8th Grade
Mathematics
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.
Unit 01: Value and Magnitude of Rational Numbers
(6 classes for the entire unit)
Students continue to examine the sets and subsets of rational numbers and use a visual representation, such as a Venn diagram, to describe the relationships between the sets and subsets. Rational numbers are the focus of this unit as students order a set of rational numbers that arise from mathematical and real-world situations. Students extend previous understandings of the relationships within the base-10 place value system as they convert between standard decimal notation and scientific notation. Both positive and negative numbers are represented with standard decimal notation and scientific notation, including values greater than and less than one.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.2A, 8.2C, 8.2D
Unit 02: Statistics with Univariate Data
(6 classes for the entire unit)
Students extend their knowledge of ordering numbers and finding the mean to calculate the mean absolute deviation of up to 10 data points and describe the data by comparing each data point to the mean absolute deviation. Univariate data, data with one variable, is examined as students describe the spread and shape of data through the lens of variation from the mean. Additionally, students develop the notion that random samples of a population with known characteristics are representative of a population from which they were selected. Students explore appropriate methods for simulating such samples.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.11B, 8.11C
Unit 03: One-Variable Equations, Inequalities, and their Applications
(13 classes for the entire unit)
Students extend their understanding of modeling and solving one-variable equations that represent mathematical and real-world problems from variables on one-side of the equality sign to variables on both sides of the equality sign using rational number coefficients and constants. When solving one-variable equations with variables on both sides of the equality sign, students distinguish between types of solutions as one solution, no solution, and infinite solutions (all real numbers). Students also extend their knowledge of writing one-variable equations or inequalities from variables on one-side of the equality sign to variables on both sides of the equality sign to represent problems using rational number coefficients and constants. Financial literacy contexts, such as calculating and comparing simple and compound interest rates and how those rates affect earnings in a savings account or the total cost of repaying a loan or credit card, are embedded in this unit.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.8A, 8.8B, 8.8C, 8.12A, 8.12B, 8.12D
Unit 04: Developing an Understanding of Slope and Y-Intercept
(8 classes for the entire unit)
Students use similar right triangles to develop an understanding of slope. This approach lends itself to the development of the formula for slope by determining the ratio of the change in y-values compared to the change in x-values is the same for any two points on the same line. Students use data from a table or graph to determine the rate of change or slope and the y-intercept.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.4A, 8.4C
Unit 05: Proportional and Non-Proportional Functions
(17 classes for the entire unit)
Students extend their previous understandings of slope and y-intercept to represent proportional and non-proportional linear situations with tables, graphs, and equations. These representations are used as students distinguish between proportional and non-proportional linear situations. Students specifically examine the relationship between the unit rate and slope of a line that represents a proportional linear situation. Problem situations involving direct variation are included within this unit as they are also proportional linear situations. Graphical representations of linear equations are examined closely as students begin to develop the understandings of systems of equations. Students are expected to identify 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. Students must also verify these values algebraically with the equations that represent the two graphed linear equations. The study of proportional and non-proportional linear situations allows students to enrich their understanding of financial situations by explaining how small amounts of money, without interest, invested regularly grow over time. Students also examine how periodic savings plans can be used to contribute to the cost of attending a two-year or four-year college after estimating the financial costs associated with obtaining a college education. Exploring money invested over time helps students begin to consider the benefits of savings for retirement. Students are formally introduced to functions as a relation in which each element of the input (x) is paired with exactly one element of the output (y). Students must identify functions using sets of ordered pairs, tables, mappings, and graphs. Examining proportional and non-proportional linear relationships is extended to include identifying proportional and non-proportional linear functions in mathematical and real-world problems. A deep understanding of the characteristics of functions is essential to future mathematics coursework beyond Grade 8.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.4B, 8.5A, 8.5B, 8.5E, 8.5F, 8.5G, 8.5H, 8.9A, 8.12C, 8.12G
