(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 Grade 2 are expected to perform their work without the use of calculators.
(4) The primary focal areas in Grade 2 are making comparisons
within the base10 place value system, solving problems with addition
and subtraction within 1,000, and building foundations for multiplication.
(A) Students develop an understanding of the base10
place value system and place value concepts. The students' understanding
of base10 place value includes ideas of counting in units and multiples
of thousands, hundreds, tens, and ones and a grasp of number relationships,
which students demonstrate in a variety of ways.
(B) Students identify situations in which addition
and subtraction are useful to solve problems. Students develop a variety
of strategies to use efficient, accurate, and generalizable methods
to add and subtract multidigit whole numbers.
(C) Students use the relationship between skip counting
and equal groups of objects to represent the addition or subtraction
of equivalent sets, which builds a strong foundation for multiplication
and division.
(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 related to place value.
The student is expected to:
(A) use concrete and pictorial models to compose and
decompose numbers up to 1,200 in more than one way as a sum of so
many thousands, hundreds, tens, and ones;
(B) use standard, word, and expanded forms to represent
numbers up to 1,200;
(C) generate a number that is greater than or less
than a given whole number up to 1,200;
(D) use place value to compare and order whole numbers
up to 1,200 using comparative language, numbers, and symbols (>, <,
or =);
(E) locate the position of a given whole number on
an open number line; and
(F) name the whole number that corresponds to a specific
point on a number line.
(3) Number and operations. The student applies mathematical
process standards to recognize and represent fractional units and
communicates how they are used to name parts of a whole. The student
is expected to:
(A) partition objects into equal parts and name the
parts, including halves, fourths, and eighths, using words;
(B) explain that the more fractional parts used to
make a whole, the smaller the part; and the fewer the fractional parts,
the larger the part;
(C) use concrete models to count fractional parts beyond
one whole using words and recognize how many parts it takes to equal
one whole; and
(D) identify examples and nonexamples of halves, fourths,
and eighths.
(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 addition and subtraction problems
with efficiency and accuracy. The student is expected to:
(A) recall basic facts to add and subtract within 20
with automaticity;
(B) add up to four twodigit numbers and subtract twodigit
numbers using mental strategies and algorithms based on knowledge
of place value and properties of operations;
(C) solve onestep and multistep word problems involving
addition and subtraction within 1,000 using a variety of strategies
based on place value, including algorithms; and
(D) generate and solve problem situations for a given
mathematical number sentence involving addition and subtraction of
whole numbers within 1,000.
(5) Number and operations. The student applies mathematical
process standards to determine the value of coins in order to solve
monetary transactions. The student is expected to:
(A) determine the value of a collection of coins up
to one dollar; and
(B) use the cent symbol, dollar sign, and the decimal
point to name the value of a collection of coins.
(6) Number and operations. The student applies mathematical
process standards to connect repeated addition and subtraction to
multiplication and division situations that involve equal groupings
and shares. The student is expected to:
(A) model, create, and describe contextual multiplication
situations in which equivalent sets of concrete objects are joined;
and
(B) model, create, and describe contextual division
situations in which a set of concrete objects is separated into equivalent
sets.
(7) 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) determine whether a number up to 40 is even or
odd using pairings of objects to represent the number;
(B) use an understanding of place value to determine
the number that is 10 or 100 more or less than a given number up to
1,200; and
(C) represent and solve addition and subtraction word
problems where unknowns may be any one of the terms in the problem.
(8) 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) create twodimensional shapes based on given attributes,
including number of sides and vertices;
(B) classify and sort threedimensional solids, including
spheres, cones, cylinders, rectangular prisms (including cubes as
special rectangular prisms), and triangular prisms, based on attributes
using formal geometric language;
(C) classify and sort polygons with 12 or fewer sides
according to attributes, including identifying the number of sides
and number of vertices;
(D) compose twodimensional shapes and threedimensional
solids with given properties or attributes; and
(E) decompose twodimensional shapes such as cutting
out a square from a rectangle, dividing a shape in half, or partitioning
a rectangle into identical triangles and identify the resulting geometric
parts.
(9) Geometry and measurement. The student applies mathematical
process standards to select and use units to describe length, area,
and time. The student is expected to:
(A) find the length of objects using concrete models
for standard units of length;
(B) describe the inverse relationship between the size
of the unit and the number of units needed to equal the length of
an object;
(C) represent whole numbers as distances from any given
location on a number line;
(D) determine the length of an object to the nearest
marked unit using rulers, yardsticks, meter sticks, or measuring tapes;
(E) determine a solution to a problem involving length,
including estimating lengths;
(F) use concrete models of square units to find the
area of a rectangle by covering it with no gaps or overlaps, counting
to find the total number of square units, and describing the measurement
using a number and the unit; and
(G) read and write time to the nearest oneminute increment
using analog and digital clocks and distinguish between a.m. and p.m.
(10) Data analysis. The student applies mathematical
process standards to organize data to make it useful for interpreting
information and solving problems. The student is expected to:
(A) explain that the length of a bar in a bar graph
or the number of pictures in a pictograph represents the number of
data points for a given category;
(B) organize a collection of data with up to four categories
using pictographs and bar graphs with intervals of one or more;
(C) write and solve onestep word problems involving
addition or subtraction using data represented within pictographs
and bar graphs with intervals of one; and
(D) draw conclusions and make predictions from information
in a graph.
(11) 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) calculate how money saved can accumulate into a
larger amount over time;
(B) explain that saving is an alternative to spending;
(C) distinguish between a deposit and a withdrawal;
(D) identify examples of borrowing and distinguish
between responsible and irresponsible borrowing;
(E) identify examples of lending and use concepts of
benefits and costs to evaluate lending decisions; and
(F) differentiate between producers and consumers and
calculate the cost to produce a simple item.
