Sunshine State Standards

MA.912.A: Algebra Body of Knowledge

MA.912.A.1: Students expand and deepen their understanding of real and complex numbers by comparing expressions and performing arithmetic computations, especially those involving square roots and exponents. They use the properties of real numbers to simplify algebraic expressions and equations, and they convert between different measurement units using dimensional analysis.

MA.912.A.1.3: Simplify real number expressions using the laws of exponents.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

MA.912.A.1.7: Represent complex numbers geometrically.

Points in the Complex Plane - Activity A

MA.912.A.1.8: Use the zero product property of real numbers in a variety of contexts to identify solutions to equations.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

MA.912.A.2: Students draw and interpret graphs of relations. They understand the notation and concept of a function, find domains and ranges, and link equations to functions.

MA.912.A.2.1: Create a graph to represent a real-world situation.

Describing Data Using Statistics

MA.912.A.2.3: Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions.

Introduction to Functions

Linear Functions

Using Algebraic Equations

MA.912.A.2.4: Determine the domain and range of a relation.

MA.912.A.2.5: Graph absolute value equations and inequalities in two variables.

Defining a Line with Two Points

Ellipse - Activity A

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

MA.912.A.2.6: Identify and graph common functions (including but not limited to linear, rational, quadratic, cubic, radical, absolute value).

Cubic Function Activity

Functions Involving Square Roots

General Form of a Rational Function

Linear Functions

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Roots of a Quadratic

MA.912.A.2.7: Perform operations (addition, subtraction, division and multiplication) of functions algebraically, numerically, and graphically.

Addition and Subtraction of Polynomials

Linear Functions

MA.912.A.2.10: Describe and graph transformations of functions

Logarithmic Functions: Translating and Scaling

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

MA.912.A.2.11: Solve problems involving functions and their inverses.

Logarithmic Functions - Activity A

MA.912.A.2.12: Solve problems using direct, inverse, and joint variations.

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

MA.912.A.2.13: Solve real-world problems involving relations and functions.

Introduction to Functions

Linear Functions

MA.912.A.3: Students solve linear equations and inequalities.

MA.912.A.3.1: Solve linear equations in one variable that include simplifying algebraic expressions.

Solving Equations By Graphing Each Side

MA.912.A.3.2: Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Formulas for any Variable

Solving Two-Step Equations

MA.912.A.3.3: Solve literal equations for a specified variable.

Solving Formulas for any Variable

MA.912.A.3.4: Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution.

Compound Inequalities

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Linear Programming - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Systems of Linear Inequalities (Slope-intercept form) - Activity A

MA.912.A.3.5: Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities.

Modeling and Solving Two-Step Equations

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Solving Two-Step Equations

MA.912.A.3.6: Solve and graph the solutions of absolute value equations and inequalities with one variable.

Ellipse - Activity A

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

MA.912.A.3.7: Rewrite equations of a line into slope-intercept form and standard form.

Defining a Line with Two Points

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

Using Tables, Rules and Graphs

MA.912.A.3.8: Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or point-slope form.

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

Using Tables, Rules and Graphs

MA.912.A.3.9: Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line.

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

MA.912.A.3.10: Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line.

Point-Slope Form of a Line - Activity A

Slope - Activity B

MA.912.A.3.11: Write an equation of a line that models a data set and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.

Defining a Line with Two Points

Direct Variation

Direct and Inverse Variation

Modeling Linear Systems - Activity A

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

MA.912.A.3.12: Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph.

Defining a Line with Two Points

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Linear Programming - Activity A

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Standard Form of a Line

Systems of Linear Inequalities (Slope-intercept form) - Activity A

MA.912.A.3.13: Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology.

Linear Programming - Activity A

Modeling Linear Systems - Activity A

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

Systems of Linear Inequalities (Slope-intercept form) - Activity A

MA.912.A.3.14: Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods.

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

MA.912.A.3.15: Solve real-world problems involving systems of linear equations and inequalities in two and three variables.

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Systems of Linear Inequalities (Slope-intercept form) - Activity A

MA.912.A.4: Students perform operations on polynomials. They find factors of polynomials, learning special techniques for factoring quadratics. They understand the relationships among the solutions of polynomial equations, the zeros of a polynomial function, the x-intercepts of a graph, and the factors of a polynomial.

