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Rice University School Mathematics Project
 

Deconstructing the Language of Mathematics in the Revised TEKS for High School Algebra and Geometry

Mathematics teachers who participated in Rice University School Mathematics Project's 2014 Spring Networking Conference on February 1 provided material for this wonderful resource for K-12 Texas mathematics teachers. Attendees identified mathematical terms new to their grade level in the revised TEKS; these terms are bold typed.  

TEKS Revised Language   Reporting Category
A.2E Write the equation of a line that contains a given point and is parallel to a given line.
Linear Functions, Equations, and Inequalities
A.2F Write the equation of a line that contains a given point and is perpendicular to a given line.
Linear Functions, Equations, and Inequalities
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).

Linear Functions, Equations, and Inequalities
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.
Linear Functions, Equations, and Inequalities
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
.

Linear Functions, Equations, and Inequalities
A.4B Compare and contrast association and causation in real-world problems.
Linear Functions, Equations, and Inequalities
A.4C Write linear functions, with and without technology, that provide a reasonable fit to data to make predictions for real-world problems.
Linear Functions, Equations, and Inequalities
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.
Linear Functions, Equations, and Inequalities
A.6B Write equations of quadratic functions given the vertex and another point on the graph, write this equation in vertex form (f(x) = a(x+h)2 + k), and then rewrite this equation from vertex form to standard form (f(x) = ax2 + bx + c). 
Quadratic Functions, and Equations
A.6C Write quadratic functions when given real solutions and graphs of their related equations.
Quadratic Functions, and Equations
A.7B Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions.
Quadratic Functions, and Equations
A.8A Solve quadratic equations, having real solutions by factoring, taking square roots, completing the square, and applying the  quadratic formula.
Quadratic Functions, and Equations
A.8B Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.
Quadratic Functions, and Equations
A.9A Determine the domain and range of exponential functions of the form f(x) = a·bx and represent the domain and range using inequalities.
Exponential Functions, and Equations
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.
Exponential Functions, and Equations
A.10A Add and subtract polynomials of degree one and degree two.
Number and Algebraic Methods
A.10B Multiply polynomials of degree one and degree two.
Exponential Functions, and Equations
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 excees the degree of the dividend.
Number and Algebraic Methods
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. 
Number and Algebraic Methods
A.11A Simplify numerical radical expressions involving square roots.
Number and Algebraic Methods
A.11B Simplify numeric and algebraic expressions using the law of exponents, including integral and rational exponents.
Number and Algebraic Methods
A.12C Identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes.
Number and Algebraic Methods
A.12D Write the formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms.
Number and Algebraic Methods
A.12E Solve mathematic and scientific formulas, and other literal equations, for a specified variable.
Number and Algebraic Methods




G.3B Determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point on the plane.
Coordinate and Transformational Geometry
G.3C Identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane.
Coordinate and Transformational Geometry
G.4A Distinguish between undefined terms, definitions, postulates, conjectures, and theorems.
Logical Argument and  Constructions
G.4B Identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse.
Logical Argument and  Constructions
G.4D Compare geometric relationship between Euclidian and spherical geometries, including parallel lines and the sum of the angles in a triangle.
Logical Argument and  Constructions
G.5A Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools.
Logical Argument and  Constructions
G.5B Construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector
of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge.

Logical Argument and  Constructions
G.5C Use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships.
Logical Argument and  Constructions
G.5D Verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems.
Logical Argument and  Constructions
G.6A Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, angles formed by parallel lines cut by a transversal, and prove equidistance between the endpoints of a segment and points on its perpendicular bisector, and apply these relationships to solve problems.
Proof and Congruence
G.10A Identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes.
Two-Dimensional and
Three-Dimensional Figures
G.12A Apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems.
Circles