(a) Introduction.
  (1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on computational thinking, mathematical fluency, and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century.
  (2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will 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. Students will select appropriate tools such as real objects, manipulatives, algorithms, paper and pencil, and technology and techniques such as mental math, estimation, number sense, and generalization and abstraction to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, computer programs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
  (3) The primary focal areas in Grade 8 are proportionality; expressions, equations, relationships, and foundations of functions; and measurement and data. Students use concepts, algorithms, and properties of real numbers to explore mathematical relationships and to describe increasingly complex situations. Students use concepts of proportionality to explore, develop, and communicate mathematical relationships. Students use algebraic thinking to describe how a change in one quantity in a relationship results in a change in the other. Students connect verbal, numeric, graphic, and symbolic representations of relationships, including equations and inequalities. Students begin to develop an understanding of functional relationships. Students use geometric properties and relationships, as well as spatial reasoning, to model and analyze situations and solve problems. Students communicate information about geometric figures or situations by quantifying attributes, generalize procedures from measurement experiences, and use the procedures to solve problems. Students use appropriate statistics, representations of data, and reasoning to draw conclusions, evaluate arguments, and make recommendations. While the use of all types of technology is important, the emphasis on algebra readiness skills necessitates the implementation of graphing technology.
  (4) Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples.
(b) Knowledge and skills.
  (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.
  (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:
    (A) extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers;
    (B) 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;
    (C) convert between standard decimal notation and scientific notation; and
    (D) 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:
    (A) generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation;
    (B) compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; and
    (C) 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:
    (A) use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y- values to the change in x- values, (y2 - y1 ) / (x2 - x1 ), is the same for any two points (x1 , y1 ) and (x2, y2) on the same line;
    (B) graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; and
    (C) use data from a table or graph to determine the rate of change or slope and y- intercept in mathematical and real-world problems.
  (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:
    (A) represent linear proportional situations with tables, graphs, and equations in the form of y = kx;
    (B) represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0;
    (C) 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;
    (D) use a trend line that approximates the linear relationship between bivariate sets of data to make predictions;
    (E) solve problems involving direct variation;
    (F) distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0;
    (G) identify functions using sets of ordered pairs, tables, mappings, and graphs;
    (H) identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; and
    (I) 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:
    (A) describe the volume formula V = Bh of a cylinder in terms of its base area and its height;
    (B) 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; and
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