BISD
Algebra 1 PRE-AP
Super TEKS
The new Algebra 1 Super TEKS are created to integrate Algebra 2 and Geometry
TEKS to the current Algebra 1 grade state standards. These TEKS ensure the
differentiation of instruction between regular and Pre-AP Math courses. The overall
intention is to promote a challenging environment to reach the students’ full
potential and to prepare the students for the demands of Advanced Placement
Math Courses.
Markings throughout the document need to be considered in the following manner:
Bolded – More emphasis needed during the course
Lightened – Less emphasis needed during the course
Highlighted – Teacher notes that clarify TEKS further
Red – TEKS brought down from Algebra 2 that need to be taught during Algebra 1 Pre-AP
Blue - TEKS brought down from Geometry that need to be taught during Algebra 1 Pre-AP
§111.32. Algebra I (One Credit).
(a) Basic understandings.
(1) Foundation concepts for high school mathematics. As presented in Grades K-8, the
basic understandings of number, operation, and quantitative reasoning; patterns,
relationships, and algebraic thinking; geometry; measurement; and probability and statistics
are essential foundations for all work in high school mathematics. Students will continue to
build on this foundation as they expand their understanding through other mathematical
experiences.
(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. Students study algebraic concepts and the relationships among them to better
understand the structure of algebra.
(3) Functions, equations, and their relationship. A function is a fundamental mathematical
concept; it expresses a special kind of relationship between two quantities. Students use
functions to determine one quantity from another, to represent and model problem
situations, and to analyze and interpret relationships. Students perceive functions and
equations as means for analyzing and understanding a broad variety of relationships and as a
useful tool for expressing generalizations.
(4) Relationship between equations and functions. Equations and inequalities arise as a way
of asking and answering questions involving functional relationships. Students work in
many situations to set up equations and inequalities and use a variety of methods to solve
them.
(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.
(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. Students also use multiple representations, technology, applications
and modeling, and numerical fluency in problem-solving contexts.
(b) Knowledge and skills.
(1) Foundations for functions. The student understands that a function represents a
dependence of one quantity on another and can be described in a variety of ways. The
student is expected to:
(A) describe independent and dependent quantities in functional relationships;
A2 (b1A) identify the mathematical domains and ranges of functions and determine
reasonable domain and range values for continuous and discrete situations; and
(B) gather and record data and use data sets to determine functional relationships
between quantities;
A2 (b1B) collect and organize data, make and interpret scatterplots, fit the graph of a
function to the data, interpret the results, and proceed to model, predict, and make
decisions and critical judgments.
(C) describe functional relationships for given problem situations and write
equations or inequalities to answer questions arising from the situations;
(D) represent relationships among quantities using concrete models, tables, graphs,
diagrams, verbal descriptions, equations, and inequalities; and
(E) interpret and make decisions, predictions, and critical judgments from functional
relationships.
A2 (b3C) interpret and determine the reasonableness of solutions (approximation) to
systems of equations or inequalities for given contexts.
(2) Foundations for functions. The student uses the properties and attributes of functions.
The student connects algebraic and geometric representations of functions. The student is
expected to:
(A) identify and sketch the general forms of linear (y = x, emphasize that
= y, hence f(x) = x) and quadratic (y = x2), (f(x) = x2) parent functions;
f(x)
A2 (b4A) identify and sketch graphs of parent functions, including linear
x), quadratic (f(x) = x2), exponential and square roots
(f(x) =
A2 (b2A) use tools including factoring and properties of exponents to simplify
expressions and to transform and solve equations,( emphasize x-a = 1/xa), ; and
(B) identify mathematical domains and ranges and determine reasonable domain and
range values for given situations, both continuous and discrete;
A2 (b6A) determine the reasonable domain and range values of quadratic functions,
as well as interpret and determine the reasonableness of solutions to quadratic
equations and inequalities;
(C) interpret situations in terms of given graphs or creates situations that fit given
graphs; and
(D) 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.
(3) Foundations for functions. The student understands how algebra can be used to express
generalizations and recognizes and uses the power of symbols to represent situations. The
student is expected to:
(A) use symbols to represent unknowns and variables;
TEACHER NOTE: introduce other variables such as (  ,  ,  ,  , , ,  , )
(B) look for patterns and represent generalizations algebraically.
(4) Foundations for functions. The student understands the importance of the skills required
to manipulate symbols in order to solve problems and uses the necessary algebraic skills
required to simplify algebraic expressions and solve equations and inequalities in problem
situations. The student is expected to:
(A) find specific function values, simplify polynomial expressions, transform and
solve equations, and factor as necessary in problem situations;
(B) use the commutative, associative, and distributive properties to simplify
algebraic expressions; and
(C) connect equation notation with function notation, such as y = x + 1 and f(x) = x
+ 1.
