Content Map For Mathematics

Henry County Public Schools Teacher’s Guide For Curriculum, Instruction, & Assessment School Year 2001-2002

Content Map For Mathematics

Concepts of Problem Solving Probability & Statistics

MA-CPSTAT-1 Reinforce basic algebra skills. A. Perform operations with signed numbers. B. Write mathematical expressions. C. Solve simple equations (1 and 2 step). D. Plot ordered pairs using coordinate plane. E. Use order of operations.

MA-CPSTAT-2 Gather, explore, and interpret data.

A. Collect data, discuss and interpret results. B. Construct and interpret circle graphs, line graphs, pictographs, bar graphs,

histograms, stem-and-leaf plots, and box-and-whisker plots. C. Compare several data sets. D. Calculate and appropriately apply mean, median, mode, range, quantities,

and percentiles. E. Identify trends in data. F. Construct, interpret, and make predictions using scatter plots. G. Understand the concept of correlation. H. Construct and interpret a plot of data over time.

MA-CPSTAT-3 Explore simulation and calculate probability.

A. Observe and collect real data for applications in experimental probability. B. Use random number tables for practical problems. C. Assign theoretical probabilities to equally likely events. D. Recognize and assign probabilities to complementary events. E. Evaluate the probability of a compound event. F. Distinguish between independent and dependent events. G. Compute expected values for simple experimental situations. H. Perform simulations for practical problems.

MA-CPSTAT-4 Apply statistical inference.

A. Plot and interpret experimental data. B. Use student investigations and simulations to construct sampling

distributions. C. Use box plots to summarize sampling distributions. D. Construct confidence intervals. E. Apply capture-recapture model. F. Formulate and test hypotheses informally through confidence interval

arguments.



Concepts of Probability & StatisticsProblem Solving

MA-CPSTAT-5 Explore geometry and measurement A. Estimate and apply metric and customary measurements. B. Classify angles and triangles (obtuse, right, acute, equiangular, equilateral,

isosceles, scalene). C. Use Pythagorean Theorem to solve problems. D. Identify geometric figures in everyday life (lines, angles, circles, polygons,

cylinders, cones, rectangular solids, and spheres). E. Calculate perimeter, area, and volume of geometric figures. F. Apply geometric properties (missing angles, parallel sides of figures). G. Identify figures that have been transformed by reflection, rotation, and

translation. H. Use ratios and proportions to solve problems. I. Solves problems involving congruent and similar figures and scale

drawings. MA-CPSTAT-6 Examine statistics in society.

A. Plan, conduct, and analyze experiments realizing the impact of sample size and bias.

B. Distinguish among sampling schemes and understand the concept of randomness.

C. Interpret results of polls and surveys discussed in the media including public opinion polls, the Nielsen ratings, the U.S. Census, and surveys that determine the consumer price indices.

D. Examine the use of statistics in areas such as business, medicine, agriculture, engineering, and industry.

E. Use the media to identify correct uses and misuses of statistics. MA-CPSTAT-7 Apply appropriate strategies to communicate and solve problems throughout the

course. A. Reach a valid and supportable conclusion. B. Judge the reasonableness of a proposed solution. C. Express mathematical ideas both orally and in writing. D. Interpret written presentations of mathematics.

MA-CPSTAT-8 Apply reasoning skills.

A. Make and test conjectures. B. Formulate counter examples. C. Follow logical arguments. D. Judge the validity for arguments. E. Construct simple arguments.



Fundamentals of Algebra

MA-FOA-1 Learn to name, manipulate, and apply concepts using Lab Gear. A. Find perimeter and area of geometric figures and label with appropriate unit

measures. B. Simplify expressions using the order of operations, combination of like terms, and

the distributive property using manipulatives and algebraically. C. Evaluate expressions using manipulatives and algebraically. D. Use physical models to explain mathematical relationships. MA-FOA-2 Understand functions and operations. A. Add, subtract, multiply, and divide real numbers using calculators, mental

computation, and Lab Gear. B. Find the absolute value of a given number. C. Write an equation from a data table. D. Show the relationship of quantities by graphing, data tables, and function diagrams. E. Read and interpret function diagrams. F. Use patterns and sequences to predict future outcomes. MA-FOA-3 Explore algebraic concepts utilizing problem solving skills and Lab Gear. A. Solve linear equations using number sense. B. Determine the reasonableness of an answer using estimation. C. Graph points and lines. D. Combine two functions on a function diagram and write the equation for the

