MA-HS-1: High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. This becomes the foundation for algebra and working with algebraic symbols. They understand large and small numbers and their representations, powers and roots. They compare and contrast properties of numbers and number systems and develop strategies to estimate the results of operations on real numbers. Students will use, and understand the limitations of, graphing calculators and computer spreadsheets appropriately as learning tools.

MA-HS-1.1: Number Sense

MA-HS-1.1.1: Students will compare real numbers using order relations (less than, greater than, equal to) and represent problems using real numbers.

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

MA-HS-1.1.3: Students will use scientific notation to express very large or very small quantities.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

MA-HS-1.3: Number Operations

MA-HS-1.3.1: Students will solve real-world and mathematical problems to specified accuracy levels by simplifying expressions with real numbers involving addition, subtraction, multiplication, division, absolute value, integer exponents, roots (square, cube) and factorials.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Radical Expressions

MA-HS-1.3.2: Students will:

MA-HS-1.3.2.a: describe and extend arithmetic and geometric sequences;

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

MA-HS-1.3.2.b: determine a specific term of a sequence given an explicit formula;

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MA-HS-1.3.2.c: determine an explicit rule for the nth term of an arithmetic sequence and

Arithmetic Sequences

MA-HS-1.3.2.d: apply sequences to solve real-world problems.

Arithmetic Sequences
Estimating Population Size
Geometric Sequences

MA-HS-1.3.3: Students will write an explicit rule for the nth term of a geometric sequence.

Geometric Sequences

MA-HS-1.4: Ratios and Proportional Reasoning

MA-HS-1.4.1: Students will apply ratios, percents and proportional reasoning to solve real-world problems (e.g., those involving slope and rate, percent of increase and decrease) and will explain how slope determines a rate of change in linear functions representing real-world problems.

Beam to Moon (Ratios and Proportions)
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percent of Change
Point-Slope Form of a Line
Real-Time Histogram
Slope-Intercept Form of a Line

MA-HS-1.5: Properties of Numbers and Operations

MA-HS-1.5.1: Students will identify real number properties (commutative properties of addition and multiplication, associative properties of addition and multiplication, distributive property of multiplication over addition and subtraction, identity properties of addition and multiplication and inverse properties of addition and multiplication) when used to justify a given step in simplifying an expression or solving an equation.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II

MA-HS-2: High school students continue to measure and estimate measurements including fractions and decimals. They use formulas to find surface area and volume. They use US Customary and metric units of measurement. They use the Pythagorean theorem and other right triangle relationships to solve real-world problems.

MA-HS-2.1: Measuring Physical Attributes

MA-HS-2.1.1: Students will determine the surface area and volume of right rectangular prisms, pyramids, cylinders, cones and spheres in real-world and mathematical problems.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

MA-HS-2.1.2: Students will describe how a change in one or more dimensions of a geometric figure affects the perimeter, area and volume of the figure.

Perimeter and Area of Rectangles

MA-HS-2.1.3: Students will apply definitions and properties of right triangle relationships (right triangle trigonometry and the Pythagorean theorem) to determine length and angle measures to solve real-world and mathematical problems.

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Cosine Function
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

MA-HS-2.1.4: Students will apply special right triangles and the converse of the Pythagorean theorem to solve real-world problems.

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine, Cosine, and Tangent Ratios
Surface and Lateral Areas of Pyramids and Cones

MA-HS-3: High school students expand analysis of two-dimensional shapes and three-dimensional shapes. They translate shapes in a coordinate plane. They extend work with congruent and similar figures, including proportionality.

MA-HS-3.1: Shapes and Relationships

MA-HS-3.1.1: Students will analyze and apply spatial relationships (not using Cartesian coordinates) among points, lines and planes (e.g., betweenness of points, midpoint, segment length, collinear, coplanar, parallel, perpendicular, skew).

Parallel, Intersecting, and Skew Lines
Points in the Coordinate Plane

MA-HS-3.1.3: Students will analyze and apply angle relationships (e.g., linear pairs, vertical, complementary, supplementary, corresponding and alternate interior angles) in real-world and mathematical problems.

Investigating Angle Theorems
Triangle Angle Sum

MA-HS-3.1.4: Students will use angle relationships to prove basic theorems.