MA.912.A.4.1: Simplify monomials and monomial expressions using the laws of integral exponents.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

MA.912.A.4.2: Add, subtract, and multiply polynomials.

Addition of Polynomials - Activity A

MA.912.A.4.3: Factor polynomial expressions.

Factoring Special Products

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

Polynomials and Linear Factors

MA.912.A.4.4: Divide polynomials by monomials and polynomials with various techniques, including synthetic division.

Dividing Exponential Expressions

Dividing Polynomials Using Synthetic Division

MA.912.A.4.5: Graph polynomial functions with and without technology and describe end behavior.

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

MA.912.A.4.6: Use theorems of polynomial behavior (including but not limited to the Fundamental Theorem of Algebra, Remainder Theorem, the Rational Root Theorem, Descartes' Rule of Signs, and the Conjugate Root Theorem) to find the zeros of a polynomial function.

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

Polynomials and Linear Factors

MA.912.A.4.7: Write a polynomial equation for a given set of real and/or complex roots.

Polynomials and Linear Factors

MA.912.A.4.8: Describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression, with and without technology.

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

Point-Slope Form of a Line - Activity A

Polynomials and Linear Factors

Slope-Intercept Form of a Line - Activity A

Using Algebraic Equations

MA.912.A.4.9: Use graphing technology to find approximate solutions for polynomial equations.

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

MA.912.A.4.10: Use polynomial equations to solve real-world problems.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

MA.912.A.4.11: Solve a polynomial inequality by examining the graph with and without the use of technology.

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Linear Programming - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Systems of Linear Inequalities (Slope-intercept form) - Activity A

MA.912.A.5: Students simplify rational expressions and solve rational equations using what they have learned about factoring polynomials.

MA.912.A.5.1: Simplify algebraic ratios.

Estimating Population Size

Part:Part and Part:Whole Ratios

Polling: Neighborhood

MA.912.A.5.4: Solve algebraic proportions.

MA.912.A.5.6: Identify removable and non-removable discontinuities and vertical, horizontal, and oblique asymptotes of a graph of a rational function, find the zeros, and graph the function.

General Form of a Rational Function

Polynomials and Linear Factors

Rational Functions

MA.912.A.6: Students simplify and perform operations on radical expressions and equations. They also rationalize square root expressions and understand and use the concepts of negative and rational exponents. They add, subtract, multiply, divide, and simplify radical expressions and expressions with rational exponents. Students will solve radical equations and equations with terms that have rational exponents.

MA.912.A.6.1: Simplify radical expressions.

Operations with Radical Expressions

Simplifying Radicals - Activity A

MA.912.A.6.2: Add, subtract, multiply and divide radical expressions (square roots and higher).

Operations with Radical Expressions

Simplifying Radicals - Activity A

Square Roots

MA.912.A.6.4: Convert between rational exponent and radical forms of expressions.

Simplifying Radicals - Activity A

MA.912.A.6.5: Solve equations that contain radical expressions.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Simplifying Radicals - Activity A

Solving Two-Step Equations

MA.912.A.7: Students draw graphs of quadratic functions. They solve quadratic equations and solve these equations by factoring, completing the square and by using the quadratic formula. They also use graphing calculators to find approximate solutions of quadratic equations.

MA.912.A.7.1: Graph quadratic equations with and without graphing technology.

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

MA.912.A.7.2: Solve quadratic equations over the real numbers by factoring, and by using the quadratic formula.

Factoring Special Products

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

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

Roots of a Quadratic

MA.912.A.7.3: Solve quadratic equations over the real numbers by completing the square.

MA.912.A.7.4: Use the discriminant to determine the nature of the roots of a quadratic equation.

MA.912.A.7.5: Solve quadratic equations over the complex number system.

MA.912.A.7.6: Identify the axis of symmetry, vertex, domain, range and intercept(s) for a given parabola.

Holiday Snowflake Designer

Introduction to Functions

Parabolas - Activity A

MA.912.A.8: Students understand the concepts of logarithmic and exponential functions. They graph exponential functions and solve problems of growth and decay. They understand the inverse relationship between exponents and logarithms and use it to prove laws of logarithms and to solve equations. They convert logarithms between bases and simplify logarithmic expressions.

