Download K-5 Curriculum Document - Rapid City Area Schools

Rapid City Area Schools
ELEMENTARY SCHOOL
Mathematics Curriculum
Approved by the Boards of Education, November 2002
Revision approved by the board of Education, June 2005
RAPID CITY AREA SCHOOLS
300 6TH Street
Rapid City, South Dakota 57701
BOARD OF EDUCATION
Mrs. Margie Rosario
Mrs. Sheryl Kirkeby
Mrs. Leah Lutheran
Mrs. Holly Lemay
Mr. David Janak
Mr. Douglas Kinneburgh
President
1st Vice President
2nd Vice President
ADMINISTRATION
Dr. Peter M. Wharton, Superintendent of Schools
Dr. Patricia Smith Peel, Director of Student Achievement and Staff
Development
Ms. Nancy Ward, Mathematics Coordinator
Mrs. Lisa Plumb, Facilitator of Mathematics Curriculum Committee
COMMUNITY ADVISORY COMMITTEE
Mrs. Micheline Hickenbotham
Mrs. Vicki Kapust
Mrs. Danielle Goodwin
Black Hills State University
Center for Advancement of Math and
Science Education
Center for Advancement of Math and
Science Education
MATHEMATICS CURRICULUM WRITING COMMITTEE
Name
School
Grade
Anderson, Judy
Barker, Gaylene
Beaumont, Rosella
Boechler, Tara
Conrad, Dan
Dahme, Linda
Darrow, Sharon
Rapid Valley
Grandview
Corral Drive
Valley View
Central
South Canyon
Central
Fifth Grade
First Grade
First Grade
First Grade
Fourth Grade
Dormann, Carol
Fincher, Shannon
Gilliland, Deb
Greenwalt, Donna
Heberlein, Sally
Heck, Suzy
Hunt, Peggy
Johns, Connie
Johnson, Al
Johnson, Rosemary
Johnston, Mary
Keck, Jeanette
Keck, Tom
Kertzman, Deann
Kundel, Ken
Larsen, Pat
Liggett, Carol
Loomer, Lynn
Miller, Glenda
Olson, Robin
Olson, Shelly
Peterson, Leslie
Pratt, Peg
Reiling, Ann
Renner, Misty
Richardson, Kim
Schara, Kim
Schaefer, Kim
Shelton, Debi
Steinberg, Craig
Stephens, Danelle
Tschetter, Stacie
Uecker, Judy
Weaver, Bernetta
Webber, Kim
Zimiga, Cheryl
Southwest
9th Gr. Academy
Grandview
Southwest
South
Black Hawk
Pinedale
Corral Drive
South
West
Horace Mann
Bergquist
Stevens
Rapid Valley
North
Wilson
Robbinsdale
South Canyon
Bergquist
South Canyon
WDTI
South Park
Horace Mann
South Park
Valley View
Central
Dakota
West
General Beadle
Wilson
Pinedale
Canyon Lake
Meadowbrook
Central
Black Hawk
Meadowbrook
Sixth Grade
Third Grade
Seventh Grade
Eighth Grade
Fifth Grade
Fourth Grade
Fifth Grade
Eighth Grade
Sixth Grade
Third Grade
First Grade
First Grade
Sixth Grade
Special Education
First Grade
Third Grade
Fourth Grade
First Grade
Preschool
Second Grade
Second Grade
Fourth Grade
Kindergarten
Sixth Grade
Eighth Grade
Third Grade
Fifth Grade
First Grade
Fifth Grade
First Grade
Second Grade
Fourth Grade
MATHEMATICS CURRICULUM REALIGNMENT
COMMITTEE
Name
School
Grade
Ahrens, Connie
Gilliland, Deb
Heberlein, Sally
Goodell, Donna
Johnston, Mary
Knollwood
Grandview/Wilson
North
Wilson
Valley View
Math Teacher Leader
Math Teacher Leader
Math Teacher Leader
Math Recovery
Math Teacher Leader
Kramer, Linda
Manning, Jennifer
Pierce, Paula
Ritten, Marie
Stewart, Chris
Swanson, Jackie
Tschetter, Stacie
Webber, Kim
Black Hawk/Corral Drive
Knollwood
Grandview
District
Meadowbrook
General Beadle
Canyon Lake/Pinedale
Meadowbrook
Math Teacher Leader
Math Teacher Leader
First Grade
Secondary Math Coordinator
Fifth Grade
Math Recovery
Math Teacher Leader
Math Teacher Leader
ELEMENTARY SCHOOL TABLE OF CONTENTS
Introduction
Introduction
Philosophy
Essential Knowledge
Principles of National Council of Teachers of Mathematics
Nation Council of Teachers of Mathematics Content Standards
Nation Council of Teachers of Mathematics Process Standards
Elementary School Curriculum
South Dakota Mathematics Standards, Goals, and Indicators
Guide to Document Numbering
Pre-Kindergarten Standards
Kindergarten Standards
First Grade Standards
Second Grade Standards
Third Grade Standards
Fourth Grade Standards
Fifth Grade Standards
Vertical Alignment
Glossary
Introduction
This document was written by the members of the Mathematics Curriculum Writing
Committee to reflect the National and South Dakota Standards for Mathematics Instruction.
The committee was facilitated by Lisa Plumb, Administrator, and Nancy Ward, Math
Coordinator, approved by the members of the Mathematics Curriculum Advisory
Committee and the Instructional Council and authorized by the Board of Education for the
Rapid City Area Schools.
The document was realigned by the Math Curriculum Realignment Committee to the South
Dakota Math Content Standards approved on May 17, 2004. The 2004 South Dakota
standards is simple a place to begin – it lays the foundation for measurable, consistent,
high-level student learning; however, the curriculum of each district must provide students
with rigor and topics beyond those of the standards in order to ensure mastery.
Vision Statement
Our vision is the development of a curriculum with common language and continuity that
provides a strong and diverse foundation where the teaching and learning of mathematics
are in harmony to meet individual needs that promote success, confidence and an insatiable
thirst for learning.
Introduction
We live in a time of extraordinary and accelerating change. New knowledge, tools, and
ways of doing and communicating mathematics continue to emerge and evolve.
Quantitative information available to limited numbers of people a few years ago is now
widely disseminated through popular media outlets.
The need to understand and be able to use mathematics in everyday life and in the
workplace has never been greater and will continue to increase. In this changing world,
those who understand and can do mathematics will have significantly enhanced
opportunities and options for shaping their futures. Mathematical competence opens doors
to productive futures.
The Mathematics Curriculum committee was formed in 2000 and charged with the task of
reviewing and revising the K-12 Mathematics curriculum to align with the South Dakota
Mathematics Content Standards and the National Council of Teachers of Mathematics
Principles and Standards 2000. The committee used relevant research from a variety of
resources including the National Council of Teachers of Mathematics and the South Dakota
State Mathematics Content Standards adopted in 1998.
Persons desiring in-depth information regarding this research are directed to the following
publications:
- South Dakota Mathematics Content Standards: South Dakota Department of Education
and Cultural Affairs. Adopted May 17, 2005
- National Council of Teachers of Mathematics Principles and Standards 2000
Mathematics Curriculum Foundation – Grades Pre-K-12
Philosophy
The educational mission of the Rapid City Area Schools is to prepare students to lead
fulfilling and responsible lives. Mathematics education should provide students with a
useful base of mathematical knowledge, skills, and understanding that will enable them to
think and reason mathematically. The mathematics curriculum is designed to develop
mathematically powerful students who:
 Value mathematics
 Are confident and proficient in their ability to do mathematics
 Are mathematical problem solvers