combined function. E. Multiply and divide polynomials with Lab Gear, transferring to abstract operation. MA-FOA-4 Draw and interpret graphs and make predictions using graphs. A. Recognize slope as a ratio and/or rate of change. B. Recognize parallel lines and perpendicular lines. C. Graph and recognize characteristics of linear functions in slope-intercept form. D. Graph and recognize the characteristics of quadratic functions f(x)=ax2 and cubic

function (f)x=ax3. E. Graph equations with a calculator. F. Use physical models to explain mathematical relationships. G. Use estimation to determine if an answer is appropriate. H. Solve rate of change problems involving velocity. I. Find the mean, median, mode and range of a set of data. J. Use algebraic concepts to formulate solutions to everyday problems.



Fundamentals of Algebra

MA-FOA-5 Explore more advanced concepts of algebra. A. Recognize rational and irrational numbers. B. Simplify square roots. C. Simplify and evaluate radical and exponential expressions. D. Apply the Pythagorean Theorem. E. Solve systems of linear equations by graphing, substitution, and linear combination. F. Solve quadratic equations by factoring, a table of values, the quadratic formula, and

graphing.



Applied Problem Solving

MA-APSMI-1 Perform four basic operations using the calculator. MA-APSMI-2 Evaluate expressions using parentheses to group the four basic operations. MA-APSMI-3 Convert between standard, scientific, and exponential notation. MA-APSMI-4 Convert between fractions, decimals, and percentages. MA-APSMI-5 Solve problems that contain information in the form of whole numbers,

fractions, decimals, or percentages. MA-APSMI-6 Solve problems using the four basic steps for problem solving. MA-APSMI-7 Use patterns, charts, and tables to develop models for problem-solving. MA-APSMI-8 Determine the reasonableness of the model for problem-solving. MA-APSMI-9 Identify place value. MA-APSMI-10 Estimate using rounding and truncating; recognize appropriate situations in

which to use exact and approximate numbers. MA-APSMI-11 Determine the reasonableness of result of calculations. MA-APSMI-12 Use tools to measure in English and Metric units and solve problems

involving these measurements. MA-APSMI-13 Convert within systems of measurements and between systems of

measurements. MA-APSMI-14 Define and use geometric terms to measure segments and circles, and

measure and classify angles. MA-APSMI-15 Measure and draw segments and angles using appropriate tools. MA-APS-16 Identify the parts of a triangle and classify triangles. MA-APSMI-167 Apply angle relationships to determine supplementary, complementary,

vertical and right angles. MA-APSMI-178 Identify parallel and perpendicular lines. MA-APSMI-189 Identify and apply angle relationships between parallel and perpendicular

lines (corresponding, alternate interior/exterior, and same-side interior angles).



Applied Problem Solving

MA-APSMI-1920 Identify formulas for two-dimensional geometric figures which involve area and perimeter.

MA-APSMI-201 Apply formulas to solve problems using two-dimensional geometric

figures.

MA-APSMI-212 Identify formulas for three-dimensional geometric figures which involve surface area and volume.

MA-APSMI-223 Apply formulas to solve problems using three-dimensional geometric

figures.

MA-APSMI-234 Write and solve ratio and proportion equations.

MA-APSMI-245 Apply ratios and proportions to scale drawings.

MA-APSMI-256 Perform the four basic operations using real numbers.

MA-APSMI-267 Graph and identify points and vectors on a coordinate plane.

MA-APSMI-278 Recognize that roots and powers are inverse operations.

MA-APSMI-289 Evaluate roots and powers with and without a calculator.

MA-APSMI-2930 Simplify radicals. MA-APS-31 Use the Pythagorean Theorem to determine the length of the side of a right

triangle and the distance between two points. MA-APSMI-302 Solve one and two step equations. MA-APSMI-313 Combine like terms on both sides of an equation. MA-APSMI-324 Use the distributive property in simplifying equations.