MA.912.A.8.1: Define exponential and logarithmic functions and determine their relationship.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

MA.912.A.8.3: Graph exponential and logarithmic functions.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

MA.912.A.8.7: Solve applications of exponential growth and decay.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Half-life

MA.912.A.9: Students write equations and draw graphs of conic sections (circle, ellipse, parabola, and hyperbola), thus relating an algebraic representation to a geometric one.

MA.912.A.9.1: Write the equations of conic sections in standard form and general form, in order to identify the conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.).

Circles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

Standard Form of a Line

MA.912.A.9.2: Graph conic sections with and without using graphing technology.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

MA.912.A.9.3: Solve real-world problems involving conic sections

Ellipse - Activity A

Hyperbola - Activity A

MA.912.A.10: In a general sense, all of mathematics is problem solving. In all of their mathematics, students use problem-solving skills: they choose how to approach a problem, they explain their reasoning, and they check their results.

MA.912.A.10.3: Decide whether a given statement is always, sometimes, or never true (statements involving linear or quadratic expressions, equations, or inequalities rational or radical expressions or logarithmic or exponential functions).

Conditional Statement

Exponential Functions - Activity A

Logarithmic Functions - Activity A

Quadratic Inequalities - Activity A

MA.912.C: Calculus Body of Knowledge

MA.912.C.1: Students develop an understanding of the concept of limit by estimating limits graphically and numerically, and evaluating limits analytically. They extend the idea of a limit to one-sided limits and limits at infinity. They use limits to define and understand the concept of continuity, decide whether a function is continuous at a point, and find types of discontinuities. They understand and apply continuity theorems.

MA.912.C.1.1: Understand the concept of limit and estimate limits from graphs and tables of values.

Using Tables, Rules and Graphs

MA.912.C.1.4: Find limits of rational functions that are undefined at a point.

General Form of a Rational Function

Rational Functions

MA.912.C.1.11: Find the types of discontinuities of a function.

Functions Involving Square Roots

MA.912.C.3: Students apply what they learn about derivatives to find slopes of curves and the related tangent lines. They analyze and graph functions, finding where they are increasing or decreasing, their maximum and minimum points, their points of inflection, and their concavity. They solve optimization problems, find average and instantaneous rates of change (including velocities and accelerations), and model rates of change. Students find slopes and equations of tangent lines, maximum and minimum points, and points of inflection. They solve optimization problems and find rates of change.

MA.912.C.3.9: Find average and instantaneous rates of change. Understand the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed, and acceleration.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

MA.912.C.3.10: Find the velocity and acceleration of a particle moving in a straight line.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

MA.912.C.4: Students understand that integration is used to find areas and they evaluate integrals using rectangular approximations. From this, they develop the idea that integration is the inverse operation to differentiation - the Fundamental Theorem of Calculus. They use this result to find definite and indefinite integrals, including using the method of integration by substitution. They also apply approximate methods, such as the Trapezoidal Rule, to find definite integrals. Students define integrals using Riemann sums, use the Fundamental Theorem of Calculus to find integrals using antiderivatives, and use basic properties of integrals. They integrate by substitution and find approximate integrals.

MA.912.C.4.2: Calculate the values of Riemann Sums over equal subdivisions using left, right, and midpoint evaluation points.

MA.912.C.4.3: Interpret a definite integral as a limit of Riemann sums.

MA.912.C.4.8: Use Riemann Sums, the Trapezoidal Rule, and technology to approximate definite integrals of functions represented algebraically, geometrically, and by tables of values.

MA.912.D: Discrete Mathematics Body of Knowledge

MA.912.D.6: Students develop an understanding of the fundamentals of propositional logic, arguments, and methods of proof.

MA.912.D.6.3: Determine whether two propositions are logically equivalent.

MA.912.D.6.4: Use methods of direct and indirect proof and determine whether a short proof is logically valid.

Biconditional Statement

Conditional Statement

Proving Triangles Congruent

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

MA.912.D.6.5: Identify and give examples of:

MA.912.D.6.5.a: undefined terms;

MA.912.D.6.5.d: inductive and deductive proofs; and,

Biconditional Statement

Conditional Statement

MA.912.D.6.5.e: inductive and deductive reasoning.

Biconditional Statement

Conditional Statement

MA.912.D.6.7: Use applications of the universal and existential quantifiers to propositional statements.

