2014 STAAR Algebra I Assessed Curriculum

Algebra I

Assessment

Eligible Texas Essential

Knowledge and Skills

Texas Education Agency

Student Assessment Division

January 2014

STAAR Algebra I Assessment

Mathematical Process Standards

These student expectations will not be listed under a separate reporting

category. Instead, they will be incorporated into test questions across

reporting categories since the application of mathematical process

standards is part of each knowledge statement.

(A.1) Mathematical process standards. The student uses mathematical

processes to acquire and demonstrate mathematical understanding. The

student is expected to

(A) apply mathematics to problems arising in everyday life, society, and

the workplace;

(B) 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;

(C) select tools, including real objects, manipulatives, paper and pencil,

and technology as appropriate, and techniques, including mental

math, estimation, and number sense as appropriate, to solve

problems;

(D) communicate mathematical ideas, reasoning, and their implications

using multiple representations, including symbols, diagrams, graphs,

and language as appropriate;

(E) create and use representations to organize, record, and

communicate mathematical ideas;

(F) analyze mathematical relationships to connect and communicate

mathematical ideas; and

(G) display, explain, and justify mathematical ideas and arguments using

precise mathematical language in written or oral communication.

STAAR Algebra I Page 2 of 11

Texas Education Agency

Student Assessment Division

January 2014

Reporting Category 1:

Number and Algebraic Methods

The student will demonstrate an understanding of how to use algebraic

methods to manipulate numbers, expressions, and equations.

(A.10) Number and algebraic methods. 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) add and subtract polynomials of degree one and degree two;

Supporting Standard

(B) multiply polynomials of degree one and degree two;

Supporting Standard

(C) 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; Supporting Standard

(D) rewrite polynomial expressions of degree one and degree two in

equivalent forms using the distributive property;

Supporting Standard

(E) factor, if possible, trinomials with real factors in the form ax

2

+ bx + c,

including perfect square t rinomials of degree two; and

Readiness Standard

(F) 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. Supporting Standard

(A.11) Number and algebraic methods. The student applies the mathematical

process standards and algebraic methods to rewrite algebraic expressions

into equivalent forms. The s tudent is expected to

(A) simplify numerical radical expressions involving square roots; and

Supporting Standard

(B) simplify numeric and algebraic expressions using the laws of

exponents, including integral and rational exponents.

Readiness Standard

STAAR Algebra I Page 3 of 11

Texas Education Agency

Student Assessment Division

January 2014

(A.12) Number and algebraic methods. 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) decide whether relations represented verbally, tabularly, graphically,

and symbolically define a function; Supporting Standard

(B) evaluate functions, expressed in function notation, given one or more

elements in their domains; Supporting Standard

(C) identify terms of arithmetic and geometric sequences when the

sequences are given in function form using recursive processes;

Supporting Standard

(D) write a formula for the n

th

term of arithmetic and geometric

sequences, given the value of several of their terms; and

Supporting Standard

(E) solve mathematic and scientific formulas, and other literal equations,

for a specified variable. Supporting Standard

STAAR Algebra I Page 4 of 11

Texas Education Agency

Student Assessment Division

January 2014

Reporting Category 2:

Describing and Graphing Linear Functions, Equations, and

Inequalities

The student will demonstrate an understanding of how to describe and

graph linear functions, equations, and inequalities.

(A.3) Linear functions, equations, and inequalities. 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 sy stems of

equations. The student is expected to

(A) 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 – y

1

= m(x – x

1

);

Supporting Standard

(B) calculate the rate of change of a linear function represented

tabularly, graphically, or algebraically i n context of mathematical and

real-world problems; Readiness Standard

(C) graph linear f unctions on the coordinate plane and identify key

features, including x-intercept, y-intercept, zeros, and slope, in

mathematical and real-world problems; Readiness Standard

(D) graph the solution set of linear inequalities in two variables on the

coordinate plane; Readiness Standard

(E) 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 o f a, b, c, and d; Supporting Standard

(F) graph systems of two linear equations in two variables on the

coordinate plane and d etermine the solutions if they exist;

Supporting Standard

(G) estimate graphically the solutions to systems of two linear equations

with two variables in real-world problems; and

Supporting Standard

(H) graph the solution set of systems of two linear inequalities in two

variables o n the coordinate plane. Supporting Standard

STAAR Algebra I Page 5 of 11

Texas Education Agency

Student Assessment Division

January 2014

(A.4) Linear functions, equations, and inequalities. 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) calculate, using technology, the correlation coefficient between two

quantitative variables and interpret this quantity a s a measure of the

strength of the linear association; Supporting Standard

(B) compare and co ntrast association and causation in real-world

problems; and Supporting Standard

(C) write, with and without technology, linear functions that provide a

reasonable fit to data to estimate solutions and make predictions for

real-world problems. Supporting Standard

STAAR Algebra I Page 6 of 11

Texas Education Agency

Student Assessment Division

January 2014

Reporting Category 3:

Writing and Solving Linear Functions, Equations, and

Inequalities

The student will demonstrate an understanding of how to write and solve

linear functions, equations, and inequalities.

