Accelerated Algebra 1

MAAC: Accelerated Algebra 1

MAAC.A: Algebra

MAAC.B: Statistics and Probability

MAAC.C: Geometry

MAAC.D: Functions

MAAC.E: Numbers and Quantity

MAAC.A.1: add, subtract, and multiply polynomials

MAAC.A.2: interpret parts of an expression, such as terms, factors, and coefficients in context

MAAC.A.3: interpret the meaning of given formulas or expressions in context of individual terms or factors when given in situations which utilize the formulas or expressions with multiple terms and/or factors

MAAC.A.4: create linear equations and inequalities in one variable and use them to solve problems

MAAC.A.5: solve linear equations and inequalities in one variable, including equations with coefficients represented by letters (i.e., solve multi-step linear equations with one solution, infinitely many solutions, or no solutions; extend this reasoning to solve compound linear inequalities and literal equations); express solution sets to inequalities using both interval notation (e.g., (2, 10]) and set notation (e.g., {x \ 2 < x = 10})

MAAC.A.6: rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations (e.g., rearrange Ohm's law V=IR to highlight resistance R)

MAAC.A.7: justify the steps of a simple one-solution equation using algebraic properties and the properties of real numbers; justify each step, or if given two or more steps of an equation, explain the progression from one step to the next using properties

MAAC.A.8: demonstrate that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane

MAAC.A.9: graph the solutions to a linear inequality in two variables as a half plane, excluding the boundary in the case of a strict inequality

MAAC.A.10: graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes

MAAC.A.11: represent constraints by equations or inequalities, and interpret data points as possible (i.e., a solution) or not possible (i.e., a non-solution) under the established constraints

MAAC.A.12: represent constraints by systems of equations and/or inequalities, and interpret data points as possible (i.e., a solution) or not possible (i.e., a non-solution) under the established constraints

MAAC.A.13: create linear equations in two variables to represent relationships between quantities expressed in a table of values or verbal representation, including writing equations when given a slope and a y-intercept or slope and a point; graph these linear equations on coordinate axes with appropriate labels and scales

MAAC.A.14: solve systems of linear equations exactly (i.e., algebraically) and approximately (i.e., with graphs), focusing on pairs of linear equations in two variables; solve simple cases by inspection (e.g., 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6)

MAAC.A.15: show and explain why the elimination method works to solve a system of two-variable equations

MAAC.A.16: explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately (e.g., using technology to graph the functions, make tables of values, or find successive approximations)

MAAC.A.17: use the structure of an expression to rewrite it in different equivalent forms [i.e., see x4 - y4 as ((x²) -(y²))², thus recognizing it as a difference of squares that can be factored as (x²-y²)(x²+y²)]

MAAC.A.18: choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression (e.g., reveal the zeros, minimum, or maximum)

MAAC.A.19: factor any quadratic expression to reveal the zeros of the function it defines

MAAC.A.20: complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines

MAAC.A.21: use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions; derive the quadratic formula from ax² + bx + c = 0

MAAC.A.22: solve quadratic equations by inspection, taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions)

MAAC.A.23: create quadratic equations in one variable and use them to solve problems

MAAC.A.24: create quadratic equations in two variables to represent relationships between quantities expressed in a table of values or verbal representation; graph these quadratic equations on coordinate axes with appropriate labels and scales

MAAC.A.25: create exponential equations in two variables to represent relationships between quantities expressed in a table of values or verbal representation, graph these exponential equations on coordinate axes with appropriate labels and scales

MAAC.A.26: create exponential equations in one variable and use them to solve simple equations

MAAC.B.27: represent data with plots on the real number line (e.g., dot plots, histograms, and box plots)

MAAC.B.28: use statistics appropriate to the shape of the data distribution to compare center (i.e., median, mean) and spread (i.e., interquartile range, mean absolute deviation) of two or more different data sets

MAAC.B.29: interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (i.e., outliers)

