Texas

$Texas flag$

Skills available for Texas eighth-grade math standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

Show alignments for:

State of Texas Assessments of Academic Readiness (STAAR) State of Texas Assessments of Academic Readiness (STAAR)
Texas Essential Knowledge and Skills (TEKS): Grade 8 Texas Essential Knowledge and Skills (TEKS): Grade 8
Texas Essential Knowledge and Skills (TEKS): Mathematical processes Texas Essential Knowledge and Skills (TEKS): Mathematical processes

Actions

Print standards

These student expectations will not be listed under a separate reporting category. Instead, they will be incorporated into test questions across reporting categories since the application of mathematical process standards is part of each knowledge statement.

8.1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.
- 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;
  - Solve multi-step equations: complete the solution (8-Y.18)
- 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.
  - Solve multi-step equations: complete the solution (8-Y.18)

1 The student will demonstrate an understanding of how to represent and manipulate numbers and expressions.

8.2 The student applies mathematical process standards to represent and use real numbers in a variety of forms.
- A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers;
  - Classify numbers (8-I.3)
- 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;
  - Estimate positive and negative square roots (8-F.4)
  - Identify rational and irrational numbers (8-I.2)
- C convert between standard decimal notation and scientific notation; and
  - Convert between standard and scientific notation (8-E.1)
- D order a set of real numbers arising from mathematical and real-world contexts.

2 The student will demonstrate an understanding of how to perform operations and represent algebraic relationships.

8.4 The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope.
- 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, (y? - y?)/ (x? - x?), is the same for any two points (x?, y?) and (x?, y?) on the same line;
  - Find the slope of a graph (8-AA.1)
  - Find the slope from two points (8-AA.2)
- 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.
  - Write a linear equation from a graph (8-AA.9)
  - Write a linear function from a table (8-BB.14)
8.5 The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions.
- 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;
- E solve problems involving direct variation;
  - Interpret graphs of proportional relationships (8-K.10)
  - Write and solve equations for proportional relationships (8-K.11)
- 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;
  - Identify proportional relationships from graphs and equations (8-K.6)
- 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.
8.8 The student applies mathematical process standards to use one-variable equations or inequalities in problem situations.
- A write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants;
  - Write and solve equations that represent diagrams (8-Y.4)
- 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; and
- 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.
8.9 The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations.
- A 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.

3 The student will demonstrate an understanding of how to represent and apply geometry and measurement concepts.

8.3 The student applies mathematical process standards to use proportional relationships to describe dilations.
- 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
  - Dilations: graph the image (8-S.2)
  - Dilations: find the coordinates (8-S.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.
  - Dilations: find the scale factor (8-S.4)
8.6 The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas.
- A describe the volume formula V = Bh of a cylinder in terms of its base area and its height; and
  - Volume of cubes, prisms, and pyramids (8-V.8)
- C use models and diagrams to explain the Pythagorean theorem.
8.7 The student applies mathematical process standards to use geometry to solve problems.
- A solve problems involving the volume of cylinders, cones, and spheres;
- 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;
- C use the Pythagorean Theorem and its converse to solve problems; and
- D determine the distance between two points on a coordinate plane using the Pythagorean Theorem.
  - Find the distance between two points (8-P.4)
8.8 The student applies mathematical process standards to use one-variable equations or inequalities in problem situations.
- 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.
8.10 The student applies mathematical process standards to develop transformational geometry concepts.
- A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane;
- B differentiate between transformations that preserve congruence and those that do not;
- 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
- D model the effect on linear and area measurements of dilated two-dimensional shapes.
  - Perimeter and area: changes in scale (8-V.17)

4 The student will demonstrate an understanding of how to represent and analyze data and how to describe and apply personal financial concepts.

8.5 The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions.
- 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; and
  - Identify trends with scatter plots (8-EE.17)
- D use a trend line that approximates the linear relationship between bivariate sets of data to make predictions.
  - Write equations for lines of best fit (8-FF.11)
  - Write equations for lines of best fit (A1-MM.12)
8.11 The student applies mathematical process standards to use statistical procedures to describe data.
- 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; and
  - Identify trends with scatter plots (8-EE.17)
- 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.
  - Calculate mean absolute deviation (8-FF.5)
  - Mean absolute deviation (A1-MM.6)
8.12 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.
- A solve real-world problems comparing how interest rate and loan length affect the cost of credit;
- C explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time;
- D calculate and compare simple interest and compound interest earnings; and
  - Simple interest (8-M.10)
  - Compound interest (8-M.11)
- 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.

Texas

Show alignments for:

Actions

These student expectations will not be listed under a separate reporting category. Instead, they will be incorporated into test questions across reporting categories since the application of mathematical process standards is part of each knowledge statement.

8.1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.

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.

1 The student will demonstrate an understanding of how to represent and manipulate numbers and expressions.

8.2 The student applies mathematical process standards to represent and use real numbers in a variety of forms.

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.

2 The student will demonstrate an understanding of how to perform operations and represent algebraic relationships.

8.4 The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope.

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, (y? - y?)/ (x? - x?), is the same for any two points (x?, y?) and (x?, y?) 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.

8.5 The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions.

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;

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.

8.8 The student applies mathematical process standards to use one-variable equations or inequalities in problem situations.

A write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants;

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; and

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.

8.9 The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations.

A 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.

3 The student will demonstrate an understanding of how to represent and apply geometry and measurement concepts.

8.3 The student applies mathematical process standards to use proportional relationships to describe dilations.

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.

8.6 The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas.

A describe the volume formula V = Bh of a cylinder in terms of its base area and its height; and

C use models and diagrams to explain the Pythagorean theorem.

8.7 The student applies mathematical process standards to use geometry to solve problems.

A solve problems involving the volume of cylinders, cones, and spheres;

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;

C use the Pythagorean Theorem and its converse to solve problems; and

D determine the distance between two points on a coordinate plane using the Pythagorean Theorem.

8.8 The student applies mathematical process standards to use one-variable equations or inequalities in problem situations.

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.

8.10 The student applies mathematical process standards to develop transformational geometry concepts.

A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane;

B differentiate between transformations that preserve congruence and those that do not;

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

D model the effect on linear and area measurements of dilated two-dimensional shapes.

4 The student will demonstrate an understanding of how to represent and analyze data and how to describe and apply personal financial concepts.

8.5 The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions.

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; and

D use a trend line that approximates the linear relationship between bivariate sets of data to make predictions.

8.11 The student applies mathematical process standards to use statistical procedures to describe data.

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; and

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.

8.12 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.

A solve real-world problems comparing how interest rate and loan length affect the cost of credit;

C explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time;

D calculate and compare simple interest and compound interest earnings; and

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.