Biconditional Statement

Conditional Statement

MA.912.D.7: Students operate with sets and use set theory to solve problems.

MA.912.D.7.2: Use Venn diagrams to explore relationships and patterns, and to make arguments about relationships between sets.

Arithmetic and Geometric Sequences

Geometric Sequences

MA.912.D.8: Students understand how matrices can be used to store and organize data and to solve systems of equations. They also use matrices to solve Markov chain problems that link present events to future events using probabilities.

MA.912.D.8.6: Use matrices to solve Markov chain problems that link present events to future events using probabilities.

Binomial Probabilities

Geometric Probability - Activity A

MA.912.D.9: Students recognize vectors in both two- and three-dimensions and that they are represented geometrically and algebraically. Students perform basic operations on vectors, including addition, scalar multiplication, dot product, and cross product. Students solve problems using vectors.

MA.912.D.9.1: Demonstrate an understanding of the geometric interpretation of vectors and vector operations including addition, scalar multiplication, dot product and cross product in the plane and in three-dimensional space.

MA.912.D.9.2: Demonstrate an understanding of the algebraic interpretation of vectors and vector operations including addition, scalar multiplication, dot product and cross product in the plane and in three-dimensional space.

MA.912.D.11: Students define and use arithmetic and geometric sequences and series.

MA.912.D.11.1: Define arithmetic and geometric sequences and series.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

MA.912.D.11.2: Use sigMAnotation to describe series.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

MA.912.D.11.3: Find specified terms of arithmetic and geometric sequences.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

MA.912.D.11.4: Find partial sums of arithmetic and geometric series, and find sums of infinite convergent geometric series. Use SigMAnotation where applicable.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

MA.912.D.11.5: Explore and use other sequences found in nature such as the Fibonacci sequence and the golden ratio.

Arithmetic and Geometric Sequences

Geometric Sequences

MA.912.F: Financial Literacy Body of Knowledge

MA.912.F.1: Simple and Compound Interest

MA.912.F.1.1: Explain the difference between simple and compound interest.

MA.912.F.1.2: Solve problems involving compound interest.

MA.912.F.1.3: Demonstrate the relationship between simple interest and linear growth

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Simple and Compound Interest

MA.912.F.1.4: Demonstrate the relationship between compound interest and exponential growth

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Half-life

Simple and Compound Interest

MA.912.F.3: Students are familiar with and can describe the advantages and disadvantages of short-term purchases, long-term purchases, and mortgages.

MA.912.F.3.8: Substitute to solve a variety of mortgage formulas, including but not limited to Front End Ratio, Total Debt-to-Income Ratio, Loan-to-Value Ratio (LTV), Combined Loan-to-Value Ratio (CLTV), and Amount of Interest Paid Over the Life of a Loan.

MA.912.F.3.10: Calculate the effects on the monthly payment in the change of interest rate based on an adjustable rate mortgage.

MA.912.F.3.12: Compare the cost of paying a higher interest rate and lower points versus a lower interest rate and more points.

MA.912.F.3.13: Calculate the total amount paid for the life of a loan for a house including the down payment, points, fees, and interest.

MA.912.F.3.17: Compare interest rate calculations and annual percentage rate calculations to distinguish between the two rates.

MA.912.G: Geometry Body of Knowledge

MA.912.G.1: Students understand geometric concepts, applications, and their representations with coordinate systems. They find lengths and midpoints of line segments, slopes, parallel and perpendicular lines, and equations of lines. Using a compass and straightedge, patty paper, a drawing program or other techniques, students also construct lines and angles, explaining and justifying the processes they use.

MA.912.G.1.1: Find the lengths and midpoints of line segments in two-dimensional coordinate systems.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

MA.912.G.1.2: Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass or a drawing program, explaining and justifying the process used.

Construct Parallel and Perpendicular Lines

Constructing Congruent Segments and Angles

MA.912.G.1.3: Identify and use the relationships between special pairs of angles formed by parallel lines and transversals.

Investigating Angle Theorems - Activity A

MA.912.G.1.4: Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.

