mathematical process standards algebra icurriculum.austinisd.org/schoolnetdocs/mathematics/... ·...

Key: Change of grade level Change of strand NEW Standard © 2012 lead4ward

Mathematical Process Standards Algebra I

+A.1 The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:Change New Standard

(Implementation Year 2015‐2016) Current Standard Cognitive Change Content Change

A.1A apply mathematics to problems arising in everyday life, society, and the workplace A.1B use a problem‐solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem‐solving process and the reasonableness of the solution A.1F analyze mathematical relationships to connect and communicate mathematical ideas A.1G display, explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communications

a(6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem‐solving, language and communication, and reasoning (justification and proof) to make connections within and outside mathematics…

changed “make connections” to “apply mathematics”

changed “use communication” to “display” and “communicate ideas”

changed “use reasoning (justification and proof)” to “explain and justify”

added “analyze mathematical relationships”

moved “Underlying mathematical processes” from introductory “Basic Understandings” to the “Mathematical Process Standards”

changed “within and outside mathematics” to “in everyday life, society, and the workplace”

changed “language” to “precise mathematical language in written or oral communications”

expanded the problem‐solving process to include: analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem‐solving process and the reasonableness

A.1E interpret and make decisions, predictions, and critical judgments from functional relationships

changed “interpret” to “analyze” and “display”

changed strand from “Foundations for Functions” to “Mathematical Process Standards”

changed “functional relationships” to “mathematical relationships”

changed “predictions and critical judgments” to “mathematical ideas and arguments”

3

Key: Change of grade level Change of strand NEW Standard © 2012 lead4ward

Mathematical Process Standards Algebra I

A.1 The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:Change New Standard

(Implementation Year 2015‐2016) Current Standard Cognitive Change Content Change

A.1C select tools, including real objects, manipulatives, paper/pencil, and technology, as appropriate and techniques, including mental math, estimation, and number sense, as appropriate to solve problems A.1D communicate mathematical ideas, reasoning, and their implications using multiple representation, including symbols, diagrams, graphs, and language as appropriate

a(6) Underlying mathematical processes…Students also use multiple representations, technology, applications and modeling, and numerical fluency in problem‐solving contexts. a(5) Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model mathematical situations to solve meaningful problems.

changed “use tools” to “select tools” changed “use a variety of

representations” to “communicate ideas, reasoning, and their implications using multiple representation”

deleted “use modeling” and “model mathematical situations”

moved “Underlying mathematical processes” and “Tools for algebraic thinking” from introductory “Basic Understandings” to the “Mathematical Process Standards”

expanded “numerical fluency” to include mental math, estimation, and number sense

added use of paper/pencil deleted list of specific types of

technology (calculators with graphing capabilities, data collection devices, and computers)

changed “concrete” representations to “real objects [and] manipulatives”

changed “pictorial” representations to “diagrams”

changed “verbal” representations to “language”

A.1D represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities A.2C interpret situations in terms of given graphs or creates situations that fit given graphs A.3A use symbols to represent unknowns and variables

changed “represent,” “interpret” and “use” to “communicate”

changed strand from “Foundations for Functions” to “Mathematical Process Standards”

A.1E create and use representations to organize, record and communicate mathematical ideas

a(2) Algebraic thinking and symbolic reasoning. Symbolic reasoning plays a critical role in algebra; symbols provide powerful ways to represent mathematical situations and to express generalizations. Students use symbols in a variety of ways to study relationships among quantities.

changed “represent situations” to “create and use representations”

changed “study relationships” and “express generalizations” to “organize, record, and communicate ideas”

moved “Algebraic thinking and symbolic reasoning” from introductory “Basic Understandings” to the “Mathematical Process Standards”

deleted “symbols;” however, included in “representations”

deleted “relationships;” however, included in A.1F

4

Key: Change of grade /course Change of strand NEW Standard © 2012 lead4ward

Linear Functions, Equations, and Inequalities Algebra I

A.2 The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations. The student is expected to:

Change New Standard (Implementation Year 2015‐2016)

Current Standard Cognitive Change Content Change

A.2A determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real‐world situations, both continuous and discrete; and represent domain and range using inequalities

A.2B identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete A.5B determine the domain and range for linear functions in given situations

specified the use of inequalities to represent domain and range

A.2B write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1), given one point and the slope and given two points

A.6D graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y‐intercept

deleted “graph;” however, included in A.3C

deleted “slope and y‐intercept,” as it can be included in “one point and the slope”

specified the various forms of linear equations (y = mx + b, Ax + By = C, and y – y1 = m(x – x1))

A.2C write linear equations in two variables given a table of values, a graph, and a verbal description