(5) Linear functions. The student understands that linear functions can be represented in
different ways and translates among their various representations. The student is expected
to:
(A) determine whether or not given situations can be represented by linear
functions;
(B) determine the domain and range for linear functions in given situations; and
(C) use, translate, and make connections among algebraic, tabular, graphical, or
verbal descriptions of linear functions.
(6) Linear functions. The student understands the meaning of the slope and intercepts of the
graphs of linear functions and zeros of linear functions and interprets and describes the
effects of changes in parameters of linear functions in real-world and mathematical
situations. The student is expected to:
(A) develop the concept of slope as rate of change and determine slopes from
graphs, tables, and algebraic representations;
G (b7B) use slopes and equations of lines to investigate geometric relationships,
including parallel lines, perpendicular(normal) lines, and special segments of
triangles and other polygons ; and
G (b7c) derive and use formulas involving length, slope, and midpoint,.
(B) interpret the meaning of slope (introduce slope as rate of change) and intercepts
in situations using data, symbolic representations, or graphs;
(C) investigate, describe, and predict the effects of changes in m and b on the graph
of y = mx + b;
TEACHER NOTE: place emphasis on using y – y1 = m(x – x1)
(D) graph and write equations of lines given characteristics such as two points, a
point and a slope, or a slope and y-intercept;
(E) determine the intercepts of the graphs of linear functions and zeros of linear
functions from graphs, tables, and algebraic representations;
(F) interpret and predict the effects of changing slope and y-intercept in applied
situations; and
(G) relate direct variation to linear functions and solve problems involving
proportional change.
(7) Linear functions. The student formulates equations and inequalities based on linear
functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the
situation. The student is expected to:
(A) analyze situations involving linear functions and formulate linear equations or
inequalities to solve problems;
(B) 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; and
(C) interpret and determine the reasonableness of solutions to linear equations and
inequalities.
A2 (b8D) solve quadratic equations and inequalities using graphs, tables, and
algebraic methods.
(8) Linear functions. The student formulates systems of linear equations from problem
situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the
situation. The student is expected to:
(A) analyze situations and formulate systems of linear equations in two unknowns to
solve problems;
(B) solve systems of linear equations using concrete models, graphs, tables, and
algebraic methods; and
(C) interpret and determine the reasonableness of solutions to systems of linear
equations.
(9) Quadratic and other nonlinear functions. The student understands that the graphs of
quadratic functions are affected by the parameters of the function and can interpret and
describe the effects of changes in the parameters of quadratic functions. The student is
expected to:
(A) determine the domain and range for quadratic functions in given situations;
(B) investigate, describe, and predict the effects of changes in a on the graph of y =
ax2 + c;
(C) investigate, describe, and predict the effects of changes in c on the graph of y =
ax2 + c; and
(D) analyze graphs of quadratic functions and draw conclusions.
A2 (b6) Quadratic and square root functions. The student understands that quadratic
functions can be represented in different ways and translates among
their various
representations. The student is expected to:
A2 (b6A) determine the reasonable domain and range values of quadratic functions,
as well as interpret and determine the reasonableness of solutions to quadratic
equations and inequalities;
A2 (b6B) relate representations of quadratic functions, such as algebraic, tabular,
graphical, and verbal descriptions; and
A2 (b6C) determine a quadratic function from its roots (real and complex) or a graph.
A2 (b7) Quadratic and square root functions. The student interprets and describes
the effects of changes in the parameters of quadratic functions in applied and
mathematical situations. The student is expected to:
A2 (b7A) 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; and
A2 (b7B) 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.
(10) Quadratic and other nonlinear functions. The student understands there is
more than
one way to solve a quadratic equation and solves them using
appropriate methods.
The student is expected to:
(A) solve quadratic equations and inequalities using concrete models, tables, graphs,
and algebraic methods; and
A2 (b8A) analyze situations involving quadratic functions and formulate quadratic
equations or inequalities to solve problems;
(B) 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.
A2 (b8B) Algebra II TEKS) (D) analyze and interpret the solutions of quadratic
equations using discriminants and solve quadratic equations using the quadratic
formula;
A2 (b8C) compare and translate between algebraic and graphical solutions of
quadratic equations; and
A2 (b8D) solve quadratic equations and inequalities using graphs, tables, and
algebraic methods.
A2 (b5E) use the method of completing the square.
(11) Quadratic and other nonlinear functions. The student understands there are situations
modeled by functions that are neither linear nor quadratic and models the situations. The
student is expected to:
(A) use patterns to generate the laws of exponents and apply them in problemsolving situations;
(B) analyze data and represent situations involving inverse variation using concrete
models, tables, graphs, or algebraic methods; and
(C) analyze data and represent situations involving exponential growth and decay
using concrete models, tables, graphs, or algebraic methods.
A2 (b11) Exponential and logarithmic functions. The student formulates equations
and inequalities based on exponential and logarithmic functions, uses a
variety of
methods to solve them, and analyzes the solutions in terms of the situation.
Source: §111.32, §111.33, §111.34