# Texas Essential Knowledge and Skills - Mathematics — Grade 8

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Plan, assess, and analyze learning aligned to these standards using Kiddom.

#### 111.28.b.1

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;

#### 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;

#### 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;

#### 111.28.b.1.D

communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

#### 111.28.b.1.E

create and use representations to organize, record, and communicate mathematical ideas;

#### 111.28.b.1.F

analyze mathematical relationships to connect and communicate mathematical ideas; and

#### 111.28.b.1.G

display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

#### 111.28.b.10

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;

#### 111.28.b.10.B

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

#### 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

#### 111.28.b.10.D

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

#### 111.28.b.11

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;

#### 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

#### 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.

#### 111.28.b.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. 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;

#### 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;

#### 111.28.b.12.C

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

#### 111.28.b.12.D

calculate and compare simple interest and compound interest earnings;

#### 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

#### 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.

#### 111.28.b.2

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;

#### 111.28.b.2.B

approximate the value of an irrational number, including and square roots of numbers less than 225, and locate that rational number approximation on a number line;

#### 111.28.b.2.C

convert between standard decimal notation and scientific notation; and

#### 111.28.b.2.D

order a set of real numbers arising from mathematical and real-world contexts.

#### 111.28.b.3

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;

#### 111.28.b.3.B

compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; and

#### 111.28.b.3.C

use an algebraic representation to explain the effect of a given positive rational scale factorapplied to two-dimensional figures on a coordinate plane with the origin as the center of dilation.

#### 111.28.b.4

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;

#### 111.28.b.4.B

graph proportional relationships, interpreting the unit rate as the slope of the line that modelsthe relationship; and

#### 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.

#### 111.28.b.5

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;

#### 111.28.b.5.B

represent linear non-proportional situations with tables, graphs, and equations in the form ofy = mx + b, where b 0;

#### 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;

#### 111.28.b.5.D

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

#### 111.28.b.5.E

solve problems involving direct variation;

#### 111.28.b.5.F

distinguish between proportional and non-proportional situations using tables, graphs, andequations in the form y = kx or y = mx + b, where b 0;

#### 111.28.b.5.G

identify functions using sets of ordered pairs, tables, mappings, and graphs;

#### 111.28.b.5.H

identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; and

#### 111.28.b.5.I

write an equation in the form y = mx + b to model a linear relationship between two quantitiesusing verbal, numerical, tabular, and graphical representations.

#### 111.28.b.6

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;

#### 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

#### 111.28.b.6.C

use models and diagrams to explain the Pythagorean theorem.

#### 111.28.b.7

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;

#### 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;

#### 111.28.b.7.C

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

#### 111.28.b.7.D

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

#### 111.28.b.8

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 representproblems using rational number coefficients and constants;

#### 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;

#### 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

#### 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.

#### 8.1.A

Apply mathematics to problems arising in everyday life, society, and the workplace.

#### 8.1.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.

#### 8.1.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.

#### 8.1.D

Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

#### 8.1.E

Create and use representations to organize, record, and communicate mathematical ideas.

#### 8.1.F

Analyze mathematical relationships to connect and communicate mathematical ideas.

#### 8.1.G

Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

#### 8.10.A

Generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane.

#### 8.10.B

Differentiate between transformations that preserve congruence and those that do not.

#### 8.10.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.

#### 8.10.D

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

#### 8.11.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.

#### 8.11.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.

#### 8.11.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.

#### 8.12.A

Solve real-world problems comparing how interest rate and loan length affect the cost of credit.

#### 8.12.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.

#### 8.12.C

Explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time.

#### 8.12.D

Calculate and compare simple interest and compound interest earnings.

#### 8.12.F

Analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility.

#### 8.12.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.

#### 8.2.A

Extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers.

#### 8.2.B

Approximate the value of an irrational number, including and square roots of numbers less than 225, and locate that rational number approximation on a number line.

#### 8.2.C

Convert between standard decimal notation and scientific notation.

#### 8.2.D

Order a set of real numbers arising from mathematical and real-world contexts.

#### 8.3.A

Generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation.

#### 8.3.B

Compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane.

#### 8.3.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.

#### 8.4.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.

#### 8.4.B

Graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship.

#### 8.4.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.

#### 8.5.A

Represent linear proportional situations with tables, graphs, and equations in the form of y = kx.

#### 8.5.B

Represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b 0.

#### 8.5.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.

#### 8.5.D

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

#### 8.5.E

Solve problems involving direct variation.

#### 8.5.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.

#### 8.5.G

Identify functions using sets of ordered pairs, tables, mappings, and graphs.

#### 8.5.H

Identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems.

#### 8.5.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.

#### 8.6.A

Describe the volume formula V = Bh of a cylinder in terms of its base area and its height.

#### 8.6.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.

#### 8.6.C

Use models and diagrams to explain the Pythagorean theorem.

#### 8.7.A

Solve problems involving the volume of cylinders, cones, and spheres.

#### 8.7.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.

#### 8.7.C

Use the Pythagorean Theorem and its converse to solve problems.

#### 8.7.D

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

#### 8.8.A

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

#### 8.8.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.

#### 8.8.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.

#### 8.8.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.