Investigating Angle Theorems
Triangle Angle Sum

MA-HS-3.1.5: Students will classify and apply properties of two-dimensional geometric figures (e.g., number of sides, vertices, length of sides, sum of interior and exterior angle measures).

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Special Parallelograms

MA-HS-3.1.6: Students will know the definitions and basic properties of a circle and will use them to prove basic theorems and solve problems.

Chords and Arcs
Inscribed Angles

MA-HS-3.1.7: Students will solve real-world and mathematical problems by applying properties of triangles (e.g., Triangle Sum theorem and Isosceles Triangle theorems).

Concurrent Lines, Medians, and Altitudes
Similarity in Right Triangles
Triangle Angle Sum
Triangle Inequalities

MA-HS-3.1.8: Students will use the properties of triangles to prove basic theorems.

Isosceles and Equilateral Triangles
Triangle Angle Sum
Triangle Inequalities

MA-HS-3.1.11: Students will visualize solids and surfaces in three-dimensional space when given two-dimensional representations (e.g., nets, multiple views) and create two-dimensional representations for the surfaces of three-dimensional objects.

Surface and Lateral Areas of Prisms and Cylinders

MA-HS-3.1.12: Students will apply the concepts of congruence and similarity to solve real-world and mathematical problems.

Circles
Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Similarity in Right Triangles

MA-HS-3.1.13: Students will prove triangles congruent and similar.

Congruence in Right Triangles
Proving Triangles Congruent
Similar Figures

MA-HS-3.3: Coordinate Geometry

MA-HS-3.3.1: Students will apply algebraic concepts and graphing in the coordinate plane to analyze and solve problems (e.g., finding the final coordinates for a specified polygon, midpoints, between-ness of points, parallel and perpendicular lines, the distance between two points, the slope of a segment).

Points in the Coordinate Plane

MA-HS-3.4: Foundational Statements

MA-HS-3.4.1: Students will identify definitions, axioms and theorems, explain the necessity for them and of and give examples of them.

Investigating Angle Theorems

MA-HS-3.4.3: Students will be able to perform constructions such as a line parallel to a given line through a point not on the line, the perpendicular bisector of a line segment and the bisector of an angle.

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Parallel, Intersecting, and Skew Lines
Segment and Angle Bisectors

MA-HS-4: High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They relate curve of best fit with two-variable data and determine line of best fit for a given set of data. They distinguish between combinations and permutations and compare and contrast theoretical and experimental probability.

MA-HS-4.1: Data Representations

MA-HS-4.1.2: Students will construct data displays for data with no more than two variables.

Correlation

MA-HS-4.2: Characteristics of Data Sets

MA-HS-4.2.1: Students will describe and compare data distributions and make inferences from the data based on the shapes of graphs, measures of center (mean, median, mode) and measures of spread (range, standard deviation).

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

MA-HS-4.2.2: Students will know the characteristics of the Gaussian normal distribution (bell-shaped curve).

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

MA-HS-4.2.3: Students will:

MA-HS-4.2.3.a: identify an appropriate curve of best fit (linear, quadratic, exponential) for a set of two-variable data;

Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

MA-HS-4.2.3.b: determine a line of best fit equation for a set of linear two-variable data and

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

MA-HS-4.2.3.c: apply a line of best fit to make predictions within and beyond a given set of two-variable data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

MA-HS-4.2.4: Students will recognize when arguments based on data confuse correlation and causation.

Correlation

MA-HS-4.3: Experiments and Samples

MA-HS-4.3.1: Students will recognize potential for bias resulting from the misuse of sampling methods (e.g., non-random sampling, polling only a specific group of people, using limited or extremely small sample sizes) and explain why these samples can lead to inaccurate inferences.

Populations and Samples

MA-HS-4.3.2: Students will design simple experiments or investigations to collect data to answer questions of interest.

Correlation
Describing Data Using Statistics
Real-Time Histogram

MA-HS-4.3.3: Students will explain the differences between randomized experiments and observational studies.

Polling: Neighborhood

MA-HS-4.4: Probability

MA-HS-4.4.1: Students will:

MA-HS-4.4.1.a: determine theoretical and experimental (from given data) probabilities;

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

MA-HS-4.4.1.b: make predictions and draw inferences from probabilities;

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

MA-HS-4.4.1.c: compare theoretical and experimental probabilities and

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

MA-HS-4.4.1.d: determine probabilities involving replacement and non-replacement.

