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Curriculum Expectations:   Algebra 1 (High School Math)
Local VA Standards (End of Course Expectations)
Linked Core Standard:
By the end of Algebra 1, the student will:


LVAS

Local VA Standard

Domain

1

write verbal expression algebraically and evaluate them for given replacement sets.

Expressions and Operations

2

apply laws of exponents to add, subtract, multiply, and divide polynomials and to factor first and second degree binomials and trinomials in one or two variables.

Expressions and Operations

3

express square and cube roots of monomial expressions in simplest radical form.

Expressions and Operations

4

solve literal equations, linear equations, quadratic equations,linear inequalities, systems of linear equations, and systems of linear inequalities for a given variable algebraically and graphically.  Justify the steps used to solve or simplify equations, inequalities, and expressions. Solve real world problems involving equations, inequalities, systems of equations, and systems of inequalities.

Equations and Inequalities

5

graph and write the equations and inequalities of linear relationships by determining slope and whether it is positive, negative, zero, or undefined given the equation of a line, the graph of a line, two points on the line, or the slope and a point on the line.

Equations and Inequalities

6

analyze real world and theoretical situations to determine: whether a realtion is a function, domain, range, zeros, x- and y- intercepts, the values of a function given a set of the values of the domain, and whether a direct or indirect variation exists and represent direct or indirect variations algebraically and graphically. Make connections between and among mutliple respresentations of functions which include concrete, verbal numeric, graphic, and algebraic.

Functions

7

interpret and calculate mean absolute deviations, standard deviation, and z-score and apply to real-world contexts.

Statistics

8

compare and contrast data sets using box-and-whisker plots and will collect and analyze data to determine the curve/line or best fit in order to make predictions, and solve real-world problems, using mathematical models.

Statistics

Instructional Objective (End of Term Expectations)


Term

Instructional Objective
Number

 Instructional Objective  (VASoL)

LVAS

1

Algebra 1-1.189ALG Expressions and Operations-O1.1

analyze an algebraic expression and create a verbal expression to represent the algebraic expression and create an algebraic expression from a verbal expressions.  describe the words and phrases necessary to represent an algebraic expression as a verbal expression and defend their choice of wording and/or algebraic expression written given the original expression. (A.1)

1

1

Algebra 1-1.189ALG Expressions and Operations-O1.2

rewrite an algebraic expression with its replacement values and evaluate the new numeric expression using the order of operations to explain each step that has taken place. arrange real numbers on a number line and be able to explain what a square root is and how to know that the square root of a certain value belongs between two numbers.  apply properties of real numbers and tell what properties apply to each step of an expression when simplifying. (A.1)

1

1

Algebra 1-4.189ALG Equations and Inequalities-O1.3

understand what an ordered pair and its parts are and use an ordered pair to graph points on a coordinate plane. (A.4.a, A.4.b, A.4.c, A.4.d, A.4.e, A.4.f, A.5.a, A.5.b, A.5.c, A.5.d)

4

1

Algebra 1-4.189ALG Equations and Inequalities-O1.4

classify equations as open sentences and determine the solutions to simple one variable equations using mental math to find the missing value.  recognize two different variables in an equation and plug in given values for those variable to verify if they are solutions to the given two variable equation. (A.4.a, A.4.b, A.4.c, A.4.d, A.4.e, A.4.f, A.5.a, A.5.b, A.5.c, A.5.d)

4

1

Algebra 1-4.189ALG Equations and Inequalities-O1.5

differentiate between one step, two step, multi-step, and literal equations and solve each level of equation for the given variable while justifying each step using properties of equality and properties of real numbers. solve proportions using properties of equality and real numbers.  evaluate and explain a percentage problem and how to find a sales tax or discount given certain parameters and solve mixtures problems.  create algebraic equations given word problems and solve for a given variable, value, or quantity. (A.4.a, A.4.b, A.4.c, A.4.d, A.4.e, A.4.f, A.5.a, A.5.b, A.5.c, A.5.d)

4

1

Algebra 1-4.189ALG Equations and Inequalities-O1.6

differentiate between an equation and an inequality as well as one step, two step, multi-step, compound, and absolute value inequalities.  solve inequalities for a given variable justifying each step using properties of inequality and properties of real numbers.  assess the variables needed to write an algebraic inequality from a verbal statement (word problem) and solve that inequality for the given variable or value. (A.4.a, A.4.b, A.4.c, A.4.d, A.4.e, A.4.f, A.5.a, A.5.b, A.5.c, A.5.d)

4

1

Algebra 1-4.189ALG Equations and Inequalities-O1.7

identify the zeros of a quadratic function given the graph of the function. explain why the zeros of a quadratic function are the x-intercepts of the graph. appraise a quadratic equation to determine if it would be best solved algebraically using square roots, factoring, or the quadratic formula.  use the discriminant to determine the number and type of roots of quadratic equations. (A.4.a, A.4.b, A.4.c, A.4.d, A.4.e, A.4.f, A.5.a, A.5.b, A.5.c, A.5.d)

4

2

Algebra 1-5.189ALG Equations and Inequalities-O2.1

relate two variables using a graph to determine whether when one variable increases/decreases that the other increases/decreases. (A.6.a, A.6.b)

5

2

Algebra 1-5.189ALG Equations and Inequalities-O2.2

analyze a pattern or situation and use the pattern formed to determine a two variable equation which will fit the pattern and give a correct output for the pattern found given an input. (A.6.a, A.6.b)

5

2

Algebra 1-6.189ALG Functions-O2.3

relate two variables using a graph to determine whether when one variable increases/decreases that the other increases/decreases. (A.7.a, A.7.b, A.7.c, A.7.d, A.7.e, A.7.f, A.8)