Construct Parallel and Perpendicular Lines

Point-Slope Form of a Line - Activity A

Slope - Activity B

MA.912.G.2: Students identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. They find measures of angles, sides, perimeters, and areas of polygons, justifying their methods. They apply transformations to polygons. They relate geometry to algebra by using coordinate geometry to determine transformations. Students use algebraic reasoning to determine congruence, similarity, and symmetry. Students create and verify tessellations of the plane using polygons.

MA.912.G.2.2: Determine the measures of interior and exterior angles of polygons, justifying the method used.

Triangle Angle Sum - Activity A

MA.912.G.2.3: Use properties of congruent and similar polygons to solve mathematical or real-world problems.

Classifying Triangles

Congruence in Right Triangles

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures - Activity A

Similar Polygons

MA.912.G.2.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons. to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations of the plane using polygons.

Dilations

Holiday Snowflake Designer

Perimeters and Areas of Similar Figures

Reflections

Rotations, Reflections and Translations

Similar Figures - Activity A

Similar Polygons

Translations

MA.912.G.2.5: Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.).

Area of Parallelograms - Activity A

Perimeter, Circumference, and Area - Activity B

Rectangle: Perimeter and Area

MA.912.G.2.6: Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane.

Classifying Triangles

Congruence in Right Triangles

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Rotations, Reflections and Translations

Similar Figures - Activity A

Similar Polygons

MA.912.G.2.7: Determine how changes in dimensions affect the perimeter and area of common geometric figures.

Area of Parallelograms - Activity A

Circle: Circumference and Area

Minimize Perimeter

Perimeter, Circumference, and Area - Activity B

Rectangle: Perimeter and Area

MA.912.G.3: Students classify and understand relationships among quadrilaterals (rectangle, parallelogram, kite, etc.). They relate geometry to algebra by using coordinate geometry to determine regularity, congruence, and similarity. They use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas, and prove theorems involving quadrilaterals.

MA.912.G.3.1: Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus, parallelogram, trapezoid, and kite.

Classifying Quadrilaterals - Activity B

Parallelogram Conditions

Special Quadrilaterals

MA.912.G.3.2: Compare and contrast special quadrilaterals on the basis of their properties.

Classifying Quadrilaterals - Activity B

Congruence in Right Triangles

Parallelogram Conditions

Proving Triangles Congruent

Special Quadrilaterals

MA.912.G.3.3: Use coordinate geometry to prove properties of congruent, regular and similar quadrilaterals.

Classifying Quadrilaterals - Activity B

Congruence in Right Triangles

Parallelogram Conditions

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures - Activity A

Similar Polygons

Special Quadrilaterals

MA.912.G.3.4: Prove theorems involving quadrilaterals

MA.912.G.4: Students identify and describe various kinds of triangles (right, acute, scalene, isosceles, etc.). They define and construct altitudes, medians, and bisectors, and triangles congruent to given triangles. They prove that triangles are congruent or similar and use properties of these triangles to solve problems involving lengths and areas. They relate geometry to algebra by using coordinate geometry to determine regularity, congruence, and similarity. They understand and apply the inequality theorems of triangles.

MA.912.G.4.1: Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.

Classifying Triangles

Pythagorean Theorem - Activity B

Triangle Angle Sum - Activity A

MA.912.G.4.2: Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors, orthocenter, centroid, incenter, and circumcenter.

Concurrent Lines, Medians, and Altitudes

MA.912.G.4.3: Construct triangles congruent to given triangles.

Congruence in Right Triangles

Proving Triangles Congruent

MA.912.G.4.4: Use properties of congruent and similar triangles to solve problems involving lengths and areas.

Congruence in Right Triangles

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures - Activity A

Similar Polygons

MA.912.G.4.5: Apply theorems involving segments divided proportionally.

Estimating Population Size

Perimeters and Areas of Similar Figures

Polling: Neighborhood

Similar Figures - Activity A

Similar Polygons

MA.912.G.4.6: Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.

Congruence in Right Triangles

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures - Activity A

Similar Polygons

MA.912.G.4.7: Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem.

MA.912.G.4.8: Use coordinate geometry to prove properties of congruent, regular, and similar triangles.

Congruence in Right Triangles

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures - Activity A

Similar Polygons

MA.912.G.5: Students apply the Pythagorean Theorem to solving problems, including those involving the altitudes of right triangles and triangles with special angle relationships. Students use special right triangles to solve problems using the properties of triangles.