Can communicate mathematically
Reason mathematically
Our students deserve and need the best mathematics education possible, one that enables
them to fulfill personal ambitions and career goals in an ever-changing world. The NCTM
Principles for School Mathematics 2000 describe particular features of high-quality
mathematics education.
Essential Knowledge
The Rapid City Area Schools mathematics curriculum is based on the South Dakota
Mathematics content standards. Standards articulate an essential core of knowledge and
skills. They specify the understanding, knowledge, and skills that students are expected to
achieve in their K-12 academic career.
Since education is often described as a “journey through learning,” that analogy helps
clarify the components that make up a set of standards. The goals represent the
final/ultimate destination--where all students should “arrive” after the required years of
mathematics study. The indicators provide targets and guideposts throughout the journey.
The performance descriptors serve as mile markers and weigh stations along the way and
the grade level standards represent the turns, hills, traffic signs, and the white lines along
the road.
o Goals: The six broad, conceptual goals (content area/discipline standards) are
the K-12 strands that define the essence of the discipline of mathematics.
Because the goals are the “end results” of what we would expect after thirteen
years of mathematics study, they are worded the same at each grade level. This
is done to provide consistency in K-12 curricular focus and alignment. It should
also be noted that although algebra, geometry, and statistics have traditionally
been thought of as “courses,” in this document, they refer to mathematical
strands that should be addressed throughout a K-12 program.
o
Indicators: The indicators further define the goals and set the framework for
mathematics. The indicators remain the same at all instructional levels (K-2, 35, 6-8, 9-12), thereby providing an ongoing and constant focus for the standards.
The indicators also provide the targets and anchors for broad district-level,
program evaluation.
o
Performance Descriptors: The performance descriptors are organized into
proficiency levels. These proficiency levels describe how a student at that level
would be expected to perform the grade-level standards.


Advanced: A student performing at the advanced level exceeds
expectations for that grade level. The student is able to perform the
content standards for the grade at a high level of difficulty, complexity,
or fluency beyond that specified by the grade-level standards.
Proficient: A student performing at the proficient level meets
expectations for that grade level. The student is able to perform the