A.5C use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions

changed “use, translate, and make connections” to “write”

A.2D write and solve equations involving direct variation

A.6G relate direct variation to linear functions and solve problems involving proportional change

changed “relate direct variation to linear functions” to “write equations”

deleted reference to “proportional change”

A.2E write the equation of a line that contains a given point and is parallel to a given line A.2F write the equation of a line that contains a given point and is perpendicular to a given line

G.7B use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons

changed “use” and “investigate” to “write”

moved equations of parallel and perpendicular lines from Geometry to Algebra I

did not include “special segments of triangles and other polygons”

A.2G write an equation of a line that is parallel or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined

A.2H write linear inequalities in two variables given a table of values, a graph, and a verbal description

A.7A analyze situations involving linear functions and formulate linear equations or inequalities to solve problems

deleted “analyze situations;” however, included in “verbal descriptions”

deleted “solve problems;” however, included in Process Standards (see TEKS A.1)

specified that inequalities involve two variables

added the use of tables and graphs in writing inequalities

A.2I write systems of two linear equations given a table of values, a graph, and a verbal description

A.8A analyze situations and formulate systems of linear equations in two unknowns to solve problems

deleted “analyze situations;” however, included in “verbal descriptions”

deleted “solve problems;” however, included in Process Standards (see TEKS A.1)

added the use of tables and graphs in writing systems

5



A.3 The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations. The student is expected to:



A.3A determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1)

A.6A develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations

changed “develop the concept of slope” to “determine the slope”

added “two points on the line” specified the various forms of linear

equations (y = mx + b, Ax + By = C, and y – y1 = m(x – x1))

A.3B calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real‐world problems

A.6B interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs

changed “interpret the meaning of slope” to “calculate the rate of change”

deleted “intercepts” changed “using data” to “represented

tabularly” added “in context of mathematical

and real‐world problems”

A.3C graph linear functions on the coordinate plane and identify key features, including x‐intercept, y‐intercept, zeros, and slope, in mathematical and real‐world problems

A.6D graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y‐intercept

deleted “write equations;” however, included in A.2B

added “x‐intercept” and “zeros” added “in mathematical and real‐

world problems”

A.3D graph the solution set of linear inequalities in two variables on the coordinate plane

A.7B investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities

deleted “investigate methods” and “select a method”

changed “solving” linear inequalities to “graphing” the ”solution set”

deleted the use of concrete models and properties of equality in finding the solution set to inequalities; however, included in A.5B

A.3E determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d , f(x – c), f(bx) for specific values of a, b, c, and d

A.2A identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions A.6C investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b

deleted “identify and sketch” changed “investigate, describe, and

predict the effects” to “determine the effects”

changed the use of m and b (in y = mx + b) to the use of a, b, c, and d (when f(x) is replaced by af(x), f(x) + d , f(x – c), or f(bx))

A.3F graph systems of two linear equations intwo variables on the coordinate plane and determine the solutions if they exist

A.8B solve systems of linear equations using concrete models, graphs, tables, and algebraic methods

deleted the use of concrete models, tables, and algebraic methods to solve systems; however, included in the Process Standards (see A.1B, A.1C, A.1D)

included reference to systems where solutions may not exist

A.3G estimate graphically the solutions to systems of two linear equations with two variables in real‐world problems

A.8C interpret and determine the reasonableness of solutions to systems of linear equations

changed “interpret” and “determine reasonableness” to “estimate graphically”

added “in real‐world problems”

A.3H graph the solution set of systems of two linear inequalities in two variables on the coordinate plane

2 A.3B use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities

moved the graphing of systems of inequalities from Algebra II to Algebra I

did not include tables or matrices

6



A.4 The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real‐world data. The student is expected to:



A.4A calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association

P.3C use regression to determine the appropriateness of a linear function to model real‐life data (including using technology to determine the correlation coefficient)

changed “use” and “determine” to “calculate” and “interpret”

moved linear regression and correlation coefficients from Precalculus to Algebra I

changed the “appropriateness of a linear function” to “measure of strength of the linear association”

A.4B compare and contrast association and causation in real‐world problems

A.4C write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real‐world problems

A.2D collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations

deleted “collect and organize [data]” deleted “make and interpret scatterplots” changed “model” to “write functions” deleted “make decisions and critical

judgments”

deleted reference to specific types of correlation; however, skills still necessary to “provide a reasonable fit to data”

7



A.5 The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions. The student is expected to:



A.5A solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

A.4A find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations A.4B use the commutative, associative, and distributive properties to simplify algebraic expressions

specified that equations use one variable; however, other literal equations are addressed in A.12E

specified that solutions involve the use of the distributive property, and variables on both sides of the equation

