Texas homeschool hubGrade 7 · Mathematics
Grade 7 MathematicsTEKS Scope & Sequence
The Texas Essential Knowledge and Skills your grade 7 student covers in mathematics — the same standards state assessments and Texas curricula are built on.
TEKS scope & sequence
106 standardsStandards are ordered by STAAR priority — Readiness standards first, then Supporting, then the rest. Readiness standards carry the most weight on the state assessment.
ReadinessSupportingSTAAR-tested
| TEKS | Standard | STAAR |
|---|---|---|
| 7.11A | determine the circumference and area of circles; | Readiness |
| 7.12A | generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane; | Readiness |
| 7.3B | apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers. | Readiness |
| 7.4A | solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems; | Readiness |
| 7.4D | solve real-world problems comparing how interest rate and loan length affect the cost of credit; | Readiness |
| 7.5C | solve mathematical and real-world problems involving similar shape and scale drawings. | Readiness |
| 7.6G | solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents; | Readiness |
| 7.6H | solve problems using qualitative and quantitative predictions and comparisons from simple experiments; | Readiness |
| 7.6I | determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces. | Readiness |
| 7.7A | represent solutions for one-variable, two-step inequalities on number lines; | Readiness |
| 7.9A | solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids; | Readiness |
| 7.9B | determine the circumference and area of circles; | Readiness |
| 7.9C | determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles; | Readiness |
| 7.10A | use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas; | Supporting |
| 7.10B | 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; | Supporting |
| 7.10C | describe the volume formula V = Bh of a cylinder in terms of its base area and its height; | Supporting |
| 7.11B | determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles; | Supporting |
| 7.11C | write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships. | Supporting |
| 7.12B | differentiate between transformations that preserve congruence and those that do not; | Supporting |
| 7.12C | 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; | Supporting |
| 7.13A | calculate the sales tax for a given purchase and calculate income tax for earned wages; | Supporting |
| 7.13B | compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations; | Supporting |
| 7.13C | create and organize a financial assets and liabilities record and construct a net worth statement; | Supporting |
| 7.13D | 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; | Supporting |
| 7.13E | calculate and compare simple interest and compound interest earnings; | Supporting |
| 7.13F | analyze and compare monetary incentives, including sales, rebates, and coupons. | Supporting |
| 7.2A | extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers; | Supporting |
| 7.3A | add, subtract, multiply, and divide rational numbers fluently; | Supporting |
| 7.4B | calculate and compare simple interest and compound interest earnings; | Supporting |
| 7.4C | analyze and compare monetary incentives, including sales, rebates, and coupons; | Supporting |
| 7.4E | 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; | Supporting |
| 7.5A | describe π as the ratio of the circumference of a circle to its diameter; | Supporting |
| 7.5B | generalize the critical attributes of similarity, including ratios within and between similar shapes; | Supporting |
| 7.6C | make predictions and determine solutions using experimental data for simple and compound events; | Supporting |
| 7.9D | 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. | Supporting |
| 7.10 | Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations and inequalities to represent situations. The student is expected to: (A) write one-variable, two-step equations and inequalities to represent constraints or conditions within problems; (B) represent solutions for one-variable, two-step equations and inequalities on number lines; (C) write a corresponding real-world problem given a one-variable, two-step equation or inequality. | — |
| 7.10 | 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: (A) use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas; (B) 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; (C) describe the volume formula V = Bh of a cylinder in terms of its base area and its height; (D) 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; (E) 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; (F) 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; (G) use models and diagrams to explain the Pythagorean theorem; (H) 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. | — |
| 7.10A | write one-variable, two-step equations and inequalities to represent constraints or conditions within problems; | — |
| 7.10C | write a corresponding real-world problem given a one-variable, two-step equation or inequality. | — |
| 7.10D | 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; | — |
| 7.10E | 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; | — |
| 7.10F | 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; | — |
| 7.10G | use models and diagrams to explain the Pythagorean theorem; | — |
| 7.10H | 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. | — |
| 7.11 | Geometric expressions, equations, and relationships--applications of geometric concepts. The student applies mathematical process standards to solve geometric problems. The student is expected to: (A) determine the circumference and area of circles; (B) determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles; (C) 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; (D) solve problems involving the volume of rectangular pyramids and triangular pyramids; (E) solve problems involving the volume of cylinders, cones, and spheres; (F) use the Pythagorean theorem and its converse to solve problems; (G) determine the distance between two points on a coordinate plane using the Pythagorean theorem. | — |
| 7.11 | Expressions, equations, and relationships. The student applies mathematical process standards to solve one-variable equations and inequalities. The student is expected to: (A) model and solve one-variable, two-step equations and inequalities; (B) determine if the given value(s) make(s) one-variable, two-step equations and inequalities true; (C) write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships. | — |
| 7.11B | determine if the given value(s) make(s) one-variable, two-step equations and inequalities true; | — |
| 7.11C | 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; | — |
| 7.11D | solve problems involving the volume of rectangular pyramids and triangular pyramids; | — |
| 7.11E | solve problems involving the volume of cylinders, cones, and spheres; | — |
| 7.11F | use the Pythagorean theorem and its converse to solve problems; | — |
| 7.11G | determine the distance between two points on a coordinate plane using the Pythagorean theorem. | — |
| 7.12 | Geometric expressions, equations, and relationships--transformations. The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to: (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; (D) model the effect on linear and area measurements of dilated two-dimensional shapes. | — |
| 7.12B | use data from a random sample to make inferences about a population; | — |
| 7.12C | compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations. | — |
| 7.12D | model the effect on linear and area measurements of dilated two-dimensional shapes. | — |
| 7.13 | 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: (A) use data from a random sample to make inferences about a population; (B) compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations; (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; (D) 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. | — |
