 TEKS Alignment

## HS Geometry

2. Numbers and Operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:

Standard Description
2A classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers
2B identify a number, its opposite, and its absolute value
2C locate, compare, and order integers and rational numbers using a number line
2D order a set of rational numbers arising from mathematical and real-world contexts
2E extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0

3. Number and operations. The student applies mathematical process standards to represent addition, subtraction, multiplication, and division while solving problems and justifying solutions. The student is expected to:

Standard Description
3A recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values
3B determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one
3C represent integer operations with concrete models and connect the actions with the models to standardized algorithms
3D add, subtract, multiply, and divide integers fluently
3E multiply and divide positive rational numbers fluently

4. Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to:

5. Proportionality. The student applies mathematical process standards to solve problems involving proportional relationships. The student is expected to

6. Expressions, equations, and relationships. The student applies mathematical process standards to use multiple representations to describe algebraic relationships. The student is expected to

Standard Description
6A identify independent and dependent quantities from tables and graphs
6B write an equation that represents the relationship between independent and dependent quantities from a table
6C represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b

7. Expressions, equations, and relationships. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:

Standard Description
7A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization
7B distinguish between expressions and equations verbally, numerically, and algebraically
7C determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations
7D generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties

8. Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to represent relationships and solve problems. The student is expected to:

9. Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to represent situations. The student is expected to:

Standard Description
9A write one-variable, one-step equations and inequalities to represent constraints or conditions within problems
9B represent solutions for one-variable, one-step equations and inequalities on number lines
9C write corresponding real-world problems given one-variable, one-step equations or inequalities

10. Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to solve problems. The student is expected to:

Standard Description
10A model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts
10B determine if the given value(s) make(s) one-variable, one-step equations or inequalities true

12. Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to analyze problems. The student is expected to:

13. Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to solve problems. The student is expected to:

Standard Description
13A interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots
13B distinguish between situations that yield data with and without variability

14. Personal financial literacy. The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor. The student is expected to:

Standard Description
14A compare the features and costs of a checking account and a debit card offered by different local financial institutions
14B distinguish between debit cards and credit cards
14C balance a check register that includes deposits, withdrawals, and transfers
14D explain why it is important to establish a positive credit history
14E describe the information in a credit report and how long it is retained
14F describe the value of credit reports to borrowers and to lenders
14G explain various methods to pay for college, including through savings, grants, scholarships, student loans, and work-study
14H compare the annual salary of several occupations requiring various levels of post- secondary education or vocational training and calculate the effects of the different annual salaries on lifetime income

3. Number and operations. The student applies mathematical process standards to add, subtract, multiply, and divide while solving problems and justifying solutions. The student is expected to:

Standard Description
3A add, subtract, multiply, and divide rational numbers fluently
3B apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers

4. Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to:

Standard Description
4A represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt
4B calculate unit rates from rates in mathematical and real-world problems
4C determine the constant of proportionality (k = y/x) within mathematical and real-world problems
4D solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems
4E convert between measurement systems, including the use of proportions and the use of unit rates

5. Proportionality. The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships. The student is expected to:

Standard Description
5A generalize the critical attributes of similarity, including ratios within and between similar shapes
5B describe π as the ratio of the circumference of a circle to its diameter
5C solve mathematical and real-world problems involving similar shape and scale drawings

6. Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is expected to:

Standard Description
6A represent sample spaces for simple and compound events using lists and tree diagrams
6B select and use different simulations to represent simple and compound events with and without technology
6C make predictions and determine solutions using experimental data for simple and compound events
6D make predictions and determine solutions using theoretical probability for simple and compound events
6E find the probabilities of a simple event and its complement and describe the relationship between the two
6F use data from a random sample to make inferences about a population
6G solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents
6H solve problems using qualitative and quantitative predictions and comparisons from simple experiments
6I determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces

8. Expressions, equations, and relationships. The student applies mathematical process standards to develop geometric relationships with volume. The student is expected to:

9. Expressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems. The student is expected to:

Standard Description
9A solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids
9B determine the circumference and area of circles
9C determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles
9D solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net

10. Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations and inequalities to represent situations. The student is expected to:

Standard Description
10A write one-variable, two-step equations and inequalities to represent constraints or conditions within problems
10B represent solutions for one-variable, two-step equations and inequalities on number lines
10C write a corresponding real-world problem given a one-variable, two-step equation or inequality

11. Expressions, equations, and relationships. The student applies mathematical process standards to solve one-variable equations and inequalities. The student is expected to:

Standard Description
11A model and solve one-variable, two-step equations and inequalities
11B determine if the given value(s) make(s) one-variable, two-step equations and inequalities true
11C write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships

12. Measurement and data. The student applies mathematical process standards to use statistical representations to analyze data. The student is expected to:

Standard Description
12A compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads
12B use data from a random sample to make inferences about a population
12C compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations

13. Personal financial literacy. The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor. The student is expected to:

Standard Description
13A calculate the sales tax for a given purchase and calculate income tax for earned wages
13B identify the components of a personal budget, including income; planned savings for college, retirement, and emergencies; taxes; and fixed and variable expenses, and calculate what percentage each category comprises of the total budget
13C create and organize a financial assets and liabilities record and construct a net worth statement
13D use a family budget estimator to determine the minimum household budget and average hourly wage needed for a family to meet its basic needs in the student's city or another large city nearby
13E calculate and compare simple interest and compound interest earnings
13F analyze and compare monetary incentives, including sales, rebates, and coupons

2. Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:

Standard Description
2A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers
2B approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line
2C convert between standard decimal notation and scientific notation
2D order a set of real numbers arising from mathematical and real-world contexts

3. Proportionality. The student applies mathematical process standards to use proportional relationships to describe dilations. The student is expected to:

Standard Description
3A generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation
3B compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane
3C use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation

4. Proportionality. The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope. The student is expected to:

5. Proportionality. The student applies mathematical process standards to use proportional and non- proportional relationships to develop foundational concepts of functions. The student is expected to:

Standard Description
5A represent linear proportional situations with tables, graphs, and equations in the form of y = kx
5B represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0
5C contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation
5D use a trend line that approximates the linear relationship between bivariate sets of data to make predictions
5E solve problems involving direct variation
5F distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0
5G identify functions using sets of ordered pairs, tables, mappings, and graphs
5H identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems
5I write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations

6. Expressions, equations, and relationships. The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to:

Standard Description
6A describe the volume formula V = Bh of a cylinder in terms of its base area and its height
6B model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas
6C use models and diagrams to explain the Pythagorean theorem

7. Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to solve problems. The student is expected to:

Standard Description
7A solve problems involving the volume of cylinders, cones, and spheres
7B use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders
7C use the Pythagorean Theorem and its converse to solve problems
7D determine the distance between two points on a coordinate plane using the Pythagorean Theorem

8. Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:

10. Two-dimensional shapes. The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to:

Standard Description
10A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane
10B differentiate between transformations that preserve congruence and those that do not
10C explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation
10D model the effect on linear and area measurements of dilated two-dimensional shapes

11. Measurement and data. The student applies mathematical process standards to use statistical procedures to describe data. The student is expected to:

12. Personal financial literacy. The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor. The student is expected to:

## High School

### Algebra 1

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:

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 systems of equations. The student is expected to:

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:

Standard Description
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
4B compare and contrast association and causation in real-world problems
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

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:

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 without technology, quadratic equations. The student is expected to:

Standard Description
6A determine the domain and range of quadratic functions and represent the domain and range using inequalities
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)
6C write quadratic functions when given real solutions and graphs of their related equations

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:

8. Quadratic functions and equations. 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:

Standard Description
8A solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula
8B write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems

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 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:

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:

Standard Description
10A add and subtract polynomials of degree one and degree two
10B multiply polynomials of degree one and degree two
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
10D rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property
10E factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two
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

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

Standard Description
11A simplify numerical radical expressions involving square roots
11B simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents

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:

Standard Description
12A decide whether relations represented verbally, tabularly, graphically, and symbolically define a function
12B evaluate functions, expressed in function notation, given one or more elements in their domains
12C identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes
12D write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms
12E solve mathematic and scientific formulas, and other literal equations, for a specified variable

## High School

### Algebra 2

2. Attributes of functions and their inverses. The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse. The student is expected to:

3. Systems of equations and inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutions. The student is expected to:

Standard Description
3A formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations, the first linear and the second quadratic
3B solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution
3C solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation
3D determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables
3E formulate systems of at least two linear inequalities in two variables
3F solve systems of two or more linear inequalities in two variables
3G determine possible solutions in the solution set of systems of two or more linear inequalities in two variables

4. Quadratic and square root functions, equations, and inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:

Standard Description
4A write the quadratic function given three specified points in the plane
4B write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening
4C determine the effect on the graph of f(x) = x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d
4D transform a quadratic function f(x) = ax2 + bx + c to the form f(x) = a(x - h)2 + k to identify the different attributes of f(x)
4E formulate quadratic and square root equations using technology given a table of data
4F solve quadratic and square root equations
4G identify extraneous solutions of square root equations

5. Exponential and logarithmic functions and equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems. The student is expected to:

6. Cubic, cube root, absolute value and rational functions, equations, and inequalities. The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to:

Standard Description
6A analyze the effect on the graphs of f(x) = x3 and f(x) = 3√x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d
6B solve cube root equations that have real roots
6C analyze the effect on the graphs of f(x) = |x| when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d
6D formulate absolute value linear equations
6E solve absolute value linear equations
6F solve absolute value linear inequalities
6G analyze the effect on the graphs of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d
6H formulate rational equations that model real-world situations
6I solve rational equations that have real solutions
6J determine the reasonableness of a solution to a rational equation
6K determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation
6L formulate and solve equations involving inverse variation

7. Number and algebraic methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to:

Standard Description
7A add, subtract, and multiply complex numbers
7B add, subtract, and multiply polynomials
7C determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two
7D determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods
7E determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping
7F determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two
7G rewrite radical expressions that contain variables to equivalent forms
7H solve equations involving rational exponents
7I write the domain and range of a function in interval notation, inequalities, and set notation

8. Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions. The student is expected to:

Standard Description
8A analyze data to select the appropriate model from among linear, quadratic, and exponential models
8B use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data
8C predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential model

## High School

### Geometry

2. Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures. The student is expected to:

3. Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). The student is expected to:

4. Logical argument and constructions. The student uses the process skills with deductive reasoning to understand geometric relationships. The student is expected to:

Standard Description
4A distinguish between undefined terms, definitions, postulates, conjectures, and theorems
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
4C verify that a conjecture is false using a counterexample
4D compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle

5. Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures. The student is expected to:

6. Proof and congruence. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart. The student is expected to:

7. Similarity, proof, and trigonometry. The student uses the process skills in applying similarity to solve problems. The student is expected to:

Standard Description
7A apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles
7B apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems

8. Similarity, proof, and trigonometry. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart. The student is expected to:

Standard Description
8A prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems
8B identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems

9. Similarity, proof, and trigonometry. The student uses the process skills to understand and apply relationships in right triangles. The student is expected to:

Standard Description
9A determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems
9B apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean theorem, including Pythagorean triples, to solve problems

10. Two-dimensional and three-dimensional figures. The student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures. The student is expected to:

11. Two-dimensional and three-dimensional figures. The student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures. The student is expected to:

12. Circles. The student uses the process skills to understand geometric relationships and apply theorems and equations about circles. The student is expected to:

13. Probability. The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events. The student is expected to:

Standard Description
13A develop strategies to use permutations and combinations to solve contextual problems
13B determine probabilities based on area to solve contextual problems
13C identify whether two events are independent and compute the probability of the two events occurring together with or without replacement
13D apply conditional probability in contextual problems
13E apply independence in contextual problems