| (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) 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 Grade 1 are expected to perform their work without the use of calculators.
(4) The primary focal areas in Grade 1 are understanding
and applying place value, solving problems involving addition and
subtraction, and composing and decomposing two-dimensional shapes
and three-dimensional solids.
(A) Students use relationships within the numeration
system to understand the sequential order of the counting numbers
and their relative magnitude.
(B) Students extend their use of addition and subtraction
beyond the actions of joining and separating to include comparing
and combining. Students use properties of operations and the relationship
between addition and subtraction to solve problems. By comparing a
variety of solution strategies, students use efficient, accurate,
and generalizable methods to perform operations.
(C) Students use basic shapes and spatial reasoning
to model objects in their environment and construct more complex shapes.
Students are able to identify, name, and describe basic two-dimensional
shapes and three-dimensional solids.
(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 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 compare whole numbers, the relative
position and magnitude of whole numbers, and relationships within
the numeration system related to place value. The student is expected
to:
(A) recognize instantly the quantity of structured
arrangements;
(B) use concrete and pictorial models to compose and
decompose numbers up to 120 in more than one way as so many hundreds,
so many tens, and so many ones;
(C) use objects, pictures, and expanded and standard
forms to represent numbers up to 120;
(D) generate a number that is greater than or less
than a given whole number up to 120;
(E) use place value to compare whole numbers up to
120 using comparative language;
(F) order whole numbers up to 120 using place value
and open number lines; and
(G) represent the comparison of two numbers to 100
using the symbols >, <, or =.
(3) Number and operations. The student applies mathematical
process standards to develop and use strategies for whole number addition
and subtraction computations in order to solve problems. The student
is expected to:
(A) use concrete and pictorial models to determine
the sum of a multiple of 10 and a one-digit number in problems up
to 99;
(B) use objects and pictorial models to solve word
problems involving joining, separating, and comparing sets within
20 and unknowns as any one of the terms in the problem such as 2 +
4 = [ ]; 3 + [ ] = 7; and 5 = [ ] - 3;
(C) compose 10 with two or more addends with and without
concrete objects;
(D) apply basic fact strategies to add and subtract
within 20, including making 10 and decomposing a number leading to
a 10;
(E) explain strategies used to solve addition and subtraction
problems up to 20 using spoken words, objects, pictorial models, and
number sentences; and
(F) generate and solve problem situations when given
a number sentence involving addition or subtraction of numbers within
20.
(4) Number and operations. The student applies mathematical
process standards to identify coins, their values, and the relationships
among them in order to recognize the need for monetary transactions.
The student is expected to:
(A) identify U.S. coins, including pennies, nickels,
dimes, and quarters, by value and describe the relationships among
them;
(B) write a number with the cent symbol to describe
the value of a coin; and
(C) use relationships to count by twos, fives, and
tens to determine the value of a collection of pennies, nickels, and/or
dimes.
(5) Algebraic reasoning. The student applies mathematical
process standards to identify and apply number patterns within properties
of numbers and operations in order to describe relationships. The
student is expected to:
(A) recite numbers forward and backward from any given
number between 1 and 120;
(B) skip count by twos, fives, and tens to determine
the total number of objects up to 120 in a set;
(C) use relationships to determine the number that
is 10 more and 10 less than a given number up to 120;
(D) represent word problems involving addition and
subtraction of whole numbers up to 20 using concrete and pictorial
models and number sentences;
(E) understand that the equal sign represents a relationship
where expressions on each side of the equal sign represent the same
value(s);
(F) determine the unknown whole number in an addition
or subtraction equation when the unknown may be any one of the three
or four terms in the equation; and
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