| 7.13A | use data from a random sample to make inferences about a population; | — |
| 7.13C | 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; | — |
| 7.13D | 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. | — |
| 7.14 | 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: (A) 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; (B) 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; (C) analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility. | — |
| 7.14A | 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; | — |
| 7.14B | 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; | — |
| 7.14C | analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility. | — |
| 7.1B | 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; | — |
| 7.1C | 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; | — |
| 7.2 | Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to: (A) extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers. | — |
| 7.2 | 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: (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; (D) order a set of real numbers arising from mathematical and real-world contexts. | — |
| 7.2A | extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers. | — |
| 7.2B | 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; | — |
| 7.2C | convert between standard decimal notation and scientific notation; | — |
| 7.2D | order a set of real numbers arising from mathematical and real-world contexts. | — |
| 7.3 | 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: (A) add, subtract, multiply, and divide rational numbers fluently; (B) apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers. | — |
| 7.4 | Proportionality. The student applies mathematical process standards to represent and solve problems involving proportional relationships. The student is expected to: (A) represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt; (B) calculate unit rates from rates in mathematical and real-world problems; (C) determine the constant of proportionality (k = y/x) within mathematical and real-world problems; (D) solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems; (E) convert between measurement systems, including the use of proportions and the use of unit rates. | — |
| 7.4 | 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: (A) solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems; (B) calculate and compare simple interest and compound interest earnings; (C) analyze and compare monetary incentives, including sales, rebates, and coupons; (D) solve real-world problems comparing how interest rate and loan length affect the cost of credit; (E) 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; (F) explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time; (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. | — |
| 7.4B | calculate unit rates from rates in mathematical and real-world problems; | — |
| 7.4C | determine the constant of proportionality (k = y/x) within mathematical and real-world problems; | — |
| 7.4D | solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems; | — |
| 7.4E | convert between measurement systems, including the use of proportions and the use of unit rates. | — |
| 7.4F | explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time; | — |
| 7.4G | 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. | — |
| 7.5 | Proportionality. The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships. The student is expected to: (A) generalize the critical attributes of similarity, including ratios within and between similar shapes; (B) describe π as the ratio of the circumference of a circle to its diameter; (C) solve mathematical and real-world problems involving similar shape and scale drawings. | — |
| 7.5 | 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: (A) describe π as the ratio of the circumference of a circle to its diameter; (B) generalize the critical attributes of similarity, including ratios within and between similar shapes; (C) solve mathematical and real-world problems involving similar shape and scale drawings; (D) compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; (E) 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. | — |
| 7.5A | generalize the critical attributes of similarity, including ratios within and between similar shapes; | — |
| 7.5B | describe π as the ratio of the circumference of a circle to its diameter; | — |
| 7.5C | solve mathematical and real-world problems involving similar shape and scale drawings; | — |
| 7.5D | compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; | — |
| 7.5E | 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. | — |
| 7.6 | 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: (A) represent sample spaces for simple and compound events using lists and tree diagrams; (B) select and use different simulations to represent simple and compound events with and without technology; (C) make predictions and determine solutions using experimental data for simple and compound events; (D) make predictions and determine solutions using theoretical probability for simple and compound events; (E) find the probabilities of a simple event and its complement and describe the relationship between the two; (F) solve problems using qualitative and quantitative predictions and comparisons from simple experiments; (G) determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces. | — |
| 7.6B | select and use different simulations to represent simple and compound events with and without technology; | — |
| 7.6F | use data from a random sample to make inferences about a population; | — |
| 7.6F | solve problems using qualitative and quantitative predictions and comparisons from simple experiments; | — |
| 7.6G | determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces. | — |
| 7.7 | 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: (A) represent solutions for one-variable, two-step inequalities on number lines; (B) model and solve one-variable, two-step inequalities; (C) write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants; (D) 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; (E) 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. | — |
| 7.7B | model and solve one-variable, two-step inequalities; | — |
| 7.7C | write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants; | — |
| 7.7D | 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; | — |
| 7.7E | 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. | — |
| 7.8 | 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: (A) determine the constant of proportionality (k = y/x) within mathematical and real-world problems; (B) distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0; (C) identify examples of proportional and non-proportional relationships that arise from mathematical and real-world problems. | — |
| 7.8A | determine the constant of proportionality (k = y/x) within mathematical and real-world problems; | — |
| 7.8B | distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0; | — |
| 7.8B | 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; | — |
| 7.8C | identify examples of proportional and non-proportional relationships that arise from mathematical and real-world problems. | — |
| 7.9 | Expressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems. The student is expected to: (A) solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids; (B) determine the circumference and area of circles; (C) determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles; (D) 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. | — |
| 7.9 | 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: (A) represent linear proportional and non-proportional relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b. | — |
| 7.9A | represent linear proportional and non-proportional relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b. | — |