(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 problemsolving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying
the solution, and evaluating the problemsolving 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) For students to become fluent in mathematics, students
must develop a robust sense of number. The National Research Council's
report, "Adding It Up," defines procedural fluency as "skill in carrying
out procedures flexibly, accurately, efficiently, and appropriately."
As students develop procedural fluency, they must also realize that
true problem solving may take time, effort, and perseverance. Students
in Kindergarten are expected to perform their work without the use
of calculators.
(4) The primary focal areas in Kindergarten are understanding
counting and cardinality, understanding addition as joining and subtraction
as separating, and comparing objects by measurable attributes.
(A) Students develop number and operations through
several fundamental concepts. Students know number names and the counting
sequence. Counting and cardinality lay a solid foundation for number.
Students apply the principles of counting to make the connection between
numbers and quantities.
(B) Students use meanings of numbers to create strategies
for solving problems and responding to practical situations involving
addition and subtraction.
(C) Students identify characteristics of objects that
can be measured and directly compare objects according to these measurable
attributes.
(5) 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 problemsolving model that incorporates analyzing
given information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problemsolving 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 understand how to represent and compare whole
numbers, the relative position and magnitude of whole numbers, and
relationships within the numeration system. The student is expected
to:
(A) count forward and backward to at least 20 with
and without objects;
(B) read, write, and represent whole numbers from 0
to at least 20 with and without objects or pictures;
(C) count a set of objects up to at least 20 and demonstrate
that the last number said tells the number of objects in the set regardless
of their arrangement or order;
(D) recognize instantly the quantity of a small group
of objects in organized and random arrangements;
(E) generate a set using concrete and pictorial models
that represents a number that is more than, less than, and equal to
a given number up to 20;
(F) generate a number that is one more than or one
less than another number up to at least 20;
(G) compare sets of objects up to at least 20 in each
set using comparative language;
(H) use comparative language to describe two numbers
up to 20 presented as written numerals; and
(I) compose and decompose numbers up to 10 with objects
and pictures.
(3) Number and operations. The student applies mathematical
process standards to develop an understanding of addition and subtraction
situations in order to solve problems. The student is expected to:
(A) model the action of joining to represent addition
and the action of separating to represent subtraction;
(B) solve word problems using objects and drawings
to find sums up to 10 and differences within 10; and
(C) explain the strategies used to solve problems involving
adding and subtracting within 10 using spoken words, concrete and
pictorial models, and number sentences.
(4) Number and operations. The student applies mathematical
process standards to identify coins in order to recognize the need
for monetary transactions. The student is expected to identify U.S.
coins by name, including pennies, nickels, dimes, and quarters.
(5) Algebraic reasoning. The student applies mathematical
process standards to identify the pattern in the number word list.
The student is expected to recite numbers up to at least 100 by ones
and tens beginning with any given number.
(6) Geometry and measurement. The student applies mathematical
process standards to analyze attributes of twodimensional shapes
and threedimensional solids to develop generalizations about their
properties. The student is expected to:
(A) identify twodimensional shapes, including circles,
triangles, rectangles, and squares as special rectangles;
(B) identify threedimensional solids, including cylinders,
cones, spheres, and cubes, in the real world;
(C) identify twodimensional components of threedimensional
objects;
(D) identify attributes of twodimensional shapes using
informal and formal geometric language interchangeably;
(E) classify and sort a variety of regular and irregular
two and threedimensional figures regardless of orientation or size;
and
(F) create twodimensional shapes using a variety of
materials and drawings.
(7) Geometry and measurement. The student applies mathematical
process standards to directly compare measurable attributes. The student
is expected to:
(A) give an example of a measurable attribute of a
given object, including length, capacity, and weight; and
(B) compare two objects with a common measurable attribute
to see which object has more of/less of the attribute and describe
the difference.
(8) Data analysis. The student applies mathematical
process standards to collect and organize data to make it useful for
interpreting information. The student is expected to:
(A) collect, sort, and organize data into two or three
categories;
(B) use data to create realobject and picture graphs;
and
(C) draw conclusions from realobject and picture graphs.
(9) Personal financial literacy. The student applies
mathematical process standards to manage one's financial resources
effectively for lifetime financial security. The student is expected
to:
(A) identify ways to earn income;
(B) differentiate between money received as income
and money received as gifts;
(C) list simple skills required for jobs; and
(D) distinguish between wants and needs and identify
income as a source to meet one's wants and needs.