A.5B solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

A.7B investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities

deleted “investigate methods” and “select a method”

deleted the use of concrete models; however, included in the Process Standards (see A.1C)

deleted the use of graphs; however, included (for two‐variable inequalities) in A.3D

specified the use of one variable inequalities

specified that solutions involve the use of the distributive property and variables on both sides of the inequality

A.5C solve systems of two linear equations with two variables for mathematical and real‐world problems

A.8B solve systems of linear equations using concrete models, graphs, tables, and algebraic methods

deleted “using concrete models, graphs, tables, and algebraic methods;” however, included in the Process Standards (see A.1B, A.1C, A.1D)

added “for mathematical and real‐world problems”

8

Key: Change of grade/course Change of strand NEW Standard © 2012 lead4ward

Quadratic Functions and Equations Algebra I

A.6 The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations. The student is expected to:



A.6A determine the domain and range of quadratic functions and represent the domain and range using inequalities

A.9A determine the domain and range for quadratic functions in given situations

added “using inequalities” deleted “in given situations;”

however, included in the Process Standards (see A.1A)

A.6B write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x – h)2 + k), and rewrite the equation from vertex form to standard form (f(x) = ax2 + bx + c)

2A.7A use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax2 + bx + c and the y = a (x – h)2 + k symbolic representations of quadratic functions

changed “connect symbolic representations” to “write (and rewrite) equations”

deleted “sketch the graphs;” however, included in A.7A

moved vertex and standard forms of quadratic functions from Algebra II to Algebra I

specified the use of the vertex and another point on the graph

A.6C write quadratic functions when given real solutions and graphs of their related equations

A.10B make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x‐intercepts) of the graph of the function

changed “make connections” to “write functions”

deleted the terms roots, zeros, and x‐intercepts; however, included in A.7A and A.7B

9



A.7 The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations. The student is expected to:



A.7A graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x‐intercept, y‐intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

2A.7A use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax2 + bx + c and the y = a (x – h)2 + k symbolic representations of quadratic functions

moved graphing quadratic functions from Algebra II to Algebra I

changed “characteristics” to “key attributes”

added list of “key attributes,” including x‐intercept(s), y‐intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

deleted reference to vertex and standard forms; however, included in A.6B

A.7B describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions

A.10B make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x‐intercepts) of the graph of the function

changed “make connections among” to “describe the relationship between”

deleted the term “roots” added connections to “linear factors”

A.7C determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x – c), f(bx) for specific values of a, b, c, and d

A.2A identify and sketch the general forms of linear (y=x) and quadratic (y=x2) parent functions A.9B investigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c A.9C investigate, describe, and predict the effects of changes in c on the graph of y = ax2 + c 2 A.7B use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a (x – h)2 + k form of a function in applied and purely mathematical situations

deleted “identify and sketch” changed “investigate, describe, and

predict” to “determine”

moved horizontal translations (f(x – c)) of quadratic functions from Algebra II to Algebra I

changed the use of h and k (in vertex form of a quadratic function) to c and d (in the forms f(x – c) and f(x) + d)

added the use of b in f(bx)

10



A.8 The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real‐world data. The student is expected to:



A.8A solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

A.4A find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations A.10A solve quadratic equations using concrete models, tables, graphs, and algebraic methods

specified that quadratic equations have “real solutions”

deleted “using concrete models, tables, and graphs;” however, included in the Process Standards (see A.1B, A.1C, A.1D

provided a list of specific “algebraic methods,” such as factoring, taking square roots, completing the square, and applying the quadratic formula

A.8B write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real‐world problems

A.9D analyze graphs of quadratic functions and

draw conclusions deleted reference to analyzing graphs

and drawing conclusions; however, included in the Process Standards (see TEKS A.1)

11


Exponential Functions and Equations Algebra I

A.9 The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real‐world data. The student is expected to:



A.9A determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities

2A.11C determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities

moved finding domains and ranges of exponential functions from Algebra II to Algebra I

did not move logarithmic functions from Algebra II

deleted “reasonable” and “reasonableness of solutions;” however, included in the Process Standards (see A.1B)

specified the form of exponential functions (f(x) = abx)

added “using inequalities”

A.9B interpret the meaning of the values of aand b in exponential functions of the form f(x) = abx in real‐world problems A.9D graph exponential functions that model growth and decay and identify key features, including y‐intercept and asymptote, in mathematical and real‐world problems

