VIEWS: 10 PAGES: 4 POSTED ON: 4/20/2012 Public Domain
GHSGT Standards Overview for Parents (Items highlighted in red are Mathematics 3 concepts that teachers will cover only if time is available when completing a unit.) Algebra Mathematics I MM1A1b Graph the six basic functions: f(x) = xn,where n = 1 to 3, f(x) =sqrt x, f(x) = |x|, f(x) =1/x MM1A1c (transformations) Graph transformations of basic functions including vertical shifts, stretches, shrinks MM1A1c (reflections) Graph transformations of basic functions including reflections across the x & y axes MM1A1d (domain) Investigate and explain all characteristics of a function including domain MM1A1d (range) Investigate and explain all characteristics of a function including range MM1A1d (zeros) Investigate and explain all characteristics of a function including zeros and intercepts MM1A1d (intervals of Investigate and explain all characteristics of a function including intervals of increase and decrease increase/decrease) MM1A1d (max & min) Investigate and explain all characteristics of a function including maximum and minimum values MM1A1d (end behavior) Investigate and explain all characteristics of a function including end behavior. MM1A1e (characteristics of Relate to a given context the characteristics of a function graph in context) MM1A1e (use tables and Use graphs/ tables to investigate the behaviors of a function graphs) MM1A1f Recognize sequences as functions with domains that are sets of whole numbers MM1A1g (constant rates of Explore constant rates of change of linear, quadratic, square root and other functions change) MM1A1g(variable rates of Explore variable rates of change of linear, quadratic, square root and other functions change) MM1A1g (compare rates of Compare rates of change of linear, quadratic, square root, and other function families. change) MM1A1h (symmetry) Determine graphically and algebraically whether a function has symmetry MM1A1h (even/odd) Determine graphically and algebraically whether a function is even, odd or neither MM1A1i (f = g) Understand & interpret the solutions of the equation f(x)=g(x) MM1A1i (intersection) Interpret the intersection point(s) of the graphs y= f(x) and y =g(x) MM1A2a Simplify algebraic and numeric expressions involving square roots MM1A2b Perform operations with square roots MM1A2c (add polynomials) Add polynomials MM1A2c (subtract Subtract polynomials polynomials) MM1A2c (multiply Multiply polynomials polynomials) MM1A2c (divide polynomials) Divide polynomials MM1A2e (add rational) Add rational expressions MM1A2e (subtract rational) Subtract rational expressions MM1A2e (multiply rational) Multiply rational expressions MM1A2e (divide rational) Divide rational expressions MM1A2f Factor expressions by greatest common factor, grouping, trial/ error, and special products (limited to 6 specific rules) MM1A3a (factorization) Solve quadratic equations in the form ax2 + bx + c= 0, where a= 1, by using factorization MM1A3a (finding square Solve quadratic equations in the form ax2 + bx + c= 0, where a= 1, by finding square roots where applicable roots) MM1A3b Solve equations involving radicals such as (square root of x) + b = c, using algebraic techniques MM1A3c Use a variety of techniques to solve equations resulting from the investigation of x2 + bx + c= 0 MM1A3d Solve simple rational equations (results in linear equations or quadratic equations with leading coefficient of 1) Algebra Mathematics II MM2N1b Write complex numbers in the form a + bi MM2N1c (add) Add complex numbers MM2N1c (subtract) Subtract complex numbers MM2N1c (multiply) Multiply complex numbers MM2N1c (divide) Divide complex numbers MM2A2a Extend properties of exponents to include all integer exponents MM2A2b (domain) Investigate and explain domain of exponential functions MM2A2b (range) Investigate and explain range of exponential functions MM2A2b (vertex) Investigate and explain the vertex of exponential functions MM2A2b (axis of symmetry) Investigate and explain the axis of symmetry of exponential functions MM2A2b (zeros) Investigate and explain zeros and intercepts of exponential functions MM2A2b (extrema) Investigate and explain extrema of exponential functions MM2A2b (points of Investigate and explain points of discontinuity of exponential functions discontinuity) MM2A2b (increase/decrease) Investigate and explain intervals of increase or decrease of exponential functions MM2A2b (rates of change) Investigate and explain rates of change of exponential functions MM2A2b (end behavior) Investigate and explain end behavior of exponential functions MM2A2c Graph transformations of f(x) = ax MM2A2d (equations Solve simple exponential equations analytically analytically) MM2A2d (equations Solve simple exponential equations graphically graphically) MM2A2d (equations Solve simple exponential equations by using appropriate technology technology) MM2A2d (inequalities Solve simple exponential inequalities analytically analytically) MM2A2d (inequalities Solve simple exponential inequalities graphically graphically) MM2A2d (inequalities Solve simple exponential inequalities using appropriate technology