7th Grade
7th Grade
Embedded Files
Mathematics
Mathematics
Introduction
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 7 are number and operations; proportionality; expressions, equations, and relationships; and measurement and data. Students use concepts, algorithms, and properties of rational 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 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: Number and Operations
Unit 01: Number and Operations
(9 classes for the entire unit)
(9 classes for the entire unit)
Students use a visual representation to organize and display the relationship of the sets and subsets of rational numbers, which include counting (natural) numbers, whole numbers, integers, and rational numbers. Students also apply and extend operations with rational numbers to include negative fractions and decimals. Grade 7 students are expected to fluently add, subtract, multiply, and divide various forms of positive and negative rational numbers that include integers, decimals, fractions, and percents converted to equivalent decimals or fractions. Exposure to solving mathematical and real-world situations assists students in generalizing operations with positive and negative rational numbers, which builds fluency and reasonableness of solutions. Students also create and organize a financial assets and liabilities record, construct a net worth statement, calculate sales tax for a given purchase, and calculate income tax for earned wages.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.1G, 7.2A, 7.3A, 7.3B, 7.13A, 7.13C
Unit 02: One-Variable Equations and Inequalities
Unit 02: One-Variable Equations and Inequalities
(16 classes for the entire unit)
(16 classes for the entire unit)
Students extend their previous work with one-variable, one-step equations and inequalities to one-variable, two-step equations and inequalities. Students model and solve one-variable, two-step equations and inequalities with concrete and pictorial models and algebraic representations. Solutions to equations and inequalities are represented on number lines and given values are used to determine if they make an equation or inequality true. Students are expected to write an equation or inequality to represent conditions or constraints within a problem and then, conversely, when given an equation or inequality out of context, students are expected to write a corresponding real-world problem to represent the equation or inequality. Additionally, students write and solve equations using geometric concepts, including the sum of the angles in a triangle, complementary angles, supplementary angles, straight angles, adjacent angles, and vertical angles. Equations and inequalities are extended to include problem situations involving monetary incentives such as sales, rebates, or coupons. Financial literacy aspects such as calculating and comparing simple and compound interest as well as utilizing a family budget estimator to determine the minimum household budget needed for a family to meet its basic needs is also explored. Although the formula for compound interest utilizes an exponent, student experiences for writing, modeling, solving, and evaluating equations and inequalities should focus primarily on linear relationships.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.1G, 7.10A, 7.10B, 7.10C, 7.11A, 7.11B, 7.11C, 7.13D, 7.13E, 7.13F
Unit 03: Proportional Reasoning with Ratios and Rates
Unit 03: Proportional Reasoning with Ratios and Rates
(11 classes for the entire unit)
(11 classes for the entire unit)
Students examine proportional reasoning with ratios and rates through the lens of constant rates of change. Students are expected to represent constant rates of change given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt. The development of rates lends itself to students examining d = rt and reveals the amount of variation that can occur when various constant rates can be applied to a situation to reveal the same outcome (e.g., the distance traveled remains the same in a situation if the speed is doubled and the time is halved, etc.). Exploring the relationship between distance, rate, and time allows students to generalize the effects when rates within any problem situation are changed. Students solve problems involving ratios, rates, and percents. Computations with percents are now inclusive of solving problems involving percent increase, percent decrease, and financial literacy. Percents are also used as students identify the components of a personal budget and calculate what percentage each category comprises of the total budget. They also calculate unit rates from rates and determine the constant of proportionality in mathematical and real-world problems. Students use proportions and unit rates as they extend previous understandings of converting units within a measurement system to now include converting units between both customary and metric measurement systems.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.1G, 7.4A, 7.4B, 7.4C, 7.4D, 7.4E, 7.13B
Unit 04: Graphs and Two-Variable Equations
Unit 04: Graphs and Two-Variable Equations
(14 classes for the entire unit)
(14 classes for the entire unit)
Students use bivariate data, data with two variables, to reexamine constant rates of change given pictorial, tabular, verbal, numeric, graphical, and algebraic representations and extend their understandings of the constant of proportionality. Students are formally introduced to the slope intercept form of equations, y = mx + b, to represent linear relationships. Although students are not formally introduced to slope or y-intercept in linear proportional and non-proportional relationships until Grade 8, students are expected to relate the constant rate of change to m, and the y-coordinate, when the x-coordinate is zero, to b in equations that simplify to the form y = mx + b. This relationship is examined through the ratio of rise to run and the change in the y-values to the change in the x-values. Students represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.1G, 7.4A, 7.4C, 7.7A
Unit 05: Similarity
Unit 05: Similarity
(12 classes for the entire unit)
(12 classes for the entire unit)
Students extend concepts of proportionality to two-dimensional figures as they solve mathematical and real-world problems involving similar shapes and scale drawings. Students generalize the critical attributes of similarity, which include examining the multiplicative relationship within and between similar shapes.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.1G, 7.5A, 7.5C
Unit 06: Probability
Unit 06: Probability
(13 classes for the entire unit)
(13 classes for the entire unit)