6

2

Algebra 1-6.189ALG Functions-O2.4

analyze a pattern or situation and use the pattern formed to determine a two variable equation which will fit the pattern and give a correct output for the pattern found given an input. (A.7.a, A.7.b, A.7.c, A.7.d, A.7.e, A.7.f, A.8)

6

2

Algebra 1-6.189ALG Functions-O2.5

interpret an equation and determine whether it is a function or not. create a function rule for a given word problem or situation. graph function rules. create a function rule for an arithmetic sequence. (A.7.a, A.7.b, A.7.c, A.7.d, A.7.e, A.7.f, A.8)

6

2

Algebra 1-5.189ALG Equations and Inequalities-O2.6

examine the correlation between slope and rate of change and analyze a graph to determine the slope using the counting method and slope formula and determine if a line has a negative, positive, zero, or undefined slope. (A.6.a, A.6.b)

5

2

Algebra 1-5.189ALG Equations and Inequalities-O2.7

analyze a set of ordered pairs, table, or graph and determine whether it represents a direct variation, inverse variation, or neither.  relate direct and inverse variation to linear equations and rewrite and/or create a linear equation in standard, point-slope, or slope-intercept form.  identify/determine slope and  x- and y- intercepts to graph an equation.  (A.6.a, A.6.b)

5

2

Algebra 1-2.189ALG Expressions and Operations-O2.8

compare and contrast positive and negative exponents and use positive and negative exponents to write numbers in standard form into scientific notation and from scientific notation into standard form. (A.2.a, A.2.b, A.2.c)

2

2

Algebra 1-2.189ALG Expressions and Operations-O2.9

simplify variable expressions using properties of exponents and be able to justify the steps taken to get to the simplest form using properties of exponents. (A.2.a, A.2.b, A.2.c)

2

3

Algebra 1-2.189ALG Expressions and Operations-O3.1

apply properties of exponents to add, subtract, multiply and divide polynomial expressions. (A.2.a, A.2.b, A.2.c)

2

3

Algebra 1-2.189ALG Expressions and Operations-O3.2

appraise a first or second degree polynomial and determine if it is a special case polynomial or if factoring by reverse distribution, F.O.I.L method, or grouping would best work to factor the polynomial. identify when a trinomial is prime. (A.2.a, A.2.b, A.2.c)

2

3

Algebra 1-4.189ALG Equations and Inequalities-O3.3

identify a set of equations/inequalities or graphs as a system of equations.  assess a system of equations/inequalities to determine if the best method for solving would be substitution, elimination, or graphing. explain why a system of equations has one solution, infinitely many solutions, or no solution. identify the solution set for a system of inequalities. use graphing techniques and identify the region on a graph where a system of inequalities has a solution or explain why there is no solution. (A.4.a, A.4.b, A.4.c, A.4.d, A.4.e, A.4.f, A.5.a, A.5.b, A.5.c, A.5.d)

4

3

Algebra 1-3.189ALG Expressions and Operations-O3.4

evaluate the length of a side of a right triangle using the Pythagorean Theorem and make the connection from the Pythagorean Theorem to the distance formula.  use properties of exponents to explain how to simplify radical monomial expressions. Express square roots of a whole number in simplest form. Express the cube root of a whole number in simplest form. Express the principal square root of a monomial algebraic expression in simplest form where variables are assumed to have
positive values. (A.3)

3

4

Algebra 1-4.189ALG Equations and Inequalities-O4.1

analyze equations and determine whether an equation is linear or quadratic. recognize the graph of a quadratic function and know that it is called a parabola. identify the parts of a parabola. calculate the vertex and axis of symmetry of a parabola algebraically using the equation given. rewrite a quadratic equation in standard form. (A.4.a, A.4.b, A.4.c, A.4.d, A.4.e, A.4.f, A.5.a, A.5.b, A.5.c, A.5.d)

4

4

Algebra 1-8.189ALG Statistics-O4.2

Write an equation for a curve of best fit, given a set of no more than twenty data points in a table, a graph, or real-world situation. Make predictions about unknown outcomes, using the equation of the curve of best fit. Design experiments and collect data to address specific, real world questions. Evaluate the reasonableness of a mathematical model of a real world situation. (A.10, A.11)

8

4

Algebra 1-7.189ALG Statistics-O4.3

Analyze descriptive statistics to determine the implications for the real-world situations from which the data derive. Given data, including data in a real-world context, calculate and interpret the mean absolute deviation of a data set. Given data, including data in a real-world context, calculate variance and standard deviation of a data set and interpret thestandard deviation.  Given data, including data in a real-world context, calculate and interpret z-scores for a data set.  Explain ways in which standard deviation addresses dispersion by
examining the formula for standard deviation.  Compare and contrast mean absolute deviation and standard
deviation in a real-world context. (A.9)

7

4

Algebra 1-8.189ALG Statistics-O4.4

Compare, contrast, and analyze data, including data from real world situations displayed in box-and-whisker plots. (A.10, A.11)

8

 

Curriculum Expectations:   Algebra 2 (High School Math)
s (End of Course Expectations)
Linked Core Standard:
By the end of Algebra 2, the student will:


 

 

Domain

1

solve, algebraically and graphically, absolute value equations, absolute value inequalities, quadratic equations over the set of complex numbers, equations containing rational algebraic expressions, and equations containing radical expressions; and use the graphing calculator to confirm algebraic solutions.

Equations and Inequalities

2

solve, algebraically and graphically, nonlinear systems of equations that include linear-quadratic and quadratic-quadratic systems; and use the graphing calculator as a tool to visualize the graphs and make predictions on the number of solutions.