Applied Algebra

MA-AAMII-1 Read and write a formula. MA-AAMII-2 Rearrange the parts of a formula to fit particular problems. MA-AAMII-3 Substitute values into formulas and evaluate. MA-AAMII-4 Use the calculator to solve problems involving formulas and linear equations. MA-AAMII-5 Identify and evaluate linear equations for a given number in the domain. MA-AAMII-6 Solve anand check equation for a given variable. (Place linear equations in slope

intercept form.) MA-AA-7 Place linear equations in slope-intercept form. MA-AAMII-78 Construct an X-Y table for a linear equation. MA-AAMII-89 Identify and determine the slope and intercepts of a linear equation. MA-AAMII-910 Write the equation for a line given its graph or two points on the line. MA-AAMII-101 Graph lines on a coordinate plane. MA-AAMII-112 Identify parabolic, hyperbolic, and exponential equations and their graphs. MA-AAMII-123 Solve and graph parabolic, hyperbolic, and exponential equations. MA-AAMII-134 Find pairs of values for a nonlinear formula in a stated problem, graph the

formula, and evaluate the results. MA-AAMII-145 Recognize and interpret data from tables, bar graphs, line/multiline

graphs, circle graphs, scatter plots and histograms. MA-AAMII-156 Identify and use correct data collecting procedures. MA-AAMII-167 Collect and organize data, construct tables, and draw bar graphs,

line/multiline graphs, circle graphs, scatter plots and histograms. MA-AAMII-178 Determine the appropriateness of a given statistic. MA-AAMII-189 Evaluate measures of central tendency and variability of a given set of

data.



Applied Algebra

MA-AAMII-1920 Interpret the characteristics of a normal curve. MA-AAMII-201 Solve problems involving statistics. MA-AAMII-212 Use the fundamental principles of counting to find a sample space. MA-AAMII-223 Determine the sample space of a given event. MA-AAMII-234 Determine the probability and odds of a given event. MA-AMII-24 Identify the parts of a triangle and classify a triangle as acute, right, or obtuse. MA-AMII-25 Use the Pythagorean Theorem to determine the length of the side of a right

triangle, and the distance between two points. MA-AMII-26 Use sine, cosine, and tangent ratios to solve problems involving right triangles. MA-AMII-27 Use special right triangles (3-4-5, 5-12-13, 30o-60o-90o, and 45o -45o -90o) to

solve practical problems. MA-AMII-28 Find and graph values for sine and cosine. MA-AMII-29 Determine amplitude, wavelength, period, and frequency of sine waves. MA-AMII-30 Determine the phase shift between sine waves. MA-AMII-31 Use the Law of Sines and Law of Cosines to solve practical problems. MA-AAMII-3225 Identify, combine, and factor polynomial expressions. MA-AAMII-3326 Solve problems which involve factoring. MA-AAMII-3427 Use patterns to write polynomial functions. MA-AAMII-3528 Distinguish between functions and relations. MA-AAMII-3629 Use patterns and functions in problem solving.



Applied Algebra

MA-AMII-39 Identify and graph conic sections on a coordinate plane. MA-AMII-38 Evaluate conic sections for a given value. MA-AAMII-3930 Use the quadratic formula to solve quadratic equations.Solve quadratic

equations using quadratic formula, factoring, and graphing calculator. MA-AAMII-4031 Solve problems involving quadratic equations. MA-AAMII-4132 Solve systems of equations using graphing, linear combinations,

matrices, and determinants. MA-AAMII-4233 Input and manipulate matrices using a calculator. MA-AAMII-4334 Solve problems using systems of equations. MA-AAMII-4435 Graph and solve algebraic inequalities. MA-AA-36 Distinguish between counting and measuring and between precision and

accuracy. MA-AA-37 Read and write measurements to show precision and tolerance, and compares

measurements to specified tolerances. MA-AA-38 Use precision tools to measure and use significant digits to indicate the accuracy

of a measurement. MA-AA-39 Use precise measurements to calculate thickness of pipe and area, volume, and

surface area of objects.



Algebra I

MA-ALG1-1 Explore data and relationships. A. Analyze data using bar graphs and circle graphs. B. Add, subtract, multiply, and divide real numbers using calculators and mental

computation. C. Add and subtract real numbers using matrices. D. Perform scalar multiplication with matrices. E. Find measures of central tendency. F. Show the relationship between two variables by graphing points. G. Find theoretical and experimental probabilities. MA-ALG1-2 Explore, represent, and find patterns for quantities. A. Identify quantities as constant or variable. B. Describe and interpret the relationship between two quantities as inverse or

direct. C. Use algebraic notation to write expressions. MA-ALG1-3 Simplify expressions. A. Use order of operations to evaluate expressions.

B. Use the distributive property. B.C. Combine like terms.

MA-ALG1-4 Recognize and represent functional relationships. A. Write an equation from a data table. B. Find the rate of change from patterns. C. Show the relationship between two quantities by graphing points and lines.