o
content standards for the grade at the level of difficulty, complexity, or
fluency specified by the grade-level standards.
Basic: A student performing at the basic level performs below
expectations for that grade level. The student is able to perform some of
the content standards for the grade below the level of difficulty,
complexity, or fluency specified by the grade-level standards.
A student performing below the basic level is unable to perform the
content standards for the grade. Therefore, no description is provided
below the basic level.
Grade Level Standards: These statements represent the classroom learning
objectives or activities that should be provided at each grade level to help
students reach the expectations articulated in the performance descriptors,
indicators, and goal.
Mathematics in the Rapid City Area Schools will be taught according to these
six principles written by the National Council of Teachers of Mathematics.
* Equity: Excellence in mathematics education requires equity—high expectations
and strong support for all students.
* Curriculum: A curriculum is more than a collection of activities; it must be
coherent, focused on important mathematics and well articulated across the grades.
* Teaching: Effective mathematics teaching requires understanding what students
know and need to learn and then challenging and supporting them to learn it well.
* Learning: Students must learn mathematics with understanding, actively building
new knowledge from experience and prior knowledge.
* Assessment: Assessment should support the learning of important mathematics
and furnish useful information to both teachers and students.
* Technology: Technology is essential in teaching and learning mathematics; it
influences the mathematics that is taught and enhances students’ learning.
NCTM Content Standards
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
Number and
Operations
Standard
Algebra
Standard
Geometry
Standard
Measurement
Standard
Data Analysis
and Probability
Standard
understand
numbers, ways
of representing
numbers,
relationships
among numbers,
and number
systems.
understand
patterns,
relations, and
functions.
analyze
understand
formulate
characteristics
measurable
questions that
and properties
attributes of
can be
of two- and
objects and the
addressed with
threeunits, systems,
data and collect,
dimensional
and processes of organize, and
geometric
measurement.
display relevant
shapes and
data to answer
develop
them.
mathematical
arguments about
geometric
relationships.
understand
represent and
specify locations apply
select and use
meanings of
analyze
and describe
appropriate
appropriate
operations and
mathematical
spatial
techniques,
statistical
how they relate
situations and
relationships
tools, and
methods to
to one another.
structures using using coordinate formulas to
analyze data.
algebraic
geometry and
determine
symbols.
other
measurements.
representational
systems.
compute fluently use
apply
develop and
and make
mathematical
transformations
evaluate
reasonable
models to
and use
inferences and
estimates.
represent and
symmetry to
predictions that
understand
analyze
are based on
quantitative
mathematical
data.
relationships.
situations.
analyze change
use
understand and
in various
visualization,
apply basic
contexts.
spatial
concepts of
reasoning, and
probability.
geometric
modeling to
solve problems.
These standards describe mathematical content goals. Inclusion of content and process standards
is critical to the effective teaching of mathematics.
NCTM Process Standards
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
Problem
Reasoning and
Communicatio
Connections
Representation
Solving
Proof Standard
n Standard
Standard
Standard
Standard
build new
mathematical
knowledge
through
problem
solving.
recognize
reasoning and
proof as
fundamental
aspects of
mathematics.
organize and
recognize and
create and use
consolidate
use connections representations
their
among
to organize,
mathematical
mathematical
record, and
thinking
ideas.
communicate
through
mathematical
communication
ideas.
.
solve
make and
communicate
understand how select, apply, and
problems that
investigate
their
mathematical
translate among
arise in
mathematical
mathematical
ideas
mathematical
mathematics
conjectures.
thinking
interconnect
representations
and in other
coherently and and build on
to solve
contexts.
clearly to peers, one another to
problems.
teachers, and
produce a
others.
coherent whole.
apply and
develop and
analyze and
Recognize and
use
adapt a variety evaluate
evaluate the
apply
representations
of appropriate mathematical
mathematical
mathematics in
to model and
strategies to
arguments and
thinking and
contexts outside interpret
solve
proofs.
strategies of
of mathematics. physical, social,
problems.
others.
and
mathematical
monitor and
select and use
use the
phenomena.
reflect on the
various types of
language of
process of
reasoning and
mathematics to
mathematical
methods of proof. express
problem
mathematical
solving.
ideas precisely.
These standards describe mathematical process goals. Inclusion of content and process standards
is critical to the effective teaching of mathematics.
K-12 – Mathematics Standards
Goals and Indicators
ALGEBRA STANDARDS
Goal 1: Students will use the language of algebra to explore, describe, represent, and
analyze number expressions and relations that represent variable quantities.
An understanding of patterns is basic to all mathematical thinking. Early experiences in
learning about, understanding, and using patterns is foundational to algebraic reasoning.
This algebraic reasoning encompasses the relationships among quantities, the use of
symbols, the modeling of phenomena, and the mathematical study of change. From
investigations of the properties of whole numbers to the use of mathematical models to
represent quantitative relationships, algebra is linked to all areas of mathematics. A strong
foundation in algebra is an expectation for every South Dakota high school graduate.
Indicator 1: Use procedures to transform algebraic expressions.
Indicator 2:
Indicator 3:
Indicator 4:
Use a variety of algebraic concepts and methods to solve equations and
inequalities.
Interpret and develop mathematical models.
Describe and use properties and behaviors of relations, functions and
inverses.
GEOMETRY STANDARDS
Goal 2: Students will use the language of geometry to discover, analyze, and
communicate geometric concepts, properties, and relationships.
Spatial sense is fundamental to mathematics both as a means of interpreting and
representing the physical environment, and as a tool for the study of other topics in
mathematics and science. The study of relationships among shapes and their properties is
essential to their representation in abstract form and their translation into definitions,
theorems, and proofs. The study of geometry allows students to use visualization, spatial
reasoning, and geometric modeling to solve problems.
Indicator 1: Use deductive and inductive reasoning to recognize and apply properties of
geometric figures.
Indicator 2: Use properties of geometric figures to solve problems from a variety of
perspectives.
MEASUREMENT STANDARDS
Goal 3: Students will apply systems of measurement and use appropriate
measurement tools to describe and analyze the world around them.
The study of measurement is essential to an understanding of the measurable attributes of
objects and the units, systems, and processes of measurement that are used in personal and
professional work. In the early grades, students learn to use these measurable attributes of
objects to compare them for relative length, weight, and other characteristics. Students
increase their precision in collecting information about the measurable attributes of objects
as they encounter increasing demands for these skills. Measurement skills and the accurate
use of measurement tools and formulas become critical in other mathematical applications
including geometry and statistics.
Indicator 1: Apply measurement concepts in practical applications.
NUMBER SENSE STANDARDS
Goal 4: Students will develop and use number sense to investigate the characteristics
of numbers in a variety of forms and modes of operation.
Number sense is the most basic skill of mathematics. From simple counting to the fluent
use of computations skills, students use number sense to operationalize mathematics. An
understanding of basic mathematics operations is critical to all other mathematical pursuits.
Students should exhibit fluency in applying number sense to mathematical operations by
the end of the elementary years. Students should be able to perform computation through
mental calculation, estimation, and paper-pencil calculations.
Indicator 1: Analyze the structural characteristics of the real number system and its
various subsystems. Analyze the concept of value, magnitude, and relative
magnitude of real numbers.
Indicator 2: Apply number operations with real numbers and other number systems.
Indicator 3:
Develop conjectures, predictions, or estimations to solve problems and
verify or justify the results.
STATISTICS & PROBABILITY STANDARDS
Goal 5: Students will apply statistical methods to analyze data and explore probability
for making decisions and predictions.
Statistics are encountered in every public forum from newspapers to consumer and
employment data. The ability to define and investigate statistical questions and the
probability of outcomes is essential to informed consumer decision-making. Students need
the skills necessary to analyze and evaluate the barrage of statistical information they will
encounter in their personal and professional lives. Through experiences in collecting and
analyzing data, students learn to interpret and evaluate the usefulness of information.
Indicator 1: Use statistical models to gather, analyze, and display data to draw
conclusions.
Indicator 2: Apply the concepts of probability to predict events/outcomes and solve
problems.
Guide to the Numbering and Symbol System Used in the Document
Standards are coded to cross-reference grades, goals/strands, indicators, and standards.
1.N.1.1.
Grade.Goal/Strand.Indicator.Standard.
Grade refers to the grade level at which the standards are to be mastered by students.
Goal or Strand refers to the major area of mathematics (e.g., algebra, geometry,
measurement, number sense, statistics and probability) this group of standards address.
These strands are coded:
A for Algebra
G for Geometry
M for Measurement
N for Number Sense
S for Statistics and Probability
Indicator refers to the number of the indicator for this goal or strand. Each goal has one or
more related indicators that describe key aspects of the goal.
Standard refers to the number of the grade-level standard for the indicator. Each indicator
has one or more grade-level standard(s) that describes what students will know and be able
to do related to the indicator at the specific grade level.
Examples in bold type are directly related and aligned to the level of the standard. These
examples represent the level of difficulty intended in the grade-level standard and possible
materials, activities, or sub-skills classroom instructors could use in teaching the standards.
Grade-level supporting skills represent enabling skills students may need to be taught in
order to achieve the standards.
(•) Bullets represent enabling skills to the current grade-level standard students may
need to be taught in order to achieve the standards.
(√) Checkmarks are enabling skills to the next higher grade-level standards that are
related to current grade-level standards and thus may be introduced at an earlier time.
Examples that are NOT in bold type are related and aligned to the level of the
bullets/supporting skills and checkmarks. These examples represent the level of difficulty
intended in the grade-level standard. They represent some possible materials, activities, or
sub-skills classroom instructors could use in teaching the supporting skills.
Pre-Kindergarten