MA.912.G.5.1: Prove and apply the Pythagorean Theorem and its converse.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

MA.912.G.5.2: State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.

MA.912.G.5.4: Solve real-world problems involving right triangles.

MA.912.G.6: Students define and understand ideas related to circles (radius, tangent, chord, etc.). They perform constructions and prove theorems related to circles. They find measures of arcs and angles related to them, as well as measures of circumference and area. They relate geometry to algebra by finding the equation of a circle in the coordinate plane.

MA.912.G.6.1: Determine the center of a given circle. Given three points not on a line, construct the circle that passes through them. Construct tangents to circles. Circumscribe and inscribe circles about and within triangles and regular polygons.

MA.912.G.6.2: Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.

Chords and Arcs

Circle: Circumference and Area

MA.912.G.6.3: Prove theorems related to circles, including related angles, chords, tangents, and secants.

MA.912.G.6.4: Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).

Chords and Arcs

Inscribing Angles

MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

Circle: Circumference and Area

Perimeter, Circumference, and Area - Activity B

MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.

MA.912.G.6.7: Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of the circle.

MA.912.G.7: Students describe and make regular and nonregular polyhedra (cube, pyramid, tetrahedron, octahedron, etc.). They explore relationships among the faces, edges, and vertices of polyhedra. They describe sets of points on spheres, using terms such as great circle. They describe symmetries of solids and understand the properties of congruent and similar solids.

MA.912.G.7.1: Describe and make regular, non-regular, and oblique polyhedra and sketch the net for a given polyhedron and vice versa.

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

MA.912.G.7.3: Identify, sketch, and determine areas and/or perimeters of cross sections of three-dimensional solids.

Minimize Perimeter

Perimeter, Circumference, and Area - Activity B

Rectangle: Perimeter and Area

MA.912.G.7.4: Identify chords, tangents, radii, and great circles of spheres.

MA.912.G.7.5: Explain and use formulas for lateral area, surface area, and volume of three-dimensional solids.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

MA.912.G.7.6: Identify and use properties of congruent and similar three-dimensional solids.

Congruence in Right Triangles

Constructing Congruent Segments and Angles

Proving Triangles Congruent

MA.912.G.7.7: Determine how changes in dimensions affect the surface area and volume of common three-dimensional geometric solids.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

MA.912.G.8: In a general sense, mathematics is problem solving. In all mathematics, students use problem-solving skills: they choose how to approach a problem, they explain their reasoning, and they check their results. At this level, students apply these skills to making conjectures, using axioms and theorems, constructing logical arguments, and writing geometric proofs. They also learn about inductive and deductive reasoning and how to use counterexamples to show that a general statement is false.

MA.912.G.8.4: Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

Biconditional Statement

Conditional Statement

Proving Triangles Congruent

MA.912.G.8.5: Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs.

Biconditional Statement

Conditional Statement

Proving Triangles Congruent

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

MA.912.G.8.6: Perform basic constructions using straightedge and compass, and/or drawing programs describing and justifying the procedures used. Distinguish between sketching, constructing and drawing geometric figures.

Construct Parallel and Perpendicular Lines

Constructing Congruent Segments and Angles

MA.912.P: Probability Body of Knowledge

MA.912.P.1: Students understand the counting principle, permutations, and combinations and use them to solve problems.

MA.912.P.1.1: Use counting principles, including the addition and the multiplication principles, to determine size of finite sample spaces and probabilities of events in those spaces.

Binomial Probabilities

Geometric Probability - Activity A

MA.912.P.1.2: Use formulas for permutations and combinations to count outcomes and determine probabilities of events.

Binomial Probabilities

Permutations

Permutations and Combinations

MA.912.P.2: Students develop rules for finding probabilities of combined and complementary events. They understand and use conditional probability and the related Bayes' Theorem.

MA.912.P.2.2: Determine probabilities of independent events.

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

MA.912.P.3: Students investigate probability distributions and calculate and interpret their means and variances. They use and apply the normal distribution, including using the central limit theorem.