technology) MM2A2f Understand and recognize geometric sequences as exponential functions with domains that are whole numbers MM2A2g Interpret the constant ratio in a geometric sequence as the base of the associated exponential function MM2A3a Convert quadratic functions between standard form and vertex form MM2A3b Graph quadratic functions as transformations of the function f(x) = x2 MM2A3c (domain) Investigate and explain domain of quadratic functions MM2A3c (range) Investigate and explain range of quadratic functions MM2A3c (vertex) Investigate and explain the vertex of quadratic functions MM2A3c (axis of symmetry) Investigate and explain the axis of symmetry of quadratic functions MM2A3c (zeros) Investigate and explain the zeros and intercepts of quadratic functions MM2A3c (extrema) Investigate and explain the extrema of quadratic functions MM2A3c (intervals of Investigate and explain the intervals of increase and decrease of quadratic functions increase/decrease) MM2A4b (factoring) Find real and complex roots of quadratic equations by factoring MM2A4b (squre roots) Find real and complex roots of quadratic equations by taking square roots MM2A4b (quadratic formula) Find real and complex roots of quadratic equations by applying the quadratic formula Algebra Mathematics III MM3A1a Graph simple polynomial functions as translations fo the function f(x)=axn MM3A1b (degree) Understand the effect of the degree on a polynomial function MM3A1b (leading coefficient) Understand the effect of the leading coefficient on a polynomial MM3A1b (multiplicity) Understand the effect of the multiplicity of real zeros on a polynomial MM3A1c Determine whether a function has symmetry and whether it is even, odd or neither MM3A1d (domain) Investigate and explain domain of polynomial functions MM3A1d (range) Investigate and explain range of polynomial functions MM3A1d (zeros) Investigate and explain zeros and intercepts of polynomial functions MM3A1d (extrema) Investigate and explain extrema of polynomial functions MM3A1d (increase/decrease) Investigate and explain intervals of increase or decrease of polynomial functions MM3A1d (end behavior) Investigate and explain end behavior of polynomial functions MM3A2a Define and understand the properties of nth roots MM3A2b Extend properties of exponents to include rational exponents MM3A2c Define logarithmic functions as inverses of exponential functions MM3A2d Understand and use properties of logarithms by extending laws of exponents MM3A2e (domain) Investigate and explain domain of exponential and logarithmic functions MM3A2e (range) Investigate and explain range of exponential and logarithmic functions MM3A2e (asymptotes) Investigate and explain asymptotes of exponential and logarithmic functions MM3A2e (zeros) Investigate and explain zeros and intercepts of exponential and logarithmic functions MM3A2e (increase/decrease) Investigate and explain intervals of increase or decrease of exponential and logarithmic functions MM3A2e (rate of change) Investigate and explain rate of change of exponential and logarithmic functions MM3A2f Graph functions as transformations of f(x)=ax, f(x) = logax, f(x)=ex, f(x)=ln x MM3A2g Explore real phenomena related to exponential and logarithmic functions including half-life and double time MM3A3a (factor theorem) Find real and complex roots of higher degree polynomial equations using the factor theorem, incorporating complex and radical conjugates MM3A3a (remainder theorem) Find real and complex roots of higher degree polynomial equations using the remainder theorem, incorporating complex and radical conjugates MM3A3a (rational root Find real and complex roots of higher degree polynomial equations using the rational root theorem, incorporating theorem) complex and radical conjugates MM3A3a (fundamental Find real and complex roots of higher degree polynomial equations using the fundamental theorem of algebra, theorem) incorporating complex and radical conjugates MM3A3b (polynomial Solve polynomial equations analytically, graphically and using appropriate technology equations) MM3A3b (exponential Solve exponential equations analytically, graphically and using appropriate technology equations) MM3A3b (logarithmic Solve logarithmic equations analytically, graphically and using appropriate technology equations) MM3A3c (polynomial Solve polynomial inequalities analytically, graphically and using appropriate technology inequalities) MM3A3c (exponential Solve exponential inequalities analytically, graphically and using appropriate technology inequalities) MM3A3c (logarithmic Solve logarithmic inequalities analytically, graphically and using appropriate technology inequalities) MM3A3d Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology MM3A4a (add) Add matrices choosing appropriate methods, including technology MM3A4a (subtract) Subtract matrices choosing appropriate methods, including technology MM3A4a (multiply) Multiply matrices choosing appropriate methods, including technology MM3A4a (invert) Invert matrices choosing appropriate methods, including technology MM3A4b (pencil and paper) Find the inverses of