D. Graph and recognize characteristics of linear functions. D.E. Identify domain and range.

MA-ALG1-5 Solve linear equations. A. Solve linear equations using number sense. B. Solve linear equations using graphing. C. Solve linear equations using the properties of equality. MA-ALG1-6 Solve linear inequalities. A. Solve linear inequalities with one variable using properties of equality. B. Graph linear inequalities with one variable.



Algebra I

MA-ALG1-7 Analyze linear functions. A. Recognize slope as a ratio. B. Recognize slope as a rate of change. C. Determine the slope of a line. D. Determine the equation of a line. E. Graph and recognize the characteristics of linear equations in slope-

intercept form. F. Graph and recognize slopes of parallel and perpendicular lines. G. Graph linear equations with a calculator. MA-ALG1-8 Solve systems of linear equations. A. Solve systems of linear equations by graphing, substitution, linear

combination and matrices. B. Solve problems using systems of equations. MA-ALG1-9 Solve systems of linear inequalities. A. Graph linear inequalities with two variables and solve related problems. B. Solve systems of linear inequalities by graphing. MA-ALG1-10 Find distances on a number line and plane. A. Find the absolute value of a given number. B. Solve absolute value equations. C. Graph and recognize the characteristics of absolute value functions. D. Simplify square roots. E. Recognize rational and irrational numbers. F. Graph and recognize the characteristics of square root functions. G. Measure distances using the distance formula and Pythagorean Theorem. MA-ALG1-11 Perform mathematical operations with polynomials. A. Identify polynomial expressions. B. Add and subtract polynomials. C. Multiply and divide monomials using laws of exponents. D. Multiply polynomials. E. Factor polynomials following whole number factorization including GCF. F. Simplify polynomial fractions using factoring.



Algebra I

MA-ALG1-12 Graph and solve quadratic function. A. Graph and recognize the characteristics of quadratic functions f(x)=ax2 B. Show the relationship between two variables by graphing parabolas. C. Solve quadratic equations using factoring, square roots, and the quadratic

formula. TO BE USED THROUGHOUT THE COURSE: MA-ALG1-13 Use correct measurement units, solve problems involving units of

measurement. MA-ALG1-14 Use physical models to explain mathematical relationships. MA-ALG1-15 Use algebraic concepts to formulate solutions to everyday problems. MA-ALG1-16 Use estimation to determine if an answer is appropriate. MA-ALG1-17 Select and apply best strategy to solve problems.



Informal Geometry

MA-IG-1 Reinforce basic algebra skills. A. Perform operations with signed numbers. B. Write mathematical expressions. C. Solve simple equations (1 and 2 step). D. Plot ordered pairs using coordinate plane. E. Use order of operations.

MA-IG-2 Explore measurement.

A. Estimate metric and customary measurements. B. Apply metric and customary measurements to problems.

MA-IG-3 Introduce geometric terms and ideas.

A. Identify and define basic geometric terms (point, line, plane, segment, angle, ray, congruence, complementary, supplementary, parallel, perpendicular, bisect, midpoint, vertical, radius, diameter, circumference).

B. Apply basic facts about points, lines, planes, perpendicular and parallel lines and planes.

C. Identify and recognize congruence in practical application. D. Identify geometric figures in everyday life (lines, angles, circles,

polygons, cylinders, cones, rectangular solids, and spheres). MA-IG-4 Explore properties of geometric figures.

A. Classify angles and triangles (obtuse, right, acute, equiangular, equilateral, isosceles, scalene).

B. Use Pythagorean Theorem to solve problems. C. Calculate perimeter, area, and volume of geometric figures with correct

units. D. Find missing angle measures. E. Identify figures that have been transformed by reflection, rotation, and

translation. F. Use ratios and proportions to solve problems. G. Solves problems involving congruent and similar figures and scale

drawings.



Geometry

MA-GEOM-1 Create mathematical models (geometric, algebraic, and Venn diagrams) to represent real world concepts.

MA-GEOM-2 Continually use algebra with geometric logic to solve problems and judge

reasonableness of results. MA-GEOM-3 Use given information, learned facts, and laws of logic to reach valid

conclusions through inductive and deductive reasoning (including proofs). MA-GEOM-4 Restate conditional statements in their converse, inverse, and contrapositive

form, testing the validity of each. MA-GEOM-5 Name, classify, and identify geometric figures using accepted notation. MA-GEOM-6 Use tools, definitions, axioms, and theorems to determine segment or angle

measures. Extend to encompass midpoints, distance formula, bearings, and vectors.