Standards
Examples
Performance Descriptors
Pre-Kindergarten Algebra
Indicator 4: Describe and use properties and behaviors of relations, functions, and
inverses.
Pre-Kindergarten Standards, Supporting Skills, and Examples
Students are able to identify the next element in two-part repeating patterns.
Example: Identify the next element in a pattern using color, size, or shape.
Students are able to match objects according to one or more attributes.
Example: Button sorting: puts all the two-hole buttons in one pile and four-hole buttons
in another pile.
Pre-Kindergarten Algebra Performance Descriptors
Pre-Kindergarten students performing at the advanced level:
Advanced
 Create and extend repeating patterns.
Pre-Kindergarten students performing at the proficient level:
 Identify the next element in two-part repeating patterns.
Proficient
 Match objects according to one or more attributes.
Pre-Kindergarten students performing at the basic level:
Basic
 Duplicate two-part repeating patterns.
Pre-Kindergarten Geometry
Indicator 1: Use deductive and inductive reasoning to recognize and apply properties of
geometric figures.
Pre-Kindergarten Standard
Students are able to duplicate block designs using models.
Students are able to identify circles, squares, and triangles.
Indicator 2: Use properties of geometric figures to solve problems from a variety of
perspectives.
Pre-Kindergarten Standard
Students are able to place objects in designated positions.
Examples: Put the ball on the chair.
Pre-Kindergarten Geometry Performance Descriptors
Pre-Kindergarten students performing at the advanced level:
Advanced
 Recognizes and names squares, circles and triangles.
 Describes the position of objects.
Pre-Kindergarten students performing at the proficient level:
 Duplicate block designs using models.
Proficient
 Identify circles, squares, and triangles.
 Place objects in designated positions.
Pre-Kindergarten students performing at the basic level:
Basic
 Sort pattern blocks by shape.
Pre-Kindergarten Measurement
Indicator 1: Apply measurement concepts in practical applications.
Pre-Kindergarten Standards, Supporting Skills, and Examples
Students are able to sort and match pennies, nickels, dimes, and quarters.
Students are able to identify the longer/shorter of two objects.
Students are able to name objects that are hot or cold.
Example: The sun is hot.
Pre-Kindergarten Measurement Performance Descriptors
Advanced
Pre-Kindergarten students performing at the advanced level:
 Identify pennies and nickels.
 Order objects by length.
 Compare objects and situations for temperature.
Proficient
Pre-Kindergarten grade students performing at the proficient level:
 Sort and match pennies, nickels, dimes, and quarters.
 Identify the longer/shorter of two objects.
 Name objects that are hot or cold.
Pre-Kindergarten grade students performing at the basic level:
 Sort and match pennies and nickels.
Basic
 Identify the bigger/smaller of two objects.
 Tell whether specific objects are hot or cold.
Pre-Kindergarten Number Sense
Indicator 1: Analyze the structural characteristics of the real number system and its
various subsystems. Analyze the concept of value, magnitude, and relative magnitude of
real numbers.
Kindergarten Standards Supporting Skills, and Examples
Read and count numerals to 10.