two-by-two matrices using pencil and paper MM3A4b (technology) Find the inverses of larger matrices using technology MM3A4c Examine the properties of matrices, contrasting them with properties of real numbers MM3A5a Represent a system of linear equations as a matrix equation MM3A5b Solve matrix equations using inverse matrices MM3A5c Represent and solve realistic problems using systems of linear equations MM3A6a Solve systems of inequalities in two variables, showing the solutions graphically MM3A6b Represent and solve realistic problems using linear programming MM3A7a Use graphs to represent realistic situations MM3A7b Use matrices to represent graphs and solve problems that can be represented by graphs Geometry Mathematics I MM1G1a Determine the distance between two points MM1G1b Determine the distance between a point and a line MM1G1c Determine the midpoint of a segment MM1G1d Understand distance formula as an application of the Pythagorean Theorem MM1G1e Use the coordinate plane to investigate properties and verify conjectures related to triangles and quadrilateral MM1G2a Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate MM1G2b (converse) Understand and use the relationships among a statement and its converse MM1G2b (inverse) Understand and use the relationships among a statement and its inverse MM1G2b (contrapositive) Understand and use the relationships among a statement and its contrapositive MM1G3a (interior) Determine the sum of interior angles in a polygon MM1G3a (exterior) Determine the sum of exterior angles in a polygon MM1G3b Understand and use the triangle inequalitiy, the side-angle inequality and the exterior-angle inequality MM1G3c Understand/ use congruence postulates/ theorems for triangles (SSS, SAS, ASA, AAS, HL) MM1G3d Understand, use, and prove properties of and relationships among special quadrilaterals MM1G3e (incenter) Find and use points of concurrency in triangles: incenter MM1G3e (orthocenter) Find and use points of concurrency in triangles: orthocenter MM1G3e (circumcenter) Find and use points of concurrency in triangles: circumcenter MM1G3e (centroid) Find and use points of concurrency in triangles: centroid Geometry Mathematics II MM2G1a Determine the lengths of sides of 30° - 60°- 90° triangles MM2G1b Determine the lengths of sides of 45° - 45°- 90° triangles MM2G2c Solve right triangle application problems using the trigonometric ratios MM2G3b Understand and use properties of central, inscribed and related angles MM2G3c (arc) Use the properties of circles to solve problems involving the length of an arc MM2G3c (sector area) Use the properties of circles to solve problems involving the area of a sector MM2G4a (volume) Use and apply volume of a sphere MM2G4b Determine the effect on surface area and volume of changing the radius or diameter of a sphere Geometry Mathematics III MM3G1a Find equations of circles MM3G1b Graph a circle given an equation in general form MM3G1c Find the equation of a tangent line to a circle at a given point MM3G1d Solve a system of equations involving a circle and a line MM3G1e Solve a system of equations involving two circles MM3G2a Convert equations of conics (parabolas, circles, ellipses, and hyperbolas) by completing the square MM3G2b Graph conics (parabolas, circles, ellipses, and hyperbolas) and identify fundamental characteristics MM3G2c Write equations of conics (parabolas, circles, ellipses, and hyperbolas) given appropriate information MM3G3a Plot the point (x, y, z) and understand it as a vertex of a rectangular prism MM3G3b Apply the distance formula in 3-space MM3G3c Recognize and understand equations of planes and spheres Data Analysis Mathematics I MM1D1a Apply the addition and multiplication principles of counting MM1D1b (combinations) Calculate and use simple combinations MM1D1b (permutations) Calculate and use simple permutations MM1D2a Find the probabilities of mutually exclusive events MM1D2b Find the probabilities of dependent events MM1D2c Calculate conditional probabilities MM1D2d Use expected value to predict outcomes MM1D3a Compare summary statistics from one sample data distribution to another in describing center and variability of the data distributions MM1D3c Understand the purpose of a random sample Data Analysis Mathematics II MM2D1a Pose a question and collect sample data from at least two different populations MM2D1c Use means and standard deviations to compare data sets MM2D2b Examine the issues of curve fitting using median-median line and eyeballing MM2D2d Investigate issues that arise when using data to explore the relationship between two variables, including confusion between correlation and causation Data Analysis Mathematics II MM3D1 Create probability histograms of discrete random variables, using both experimental and theoretical probabilities MM3D2a Determine intervals about the mean that include a given percent of data MM3D2b Determine the probability that a given value falls within a specified interval MM3D2c Estimate how many items in a population will fall within a specified interval MM3D3 Understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data