(A.2) Linear functions, equations, and inequalities. 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

(A) determine the domain and range of a linear function in mathematical

problems; determine reasonable domain and range values for r eal-

world situations, both continuous and discrete; and represent domain

and range using inequalities; Readiness Standard

(B) write linear equations in two variables in various forms, including

y = mx + b, Ax + By = C, and y – y

1

= m(x – x

1

), given one point

and the slope and given two points; Supporting Standard

(C) write linear equations in two variables given a table of values, a

graph, and a verbal description; Readiness Standard

(D) write and solve equations involving direct v ariation;

Supporting Standard

(E) write the equation of a line that contains a given point and is parallel

to a given line; Supporting Standard

(F) write the equation of a line that contains a given point and is

perpendicular t o a given line; Supporting Standard

(G) 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; Supporting Standard

(H) write linear inequalities in two variables given a table of values, a

graph, and a verbal description; and Supporting Standard

(I) write systems of two linear equations given a table of values, a

graph, and a verbal description. Readiness Standard

STAAR Algebra I Page 7 of 11

Texas Education Agency

Student Assessment Division

January 2014

(A.5) Linear functions, equations, and inequalities. 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) 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; Readiness Standard

(B) 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; and Supporting Standard

(C) solve systems of two linear equations with two variables for

mathematical and real-world problems. Readiness Standard

STAAR Algebra I Page 8 of 11

Texas Education Agency

Student Assessment Division

January 2014

Reporting Category 4:

Quadratic Functions and Equations

The student will demonstrate an understanding of how to describe, write,

and solve quadratic functions and equations.

(A.6) Quadratic functions and equations. The student applies the

mathematical process standards when using properties of quadratic

functions to write and represent in multiple ways, with and w ithout

technology, quadratic equations. The student is expected to

(A) determine the domain and range of quadratic functions and

represent the domain and range using inequalities;

Readiness Standard

(B) 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) = ax

2

+ bx + c); and Supporting Standard

(C) write quadratic functions when given real solutions and graphs of

their related equations. Supporting Standard

(A.7) Quadratic functions and equations. 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) 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; Readiness Standard

(B) describe the relationship between the linear factors of quadratic

expressions and the zeros of their associated quadratic functions;

and Supporting Standard

(C) determine the effects on the graph of the parent function f(x) = x

2

when f(x) is replaced by af(x), f(x) + d, f(x – c), f(bx) for specific

values o f a, b, c, and d. Readiness Standard

STAAR Algebra I Page 9 of 11

Texas Education Agency

Student Assessment Division

January 2014

(A.8) Quadratic functions and equations. The student applies the

mathematical process standards to solve, with and without t echnology,

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) solve quadratic equations having real solutions by factoring, taking

square roots, completing the square, and applying the quadratic

formula; and Readiness Standard

(B) write, using technology, quadratic functions that provide a

reasonable fit to data to estimate solutions and make predictions for

real-world problems. Supporting Standard

STAAR Algebra I Page 10 of 11

Texas Education Agency

Student Assessment Division

January 2014

Reporting Category 5:

Exponential Functions and Equations

The student will demonstrate an understanding of how to describe and

write exponential f unctions and equations.

(A.9) Exponential functions and equations. The student applies the

mathematical process standards when using properties of exponential

functions and their related transformations to write, graph, and represent

in multiple w ays 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) determine the domain and range of exponential functions of the form

f(x) = ab

x

and represent the domain and range using inequalities;

Supporting Standard

(B) interpret the m eaning of the values of a and b in exponential

functions of the form f(x) = ab

x

in

real-world

problems;

Supporting

Standard

(C)

write exponential

functions in

the form

f(x) =

ab

x

(where b is a

rational number) to describe problems arising from mathematical

and real-world situations, including growth and decay;

Readiness Standard

(D) graph exponential functions that model growth and decay and

identify key features, including y-intercept and asymptote, in

mathematical and real-world problems; and Readiness Standard

(E) write, using technology, exponential functions that provide a

reasonable fit to data and make predictions for real-world problems.

Supporting Standard

STAAR Algebra I Page 11 of 11

Texas Education Agency

Student Assessment Division

January 2014