Grade 7 Math GSE Standards

Personal financial literacy

Measurement and data

Expressions, equations, and relationships

Proportionality

Mathematical process standards

The student uses mathematical processes to acquire and demonstrate mathematical understanding

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

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

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

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

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

analyze mathematical relationships to connect and communicate mathematical ideas

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

The student applies mathematical process standards to use one-variable equations and inequalities to represent situations

write one-variable, two-step equations and inequalities to represent constraints or conditions within problems

represent solutions for one-variable, two-step equations and inequalities on number lines

write a corresponding real-world problem given a one-variable, two-step equation or inequality

The student applies mathematical process standards to solve one-variable equations and inequalities

model and solve one-variable, two-step equations and inequalities

determine if the given value(s) make(s) one-variable, two-step equations and inequalities true

write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships

The student applies mathematical process standards to use statistical representations to analyze data

compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads

use data from a random sample to make inferences about a population

compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations

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

calculate the sales tax for a given purchase and calculate income tax for earned wages

identify the components of a personal budget, including income; planned savings for college, retirement, and emergencies; taxes; and fixed and variable expenses, and calculate what percentage each category comprises of the total budget

create and organize a financial assets and liabilities record and construct a net worth statement

use a family budget estimator to determine the minimum household budget and average hourly wage needed for a family to meet its basic needs in the student's city or another large city nearby

calculate and compare simple interest and compound interest earnings

analyze and compare monetary incentives, including sales, rebates, and coupons

The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers

Number and operations

The student applies mathematical process standards to add, subtract, multiply, and divide while solving problems and justifying solutions

add, subtract, multiply, and divide rational numbers fluently

apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers

The student applies mathematical process standards to represent and solve problems involving proportional relationships

represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt

calculate unit rates from rates in mathematical and real-world problems

determine the constant of proportionality (k = y/x) within mathematical and real-world problems

solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems

convert between measurement systems, including the use of proportions and the use of unit rates

The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships

generalize the critical attributes of similarity, including ratios within and between similar shapes

describe π as the ratio of the circumference of a circle to its diameter

solve mathematical and real-world problems involving similar shape and scale drawings

The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships

represent sample spaces for simple and compound events using lists and tree diagrams

select and use different simulations to represent simple and compound events with and without technology

make predictions and determine solutions using experimental data for simple and compound events

make predictions and determine solutions using theoretical probability for simple and compound events

find the probabilities of a simple event and its complement and describe the relationship between the two

use data from a random sample to make inferences about a population

solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents;

solve problems using qualitative and quantitative predictions and comparisons from simple experiments; and

determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces.

The student applies mathematical process standards to represent linear relationships using multiple representations. The student is expected to represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b

The student applies mathematical process standards to develop geometric relationships with volume

model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas

explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to the formulas

use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas

The student applies mathematical process standards to solve geometric problems

solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids

determine the circumference and area of circles

determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles

solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net

Implementation. The provisions of this section may be implemented by school districts beginning with the 2025-2026 school year.

Introduction.

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.

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.

To increase the number of students who complete advanced mathematics courses in high school, the middle school advanced mathematics courses are designed to enable students to complete Algebra I by the end of Grade 8.

The primary focal areas in Grade 7, Middle School Advanced Mathematics are numeracy; proportionality; expressions, equations, and relationships; and data science. 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, including number, geometry and measurement, and statistics and probability. 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 continue to develop a foundational understanding of functions. 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. The use of technology, including graphing tools, is essential in middle school advanced mathematics courses to master algebra readiness skills by bridging conceptual understanding and procedural fluency.

Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples.

Knowledge and skills.

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

analyze mathematical relationships to connect and communicate mathematical ideas; and

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

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

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;

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;

apply mathematics to problems arising in everyday life, society, and the workplace;

Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is 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.

use models and diagrams to explain the Pythagorean theorem; and

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;

explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to the formulas;

model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas;

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

solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net;

use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas;

Geometric expressions, equations, and relationships--foundations of geometric concepts. The student applies mathematical process standards to develop geometric relationships and solve problems. The student is expected to:

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

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

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

solve problems involving the volume of rectangular pyramids and triangular pyramids;

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;

determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles;

determine the circumference and area of circles;

Geometric expressions, equations, and relationships--applications of geometric concepts. The student applies mathematical process standards to solve geometric problems. The student is expected to:

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

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

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

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

Geometric expressions, equations, and relationships--transformations. The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to:

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.

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; and

compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations;

use data from a random sample to make inferences about a population;

Data science--applications of measurement and data. The student applies mathematical process standards to use statistical representations and procedures to analyze and describe data. The student is expected to:

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

use a family budget estimator to determine the minimum household budget and average hourly wage needed for a family to meet its basic needs in the student's city or another large city nearby; and

identify the components of a personal budget, including income; planned savings for college, retirement, and emergencies; taxes; and fixed and variable expenses, and calculate what percentage each category comprises of the total budget;

Personal financial literacy--money management. 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:

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

convert between standard decimal notation and scientific notation; and

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;

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

Numeracy--foundations of real numbers. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:

apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers.

add, subtract, multiply, and divide rational numbers fluently; and

Numeracy--operations with rational numbers. The student applies mathematical process standards to add, subtract, multiply, and divide while solving problems and justifying solutions. The student is expected to:

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.

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

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;

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

analyze and compare monetary incentives, including sales, rebates, and coupons;

calculate and compare simple interest and compound interest earnings;

solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems;

Numeracy--applications of percents. The student applies mathematical process standards to represent and solve problems involving percents as proportional relationships. The student is expected to:

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.

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

solve mathematical and real-world problems involving similar shape and scale drawings;

generalize the critical attributes of similarity, including ratios within and between similar shapes;

describe π as the ratio of the circumference of a circle to its diameter;

Proportionality--geometric ratios. The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships such as dilations. The student is expected to:

determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces.

solve problems using qualitative and quantitative predictions and comparisons from simple experiments; and

find the probabilities of a simple event and its complement and describe the relationship between the two;

make predictions and determine solutions using theoretical probability for simple and compound events;

make predictions and determine solutions using experimental data for simple and compound events;

select and use different simulations to represent simple and compound events with and without technology;

represent sample spaces for simple and compound events using lists and tree diagrams;

Proportionality--probability. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is expected to:

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.

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

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

model and solve one-variable, two-step inequalities;

represent solutions for one-variable, two-step inequalities on number lines;

One-variable expressions, equations, and relationships--applications of one-variable relationships. The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:

identify examples of proportional and non-proportional relationships that arise from mathematical and real-world problems.

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

determine the constant of proportionality (k = y/x) within mathematical and real-world problems;

Two-variable equations and relationships--foundations of linear relationships. The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions. The student is expected to:

Two-variable equations and relationships--applications of linear relationships. The student applies mathematical process standards to represent linear relationships using multiple representations. The student is expected to represent linear proportional and non-proportional relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b.