MA.912.P.3.1: Determine probabilities of events from distributions, including:

MA.912.P.3.1.a: discrete uniform (all outcomes in a finite set equally likely)

Binomial Probabilities

Geometric Probability - Activity A

MA.912.P.3.1.b: binomial

Binomial Probabilities

Geometric Probability - Activity A

MA.912.P.3.1.d: exponential

Binomial Probabilities

Geometric Probability - Activity A

MA.912.P.3.2: Determine the mean and variance of distributions, including:

MA.912.P.3.2.b: binomial

MA.912.P.3.4: Apply the Central Limit Theorem to determine the probability that a sample mean will be in a certain interval.

Geometric Probability - Activity A

MA.912.S: Statistics Body of Knowledge

MA.912.S.2: Students learn key methods for collecting data and basic sampling principles.

MA.912.S.2.2: Apply the definition of random sample and basic types of sampling, including representative samples, stratified samples, censuses.

MA.912.S.3: Students learn to work with summary measures of sets of data, including measures of the center, spread, and strength of relationship between variables. Students learn to distinguish between different types of data and to select the appropriate visual form to present different types of data.

MA.912.S.3.1: Read and interpret data presented in various formats. Determine whether data is presented in appropriate format, and identify possible corrections. Formats to include:

MA.912.S.3.1.c: stem and leaf plots

MA.912.S.3.1.e: histograms

Histograms

Populations and Samples

MA.912.S.3.1.f: box and whiskers plots

MA.912.S.3.1.g: scatter plots

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

MA.912.S.3.1.h: cumulative frequency (ogive) graphs

Box-and-Whisker Plots

Line Plots

Stem-and-Leaf Plots

MA.912.S.3.2: Collect, organize, and analyze data sets, determine the best format for the data and present visual summaries from the following:

MA.912.S.3.2.c: stem and leaf plots

MA.912.S.3.2.e: histograms

Histograms

Populations and Samples

MA.912.S.3.2.f: box and whisker plots

MA.912.S.3.2.g: scatter plots

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

MA.912.S.3.2.h: cumulative frequency (ogive) graphs

Box-and-Whisker Plots

Line Plots

Stem-and-Leaf Plots

MA.912.S.3.3: Calculate and interpret measures of the center of a set of data, including mean, median, and weighted mean, and use these measures to make comparisons among sets of data.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

Populations and Samples

MA.912.S.3.4: Calculate and interpret measures of variance and standard deviation. Use these measures to make comparisons among sets of data.

MA.912.S.3.5: Calculate and interpret the range and quartiles of a set of data.

Box-and-Whisker Plots

Describing Data Using Statistics

Line Plots

MA.912.S.3.6: Use empirical rules (e.g. 68-95-99.7 rule) to estimate spread of distributions and to make comparisons among sets of data.

MA.912.S.3.7: Calculate the correlation coefficient of a set of paired data, and interpret the coefficient as a measure of the strength and direction of the relationship between the variables.

MA.912.S.3.9: Identify outliers in a set of data based on an appropriate graphical presentation of the data, and describe the effect of outliers on the mean, median, and range of the data.

Describing Data Using Statistics

Mean, Median and Mode

MA.912.S.4: Students learn to use simulations of standard sampling distributions to determine confidence levels and margins of error. They develop measures of association between two numerical or categorical variables. They can use technological tools to find equations of regression lines and correlation coefficients.

MA.912.S.4.2: Use a simulation to approximate sampling distributions for the mean, using repeated sampling simulations from a given population.

Mean, Median and Mode

Polling: City

Populations and Samples

Probability Simulations

MA.912.S.4.4: Approximate confidence intervals for means using simulations of the distribution of the sample mean.

Line Plots

Mean, Median and Mode

Populations and Samples

Probability Simulations

MA.912.S.4.5: Find the equation of the least squares regression line for a set of data.

Correlation

Solving Using Trend Lines

MA.912.S.5: Students use simulations of sampling distributions to determine confidence intervals to make inferences about means, use hypothesis tests to make decisions. They learn to use simulations to approximate p-values, and to determine whether correlations between variables are significant.

MA.912.S.5.1: Analyze the relationship between confidence level, margin of error and sample size.

Polling: City

Polling: Neighborhood

MA.912.S.5.5: Perform hypothesis tests of means and proportions for large samples, using simulations to determine whether a sample mean (proportion) has a low likelihood of occurring.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

Probability Simulations

MA.912.S.5.6: Interpret the results of hypothesis tests of means and proportions, and make decisions based on p-values of test.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

MA.912.S.5.7: Use simulations to approximate the p-value of a correlation coefficient, and use the results to determine whether the correlation between two variables is significant.

