| (a) 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.
(4) 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.
(b) Knowledge and skills.
(1) Mathematical process standards. The student uses
mathematical processes to acquire and demonstrate mathematical understanding.
The student is expected to:
(A) apply mathematics to problems arising in everyday
life, society, and the workplace;
(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;
(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;
(D) communicate mathematical ideas, reasoning, and
their implications using multiple representations, including symbols,
diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record,
and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and
communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas
and arguments using precise mathematical language in written or oral
communication.
(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 extend previous knowledge of
sets and subsets using a visual representation to describe relationships
between sets of rational numbers.
(3) Number and operations. 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; and
(B) apply and extend previous understandings of operations
to solve problems using addition, subtraction, multiplication, and
division of rational numbers.
(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; and
(E) convert between measurement systems, including
the use of proportions and the use of unit rates.
(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; and
(C) solve mathematical and real-world problems involving
similar shape and scale drawings.
(6) Proportionality. 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) use data from a random sample to make inferences
about a population;
(G) solve problems using data represented in bar graphs,
dot plots, and circle graphs, including part-to-whole and part-to-part
comparisons and equivalents;
(H) solve problems using qualitative and quantitative
predictions and comparisons from simple experiments; and
(I) determine experimental and theoretical probabilities
related to simple and compound events using data and sample spaces.
(7) Expressions, equations, and relationships. 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.
(8) Expressions, equations, and relationships. The
student applies mathematical process standards to develop geometric
relationships with volume. The student is expected to:
(A) 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;
(B) 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; and
(C) use models to determine the approximate formulas
for the circumference and area of a circle and connect the models
to the actual formulas.
(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; and
(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.
(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; and
(C) write a corresponding real-world problem given
a one-variable, two-step equation or inequality.
(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; and
(C) write and solve equations using geometry concepts,
including the sum of the angles in a triangle, and angle relationships.
(12) Measurement and data. The student applies mathematical
process standards to use statistical representations to analyze data.
The student is expected to:
(A) compare two groups of numeric data using comparative
dot plots or box plots by comparing their shapes, centers, and spreads;
(B) use data from a random sample to make inferences
about a population; and
(C) compare two populations based on data in random
samples from these populations, including informal comparative inferences
about differences between the two populations.
(13) Personal financial literacy. 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) calculate the sales tax for a given purchase and
calculate income tax for earned wages;
(B) 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;
(C) create and organize a financial assets and liabilities
record and construct a net worth statement;
(D) 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;
(E) calculate and compare simple interest and compound
interest earnings; and
(F) analyze and compare monetary incentives, including
sales, rebates, and coupons.
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