Equations and Inequalities

3

add, subtract, multiply, divide, and simplify rational algebraic and radical expressions containing rational numbers and variables, and expressions containing rational exponents; write radical expressions as expression containing rational exponents and vice versa; and factor polynomials completely.  These same basic operations will be performed on complex numbers and the student will express them in simplest form using the patterns of the powers of i.  Students will investigate and identify the field properties that are valid for the complex numbers.

Expressions and Operations

4

investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding nth terms, and evaluating summations formulas.

Expressions and Operations

5

recognize the general shape of functions (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and convert between graphic and symbolic forms.  Investigate and analyze functions algebraically and graphically.  Key concepts include domain, range, zeros, x- and y-intercepts, intervals of increasing or decreasing, asymptotes, end behavior, inverse functions, and composition of multiple functions.

Functions

6

collect and analyze data, and determine the equation of best fit in order to make predictions, and solve real-world problems.  Identify, create, and solve real-world problems involving inverse, joint, and a combination of direct and inverse variations.  Identify properties of a normal distribution and apply those properties to determine probabilities associated with areas under the standard normal curve.  Compute and distinguish between permutations and combinations and use technology for applications.

Statistics

 (End of Term Expectations)


Term

 

Number

   ()

 

1

Algebra 2-1.218Equations and Inequalities-O1.1

apply the skills they learned from algebra 1 to solve equations and inequalities, also involving simple square root equations, and will justify the steps used in solving these equations using the properties of real numbers. (AII.4.a, AII.4.b, AII.4.c, AII.4.d)

1

1

Algebra 2-1.218Equations and Inequalities-O1.2

solve absolute value equations and inequalities, graph their solutions, determine the absolute value equation or inequality that would produce a certain solution which may be graphed or written as an interval, explain why the solution to an absolute value equation or inequality is two numbers, and describe the situation in which the solution to an absolute value equation is the empty set. (AII.4.a, AII.4.b, AII.4.c, AII.4.d)

1

1

Algebra 2-5.218Functions-O1.3

appraise whether a relation is a function or not, determine if a function is linear;  describe the graph of a linear equation given only the equation and be able to write the equation in slope-intercept form,  point-slope form, and standard form; explain and interpret a piece-wise function,  describe the domain, range, zeros, x- and y- intercepts, and intervals of increase and decrease. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

1

Algebra 2-2.218Equations and Inequalities-O1.4

rewrite the equations/inequalities in a system of linear equations/inequalities to sovle the system of linear equations/inequalites by graphing, substitution, and elimination and will explain why a system of equations/inequalities does not have a solution(s) or why there are infinitely many solutions. (AII.5)

2

1

Algebra 2-5.218Functions-O1.5

describe the general transformations that take place within a family of functions and explain how to tell the difference between a parent graph and a graph in that family. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

1

Algebra 2-5.218Functions-O1.6

appraise an absolute value function and be able to give the vertex, axis of symmetry, and describe any transformations that have taken place, and will assess a two-variable absolute value inequality and determine whether its graph will be shaded inside the "V" of the absolute value graph or outside and whether the "V" should be dotted or solid when graphed. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

2

Algebra 2-5.218Functions-O2.1

recognize monomials, binomials, trinomials, and polynomials; identify the parent function/graph of a quadratic function and its vertex and zeros. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

2

Algebra 2-5.218Functions-O2.2

sketch the graph of a quadratic function using transformations of the parent graph and will be able to solve the quadratic for f(x) = 0 by determining where the graph crosses the x-axis. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

2

Algebra 2-5.218Functions-O2.3

investigate a quadratic function and be able to rewrite it in standard form, assess a situation which may be modeled by a quadratic function and be able to determine what the y-intercept for that model means, what the maximum (or minimum) means for that model, find a value of the range given a value of the domain or vice versa, and use the quadratic regression function on their calculators to determine the equation of best fit for a set of data that is best fit by a quadratic model. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

2

Algebra 2-5.218Functions-O2.4

assess the correct way in which to factor a quadratic expression or equation and then proceed to factor the quadratic using GCF, Binomial Factors (review FOIL), perfect square trinomials, difference of square trinomials, and grouping. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

2

Algebra 2-5.218Functions-O2.5

describe the domain, range, zeros, x- and y-intercepts, intervals of increasing and decreasing, and end behavior of a quadratic function; solve quadratic functions and equations for when f(x) = 0 by graphing, using the zero product rule, completing the square, and the quadratic formula. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

2

Algebra 2-3.218Expressions and Operations-O2.6

simplify radical expressions and operations performed with radical expressions, explain what complex numbers are, the properties of complex numbers, and compare the way that operations are performed on real number radical expressions and complex expressions; determine the complex roots of quadratic functions which have no real roots. (AII.1.a, AII.1.b, AII.1.c, AII.1.d)

3

2

Algebra 2-2.218Equations and Inequalities-O2.7

analyze the graph of systems of non-linear equations and determine the number of solutions to the sytem of equations and make preditions about the solutions and will use these predictions to check the answers they recieve when they solve the system of equations algebraically. (AII.5)

2

2

Algebra 2-5.218Functions-O2.8

determine the roots (zeros, x-intercepts, the value(s) of x when f(x) = 0, etc.) of a polynomial equation/function using a combination of factoring, difference of cubes, sum of cubes, quadratic formula, long and/or synthetic division, rational roots theorem, and the fundemental theorem of algebra. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

2

Algebra 2-5.218Functions-O2.9

assess the cubic family of functions and determine what transformations of the parent graph have taken place given an equation and sketch and explain the graph of a function that is a member of the cubic family of functions. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