Say the forward number word sequence to 10.

Use one-to one correspondence to count up to 10 objects.

Keep track of what’s been counted.

Match, select, and name numerals 0 to 10.
Pre-Kindergarten Number Sense Performance Descriptors
Pre-Kindergarten students performing at the advanced level:
 Sequence numerals to 10.
Advanced
 Read and count numerals to 20.
Pre-Kindergarten grade students performing at the proficient level:
Proficient
 Read and count numerals to 10.
Pre-Kindergarten grade students performing at the basic level:
Basic
 Count up to 5 objects using one-to-one correspondence.
Pre-Kindergarten Statistics & Probability
Indicator 1: Use statistical models to gather, analyze, and display data to draw conclusions.
Pre-Kindergarten Standards
Students are able to organize objects or pictures according to similarities.
Example: The student puts objects together that have the same use. (blocks, dishes, etc)
Pre-Kindergarten Statistics & Probability Performance Descriptors
Advanced
Proficient
Basic
Pre-Kindergarten students performing at the advanced level:
 Explain rules used for sorting.
Pre-Kindergarten students performing at the proficient level:
 Organize objects or pictures according to similarities.
Pre-Kindergarten students performing at the basic level:
 Sort objects into groups according a given attribute.
Kindergarten Algebra
Indicator 1: Use procedures to transform algebraic expressions.
Kindergarten Standard, Supporting Skills, and Examples
Students will be able to model possible arrangements for quantities to 6.
Example: There are 5 red and blue crayons in a box. How many red
and how many blue
crayons could there be?
Indicator 2: Use a variety of algebraic concepts and methods to solve equations and
inequalities.
Kindergarten Standard, Supporting Skills, and Examples
Students are able to compare collections of objects to determine more, less, and equal
(greater than and less than). (K.A.2.1.)
 Demonstrate mastery using collections of concrete objects.
Example: Are there more red cubes or blue cubes?
Indicator 3: Interpret and develop mathematical models.
Kindergarten Standards, Supporting Skills, and Examples
Students are able to use concrete objects to model the meaning of the + and - symbols .
(K.A.3.1.)

Model problem situations using physical materials.
Example: Mary had 2 crackers and Steve had 2 crackers. How many crackers did
they have together?
Example: Bob had 5 apples and he ate 1 apple. How many apples does he have
left?
Indicator 4: Describe and use properties and behaviors of relations, functions, and
inverses.
Kindergarten Standards, Supporting Skills, and Examples
Students are able to identify and extend two-part repeating
patterns using concrete objects, sounds, and movements.
(K.A.4.1.)
Example: green triangle, orange square, green triangle, orange
square,_____,
Example: tennis shoe, tennis shoe, sandal, tennis shoe, tennis
shoe,_____,
Students are able to sort and classify objects according to one attribute. (K.A.4.2.)
Examples: size, shape, or color
Kindergarten Algebra Performance Descriptors
Advanced
Kindergarten students performing at the advanced level:
 Create an addition/subtraction situation and write an appropriate
number sentence.
 Extend patterns with more than two elements.
Proficient
Basic
 Sort and classify objects according to more than one attribute.
Kindergarten students performing at the proficient level:
 Model possible arrangements for quantities to 6.
 Compare collections and identify the collection that has more or less
and collections that are equal.
 Model the meaning of the + and - symbols.
 Extend two-part repeating patterns.
 Sort and classify objects according to one attribute.
Kindergarten students performing at the basic level:
 Compare collections and identify the collection that
has more.
 Recognize two-part repeating patterns.
Kindergarten Geometry
Indicator 1: Use deductive and inductive
reasoning to recognize and apply properties of
geometric figures.
Kindergarten Standard, Supporting Skills, and
Examples
Students are able to recognize and name basic two-dimensional (plane) figures: circle,
square, triangle, rectangle. (K.G.1.1.)