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

MA-HS-4.4.2: Students will recognize and identify the differences between combinations and permutations and use them to count discrete quantities.

Binomial Probabilities
Permutations and Combinations

MA-HS-4.4.3: Students will represent probabilities in multiple ways, such as fractions, decimals, percentages and geometric area models.

Geometric Probability

MA-HS-4.4.4: Students will explain how the law of large numbers can be applied in simple examples.

Theoretical and Experimental Probability

MA-HS-5: High school students extend analysis and use of functions and focus on linear, quadratic, absolute value and exponential functions. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. They combine simple rational expressions and combine simple polynomial expressions. They factor polynomial expressions and quadratics of the form 1x² + bx +c.

MA-HS-5.1: Patterns, Relations and Functions

MA-HS-5.1.1: Students will identify multiple representations (tables, graphs, equations) of functions (linear, quadratic, absolute value, exponential) in real-world or mathematical problems.

Absolute Value Equations and Inequalities
Compound Interest
Exponential Functions
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Translating and Scaling Functions

MA-HS-5.1.2: Students will identify, relate and apply representations (graphs, equations, tables) of a piecewise function (such as long distance telephone rates) from mathematical or real-world information.

Absolute Value with Linear Functions

MA-HS-5.1.3: Students will demonstrate how equations and graphs are models of the relationship between two real-world quantities (e.g., the relationship between degrees Celsius and degrees Fahrenheit).

Linear Functions
Quadratics in Polynomial Form

MA-HS-5.1.4: Students will recognize and solve problems that can be modeled using an exponential function, such as compound interest problems.

Compound Interest

MA-HS-5.1.5: Students will:

MA-HS-5.1.5.a: determine if a relation is a function;

Introduction to Functions
Linear Functions

MA-HS-5.1.5.c: determine the slope and intercepts of a linear function;

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line

MA-HS-5.1.5.d: determine the maximum, minimum, and intercepts (roots/zeros) of a quadratic function and

Quadratics in Factored Form
Quadratics in Vertex Form
Zap It! Game

MA-HS-5.1.7: Students will apply and use direct and inverse variation to solve real-world and mathematical problems.

Direct and Inverse Variation

MA-HS-5.1.8: Students will identify the changes and explain how changes in parameters affect graphs of functions (linear, quadratic, absolute value, exponential) (e.g., compare y = x2, y = 2x2, y = (x-4)2, and y = x2+3).

Absolute Value with Linear Functions
Introduction to Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game

MA-HS-5.2: Variables, Expressions, and Operations

MA-HS-5.2.1: Students will apply order of operations, real number properties (identity, inverse, commutative, associative, distributive, closure) and rules of exponents (integer) to simplify algebraic expressions.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Solving Algebraic Equations II

MA-HS-5.2.3: Students will:

MA-HS-5.2.3.a: add, subtract and multiply polynomial expressions;

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

MA-HS-5.2.3.b: factor polynomial expressions using the greatest common monomial factor and

Factoring Special Products

MA-HS-5.2.4: Students will factor quadratic polynomials, such as perfect square trinomials and quadratic polynomials of the form ax² + bx + c when a is not equal to 1 and b and c are integers.

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form

MA-HS-5.3: Equations and Inequalities

MA-HS-5.3.1: Students will model, solve and graph first degree, single variable equations and inequalities, including absolute value, based in real-world and mathematical problems and graph the solutions on a number line.

Absolute Value Equations and Inequalities
Compound Inequalities
Exploring Linear Inequalities in One Variable
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

MA-HS-5.3.2: Students will solve for a specified variable in a multivariable equation.

Area of Triangles
Solving Formulas for any Variable

MA-HS-5.3.3: Students will model, solve and graph first degree, two-variable equations and inequalities in real-world and mathematical problems.

Absolute Value Equations and Inequalities
Circles
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

MA-HS-5.3.4: Students will model, solve and graph systems of two linear equations in real-world and mathematical problems.

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

MA-HS-5.3.5: Students will write, graph, and solve systems of two linear inequalities based on real-world or mathematical problems and interpret the solution.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

MA-HS-5.3.6: Students will model, solve and graph quadratic equations in real-world and mathematical problems.

Addition and Subtraction of Functions
Quadratics in Polynomial Form