3

Algebra 2-3.218Expressions and Operations-O3.1

recall simplifying square root expressions and apply to all radical expressions and perform operations on radical expressions; rewrite radical expressions using rational exponents. (AII.1.a, AII.1.b, AII.1.c, AII.1.d)

3

3

Algebra 2-1.218Equations and Inequalities-O3.2

solve radical equations with simply square roots by squaring either side of an equation and radical equations with radicands greater than 2 using rational exponents and inverse operations. (AII.4.a, AII.4.b, AII.4.c, AII.4.d)

1

3

Algebra 2-5.218Functions-O3.3

describe the radical function families, explain the transformations of the parent graph that are performed on a radical function to recieve the new graph, sketch a graph of the new function using the transformations of the parent graph, and describe the domain, range, zeros, x- and y-intercepts, intervals of increasing and decreasing, and end behavior. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

3

Algebra 2-5.218Functions-O3.4

evaluate a composition of functions, assess the graphs of two equations and determine if they are inverse functions, use composition of functions to determine if two functions are one to one functions, and describe the graph of the inverse of a given function and that the inverse graph of a function is found by reflecting the graph over the line y=x. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

3

Algebra 2-5.218Functions-O3.5

assess a graph and determine that it is a an exponential function, identify the transformations of the parent graph and determine the new graph of the family of functions, determine the domain, range, zeros, x- and y-intercepts, intervals of increasing and/or decreasing, asymptotes, and end behavior of exponential and logarithmic functions. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

3

Algebra 2-6.218Statistics-O3.6

assess a table of data and the correlated scatter plot made using the graphing calculator to determine the curve of best fit for a set of data and use exponential regression equations to find the curve of best fit for a real-world exponential model, recognize a logarithmic function, evaluate a logarithm, and solve equations using logarithms. (AII.9, AII.10, AII.11, AII.12)

6

4

Algebra 2-6.218Statistics-O4.1

assess whether a relationship is directly, inversely, combined, or jointly varied; evaluate the constant of variation for a direct, inverse, combined, or joint variation and then determine a value when x = a and/or z = b. (AII.9, AII.10, AII.11, AII.12)

6

4

Algebra 2-5.218Functions-O4.2

classify a function as a rational functions and assess the function and determine the domain, range, zeros, x- and y- intercepts, intercals of increasing or decreasing, asymptotes, end behavior, and any discontinuitites, explain any transformations of the parent function to produce a given graph or define the equation of a given graph using transformations of the parent function graph. (AII.6, AII.7.a, AII.7.b, AII.7.c, AII.7.d, AII.7.e, AII.7.f, AII.7.g, AII.7.h, AII.8)

5

4

Algebra 2-3.218Expressions and Operations-O4.3

add, subtract, multiply, divide, and simplify rational algebraic expressions using GCF, LCM, and properties of exponents. (AII.1.a, AII.1.b, AII.1.c, AII.1.d)

3

4

Algebra 2-1.218Equations and Inequalities-O4.4

justify the steps and solve rational equations using GCF, LCM, checking solutions with the graphing calculator, and determining if there are any extraneous solutions. (AII.4.a, AII.4.b, AII.4.c, AII.4.d)

1

4

Algebra 2-4.218Expressions and Operations-O4.5

classify a set of numbers as a sequence or series, arithmetic or geometric, and identify the common ratio or common difference and recognize the general equation to find the nth term of arithmetic and geometric sequences and recognize the general equation and identify the parts of a summation for arithmetic and geometric series. (AII.2, AII.3)

4

4

Algebra 2-4.218Expressions and Operations-O4.6

setup an equation to find the nth term of arithmetic and/or geometric sequences and the summation of arithmetic and geometric series. (AII.2, AII.3)

4

4

Algebra 2-6.218Statistics-O4.7

recognize permuations and combinations and be able to distinguish whether a permutation or combination is more appropriate for a given situatuion. (AII.9, AII.10, AII.11, AII.12)

6

4

Algebra 2-6.218Statistics-O4.8

define normal distribution, standard deviation, z-score, mean absolute deviation, and variation and will be able to recognize the graph of a normally distributed set of data, otherwise known as the bell curve. (AII.9, AII.10, AII.11, AII.12)

6

4

Algebra 2-6.218Statistics-O4.9

recall and identify the percentages underneath the bell curve associated with the area underneath the bell curve between certain intervals and use these areas to determine probabilites associated with those areas. recall that the area under any bell curve is = 1. (AII.9, AII.10, AII.11, AII.12)

6

4

Algebra 2-6.218Statistics-O4.10

summarize the relationship between z-score and standard deviation in relation to normal distribution and describe the percentages underneath the bell curve associated with the intervals created by standard deviation; appraise the percentile that a certain data element of a set of normally distributed data falls within. (AII.9, AII.10, AII.11, AII.12)

6

Curriculum Expectations:   Algebra Functions and Data Analysis (AFDA) (High School Math)
s (End of Course Expectations)
Linked Core Standard:
By the end of Algebra Functions and Data Analysis (AFDA), the student will:


 

 

Domain

1

collect data to create the curve of best fit using linear, quadratic, exponential, and logarithmic functions. Investigate and analyze functions to transfer between multiple representations of functions such as graphs, tables, and formulas.  Determine what transformations have taken place of the parent graph, continuity, local and absolute maxima and minima, domain, range, zeros, x- and y- intercepts, intervals of increasing and decreasing, end behaviors, and asymptotes. analyze and solve multi-step equations and solve word problems for better understanding of real world situations.

Algebra and Functions

2

determine important values in real world situations by identifying constraints and using linear programming techniques.