Sort and compare attributes of two-dimensional figures.

Describe their similarities and differences and identify them in the environment.

Recognize that figures remain the same when rotated (turned).
Match three-dimensional figures to shapes in the environment.
Examples: cube, sphere, cone, cylinder
Indicator 2: Use properties of geometric figures
to solve problems from a variety of perspectives.
Kindergarten Standard, Supporting Skills, and
Examples
Students are able to describe the position of two-dimensional (plane) figures. (K.G.2.1.)
Examples: above, between, next to, below, beside
Kindergarten Geometry Performance Descriptors
Advanced
Kindergarten students performing at the advanced level:
 Recognize and describe two-dimensional figures: oval, hexagon,
rhombus, trapezoid.

Proficient
Basic
Recognize and name three-dimensional shapes in the
environment: cube, sphere, cone, cylinder.
Kindergarten students performing at the proficient level:
 Recognize and name two-dimensional (plane) figures:
circle, square, triangle, rectangle.
 Match three-dimensional figures to shapes in the environment:
cube, sphere, cone, cylinder.
 Describe the position of two-dimensional (plane) figures.
Kindergarten students performing at the basic level:
 Recognize and name squares and circles.
 Place an object in a described position.
Kindergarten Measurement
Indicator 1: Apply measurement concepts in
practical applications.
Kindergarten Standards, Supporting Skills, and
Examples
Students are able tell time to the nearest hour using digital and analog clocks. (K.M.1.1.)
Students are able to name the days of the week. (K.M.1.2.)
Students are able to identify pennies, nickels, dimes, and quarters using money models
and count pennies to 20¢. (K.M.1.3.)
Students are able to estimate length using non-standard units of measure. (K.M.1.4.)
Example: A book is about ___ paperclips long.
Students are able to compare and order concrete objects by length, height, and weight.
(K.M.1.5.)
Examples:
length - longer, shorter
height - taller, shorter
weight - heavier, lighter
Students are able to compare temperatures of different objects or situations.
Example: Today is warmer/colder than yesterday. A popsicle is colder than a cookie.
Kindergarten Measurement Performance Descriptors
Kindergarten students performing at the advanced level:
Advanced
Proficient
Basic
 Tell time to the nearest 1/2 hour.

State the value of pennies and identify the number of pennies
needed to equal a nickel, dime, or quarter.
Kindergarten grade students performing at the proficient level:
 Tell time to the nearest hour.
 Name the days of the week.
 Identify pennies, nickels, dimes, and quarters.
 Estimate length using non-standard units.
 Compare and order concrete objects by length, height, and
weight.
 Compare temperatures of different objects or situations
Kindergarten grade students performing at the basic level:
 Name at least 5 days of the week.
 Identify pennies and nickels.
 Compare two concrete objects by length.
Kindergarten Number Sense
Indicator 1: Analyze the structural characteristics of the real number system and its
various subsystems. Analyze the concept of value, magnitude, and relative magnitude of
real numbers.
Kindergarten Standards Supporting Skills, and
Examples
Students are able to read, write, count, and sequence numerals to 20. (K.N.1.1.)
 Say the forward number word sequence to 20 and the backward number sequence
from 10.

Say the number before and after a given number in the range 0-20.

Use one-to-one correspondence.

Keep track of what’s been counted.

Associate verbal names and standard numerals with whole
numbers to 20.
 Count objects in a given set and write the corresponding
numeral.
 Identify ordinal positions using an ordered set of objects, 1st
through 10th.
 Associate written word names with whole numbers to 10.
Students are able instantly tell the number of objects in a regular patterning. (up to 5)
Students are able to use fraction models to create one-half of a
whole. (K.N.1.2.)
Example: Divide a cookie equally between two people.
Indicator 2: Apply number operations with real numbers and other number systems.
Kindergarten Standards, Supporting Skills, and
Examples
Students are able to recognize equivalent forms of the same number through the use of
physical models. (numbers to 10)
Example: 5 can be represented as:
a dot pattern with one dot and 4 dots
a toothpick pattern with 3 toothpicks and 2 toothpicks
Indicator 3: Develop conjectures, predictions, or estimations to solve problems and
verify or justify the results.
Kindergarten Standards, Supporting Skills, and
Examples
Students are able to solve addition and subtraction problems up
to 10 in context. (K.N.3.1.)
 Represent problem situations and solve using concrete objects,
pictures, or numbers.