MA-GEOM-7 Recognize and illustrate transformations of geometric figures, distinguishing

between those that preserve size and shape and those that do not. MA-GEOM-8 Identify and apply special relationships among lines, rays, segments, angles,

and planes including transversals, parallel lines, perpendicular lines, linear pairs, vertical angles, complementary angles, and supplementary angles.

MA-GEOM-9 Apply the interior and exterior angle sum theorems for triangles. MA-GEOM-10 Establish and prove congruence between triangles using postulates and

theorems. MA-GEOM-11 Define and illustrate medians, altitudes and points of concurrency in triangles. MA-GEOM-12 Draw a figure as described by a condition or set of conditions. MA-GEOM-13 Find perimeter and area of two-dimensional figures using formulas.



Geometry

MA-GEOM-14 Use given information to find missing measures in right triangles using the Pythagorean Theorem. Recognize common Pythagorean triples and special right triangle ratios.

MA-GEOM-15 Demonstrate knowledge of properties of convex polygons with an emphasis

on angle measures of regular polygons. MA-GEOM-16 State and apply properties of triangles and quadrilaterals such as

parallelograms, rectangles, rhombi, squares, and trapezoids. MA-GEOM-17 Write and solve proportions to find missing measures of angles and sides of

similar figures. MA-GEOM-18 Choose appropriate trigonometric ratios and solve for unknown angle

measures and side lengths in various problems including angles of elevation and depression.

MA-GEOM-19 Apply the formulas for circumference and area to circles, arcs, and sectors. MA-GEOM-20 Employ the relationships between angles and intercepted arcs to determine

unknown measures. MA-GEOM-21 Calculate lateral area, surface area, and volume of three-dimensional figures

including prisms, pyramids, spheres, cones, and cylinders.



Algebra II

MA-ALG2-1 Use mathematical models. A. Use graphical models to solve problems. B. Use probability and simulation to solve problems. C. Use matrices to organize data. D. Demonstrate calculator skills to solve problems. MA-ALG2-2 Solve and graph linear equations and inequalities. A. Solve linear equations in one variable. B. Graph linear equations in two variables. C. Identify and graph parallel and perpendicular lines. D. Use properties of lines to write an equation for the line. E. Use statistical linear models to solve problems. F. Solve and graph one variable inequalities. G. Graph linear inequalities in two variables. MA-ALG2-3 Solve systems of linear equations and inequalities. A. Solve a linear system of equations in two or three variables by a variety of

methods to include graphing, algebraic manipulation, and matrices. B. Solve a system of linear inequalities by graphing. MA-ALG2-4 Use real numbers. A. Identify properties of the real number system. B. Simplify and evaluate expressions involving imaginary and complex

numbers. MA-ALG2-5 Explore quadratic functions and relations. A. Investigate quadratic functions using the graphing calculator. B. Solve quadratic equations in one variable by a variety of methods to

include graphing, factoring, completing the square, and the quadratic formula.

C. Identify conic sections by the equation. D. Graph conic sections on a coordinate plane.



Algebra II

MA-ALG2-6 Investigate roots and powers. A. Simplify and evaluate exponential and radical expressions. B. Solve radical equations. C. Solve problems involving various types of variation to include direct and

inverse proportions. D. Combine functions to include operations with functions, composition of

functions, and inverse relationships. MA-ALG2-7 Analyze polynomials and polynomial functions. A. Analyze the graph of a polynomial function to determine the intercepts,

maximums, and minimums. B. Solve a polynomial equation by using a graphing calculator. C. Simplify rational expressions. D. Solve rational equations. MA-ALG2-8 Graph and solve exponential and logarithmic functions. A. Graph exponential and logarithmic functions. B. Simplify exponential and logarithmic expressions. C. Solve exponential and logarithmic equations. MA-ALG2-9 Use patterns and relationships to solve problems. A. Compute the nth term of an arithmetic or geometric sequence. B. Compute the sum of an arithmetic or geometric series. MA-ALG2-10 Apply counting rules for discrete objects. A. Apply fundamental counting principles. B. Count the number of permutations or combination of a given set.



Algebra III

MA-ALG3-1 Help students prepare for the SAT. A. Identify test-taking strategies. B. Practice sample problems. C. Work through sample tests. D. Interpret instructions. E. Discuss scoring methods. F. Review algebra and geometry concepts. G. Review factorials. MA-ALG3-2 Practice the conversions between fractions, decimals, and percents without

the use of calculators. A. Review of decimals. B. Use rounding to measure reasonableness.