Students extend the use of proportional reasoning to solve problems as they are formally introduced to probability concepts. Students use various representations, including lists, tree diagrams, tables, and the Fundamental Counting Principle to represent the sample spaces for simple and compound events. Compound events are inclusive of both independent events and dependent events. Students select, design, develop, and use various methods to simulate simple and compound events. Methods for simulation may or may not include the use of technology. When conducting simulations or investigating data from simulations, students develop an understanding of how the Law of Large Numbers will affect the experimental probability. Students are expected to distinguish between theoretical and experimental data and find the probabilities of a simple event. Students analyze and describe the relationship between the probability of a simple event and its complement. Probabilities may be represented as a decimal, fraction, or percent. Data and sample spaces are used to determine experimental and theoretical probabilities from simple and compound events. Data from experiments, experimental data, theoretical probability, and random samples are used to make qualitative and quantitative inferences about a population. Qualitative and quantitative predictions and comparisons from simple experiments are used to solve problems. Students should consider the proportional relationships within and between probabilistic situations when making predictions and inferences.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.6A, 7.6B, 7.6C, 7.6D, 7.6E, 7.6F, 7.6H, 7.6I
Unit 07: Circles and Composite Figures
Unit 07: Circles and Composite Figures
(13 classes for the entire unit)
(13 classes for the entire unit)
Students convert between measurement systems, customary to metric and metric to customary. Solution strategies may include dimensional analysis using unit rates, scale factor between ratios, proportions, and conversion graphs. Students use models to determine the approximate formulas for the circumference and area of a circle (e.g., the circumference of a circle is a little more than three times the length of the diameter of a circle; the circumference of a circle is a little more than three times twice the length of the radius of a circle or a little more than 6 times the radius; the area of a circle is a little more than three times the length of the radius squared). Students use the relationships from models to connect to the actual formulas for the circumference and area of a circle and apply these formulas to solve problems involving the circumference and area of circles. Students extend previous knowledge of the area of rectangles, parallelograms, trapezoids, and triangles along with the new understandings of the circumference and area of circles to solve problems involving area of composite figures that consist of rectangles, triangles, parallelograms, squares, quarter circles, semicircles, and trapezoids.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.1G, 7.4E, 7.5B, 7.8C, 7.9B, 7.9C
Unit 08: Volume and Surface Area
Unit 08: Volume and Surface Area
(12 classes for the entire unit)
(12 classes for the entire unit)
Students model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights as well as connect that relationship to their respective formulas (e.g. the volume of a rectangular prism is three times the volume of a rectangular pyramid; the volume of a rectangular pyramid is 1/3 the volume of a rectangular prism). Students are expected to explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights as well as connect that relationship to their respective formulas (e.g., the volume of a triangular prism is three times the volume of a triangular pyramid; the volume of a triangular pyramid is the volume of a triangular prism). Students solve problems involving volume, including the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids. Students also 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.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.1G, 7.8A, 7.8B, 7.9A, 7.9D
Unit 09: Data Representations
Unit 09: Data Representations
(15 classes for the entire unit)
(15 classes for the entire unit)
Students solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents. Students use data from random samples to make inferences about a population and compare two populations based on data from random samples, including informal comparative inferences about differences between the two populations. Students consider the strength of the inference based on the relative size of the sample compared to the total population. Students compare two groups of numeric data using comparative dot plots or box plots by describing their shapes, centers, and spreads. Descriptions of shape, center, and spread include skewed right, skewed left, symmetrical, mean, median, mode, range, and interquartile range. Percents are also incorporated within this unit as students calculate the components of a personal budget in conjunction with circle graphs and bar graphs.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.1G, 7.6G, 7.12A, 7.12B, 7.12C, 7.13B
Unit 10: Making Connections
Unit 10: Making Connections
(10 classes for the entire unit)
(10 classes for the entire unit)
Students continue to apply operations with rational numbers to calculate unit rates from rates and determine the constant of proportionality within mathematical and real-world problems. Students are expected to represent constant rates of change given pictorial, tabular, verbal, numeric, graphical, and algebraic representations. Students use verbal descriptions, tables, graphs, and the slope-intercept form of equations, y = mx + b, to represent linear relationships. Students revisit and apply concepts of proportionality to two-dimensional figures as they solve mathematical and real-world problems involving similar shapes.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.1G, 7.3B, 7.4A, 7.4B, 7.4C, 7.4D, 7.5C, 7.7A
Unit 11: Essential Understandings of Algebra
Unit 11: Essential Understandings of Algebra
(13 classes for the entire unit)
(13 classes for the entire unit)
Students revisit and solidify essential understandings of algebra. Students represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b. Students model and solve one-variable, two-step equations and inequalities with concrete and pictorial models and algebraic representations. Solutions to equations and inequalities are represented on number lines and given values are used to determine if they make an equation or inequality true. Students are expected to write an equation or inequality to represent conditions or constraints within a problem and then, conversely, when given an equation or inequality out of context, students are expected to write a corresponding real-world problem to represent the equation or inequality.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.1G, 7.7A, 7.10A, 7.10B, 7.10C, 7.11A, 7.11B
Unit 12: Essential Understandings of Geometry
Unit 12: Essential Understandings of Geometry
(12 classes for the entire unit)
(12 classes for the entire unit)
Students revisit and solidify essential understandings of geometry. Students use the formulas for circumference and area of a circle to solve problems. Students extend previous knowledge of the area of rectangles, parallelograms, trapezoids, and triangles along with the area of circles in determining the area of composite figures consisting of rectangles, triangles, parallelograms, squares, quarter circles, semicircles, and trapezoids. Students also solve problems involving the volume of rectangular and triangular prisms and pyramids. Students extend their algebraic understandings of writing equations to represent geometric concepts, including the sum of the angles in a triangle, and other angle relationships. Students describe angle relationships such as adjacent angles, vertical angles, complementary angles, supplementary angles, and straight angles.
TEKS in this unit: 7.1A, 7.1B, 7.1C, 7.1D, 7.1E, 7.1F, 7.1G, 7.9A, 7.9B, 7.9C, 7.11C
Texas Essential Knowledge & Skills (TEKS)
Texas Essential Knowledge & Skills (TEKS)
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