Correlation

Probability Simulations

MA.912.S.5.9: Interpret the coefficient of determination, r_, for a least-squares regression.

Correlation

Solving Using Trend Lines

MA.912.T: Trigonometry Body of Knowledge

MA.912.T.1: Students extend the definitions of the trigonometric functions beyond right triangles using the unit circle and they measure angles in radians as well as degrees. They draw and analyze graphs of trigonometric functions (including finding period, amplitude, and phase shift) and use them to solve word problems. They define and graph inverse trigonometric functions and determine values of both trigonometric and inverse trigonometric functions.

MA.912.T.1.2: Define and determine sine and cosine using the unit circle.

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Translating and Scaling Sine and Cosine Functions - Activity A

Unit Circle

MA.912.T.1.3: State and use exact values of trigonometric functions for special angles, i.e. multiples of pi/6 and pi/4 (degree and radian measures).

Cosine Function

Sine Function

Tangent Function

Unit Circle

MA.912.T.1.4: Find approximate values of trigonometric and inverse trigonometric functions using appropriate technology.

Cosine Function

Sine Function

Tangent Function

MA.912.T.1.5: Make connections between right triangle ratios, trigonometric functions, and circular functions.

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

Unit Circle

MA.912.T.1.6: Define and graph trigonometric functions using domain, range, intercepts, period, amplitude, phase shift, vertical shift, and asymptotes with and without the use of graphing technology.

Cosine Function

Introduction to Functions

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

Unit Circle

MA.912.T.1.8: Solve real-world problems involving applications of trigonometric functions using graphing technology when appropriate.

Cosine Function

Sine Function

Tangent Function

MA.912.T.2: Students understand how the trigonometric functions relate to right triangles and solve word problems involving right and oblique triangles. They understand and apply the laws of sines and cosines. They use trigonometry to find the area of triangles.

MA.912.T.2.1: Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, and cosecant) in terms of angles of right triangles.

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Ratio

MA.912.T.2.4: Use the area of triangles given two sides and an angle or three sides to solve real-world problems.

Classifying Triangles

Isosceles and Equilateral Triangles

Triangle Angle Sum - Activity A

MA.912.T.3: Students know basic trigonometric identities derived from definitions and use them to prove other identities. They use the sum, difference, double-angle, and half-angle formulas. They solve trigonometric equations and word problems using trigonometry.

MA.912.T.3.1: Verify the basic Pythagorean identities, e.g., sin_x + cos_x = 1, and show they are equivalent to the Pythagorean Theorem.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

Simplifying Trigonometric Expressions

MA.912.T.3.2: Use basic trigonometric identities to verify other identities and simplify expressions.

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

MA.912.T.3.3: Use the sum and difference, half-angle and double-angle formulas for sine, cosine, and tangent, when formulas are provided.

Cosine Function

Sine Function

Sine, Cosine and Tangent

Sum and Difference Identities for Sine and Cosine

Tangent Function

Tangent Ratio

Unit Circle

MA.912.T.4: Students define, use polar coordinates, and relate them to Cartesian coordinates. They translate equations in terms of Cartesian coordinates into polar coordinates and graph the resulting equations in the polar coordinate plane. They convert complex numbers from standard to trigonometric form, and vice-versa. They multiply complex numbers in trigonometric form and use De Moivre's Theorem.

MA.912.T.4.1: Define polar coordinates and relate polar coordinates to Cartesian coordinates with and without the use of technology.

MA.912.T.4.2: Represent equations given in rectangular coordinates in terms of polar coordinates.

MA.912.T.4.3: Graph equations in the polar coordinate plane with and without the use of graphing technology.

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

MA.912.T.5: Students use a variety of strategies to solve problems. They develop and evaluate mathematical arguments and proofs.

MA.912.T.5.3: Determine whether a given trigonometric statement is always, sometimes, or never true. Use the properties of the real numbers, order of operations, and trigonometric identities to justify the steps involved in verifying identities and solving equations.

Conditional Statement

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Simplifying Trigonometric Expressions

Solving Two-Step Equations

Sum and Difference Identities for Sine and Cosine

Correlation last revised: 10/21/2009