Explain how to solve story problems using concrete objects and pictures.
Kindergarten Number Sense Performance Descriptors
Advanced
Proficient
Basic
Kindergarten students performing at the advanced level:
 Read, write, count, and sequence numerals to 50.
 Solve addition problems up to 20.
Kindergarten students performing at the proficient level:
 Read, write, count, and sequence numerals to 20.
 Recognize up to 5 objects in a regular pattern.
 Use fraction models to create one-half of a whole.
 Recognize equivalent forms of the same number.
 Solve addition and subtraction problems up to 10.
Kindergarten students performing at the basic level:
 Read, write, count, and sequence numerals to 10.
 Solve addition and subtraction problems
up to 5.
Kindergarten Statistics & Probability
Indicator 1: Use statistical models to gather,
analyze, and display data to draw conclusions.
Kindergarten Standards, Supporting Skills, and
Examples
Students are able to describe data represented in concrete graphs
with objects and pictographs. (K.S.1.1.)
Example: Tell how many children are wearing Velcro shoes by
observing the rows of shoes.
Students are able to collect data and sort into two categories.
Example: Would you rather have pizza or tacos?
Do you have pets?
Indicator 2: Apply the concepts of probability to predict events/outcomes and solve
problems.
Kindergarten Standards, Supporting Skills, and Examples
(Mastery of this indicator does not emerge until first grade.)
Kindergarten Statistics & Probability Performance Descriptors
Advanced
Proficient
Basic
Kindergarten students performing at the advanced level:
 Collect and record data.
Kindergarten students performing at the proficient level:
 Describe data represented in pictographs.
 Collect data and sort into two categories.
Kindergarten students performing at the basic level:
 Describe data represented in concrete graphs.
 Identify which group has the most in a set of given data.
First Grade Algebra
Indicator 1: Use procedures to transform
algebraic expressions.
1st Grade Standards, Supporting Skills, and Examples
Students are able to apply the commutative property of addition by using
what they know about a + b to solve b + a.
Indicator 2: Use a variety of algebraic concepts
and methods to solve equations and inequalities.
1st Grade Standards, Supporting Skills, and
Examples
Students are able to use the concepts and language of more, less,
same, greater than, less than, and equal to compare numbers and
sets (0 to 20). (1.A.2.1.)
 For numbers 0 - 20, identify one more/one less.
 Write the words less than or more than between two numbers to
create a true statement.
 Identify a number that is more than/less than a given number.
Example: 18 is more than 4
Students are able to solve open addition and subtraction sentences with one unknown
using numbers equal to or less than 10. (1.A.2.2.)

Explain and use the equal sign as a symbol of equality.
Examples:
4=3+ 
+2=4+1
5–3=
1= –2
Indicator 3:
Interpret and develop mathematical models.
1st Grade Standard, Supporting Skills, and Examples
Students are able to write number sentences from problem situations using + or - and =
with numbers to 10. (1.A.3.1.)
 Represent problem situations using concrete objects, pictures,
numerals, symbols and words
Examples: Write a number sentence to represent the problems.
1) Mary had 8 cookies. She gave 2 cookies to Bob. How many
cookies does she have left?
2) Mary has 8 cookies. Bob has 2 cookies. How many cookies do
they have altogether?
Indicator 4: Describe and use the properties and behaviors of relations, functions, and
inverses.
1st Grade Standards, Supporting Skills, and Examples
Students are able to identify, describe and extend repeating patterns containing multiple
elements using objects and pictures. (1.A.4.1.)
 Describe or demonstrate the next element in repeating patterns, e.g., rhythm, color, and
shape.
 Find patterns or relations in data organized in tables or charts to determine what should
come next.
Students are able to determine common attributes in a given group and identify those
objects that do not belong. (1.A.4.2.)
First Grade Algebra Performance Descriptors
First grade students performing at the advanced level:
 Write number sentences from problem situations using + or – and
Advanced
= using two-digit numbers greater than 20.
 Solve open addition and subtraction sentences using two-digit
numbers greater than 20.
First grade students performing at the proficient level:
 Apply the commutative property of addition
 Compare numbers and sets (0 to 20)
 Solve open addition and subtraction sentences using numbers to
20.
Proficient
 Write number sentences from problem situations using + or – and
= using numbers to 10
 Identify, describe, and extend repeating patterns
 Determine common attributes in a given group and identify those
objects that do not belong
First grade students performing at the basic level:
 Write number sentences from problem situations using + or – and
= using numbers to 10.
Basic
 Determine common attributes in a given group and identify those
objects that belong
First Grade Geometry
Indicator 1: Use deductive and inductive reasoning to recognize and apply
properties of geometric figures.
1st Grade Standards, Supporting Skills, and Examples
Students are able to describe characteristics of plane figures. (1.G.1.1.)




Recognize and name oval, hexagon, rhombus, trapezoid.
Sort and compare attributes of two-dimensional figures.
Describe their likeness and differences and identify them in the environment.
Recognize that figures remain the same when reflected (flipped) and rotated (turned).
Examples:
A circle is round.
A triangle has three straight lines
A rhombus and a trapezoid both have 4 sides.
Students are able to sort, recognize, and name basic three-dimensional figures. (1.G.1.2.)

Identify and describe three-dimensional (solid) figures in the environment.
Examples:
sphere
cylinder
cube
cone
Indicator 2: Use properties of geometric figures to solve problems from a variety of
perspectives.
1st Grade Standard, Supporting Skills, and Examples
Students are able to describe the proximity and relative position of
objects in space. (1.G.2.1.)
Examples: near, far, up, down, below, beside
First Grade Geometry Performance Descriptors
Advanced
Proficient
Basic
First grade students performing at the advanced level:
 Draw and name a 2-D (plane) figure based on described attributes.
 Describe the position of objects in space using at least two different
positional words.
First grade students performing at the proficient level:
 Describe characteristics of plane figures.
 Sort, recognize, and name basic three-dimensional figures.
 Describe the relative position of objects in space.
First grade students performing at the basic level:
 Describe characteristics of squares, circles, and triangles.
 Place an object in a described position when given directions
containing positional words.
First Grade Measurement
Indicator 1: Apply measurement concepts in practical applications.
1st Grade Standards, Supporting Skills, and Examples
Students are able to tell time to the half-hour using digital and analog clocks and order a
sequence of events with respect to time. (1.M.1.1.)
Find a date on the calendar. (1.M.1.2.)
Students are able to use different combinations of pennies, nickels, and dimes to represent
money amounts to 25¢. (1.M.1.3.)
Example: Show different ways to make 15¢ using pennies, nickels, and dimes.