Algebra and Functions

3

identify dependent, independent, and mutually exclusive events and calculate experimental, simulated, theoretical, and conditional probability using addition and multiplication rules, permutations and combinations, and the law of large numbers.

Data Analysis

4

analyze and identify the bell curve, characteristics of normally distributed data, use and identify percentiles for each area of standard deviation under the bell curve, and normalizing data using z-scores.

Data Analysis

5

design and conduct an experiment which includes the concepts of sample size, sampling technique, controlling sources of bias and experimental error, data collection, and analysis and reporting of data.

Data Analysis

 (End of Term Expectations)


Term

 

Number

   ()

 

1

Algebra Functions and Data Analysis (AFDA)-1.211Algebra and Functions-O1.1

evaluate multi-step equations, one variable and literal, for the variable given, translate verbal and written expressions, and write equations for given real-world situations to solve for a given situation. (AFDA.2, AFDA.3, AFDA.4, AFDA.1.a, AFDA.1.b, AFDA.1.c, AFDA.1.d, AFDA.1.e, AFDA.1.f, AFDA.1.g, AFDA.1.h)

1

1

Algebra Functions and Data Analysis (AFDA)-1.211Algebra and Functions-O1.2

analyze a linear function and determine if it is direct or inverse variation, rewrite the equation in different forms, using the different forms be able to graph the equations without the use of a calculator or a table of values. (AFDA.2, AFDA.3, AFDA.4, AFDA.1.a, AFDA.1.b, AFDA.1.c, AFDA.1.d, AFDA.1.e, AFDA.1.f, AFDA.1.g, AFDA.1.h)

1

2

Algebra Functions and Data Analysis (AFDA)-2.211Algebra and Functions-O2.1

identify a system of equations, arrange the equations in different forms to be solved using graphing, substitution, or elimination, plan how to solve a system and what would have to be done to the equations to solve a system of equations each of the three different ways.  develop a plan for solving a system of equations with three equations and 3 variables. solve a system of linear inequalities and identify the solutions. (AFDA.5)

2

2

Algebra Functions and Data Analysis (AFDA)-1.211Algebra and Functions-O2.2

Write an equation of a line when given the graph of a line, Recognize graphs of parent functions for linear, quadratic, exponential and logarithmic functions, Write the equation of a linear, quadratic, exponential, or logarithmic function in (h, k) form given the graph of the parent function and transformation information, Describe the transformation from the parent function given the equation written in (h, k) form or the graph of the function, Given the equation of a function, recognize the parent function and transformation to graph the given function.
(AFDA.2, AFDA.3, AFDA.4, AFDA.1.a, AFDA.1.b, AFDA.1.c, AFDA.1.d, AFDA.1.e, AFDA.1.f, AFDA.1.g, AFDA.1.h)

1

2

Algebra Functions and Data Analysis (AFDA)-1.211Algebra and Functions-O2.3

•              Identify the domain and range for a relation, given a set of ordered pairs, a table, or a graph.
For each x in the domain of f, find f(x), Identify the zeros of the function algebraically and confirm them, using the graphing calculator, Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically, Recognize graphs of parent functions for linear, quadratic, Identify x-intercepts (zeros), y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing. (AFDA.2, AFDA.3, AFDA.4, AFDA.1.a, AFDA.1.b, AFDA.1.c, AFDA.1.d, AFDA.1.e, AFDA.1.f, AFDA.1.g, AFDA.1.h)

1

3

Algebra Functions and Data Analysis (AFDA)-1.211Algebra and Functions-O3.1

Describe continuity of a function on its domain or at a point,  Express intervals using correct interval notation and/or a compound inequality, Recognize restricted/discontinuous domains and ranges, Recognize graphs of parent functions for linear, quadratic, exponential and logarithmic functions, Continuous and discontinuous functions can be identified by their equations or graphs.  The end behavior of a function refers to the graphical behavior of a function as x goes to positive and negative infinity.

 (AFDA.2, AFDA.3, AFDA.4, AFDA.1.a, AFDA.1.b, AFDA.1.c, AFDA.1.d, AFDA.1.e, AFDA.1.f, AFDA.1.g, AFDA.1.h)

1

3

Algebra Functions and Data Analysis (AFDA)-2.211Algebra and Functions-O3.2

Describe the parent function represented by a scatterplot, Write an equation for the line of best fit, given a set of data points in a table, on a graph, or from a practical situation, Make predictions about unknown outcomes, using the equation of a line of best fit, Collect and analyze data to make decisions and justify conclusions.  Investigate scatterplots to determine if patterns exist, and identify the patterns,  Find an equation for the curve of best fit for data, using a graphing calculator. Models will include linear, quadratic, exponential, and logarithmic functions, Make predictions, using data, scatterplots, or equation of curve of best fit, Given a set of data, determine the model that would best describe the data.
(AFDA.5)

2

4

Algebra Functions and Data Analysis (AFDA)-3.211Data Analysis-O4.1

Compare and contrast permutations and combinations, Calculate the number of permutations of n objects taken r at a time, Calculate the number of combinations of n objects taken r at a time,  Define and give contextual examples of complementary, dependent, independent, and mutually exclusive events, Given two or more events in a problem setting, determine if the events are complementary, dependent, independent, and/or mutually exclusive, Find conditional probabilities for dependent, independent, and mutually exclusive events, Represent and calculate probabilities using Venn diagrams and probability trees, Analyze, interpret and make predictions based on theoretical probability within real-world context, given a real-world situation, determine when to use permutations or combinations.