2A.11B use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior

changed “use,” “investigate, describe, and predict,” “describe,” and “examine” to “graph”

added “interpret the meaning” of a and b in f(x) = abx

moved properties of exponential functions from Algebra II to Algebra I

did not move logarithmic functions from Algebra II


added “that model growth and decay”

added y‐intercept as a “key feature” of exponential functions

deleted domain and range; however, included in A.9A

A.9C write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real‐world situations, including growth and decay

A.11C analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods

changed “analyze data and represent situations” to “write functions to describe problems”

changed strand from “Quadratic and Other Nonlinear Functions” to “Exponential Functions and Equations”


deleted use of concrete models, tables and graphs; however, included in the Process Standards (see A.1B, A.1C, A.1D)

A.9E write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real‐world problems

2A.11F analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem

deleted “analyze a situation;” however, included in the Process Standards (see TEKS A.1)

changed “solve the problem” to “make predictions for real‐world problems”

moved writing exponential functions from Algebra II to Algebra I

added “using technology” added providing “a reasonable fit to

data”

12


Number and Algebraic Methods Algebra I

A.10 The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions. The student is expected to:



A.10A add and subtract polynomials of degree one and degree two A.10B multiply polynomials of degree one and degree two A.10E factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two

A.4A find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations

changed “simplify” to add, subtract, and multiply

changed strand from “Properties and Attributes of Functions” to “Number and Algebraic Methods”

deleted “find specific function values;” however, included in A.12B

deleted “solve equations;” however, included in A.5A

changed “polynomial expressions” to “polynomials of degree one and degree two”

specified that factoring is only “if possible” and “with real factors”

specified that factoring is only for trinomials of the form ax2 + bx + c, including perfect square trinomials

deleted “in problem situations;” however, included in the Process Standards (see TEKS A.1)

A.10C determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend

A.10D rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property

A.4B use the commutative, associative, and distributive properties to simplify algebraic expressions

changed “simplify” to “rewrite” changed strand from “Properties and Attributes of Functions” to “Number and Algebraic Methods”

deleted specific reference to commutative and associative properties; however, included in the process of rewriting expressions

changed “algebraic expressions” to “polynomial expressions of degree one and degree two”

A.10F decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial

13



A.11 The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to:



A.11A simplify numerical radical expressions involving square roots

A.11B simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents

A.11A use patterns to generate the laws of exponents and apply them in problem‐solving situations

changed “use” and “apply” patterns to “simplify” expressions

changed strand from “Quadratic and Other Nonlinear Functions” to “Number and Algebraic Methods”

specified the use of both numeric and algebraic expressions

specified the use of both integral and rational exponents

deleted “in problem‐solving situations;” however, included in the Process Standards (see TEKS A.1)

14



A.12 The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:



A.12A decide whether relations represented verbally, tabularly, graphically, and symbolically define a function

A.1B gather and record data and use data sets to determine functional relationships between quantities

deleted “gather and record data” changed “determine functional

relationships” to “decide whether relations define a function”

changed strand from “Functional Relationships” to “Number and Algebraic Methods”

changed “data sets” to “relations represented tabularly and graphically”

added verbal and symbolic representations of relations

A.1A describe independent and dependent

quantities in functional relationships moved independent and dependent

quantities from Algebra I to grade 6 (see 6.6A)

A.4C connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1

deleted specific connection between equation and function notations; however, included in the Process Standards (see TEKS A.1) as well as in the linear functions strand (see TEKS A.3)

A.12B evaluate functions, expressed in function notation, given one or more elements in their domains A.12E solve mathematic and scientific formulas, and other literal equations, for a specified variable

A.4A find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations

changed “find specific function values” to “evaluate functions”

changed strand from “Properties and Attributes of Functions” to “Number and Algebraic Methods”

specified that evaluating functions uses “one or more elements in their domains”

specified solving literal equations for a variable; however, solving other one‐variable equations is included in A.5A and A.8A

deleted “simplify polynomial expressions;” however, included in A.10A and A.10B

deleted factoring; however, included in A.10E

A.12C identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes A.12D write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms

8.5B find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change) A.3B look for patterns and represent generalizations algebraically P.4B use arithmetic, geometric and other sequences and series to solve real‐life problems

changed “evaluate an expression” to “identify terms” from “function form”

deleted “look for patterns”

moved arithmetic sequences from grade 8 to Algebra I

moved geometric sequences from Precalculus to Algebra I

did not include series from Precalculus changed “any term” to “the nth term” added using “recursive processes” deleted “real‐life problems;” however,

included in the Process Standards (see TEKS A.1)

15

mathematical process standards algebra icurriculum.austinisd.org/schoolnetdocs/mathematics/... ·...

Documents