| (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 3 are expected to perform their work without the use of calculators.
(4) The primary focal areas in Grade 3 are place value,
operations of whole numbers, and understanding fractional units. These
focal areas are supported throughout the mathematical strands of number
and operations, algebraic reasoning, geometry and measurement, and
data analysis. In Grades 3-5, the number set is limited to positive
rational numbers. In number and operations, students will focus on
applying place value, comparing and ordering whole numbers, connecting
multiplication and division, and understanding and representing fractions
as numbers and equivalent fractions. In algebraic reasoning, students
will use multiple representations of problem situations, determine
missing values in number sentences, and represent real-world relationships
using number pairs in a table and verbal descriptions. In geometry
and measurement, students will identify and classify two-dimensional
figures according to common attributes, decompose composite figures
formed by rectangles to determine area, determine the perimeter of
polygons, solve problems involving time, and measure liquid volume
(capacity) or weight. In data analysis, students will represent and
interpret data.
(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 and understand
relationships related to place value. The student is expected to:
(A) compose and decompose numbers up to 100,000 as
a sum of so many ten thousands, so many thousands, so many hundreds,
so many tens, and so many ones using objects, pictorial models, and
numbers, including expanded notation as appropriate;
(B) describe the mathematical relationships found in
the base-10 place value system through the hundred thousands place;
(C) represent a number on a number line as being between
two consecutive multiples of 10; 100; 1,000; or 10,000 and use words
to describe relative size of numbers in order to round whole numbers;
and
(D) compare and order whole numbers up to 100,000 and
represent comparisons using the symbols >, <, or =.
(3) Number and operations. The student applies mathematical
process standards to represent and explain fractional units. The student
is expected to:
(A) represent fractions greater than zero and less
than or equal to one with denominators of 2, 3, 4, 6, and 8 using
concrete objects and pictorial models, including strip diagrams and
number lines;
(B) determine the corresponding fraction greater than
zero and less than or equal to one with denominators of 2, 3, 4, 6,
and 8 given a specified point on a number line;
(C) explain that the unit fraction 1/b represents the quantity formed by one
part of a whole that has been partitioned into b
equal parts where b is a non-zero
whole number;
(D) compose and decompose a fraction a/b with a numerator greater than zero and
less than or equal to b as a sum of
parts 1/b;
(E) solve problems involving partitioning an object
or a set of objects among two or more recipients using pictorial representations
of fractions with denominators of 2, 3, 4, 6, and 8;
(F) represent equivalent fractions with denominators
of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models,
including number lines;
(G) explain that two fractions are equivalent if and
only if they are both represented by the same point on the number
line or represent the same portion of a same size whole for an area
model; and
(H) compare two fractions having the same numerator
or denominator in problems by reasoning about their sizes and justifying
the conclusion using symbols, words, objects, and pictorial models.
(4) Number and operations. The student applies mathematical
process standards to develop and use strategies and methods for whole
number computations in order to solve problems with efficiency and
accuracy. The student is expected to:
(A) solve with fluency one-step and two-step problems
involving addition and subtraction within 1,000 using strategies based
on place value, properties of operations, and the relationship between
addition and subtraction;
(B) round to the nearest 10 or 100 or use compatible
numbers to estimate solutions to addition and subtraction problems;
(C) determine the value of a collection of coins and
bills;
(D) determine the total number of objects when equally-sized
groups of objects are combined or arranged in arrays up to 10 by 10;
(E) represent multiplication facts by using a variety
of approaches such as repeated addition, equal-sized groups, arrays,
area models, equal jumps on a number line, and skip counting;
(F) recall facts to multiply up to 10 by 10 with automaticity
and recall the corresponding division facts;
Cont'd... |