Unit 06: Statistics with Bivariate Data
(10 classes for the entire unit)
Students continue to examine characteristics of linear relationships through the lens of trend lines that approximate the relationship between bivariate sets of data. Students contrast graphical representations of bivariate sets of data that suggest linear relationships with bivariate sets of data that do not suggest a linear relationship. Scatterplots are constructed from bivariate sets of data and used to describe the observed data. Observations include questions of association such as linear (positive or negative trend), non-linear, or no association. Students extend previous work with linear proportional and linear non-proportional situations to trend lines as they continue to represent situations with tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0, respectively. Within a scatterplot that represents a linear relationship, students use the trend line to make predictions and interpret the slope of the line that models the relationship as the unit rate of the scenario.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.4B, 8.5A, 8.5B, 8.5C, 8.5D, 8.5I, 8.11A
Unit 07: Transformational Geometry
(12 classes for the entire unit)
Students develop transformational geometry concepts as they examine orientation and congruence of transformations. Students extend concepts of similarity to dilations on a coordinate plane as they compare and contrast a shape and its dilation(s). The concept of proportionality is revisited as students generalize the ratio of corresponding sides of a shape and its dilation as well as use an algebraic representation to explain the effect of dilation(s) on a coordinate plane. Properties of orientation and congruence are examined as students generalize the properties as they apply to rotations, reflections, translations, and dilations of two-dimensional figures on a coordinate plane. Students must distinguish between transformations that preserve congruence and those that do not. Students are expected to use an algebraic representation to explain the effect of translations, reflections over the x- or y- axis, dilations when a positive rational number scale factor is applied to a shape, and rotations limited to 90°, 180°, 270°, and 360°. The relationship between linear and area measurements of a shape and its dilation are also examined as students model the relationship and determine that the measurements are affected by both the scale factor and the dimension (one- or two-dimensional) of the measurement. Students are expected to generalize when a scale factor is applied to all of the dimensions of a two-dimensional shape, the perimeter is multiplied by the same scale factor while the area is multiplied by the scale factor squared.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.3A, 8.3B, 8.3C, 8.10A, 8.10B, 8.10C, 8.10D
Unit 08: Angle and Triangle Relationships involving Real Numbers
(13 classes for the entire unit)
Students extend previous knowledge of sets and subsets to order and describe relationships between sets of real numbers, which includes rational numbers and their subsets as well as irrational numbers. Students approximate the value of irrational numbers less than 225 and locate those approximations on a number line. Students are expected to 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. Right triangles are examined more closely within this unit as students use models to explain the Pythagorean Theorem. Students use the Pythagorean Theorem and its converse to solve problems and apply these understandings to the coordinate plane as they determine the distance between two points on the coordinate plane.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.2A, 8.2B, 8.2D, 8.6C, 8.7C, 8.7D, 8.8D
Unit 09: Measurement of Three-Dimensional Figures
(12 classes for the entire unit)
Students blend previous understandings of the volume of a prism with calculating the area of a circle to determining the volume of a cylinder in terms of its base area and height. As with previous grade level investigations of the volume of three-dimensional figures, students are expected to model the relationship between the volume of a cylinder and a cone having both congruent bases and heights. Students connect these models to the actual formulas for determining the volume of a cylinder and cone, which directly coincides with formulas used for determining the volume of prisms and pyramids on the STAAR Grade 8 Mathematics Reference Materials. Students solve problems involving the volume of cylinders, cones, and spheres. The concept of surface area is extended from finding the sum of the areas of the faces from the net to abstract formulas for lateral and total surface area. Students are expected to 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.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.6A, 8.6B, 8.7A, 8.7B
Unit 10: Making Connections
(15 classes for the entire unit)
