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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.

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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

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2 Number and operations

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;
- C convert between standard decimal notation and scientific notation; and
  - Convert between standard and scientific notation (8-E.1)
  - Compare numbers written in scientific notation (8-E.3)
- D order a set of real numbers arising from mathematical and real-world contexts.
- Checkpoint opportunity

3-5 Proportionality

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: find the scale factor (8-S.4)
- 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: graph the image (8-S.2)
  - Dilations: find the coordinates (8-S.3)
- Checkpoint opportunity
  - Checkpoint: Dilations and similarity (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, (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
  - Find the constant of proportionality from a graph (8-K.4)
  - Graph proportional relationships and find the slope (8-K.9)
- 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.
- Checkpoint opportunity
  - Checkpoint: Interpret slopes and y-intercepts (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;
- 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;
  - Identify trends with scatter plots (8-EE.17)
  - Outliers in scatter plots (8-FF.9)
- 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;
  - Identify functions (8)
  - Identify functions: graphs (8-BB.2)
- 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.
- Checkpoint opportunity

6-9 Expressions, equations, and relationships

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;
- 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
- C use models and diagrams to explain the Pythagorean theorem.
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;
  - Surface area of prisms (8)
  - Surface area of cylinders (8-V.12)
- 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)
- Checkpoint opportunity
  - Checkpoint: Volume (8-V.18)
  - Checkpoint: The Pythagorean theorem (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;
  - Solve equations with variables on both sides: word problems (8-Y.)
  - Create equations with no solutions or infinitely many solutions (8-Y.20)
- 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;
- 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
- 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.
- Checkpoint opportunity
  - Checkpoint: Triangles and transversals (8-Q.22)
  - Checkpoint: Problem solving with equations and inequalities (8)
9 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.
- Checkpoint opportunity
  - Checkpoint: Systems of equations (8)

10 Two-dimensional shapes

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;
  - Dilations: find the scale factor (8-S.4)
- B differentiate between transformations that preserve congruence and those that do not;
  - Identify reflections, rotations, and translations (8-R.4)
- 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.
  - Area and perimeter of similar figures (8)
- Checkpoint opportunity
  - Checkpoint: Translations, reflections, and rotations on the coordinate plane (8)
  - Checkpoint: Properties of transformations (8)

11 Measurement and data

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;
- 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
  - Calculate mean absolute deviation (8-FF.5)
  - Interpret mean and mean absolute deviation (8)
- 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.
  - Which simulation represents the situation? (8)
  - Identify representative, random, and biased samples (8-FF.12)
- Checkpoint opportunity
  - Checkpoint: Scatter plots (8)
  - Checkpoint: Mean absolute deviation (8)

12 Personal financial literacy

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;
- 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;
- 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;
  - Simple interest (8-M.10)
  - Compound interest (8-M.11)
- E identify and explain the advantages and disadvantages of different payment methods;
  - Identify advantages and disadvantages of payment methods (8)
  - Debit cards and credit cards (8)
- 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
- 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

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Actions

2 Number and operations

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.

Checkpoint opportunity

3-5 Proportionality

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.

Checkpoint opportunity

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, (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.

Checkpoint opportunity

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;

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.

Checkpoint opportunity

6-9 Expressions, equations, and relationships

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;

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

C use models and diagrams to explain the Pythagorean theorem.

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.

Checkpoint opportunity

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;

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

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.

Checkpoint opportunity

9 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.

Checkpoint opportunity

10 Two-dimensional shapes

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.

Checkpoint opportunity

11 Measurement and data

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;

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

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.

Checkpoint opportunity

12 Personal financial literacy

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;

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;

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;

E identify and explain the advantages and disadvantages of different payment methods;

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

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.

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;