MAAC.B.30: summarize categorical data for two categories in two-way frequency tables; interpret relative frequencies in the context of the data (i.e., including joint, marginal, and conditional relative frequencies); recognize possible associations and trends in the data

MAAC.B.31: represent data on two quantitative variables on a scatter plot and describe how the variables are related

MAAC.B.32: fit a function to bivariate data; use functions fitted to data to solve problems in the context of the data; use given functions or choose a function suggested by the context; emphasize linear, quadratic, and exponential models

MAAC.B.33: determine and interpret the slope (i.e., rate of change) and the intercept (i.e., constant term) of a linear model in the context of the data

MAAC.B.34: compute (using technology) and interpret the correlation coefficient of a linear fit (e.g., by looking at a scatter plot, students should be able to tell if the correlation coefficient is positive or negative and give a reasonable estimate of the "r" value; after calculating the line of best fit using technology, describe how strong the goodness of fit of the regression is using "r")

MAAC.B.35: explain the difference between correlation and causation

MAAC.C.70: know and apply the precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc

MAAC.C.71: describe transformations as function that take points in the plane as inputs and give other points as outputs; compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

MAAC.C.72: describe the rotations and reflections that carry a rectangle, parallelogram, trapezoid, or regular polygon onto itself

MAAC.C.73: develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments

MAAC.C.74: given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using graph paper, tracing paper, or geometry software; specify a sequence of transformations that will carry a given figure onto another

MAAC.C.75: use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent

MAAC.C.76: use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent

MAAC.C.77: explain how the criteria for triangle congruence (i.e., ASA, SAS, SSS, HL, AAS) follow from the definition of congruence in terms of rigid motions

MAAC.C.78: prove theorems about lines and angles (i.e., vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints)

MAAC.C.79: prove theorems about triangles (i.e., measures of the interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point)

MAAC.C.80: prove theorems about parallelograms (i.e., opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals)

MAAC.C.81: make formal geometric constructions with a variety of tools and methods (e.g., compass and straightedge, string, reflective devices, paper folding, dynamic geometric software); copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

MAAC.C.82: construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle

MAAC.C.83: verify experimentally the properties of dilations given by a center and a scale factor (i.e., a dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged; the dilation of a line segment is longer or shorter according to the ratio given by the scale factor)

MAAC.C.84: given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides

MAAC.C.85: use the properties of similarity transformations to establish the AA criterion for two triangles to be similar

MAAC.C.86: prove theorems about triangles (i.e., a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem using triangle similarity)

MAAC.C.87: use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures

MAAC.C.88: understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles

MAAC.C.89: explain and use the relationship between the sine and cosine of complementary angles

MAAC.C.90: use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems

MAAC.D.36: understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range [i.e., if f is a function, x is the input (an element of the domain), and f(x) is the corresponding output (an element of the range); the graph of the function is the set of ordered pairs consisting of an input and the corresponding output]

MAAC.D.37: evaluate functions for inputs in their domains using function notation and interpret statements that use function notation in terms of a context

MAAC.D.38: graph linear functions expressed algebraically in slope-intercept and standard form by hand and by using technology; show and interpret key features including slope and intercepts (as determined by the function or by context)

MAAC.D.39: interpret key features of linear functions represented in graphs, tables, equations, and verbal descriptions (i.e., intercepts, positive, negative; intervals where the function is increasing, decreasing); sketch graphs showing these key features when given a verbal description of the relationship

MAAC.D.40: relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes [e.g., if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function]; represent the domain and range using both interval notation (e.g., (2, 10]) and set notation (e.g., {x\2 < x = 10})

MAAC.D.41: write a function that describes a relationship between two quantities by determining an explicit expression, a recursive process, or steps for calculation from a contextwrite a function that describes a linear relationship between two quantities by determining an explicit expression, a recursive process, or steps for calculation from a context

MAAC.D.42: write arithmetic sequences both recursively and with an explicit formula; use them to model situations, and translate between the two forms; connect arithmetic sequences to linear functions

MAAC.D.43: recognize that arithmetic sequences are functions, sometimes defined recursively, whose domain is a subset of the integers

