GHSGT Standards Overview for parents

							                                                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