Students extend their understanding of solving equations to model and solve one-variable equations with variables on both sides of the equal sign. Students use data from a table or graph to determine the rate of change or slope and the y-intercept. Students specifically examine the relationship between the unit rate and slope of a line that represents a proportional linear situation. Students must identify functions using sets of ordered pairs, tables, mappings, and graphs. Students continue to examine characteristics of linear relationships through the lens of trend lines that approximate the relationship between bivariate sets of data. Observations include questions of association such as linear, non-linear, or no association. Students use trend lines that approximate the linear relationship between bivariate sets of data to make predictions. Students extend concepts of similarity to dilations on a coordinate plane as they compare and contrast a shape and its dilation(s). The concept of proportionality is revisited as students generalize the ratio of corresponding sides of a shape and its dilation as well as use an algebraic representation to explain the effect of a dilation on a coordinate plane. Properties of orientation and congruence are examined as students generalize the properties as they apply to rotations, reflections, translations, and dilations of two-dimensional figures on a coordinate plane. Students are expected to use an algebraic representation to explain the effect of translations, reflections over the x- or y-axis, dilations when a positive rational number scale factor is applied to a shape, and rotations limited to 90°, 180°, 270°, and 360°. The relationship between linear and area measurements of a shape and its dilation are also examined as students model the relationship and determine that the measurements are affected by both the scale factor and the dimension (one- or two-dimensional) of the measurement. Students use the Pythagorean Theorem and its converse to solve problems and apply these understandings to the coordinate plane as they determine the distance between two points on the coordinate plane. Financial literacy contexts, such as calculating and comparing simple and compound interest rates and how those rates affect earnings in a savings account or the total cost of repaying a loan or credit card, are embedded in this unit.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.3C, 8.4B, 8.4C, 8.5D, 8.5G, 8.5I, 8.7C, 8.8C, 8.10C, 8.12D
Unit 11: Financial Planning
(5 classes for the entire unit)
Students extend their understanding of percent and formulas to compare interest rates, including simple and compound interest, and loan lengths. Students investigate the effect of the cost of credit and the total cost of repaying that credit, whether it be with credit cards or loans. They also use an online calculator to compare different payment methods. Students compare the advantages and disadvantages of various payment methods and analyze situations that constitute financial responsibility and irresponsibility. Lastly, students estimate the cost of attending a two-year and four-year college and devise a savings plan to pay for the total estimated costs for at least the first year of attendance.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.12A, 8.12B, 8.12C, 8.12D, 8.12E, 8.12F, 8.12G
Unit 12: Essential Understandings of Algebra
(20 classes for the entire unit)
Students revisit and solidify essential understandings of algebra. Students extend their previous understandings of slope and y-intercept to represent proportional and non-proportional linear situations with tables, graphs, and equations. These representations are used as students distinguish between proportional and non-proportional linear situations. Students specifically examine the relationship between the unit rate and slope of a line that represents a proportional linear situation. Graphical representations of linear equations are examined closely as students begin to develop the understandings of systems of equations. Students are expected to identify 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. Students must also verify these values algebraically with the equations that represent the two graphed linear equations. Examining proportional and non-proportional linear relationships is extended to include identifying proportional and non-proportional linear functions in mathematical and real-world problems. A deep understanding of the characteristics of functions is essential to future mathematics coursework beyond Grade 8. Students continue to examine characteristics of linear relationships through the lens of trend lines that approximate the relationship between bivariate sets of data. Students contrast graphical representations of bivariate sets of data that suggest linear relationships with bivariate sets of data that do not suggest a linear relationship. Scatterplots are constructed from bivariate sets of data and used to describe the observed data. Observations include questions of association such as linear, non-linear, or no association. Students use trend lines that approximate the linear relationship between bivariate sets of data to make predictions. Students extend previous work with linear proportional and linear non-proportional situations to trend lines as they continue to represent situations with tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0, respectively. Within a scatterplot, students use the trend line of a linear proportional relationship to interpret the slope of the line that models the relationship as the unit rate of the scenario.
TEKS in this unit: 8.1A, 8.1B, 8.1C, 8.1D, 8.1E, 8.1F, 8.1G, 8.4B, 8.5A, 8.5B, 8.5C, 8.5D, 8.5I, 8.9A, 8.11A
Texas Essential Knowledge & Skills (TEKS)
TEKS - Math - G8.pdf