C. Reduce simple fractions. D. Perform basic operations with fractions.

MA-ALG3-3 Factor quadratics and cubes using a variety of methods. A. Factor using grouping. B. Factor using difference of two squares. C. Factor using binomial squares. D. Factor using difference of two cubes. E. Factor using sum of two cubes. F. Factor using greatest common factor. G. Factor using trial and error. MA-ALG3-4 Perform the four basic operations on rational expressions and solve rational

equations. MA-ALG3-5 Analyze, graph and apply linear and step functions A. Determine domain and range. B. Write and solve equations and inequalities. C. Graph without a calculator. D. Graph with calculator. E. Write equations in slope-intercept form. F. Write equations in standard form. G. Write equations in point-slope form. H. Use models to interpret data. I. Solve systems of equations using graphing, linear substitutions, and

matrices.



Algebra III

MA-ALG3-6 Identify, graph, and interpret characteristics of quadratic functions. A. Determine domain and range. B. Simplify and approximate radicals. C. Write and solve equations using graphing, factoring, and the quadratic

formula. D. Graph without a calculator. E. Locate points using symmetry. F. Graph with calculator. G. Use properties to identify maximum, minimum, vertex, and image points

and to determine increasing and decreasing intervals and direction. H. Use models to interpret data. MA-ALG3-7 Identify, graph, and name characteristics of twelve parent functions (constant,

linear, quadratic and all even powers, cubic and all odd powers, exponential, absolute value, step, inverse, inverse quare, even root, odd root, logarithmic).

A. Recognize graphs. B. Determine domain and range. C. Graph without a calculator. D. Graph on calculator. E. Write equations of asymptotes. F. Determine symmetry. G. Use models to interpret data.


Content Map For Mathematics Algebra III

MA-ALG3-8 Perform transformations (translations, reflections, and scale changes) of functions on a graph and write corresponding equations.

A. Map pre-image to image. B. Write equations. C. Translate functions. D. Reflect functions. E. Scale vertically and horizontally. F. Distinguish between odd and even functions. G. Identify line and point symmetry. H. Find composites of functions. I. Find inverses of functions. MA-ALG3-9 Identify and apply properties of power, exponential, and logarithmic functions. A. Solve power equations, including fractional as well as whole number exponents. B. Solve exponential equations. C. Use exponential function to model growth and decay. D. Solve common and natural logarithmic equations. E. Explore applications of logarithmic functions.



Algebra III

MA-ALG3-10 Graph and perform related operations on polynomial functions. A. Use models to interpret data. B. Graph functions. C. Find zeros value on x axis. D. Divide using synthetic and long division. E. Apply Remainder and Factor Theorems. F. Perform operations with complex numbers. G. Use Rational Root Theorem to find roots of polynomials. MA-ALG3-11 Collect, organize, analyze, summarize, and interpret numerical information as an

introduction to basic statistics. A. Collect data. B. Calculate measures of central tendency. C. Construct and analyze tables and graphs. D. Construct and analyze scatter plots, circle, and line graphs. E. Calculate measures of spread. F. Calculate quartiles and percentiles and construct box plots. G. Create histograms. H. Calculate variance and standard deviation. I. Use models to interpret data. MA-ALG3-12 Introduce trigonometric functions and their properties A. Change values among degrees, radians, and revolutions. B. Find arc lengths. C. Find the area of a sector. D. Determine sine, cosine, and tangent ratios using special right triangles. E. Recite exact trigonometric values on the unit circle for 0, 30, 45, 60, and 90

degrees. F. Graph sine, cosine and tangent functions. MA-ALG3-13 Optional: Introduce the fundamental properties of probability. Use simulations to

model real-world applications. A. Determine sample space. B. Compute basic probability. C. Use models to interpret data. D. Determine mutually exclusive, independent, and complementary events. E. Calculate permutations. F. Calculate combinations. G. Use factorials to solve equations.