 (AFDA.6.a, AFDA.6.b, AFDA.6.c, AFDA.6.d, AFDA.6.e)

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Algebra Functions and Data Analysis (AFDA)-4.211Data Analysis-O4.2

Interpret mean, median, mode, range, interquartile range, variance, and standard deviation of a univariate data set in terms of the problem’s context, Explain the influence of outliers on a univariate data set, Explain ways in which standard deviation addresses dispersion by examining the formula for standard deviation, Identify the properties of a normal probability distribution, Describe how the standard deviation and the mean affect the graph of the normal distribution, Determine the probability of a given event, using the normal distribution.
(AFDA.7.a, AFDA.7.b, AFDA.7.c, AFDA.7.d)

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4

Algebra Functions and Data Analysis (AFDA)-5.211Data Analysis-O4.3

Compare and contrast controlled experiments and observational studies and the conclusions one may draw from each, Identify biased sampling methods, Select a data collection method appropriate for a given context, Investigate and describe sampling techniques, such as simple random sampling, stratified sampling, and cluster sampling, Determine which sampling technique is best, given a particular context, Plan and conduct an experiment or survey. The experimental design should address control, randomization, and minimization of experimental error, Design a survey instrument, Given a plan for a survey, identify possible sources of bias, and describe ways to reduce bias, Write a report describing the experiment/survey and the resulting data and analysis.
(AFDA.8.a, AFDA.8.b, AFDA.8.c, AFDA.8.d, AFDA.8.e)

5

Curriculum Expectations:   Geometry (High School Math)
s (End of Course Expectations)
Linked Core Standard:
By the end of Geometry, the student will:


 

 

Domain

1

construct logical arguments in symbolic and verbal form and determine the validity of those statements which will include identifying the converse, inverse, and contrapositive of conditional statements and using deductive reasoning on conditional statements to determine whether a logical argument may be made,  and use Venn diagrams to represent set relationships.

Reasoning, Lines, and Transformations

2

use relationships between angles formed by two lines but by a transversal to determine whether two lines are parallel, verify parallelism, and solve real-world problems involving angles formed.

Reasoning, Lines, and Transformations

3

using algebraic and coordinate methods as well as deductive proof. use pictorial representations, including computer software, constructions, and coordinate methods to solve problems involving symmetry and transformation using formulas to find slope, midpoint, and distance to help determine if two lines are parallel or perpendicular and to determine if a figure is symmetric to a point or a line or if the figure has been translated, rotated reflected, or dilated.

Reasoning, Lines, and Transformations

4

construct and justify the constructions of a segment congruent to a given segment, perpendicular bisector of a segment, a line perpendicular to a line through a point on the line and a point not on the line, the bisector of an angle, an angle congruent to a given angle, and a line parallel to a given line through a point not on the line.

Reasoning, Lines, and Transformations

5

given information concerning the lengths of sides and or measures of angles in a triangle will order the sides/angles by length/angle measures, determine whether a triangle exists, and determine the range in which the length of the third side must lie with all these concepts applied to real-world situations. prove two triangles are congruent/similar using algebraic and coordinate methods as well as deductive proofs. solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangles trigonometry.

Triangles

6

solve real-world problems involving angles of polygons using the formula 180(n-2) and will verify and use characteristics and properties of quadrilaterals to solve real-world problems. use angles, arcs, chords, tangents and secants to investigate, verify, and apply properties of circles, solve real-world problems involving properties of circles, and finding arc lengths and areas of sectors in circles. given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle.

Polygons and Circles

7

use formulas for surface area and volume of three-dimensional objects to solve real-world problems, use similar geometric objects in two- or three-dimensions to compare ratios between side lengths, perimeter, areas, and volumes, to determine how changes in one or more dimensions of an object affect are and or volume of the object, to determine how changes in area and/or volume of an object affect one or more dimensions of the object, and to solve real-world problems about similar geometric objects.

Three-Dimensional Figures

 (End of Term Expectations)


Term

 

Number

   ()

 

1

Geometry-3.210Reasoning, Lines, and Transformations-O1.1

 identify, list, and label points, lines, and planes.  Define, list, and label segments and rays.  Identify, label the intersection of two lines, two planes, and a line and a plane.  (Prerequisite Skill) (G.3.a, G.3.b, G.3.c, G.3.d)

3

1

Geometry-3.210Reasoning, Lines, and Transformations-O1.2

Apply the distance formula to find the distance between two points on the number line and employ the segment addition postulate to solve for unknown values of x regarding unknown lengths of segments. (Lesson 1-3). (G.3.a, G.3.b, G.3.c, G.3.d)

3

1

Geometry-3.210Reasoning, Lines, and Transformations-O1.3

categorize angles and angles pairs as adjacent vertical, complementary, supplementary, and linear pairs, explain the linear pair postulate, and setup equations to solve for an unknown value of an angle or variable in an expression which represents an angle measure using the properties of the angles pairs discussed.
(G.3.a, G.3.b, G.3.c, G.3.d)

3

1

Geometry-3.210Reasoning, Lines, and Transformations-O1.4

evaluate the segment on the number line and/or coordinate plane for which the length and/or midpoint of the segment needs to be found and evaluate the distance and midpoint formulas for the given segments to estimate the midpoint and distance of that segment. (Lesson 1-7) (G.3.a, G.3.b, G.3.c, G.3.d)

3

1

Geometry-1.210Reasoning, Lines, and Transformations-O1.5

discuss and recognize the patterns that are formed by certain objects and/or numbers  in a sequence and use inductive reasoning to come to a conclusion about the next object/number in the sequence. Combine the skills of recognizing patterns and making conclusions to form a conjecture about a generalized situation and also explain why a conjecture is not always true using a counterexample. (G.1.a, G.1.b, G.1.c, G.1.d)