MAAC.D.44: compare properties of two functions each represented algebraically, graphically, numerically in tables, and/or by a verbal description

MAAC.D.45: graph quadratic functions expressed algebraically by hand and by using technology; show and interpret key features including intercepts, maxima, and minima (as determined by the function or by context)

MAAC.D.46: interpret key features of quadratic functions represented in graphs, tables, equations, and verbal descriptions (i.e., intercepts, positive, negative; intervals where the function is increasing, decreasing; relative maximums and minimums; symmetries; end behavior); sketch graphs showing these key features when given a verbal description of the relationship

MAAC.D.47: calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval; estimate the rate of change from a graph

MAAC.D.48: identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs; experiment with cases and illustrate an explanation of the effects on the graph using technology; include recognizing even and odd functions from their graphs and algebraic expressions

MAAC.D.49: use second differences to write a quadratic function that describes a relationship between two quantities

MAAC.D.50: use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context (e.g., compare and contrast quadratic functions in standard, vertex, and intercept forms)

MAAC.D.51: graph exponential functions expressed algebraically by hand and by using technology; show and interpret key features including intercepts and end behavior

MAAC.D.52: interpret key features of exponential functions represented in graphs, tables, equations, and verbal descriptions (i.e., intercepts, positive, negative; intervals where the function is increasing, decreasing; relative maximums and minimums; asymptotes; end behavior); sketch graphs showing these key features when given a verbal description of the relationship

MAAC.D.53: recognize that geometric sequences are functions, sometimes defined recursively, whose domain is a subset of the integers

MAAC.D.54: write a function that describes an exponential relationship between two quantities by determining an explicit expression, a recursive process, or steps for calculation from a context

MAAC.D.55: write geometric sequences both recursively and with an explicit formula; use them to model situations, and translate between the two forms; connect geometric sequences to exponential functions

MAAC.D.56: prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals; this can be shown by algebraic proof, with a table showing differences, or by calculating average rates of change over equal intervals

MAAC.D.57: recognize situations in which one quantity changes at a constant rate per unit interval relative to another (i.e., linear)

MAAC.D.58: recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another (i.e., exponential)

MAAC.D.59: construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, table, a description of a relationship, or two input-output pairs

MAAC.D.60: interpret the parameters in a linear or exponential function in terms of a context; in context, students should describe what these parameters mean in terms of change and starting value

MAAC.D.61: graph linear, quadratic, and exponential functions algebraically and show key features of the graph by hand and by using technology

MAAC.D.62: interpret key features of linear, quadratic, and exponential functions represented in graphs, tables, equations, and verbal descriptions (i.e., intercepts, positive, negative; intervals where the function is increasing, decreasing; relative maximums and minimums; symmetries; asymptotes; end behavior); sketch graphs showing these key features when given a verbal description of the relationship

MAAC.D.63: show using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or more generally as a polynomial function

MAAC.E.64: rewrite expressions involving radicals (i.e., simplify and /or use the operations of addition, subtraction, multiplication, and division with radicals within algebraic expressions limited to square roots)

MAAC.E.65: explain why the sum or the product of rational numbers is rational, why the sum of a rational number and an irrational number is irrational, and why the product of a nonzero rational number and an irrational number is irrational

MAAC.E.66: use units of measure (linear, area, capacity, rates, and time) as a way to understand problems; identify, use, and record appropriate units of measure within context, within data displays, and on graphs; convert units and rates using dimensional analysis (English to English and Metric to Metric without conversion factor provided and between English and Metric with conversion factor); use units within multi-step problems and formulas; interpret units of input and resulting units of output

MAAC.E.67: define appropriate quantities for the purpose of descriptive modeling; given a situation, context, or problem, students will determine, identify, and use appropriate quantities for representing the situation

MAAC.E.68: choose a level of accuracy appropriate to limitations on measurement when reporting quantities (e.g., money situations are generally reported to the nearest hundredth; also, an answers' precision is limited to the precision of the data given)