Advanced Algebra/Trigonometry

MA-TRIG-1 Investigate trigonometric functions. A. Identify values of the trigonometric functions as defined on the unit circle. B. Identify values of the trigonometric functions using right triangles. C. Apply the law of sines or cosines in appropriate problem situations. D. Find the area of any triangle given appropriate information. MA-TRIG-2 Evaluate relations and functions. A. Determine if a given relation is also a function. B. Identify domain and range of a relation and functions. C. Perform operations with functions to include addition, subtraction, multiplication,

division and composition. D. Find the inverse of a function. E. Graph linear equations and inequalities. F. Write an equation for a line. MA-TRIG-3 Solve systems of equations and inequalities. A. Solve linear systems graphically. B. Solve linear systems algebraically. C. Solve linear systems by matrices. D. Graph linear systems of inequalities. E. Solve problems involving linear programming. MA-TRIG-4 Graph functions. A. Use symmetry as an aid in graphing. B. Graph absolute value, step, and rational functions. C. Graph inverse functions. D. Find critical points using derivatives. MA-TRIG-5 Solve polynomial and rational functions. A. Find the roots of given functions by factoring, graphing, or use of algebraic

theorems. B. Solve quadratics by factoring, completing the square, graphing and using the

quadratic formula. C. Graph polynomial functions and label the intercepts and critical points. D. Solve rational equations and inequalities. E. Solve radical equations and inequalities.



Advanced Algebra/Trigonometry

MA-TRIG-6 Graph trigonometric functions and their inverses. A. Graph trigonometry functions and identify amplitude, period and phase-shifts. B. Graph and evaluate inverse trigonometric functions. C. Write equations for trigonometric functions and their inverses. MA-TRIG-7 Use trigonometric identities and equations. A. Identify and use identities to include reciprocal, quotient, pythagorean, symmetry,

sum and difference, double, and half-angle identities. B. Solve trigonometric equations. MA-TRIG-8 Explore vectors and parametric equations. A. Add, subtract, multiply, and find the magnitude of vectors by algebraic or

geometric method. B. Find the inner and cross products of two vectors. C. Determine if vectors are perpendicular. D. Solve problems by using vectors and right triangle trigonometry. E. Write and graph parametric equations. F. Solve problems using parametric equations. MA-TRIG-9 Use polar coordinates and complex numbers. A. Graph polar coordinates and polar equations. B. Convert between polar coordinates and rectangular coordinates. C. Add, subtract, multiply and divide complex numbers in rectangular form and polar

form. D. Convert complex numbers between rectangular and polar form. E. Find powers and roots of complex numbers using DeMoivre’s theorem. MA-TRIG-10 Solve exponential and logarithmic functions. A. Evaluate or simplify expressions involving exponents and logarithms. B. Solve and graph exponential and logarithmic equations and inequalities. C. Solve problems using natural logarithms.



AP Calculus

MA-APCAL-1 Investigate functions, graphs, and limits. A. Analyze graphs. B. Evaluate limits of functions. C. Determine asymptotic and unbounded behavior. D. Explore continuity as a property of functions. MA-APCAL-2 Explore the concept of the derivative geometrically, numerically, and analytically. MA-APCAL-3 Determine the derivative at a point. A. Find slope of a curve at a point. B. Write the equation of the tangent line to a curve at a point. C. Determine instantaneous rate of change. MA-APCAL-4 Interpret the derivative as a function. A. Analyze the characteristics of graphs of f and fN. B. Write equations involving derivatives. C. Determine increasing, decreasing, and relative extrema. D. Define the Mean Value Theorem. MA-APCAL-5 Find second derivatives. A. Analyze characteristics of the graphs of f, fN, and fO. B. Determine concavity. C. Determine points of inflection. MA-APCAL-6 Investigate applications of derivatives. A. Analyze curves. B. Model rates of change. C. Interpret the derivative for velocity, speed, and acceleration. MA-APCAL-7 Compute derivatives of basic functions, exponential, logarithmic, trigonometric, and

inverse trigonometric functions. A. Use the basic rules for derivatives of sums, products, and quotients of functions. B. Use the Chain Rule and implicit differentiation. MA-APCAL-8 Define Riemann sums. A. Find Riemann sums over equal subdivisions. B. Compute Riemann sums using left, right, and midpoint evaluation points.



AP Calculus

MA-APCAL-10 Apply integrals by modeling physical, social, or economic situations. MA-APCAL-11 Interpret the Fundamental Theorem of Calculus. A. Evaluate definite integrals. B. Represent a particular antiderivative. C. Analyze functions and their graphs. MA-APCAL-12 Use the techniques of antidifferentiation. A. Determine antiderivative following directly from derivatives of basic functions. B. Evaluate by substitution of variables. MA-APCAL-13 Apply antidifferentiation. A. Find specific antiderivatives using initial conditions including motion along a

line. B. Solve separable differential equations. C. Solve problems with exponential growth and decay. MA-APCAL-14 Approximate definite integrals of function represented algebraically, geometrically,

and by a table of values using Riemann sums and the Trapezoidal rule.