1

1

Geometry-1.210Reasoning, Lines, and Transformations-O1.6

appraise logical statements and determine if they are conjunctions, disjunctions, or negations and recognize and use the symbols of formal logic to write a logic statement written in symbolic form as a verbal statement or vice versa and create and/or analyze a Venn Diagrams to represent sets formed using conjunctions, disjunctions, and negations. (G.1.a, G.1.b, G.1.c, G.1.d)

1

1

Geometry-1.210Reasoning, Lines, and Transformations-O1.7

identify a conditional statement as an "if, then" statement, judge the validity of that statement, identify and create the converse, inverse, and contrapositive of conditional statements and rewrite conditional statements from symbolic to verbal form or vice versa. (G.1.a, G.1.b, G.1.c, G.1.d)

1

1

Geometry-1.210Reasoning, Lines, and Transformations-O1.8

use valid forms of deductive reasoning including the law of syllogism, law of detachment, and counterexamples and use the symbols of formal logic to write the laws of syllogism and detachment in symbolic and verbal forms.
(G.1.a, G.1.b, G.1.c, G.1.d)

1

1

Geometry-1.210Reasoning, Lines, and Transformations-O1.9

apply the converse of a conditional statement and determine the validity of the original conditional and the converse of the conditional to determine if the biconditional is able to be written and if so to write the biconditional in symbolic and verbal forms. (G.1.a, G.1.b, G.1.c, G.1.d)

1

1

Geometry-3.210Reasoning, Lines, and Transformations-O1.10

apply the distance formula for the number line to determine the lengths of lines and to employ the segment addition postulate to find the measures of segments and to solve for unknown values used to represent measures of segments. (G.3.a, G.3.b, G.3.c, G.3.d)

3

1

Geometry-2.210Reasoning, Lines, and Transformations-O1.11

be able to identify parallel lines, perpendicular lines, skew lines, transversals, and angle pairs formed by two lines cut by a transversal (alternate interior, alternate exterior, corresponding, and consecutive interior angles). be able to identify the intersection of two lines, two planes, and a line and a plane. (G.2.a, G.2.b, G.2.c)

2

1

Geometry-2.210Reasoning, Lines, and Transformations-O1.12

be able to apply properties of parallel lines and transversals in that they will be able to identify pairs of angles formed by parallel lines and a transversal and will be able to use the properties of those angles, given that the lines are parallel, to determine if a certain pair of angles should be congruent or supplementary and then to be able to solve for a given value of a variable or find an unknown angle. (G.2.a, G.2.b, G.2.c)

2

1

Geometry-1.210Reasoning, Lines, and Transformations-O1.13

appraise an algebra or geometry problem and choose the types of reasoning and methods to make a proof of a problem or theorem and justify each step of the proof using properties, definitions, and theorems learned. (G.1.a, G.1.b, G.1.c, G.1.d)

1

1

Geometry-2.210Reasoning, Lines, and Transformations-O1.14

classify lines as parallel or perpendicular using theorems that relate parallel and perpendicular lines. (G.2.a, G.2.b, G.2.c)

2

1

Geometry-2.210Reasoning, Lines, and Transformations-O1.15

be able to recall that equations of lines in the coordinate plane may be written in point-slope, slope-intercept, or standard form and that they can solve an equation to put it in each different form. using slope-intercept form of an equation students will be able to identify parallel and perpendicular lines from their equations by comparing the slopes and will also be able to create the equation of a line which is parallel or perpendicular to a given line through a given point. (G.2.a, G.2.b, G.2.c)

2

1

Geometry-2.210Reasoning, Lines, and Transformations-O1.16

categorize lines as parallel or not given the measures of two angles and using the converses of the theorems regarding the angle pairs formed by parallel lines and transversals and will also determine a value of a variable such that it will prove that two given lines are parallel.  (G.2.a, G.2.b, G.2.c)

2

2

Geometry-5.210Triangles-O2.1

be able to classify a polygon is a triangle given its number of sides, classify a triangle by its angles and sides, determine the value of a missing angle in a triangle by using the fact that the interior angle sum of a triangle is 180, solve for an unknown variable with regards to angle measures or sides of a triangle, and use the remote interior angles of a triangle to determine the measure of an exterior angle of a triangle or vise versa. (G.5.a, G.5.b, G.5.c, G.5.d, G.6, G.7, G.8)

5

2

Geometry-5.210Triangles-O2.2

apply triangle inequality properties and the hinge theorem to demonstrate the range of possible values that the third side of a triangle must be between for a triangle to be made, illustrate that a triangle may be made from given side lengths, use the hinge theorem to arrange angles or sides of a triangle in ascending or descending order. (G.5.a, G.5.b, G.5.c, G.5.d, G.6, G.7, G.8)

5

2

Geometry-5.210Triangles-O2.3

compare two polygons and determine if they are similar knowing that similar polygons must be the same size, have congruent corresponding angles, and corresponding sides are proportional. explain why two triangles are similar using theorems and postulates of triangle similarity: AA~, SSS~, SAS~ and will construct proofs to prove two triangles are similar. (G.5.a, G.5.b, G.5.c, G.5.d, G.6, G.7, G.8)

5

2

Geometry-5.210Triangles-O2.4

explain using a two-column or paragraph proof why two triangles or two corresponding parts on two triangles are congruent by justifying first that two triangles are congruent and then using the CPCTC theorem to prove that corresponding parts of congruent triangles are congruent. (G.5.a, G.5.b, G.5.c, G.5.d, G.6, G.7, G.8)

