solving situations; or by solving problems involving systems of linear equations in a context (using equations or graphs) or using models or representations.

Absolute Value Equations and Inequalities

Cat and Mouse (Modeling with Linear Systems)

Linear Functions

Linear Inequalities in Two Variables

Solving Equations on the Number Line

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

Using Algebraic Equations

M.DSP.HS.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.

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

M.DSP.10.1: Interprets a given representation(s) (e.g., box-and-whisker plots, scatter plots, bar graphs, line graphs, circle graphs, histograms, frequency charts) to make observations, to answer questions, to analyze the data to formulate or justify conclusions, critique conclusions, make predictions, or to solve problems within mathematics or across disciplines or contexts (e.g., media, workplace, social and environmental situations).

Box-and-Whisker Plots

Correlation

Histograms

Least-Squares Best Fit Lines

Polling: City

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

Solving Using Trend Lines

Stem-and-Leaf Plots

Trends in Scatter Plots

M.DSP.HS.2: Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of dispersion (standard deviation, variance, and percentiles).

Box-and-Whisker Plots

Describing Data Using Statistics

Real-Time Histogram

M.DSP.10.2: Analyzes patterns, trends, or distributions in data in a variety of contexts by determining, using, or analyzing measures of central tendency (mean, median, or mode), dispersion (range or variation), outliers, quartile values, estimated line of best fit, regression line, or correlation (strong positive, strong negative, or no correlation) to solve problems; and solve problems involving conceptual understanding of the sample from which the statistics were developed.

Box-and-Whisker Plots

Correlation

Describing Data Using Statistics

Least-Squares Best Fit Lines

Mean, Median, and Mode

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

Solving Using Trend Lines

Stem-and-Leaf Plots

Trends in Scatter Plots

M.DSP.HS.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

Stem-and-Leaf Plots

M.DSP.10.3: Identifies or describes representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M:DSP:10:1.

Box-and-Whisker Plots

Reaction Time 1 (Graphs and Statistics)

Stem-and-Leaf Plots

M.DSP.HS.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.10.4: Uses counting techniques to solve problems in context involving combinations or permutations using a variety of strategies (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting Principle, or others).

Binomial Probabilities

Permutations and Combinations

M.DSP.HS.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.10.5: Solves problems involving experimental or theoretical probability.

Binomial Probabilities

Geometric Probability

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

M.DSP.HS.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

Polling: City

Polling: Neighborhood

Populations and Samples

Real-Time Histogram

Stem-and-Leaf Plots

M.PRP.HS2.b: Use informal and formal reasoning and proof to explain and justify conclusions.

M.CCR.HS2.a: Choose appropriate representations and mathematical language (e.g., spreadsheets, geometric models, algebraic symbols, tables, graphs, matrices) to present ideas clearly and logically for a given situation.

Dilations

Using Algebraic Expressions

M.CCR.HS2.b: See a common structure in mathematical phenomena that come from very different contexts (e.g., the sum of the first n odd natural numbers, the areas of square gardens, and the distance traveled by a vehicle that starts at rest and accelerates at a constant rate can be represented by functions of the form f(x) = ax_).

M.CCR.HS2.c: Find representations that model essential features of a mathematical situation (e.g., cost of postage can be modeled by a step-function).

Determining a Spring Constant

Estimating Population Size

M.CCR.HS3.a: Explain in oral or written form how mathematics connects to other disciplines, to daily life, careers, and society (e.g., geometry in art and literature, data analysis in social studies, and exponential growth in finance).

Estimating Population Size

Unit Conversions

Correlation last revised: 1/20/2017