Mathematical Money Management

MA-MMM-1 Earning Money A. Calculates total time worked from timecard. B. Calculates regular time and overtime pay, total pay for piecework, gross pay based

on hourly wages plus tips, salary, straight commission, and salary plus commission. C. Computes net pay, taking into account federal, state, and local taxes, social

security, and any miscellaneous deductions. MA-MMM-2 Budgeting

A. Prepares a budget for a given income on a weekly, monthly, and annual basis. B. Identifies and compares various pay periods. C. Explores and compares various methods of personal record keeping. D. Demonstrates an awareness of how income and personal goals affect financial

planning and decisions. MA-MMM-3 Banking

A. Compares various banking institutions (banks, credit unions, and savings & loans) and services provided by each.

B. Describes process of opening a checking and/or savings account, making deposits and withdrawals.

C. Reconciles a checking account, given a sample bank statement and a check register.

MA-MMM-4 Housing

A. Determines the percentage of income available for monthly rent or mortgage payment.

B. Investigates costs associated with renting, such as, deposits required, and renter’s insurance premium.

C. Computes the amount of down payment required to purchase a house/condominium and the price that can be afforded for a given income (rule of 2 ½).

D. Calculates monthly mortgage payment and monthly escrow amount. E. Calculates total interest paid on the loan. F. Estimates the closing costs associated with buying a house. G. Computes utility costs. H. Compares and contrasts efficiency ratings for large and small appliances. I. Determines services provided by the local telephone companies and related costs. J. Compares services available from long distance telephone providers. K. Compares services and related costs of cable and internet companies. L. Identifies advantages and disadvantages of property ownership.

MA-MMM-5 Taxes

A. Solves problems related to taxes by computing state, federal, and local income taxes, property taxes, social security tax, and estate and inheritance taxes.

B. Discusses difference types of taxes and how the funds are used. C. Completes federal (1040EX and 1040A) and state income tax forms for given data.




MA-MMM-6 Purchasing A. Identify various means used to sell products and services, such as advertising

and promotions. B. Explore instances of deceptive advertising, deceptive packaging, hard-sell

tactics, and masked credit practices (rent-to-own, deferred interest). C. Compute sales tax, total purchase price and change received in a cash purchase. D. Examine advantages and disadvantages of extended warranties. E. Calculate discount, successive discounts, and sale price of an item. F. Compare unit-price to do comparison-shopping and determine the better buy. G. Fill out a catalog order form and calculates the total cost. H. Compare various credit plans (including layaway) to determine best choice for

the specific need. I. Compute the finance charge for a charge account/credit card by unpaid balance

method and average daily balance method. J. Calculate the finance charge and monthly payment on an installment plan. K. Explain advantages and disadvantages of using a credit card. L. Calculate costs related to buying and owning a car. M. Explain advantages and disadvantages of owning or leasing a vehicle.

MA-MMM-7 Savings and Investments

A. Compare and contrasts savings accounts, money market accounts, certificates of deposit, savings bonds, stocks, and IRAs.

B. Solve problems related to the purchase of, deposits made to, and withdrawals from investments and savings.

C. Calculate simple and compound interest. MA-MMM-8 Insurance

A. Compare different kinds of life insurance and calculates premiums. B. Compute health insurance premiums and expenses incurred when a claim is

filed. C. Compute monthly retirement benefits from social security. D. Compute annual pension from a retirement plan. E. Identify sources of retirement income and map out a sample plan for retirement

income. F. Investigate other forms of insurance, such as dental, disability, and accidental

death. MA-MMM-9 Borrowing

A. Compare different lending institutes with respect to services, costs, and types of loans.

B. Compute interest and service charge for various types of loans. C. Explain how a person’s credit rating is established and how it effects your

ability to obtain loans.




MA-MMM-10 Consumer Rights and Responsibilities A. Identify resources and procedures in the event of financial difficulty. B. Interpret rights and responsibilities involved with leases, warranties, guarantees,

and sales contracts. C. Identify agencies that deal with consumer problems.

MA-MMM-12 Travel, Recreation, and Vacations

A. Compare costs of various forms of transportation and lodging. B. Select a leisure-time activity and investigates related expenses. C. Plan a vacation using a given amount of money.

Content Map For Mathematics

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