5

2

Geometry-5.210Triangles-O2.5

compare two triangles and determine if they are congruent using the triangle congruence postulates and theorems: SSS, SAS, ASA, AAS, HL. identify corresponding/congruent parts of overlapping triangles that will aid in the analysis of triangles to determine if they are congruent. (G.5.a, G.5.b, G.5.c, G.5.d, G.6, G.7, G.8)

5

2

Geometry-5.210Triangles-O2.6

find and use similarities in right triangles and apply the Side-Splitter Theorem and the Triangle-Angle-Bisector Theorem. (G.5.a, G.5.b, G.5.c, G.5.d, G.6, G.7, G.8)

5

2

Geometry-5.210Triangles-O2.7

be able to define what congruent figures are and that for two figures to be congruent they must be the same shape, corresponding angles must be congruent, and corresponding sides must be congruent. (G.5.a, G.5.b, G.5.c, G.5.d, G.6, G.7, G.8)

5

2

Geometry-5.210Triangles-O2.8

apply classifications of triangles using sides and angles and identify the different parts of isosceles, equilateral, and right triangles. solve for missing angles or values of variable using properties of the different types of triangles. (G.5.a, G.5.b, G.5.c, G.5.d, G.6, G.7, G.8)

5

3

Geometry-6.210Polygons and Circles-O3.1

identify a polygon given its number of sides, classify the polygon as regular, irregular, convex, or concave and will be able to find the interior angle sum of any convex polygon given the formula 180(n-2), find the measure of one exterior or interior angle of a regular polygon, and conclude the number of sides that a regular polygon has given one interior angle or one exterior angle. (G.11.c, G.9, G.10, G.11.a, G.11.b, G.12)

6

3

Geometry-6.210Polygons and Circles-O3.2

explain what a quadrilateral is, explain whether or not the quadrilateral is a parallelogram and if it is a parallelogram if it is a rectangle, rhombus, square. relate why a square is both a rhombus and a rectangle using the properties of each to justify. construct a proof to prove that a quadrilateral is a parallelogram.  categorize the quadrilateral as a simple quadrilateral, kite, or trapezoid if it is not a parallelogram. (G.11.c, G.9, G.10, G.11.a, G.11.b, G.12)

6

3

Geometry-6.210Polygons and Circles-O3.3

use coordinate geometry to classify triangles by their side measures, prove that two polygons are congruent, prove that a polygon is a regular polygon. (G.11.c, G.9, G.10, G.11.a, G.11.b, G.12)

6

3

Geometry-5.210Triangles-O3.4

identify the Pythagorean Theorem, legs, and hypotenuses of right triangles and apply this to real world problems where they will collect data and use the Pythagorean Theorem to find the missing measure to form a Pythagorean Triple, find one missing side of a right triangle given the measures of two other sides using the Pythagorean Theorem, explain whether three given measures could form a right triangle, acute triangle, obtuse triangle, or no triangle. (G.5.a, G.5.b, G.5.c, G.5.d, G.6, G.7, G.8)

5

3

Geometry-5.210Triangles-O3.5

assess a right triangle and determine if Pythagorean Theorem or Right Triangle Trigonometry should be used to evaluate the measure of a missing side or angle and explain why a certain trig function should be used as opposed to another. compare and contrast angles of depression and elevation and use them to determine an unknown value in real world situations where right angle trigonometry may be used in correlation with angles of elevation and depression. (G.5.a, G.5.b, G.5.c, G.5.d, G.6, G.7, G.8)

5

3

Geometry-3.210Reasoning, Lines, and Transformations-O3.6

appraise two figures to determine what transformations the pre-image or original figure has undergone to result in the image or new figure. compare and contrast translations, rotations, reflections, and dilations and determine the image of points that have been transformed using the rules for each transformation. (G.3.a, G.3.b, G.3.c, G.3.d)

3

4

Geometry-6.210Polygons and Circles-O4.1

define circle, diameter, radius, chord, secant, tangent, central angle, inscribed angle, minor arc, major arc, intercepted arc,  and identify the name of a circle, name of an angle, name of an arc. (G.11.c, G.9, G.10, G.11.a, G.11.b, G.12)

6

4

Geometry-6.210Polygons and Circles-O4.2

solve values of unknown variable using the properties of inscribed and central angles and their intercepted arcs, and properties of polygons inscribed in circles. (G.11.c, G.9, G.10, G.11.a, G.11.b, G.12)

6

4

Geometry-6.210Polygons and Circles-O4.3

set up equations using properties of chords, tangents, and secants and what happens with their lengths when they intersect inside and outside circles.  also relate the angles that are formed when a chord and a secant or tangent intersect and intercept an arc or when two secants, a secant and a tangent, or two tangents intercept an arc. (G.11.c, G.9, G.10, G.11.a, G.11.b, G.12)

6

4

Geometry-7.210Three-Dimensional Figures-O4.4

explain why a net is a possible net of a given soli or not. select the correct formula to determine perimeter, area, surface area, and/or volume of a figure or solid and describe how each of these are affected when certain dimensions of the figures or solids are changed. compare the ratios of the dimensions, surface areas, and volumes of 3-D figures to compare the surface area and volumes of similar figures in real-world situations. (G.13, G.14.a, G.14.b, G.14.c, G.14.d)

7

4

Geometry-4.210Reasoning, Lines, and Transformations-O4.5

construct segments congruent to given segments, perpendicular bisectors, angles congruent to given angles, angle bisectors, lines perpendicular to a given line through a given point on the line or a given point not on the line, and lines which are parallel to a given line using the properties of parallel lines and transversals. (G.4.a, G.4.b, G.4.c, G.4.d, G.4.e, G.4.f)

4