TEKS Grade 8 Math

The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

• 111.28(b)(1)(A)
  apply mathematics to problems arising in everyday life, society, and the workplace; apply
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• 111.28(b)(1)(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; use
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• 111.28(b)(1)(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; select
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• 111.28(b)(1)(D)
  communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; communicate
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• 111.28(b)(1)(E)
  create and use representations to organize, record, and communicate mathematical ideas; create
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• 111.28(b)(1)(F)
  analyze mathematical relationships to connect and communicate mathematical ideas; and analyze
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• 111.28(b)(1)(G)
  display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. display
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The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:

• 111.28(b)(2)(A)
  extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers; extend
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• 111.28(b)(2)(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; approximate
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• 111.28(b)(2)(C)
  convert between standard decimal notation and scientific notation; and convert
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• 111.28(b)(2)(D)
  order a set of real numbers arising from mathematical and real-world contexts. order
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The student applies mathematical process standards to use proportional relationships to describe dilations. The student is expected to:

• 111.28(b)(3)(A)
  generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation; generalize
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• 111.28(b)(3)(B)
  compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; and compare
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• 111.28(b)(3)(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. use
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The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope. The student is expected to:

• 111.28(b)(4)(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; use
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• 111.28(b)(4)(B)
  graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; and graph
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• 111.28(b)(4)(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. use
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The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions. The student is expected to:

• 111.28(b)(5)(A)
  represent linear proportional situations with tables, graphs, and equations in the form of y = kx; represent
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• 111.28(b)(5)(B)
  represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0; represent
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• 111.28(b)(5)(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; contrast
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• 111.28(b)(5)(D)
  use a trend line that approximates the linear relationship between bivariate sets of data to make predictions; use
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• 111.28(b)(5)(E)
  solve problems involving direct variation; solve
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• 111.28(b)(5)(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; distinguish
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• 111.28(b)(5)(G)
  identify functions using sets of ordered pairs, tables, mappings, and graphs; identify
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• 111.28(b)(5)(H)
  identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; and identify
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• 111.28(b)(5)(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. write
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The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to:

• 111.28(b)(6)(A)
  describe the volume formula V = Bh of a cylinder in terms of its base area and its height; describe
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• 111.28(b)(6)(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 model
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• 111.28(b)(6)(C)
  use models and diagrams to explain the Pythagorean theorem. use
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The student applies mathematical process standards to use geometry to solve problems. The student is expected to:

• 111.28(b)(7)(A)
  solve problems involving the volume of cylinders, cones, and spheres; solve
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• 111.28(b)(7)(B)
  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; use
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• 111.28(b)(7)(C)
  use the Pythagorean Theorem and its converse to solve problems; and use
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• 111.28(b)(7)(D)
  determine the distance between two points on a coordinate plane using the Pythagorean Theorem. determine
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The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:

• 111.28(b)(8)(A)
  write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants; write
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• 111.28(b)(8)(B)
  write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants; write
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• 111.28(b)(8)(C)
  model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants; and model
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• 111.28(b)(8)(D)
  use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. use
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The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations. The student is expected to identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations.

The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to:

• 111.28(b)(10)(A)
  generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane; generalize
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• 111.28(b)(10)(B)
  differentiate between transformations that preserve congruence and those that do not; differentiate
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• 111.28(b)(10)(C)
  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; and explain
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• 111.28(b)(10)(D)
  model the effect on linear and area measurements of dilated two-dimensional shapes. model
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The student applies mathematical process standards to use statistical procedures to describe data. The student is expected to:

• 111.28(b)(11)(A)
  construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data; construct
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• 111.28(b)(11)(B)
  determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points; and determine
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• 111.28(b)(11)(C)
  simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected. simulate
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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:

• 111.28(b)(12)(A)
  solve real-world problems comparing how interest rate and loan length affect the cost of credit; solve
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• 111.28(b)(12)(B)
  calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator; calculate
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• 111.28(b)(12)(C)
  explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time; explain
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• 111.28(b)(12)(D)
  calculate and compare simple interest and compound interest earnings; calculate
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• 111.28(b)(12)(E)
  identify and explain the advantages and disadvantages of different payment methods; identify
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• 111.28(b)(12)(F)
  analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility; and analyze
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• 111.28(b)(12)(G)
  estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college. estimate
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