State the value of pennies, nickels, and dimes using money models and pictures.
Students are able to measure length using non-standard units.
Example: Measuring with cube towers, paper clips, etc.
Students are able to estimate weight using non-standard units of measure. (1.M.1.4.)
Example: The cookie weighs about _____ cubes.
Students are able to identify appropriate measuring tools for length, weight, capacity, and
temperature. (1.M.1.5.)
Students are able to compare and order concrete objects by temperature and capacity.
(1.M.1.6.)
Examples: Temperature - hotter, colder; Capacity - holds more, holds less
First Grade Measurement Performance Descriptors
Advanced
Proficient
Basic
First grade students performing at the advanced level:
 Tell time to the nearest minute.
 Count and compare collections of coins up to 25¢.
First grade students performing at the proficient level:
 Tell time to the half-hour.
 Find a date on the calendar.
 Use different combinations of coins to represent amounts to 25¢.
 Measure length using non-standard units.
 Estimate weight using non-standard units.
 Identify appropriate measuring tools used to solve problems.
 Compare and order objects by temperature and capacity.
First grade students performing at the basic level:
 Tell time to the nearest hour.
 State the value of pennies, nickels, and dimes.
First Grade Number Sense
Indicator 1: Analyze the structural characteristics of the real number system and its
various subsystems. Analyze the concept of value, magnitude, and relative magnitude
of real numbers.
1st Grade Standards, Supporting Skills, and Examples
Students are able to read, write, count, and order numerals to 50. (1.N.1.1.)
 Say the forward and backward number word sequences in the range 0-50.
 Say the number before and after a given number in the range
 0-50.
 Count objects using one-to-one correspondence to 50.
 Keep track of objects counted to 50.
 Associate verbal names and standard numerals with whole numbers to 50.
 Count objects in a given set and write the corresponding numeral.
 When given a number, count out the correct number of objects.
 Identify ordinal positions using an ordered set of objects, 1st through 20th.

Associate written word names with whole numbers to 50.
Students are able to use unit fraction models to create parts of a whole. (1.N.1.2.)

Determine ways in which shapes can be divided into equal pieces.
Example: Color a square 1/4 red, 1/4 blue, 1/4 green and 1/4 yellow.
Indicator 2: Apply number operations with real numbers and other number systems.
1st Grade Standards, Supporting Skills, and Examples
Students are able to solve addition and subtraction problems with numbers 0 to 20 written
in horizontal and vertical formats using a variety of strategies. (1.N.2.1)

Interpret and illustrate addition and subtraction problems using standard notation
Strategy Examples:
Doubles
Near-doubles
Compensation
One more, one less
Making fives
Breaking apart numbers
Internalized number
combinations
Incrementing (jump strategies)
Commutative property
Using landmark numbers
Mental math
Relating numbers to money
Estimation
Inverse operations
Making tens
Students are able to apply with fluency sums to 5 and related subtraction facts.
 Can identify the whole when given two parts.
 Can identify the unknown part when given the whole and one part.


Use known combinations to solve more difficult combinations.
Either automatically knows the combination or has one quick strategy for figuring it out.
Students are able to represent equivalent forms of the same number through the use of
physical models, pictures, words, and numerical expressions (numbers to 20)
Examples: 10 can be represented as:
7 red crayons and 3 blue crayons
12 – 2
6+4
Indicator 3:
Develop conjectures, predictions, or estimations to solve problems and
verify or justify the results.
1st Grade Standard, Supporting Skills, and Examples
Students are able to solve addition and subtraction problems up to 20 in context. (1.N.3.1.)
 Represent problem situations and solve using concrete objects, pictures, or numbers.
 Explain how one arrives at solutions to problems.
 Select appropriate operation(s).
 Estimate to determine if a given answer is reasonable.
First Grade Number Sense Performance Descriptors
Advanced
Proficient
Basic
First grade students performing at the advanced level:
 Read, write, count, and order numerals to 100.
 Apply with fluency sums to 10 and related subtraction facts.
First grade students performing at the proficient level:
 Read, write, count, and order numerals to 50.
 Use fraction models to create parts of a whole.
 Solve addition and subtraction problems 0-20.
 Apply with fluency sums to 5 and related subtraction facts.
 Represent equivalent forms of the same number.
 Solve addition and subtraction problems up to 20 in context.
First grade students performing at the basic level:
 Read, write, count, and order numerals to 20.
 Use counting strategies to compute sums to 5 and related subtraction
facts.
 Identify fractional parts of a whole using unit fractions.
First Grade Statistics & Probability
Indicator 1:
conclusions.
Use statistical models to gather, analyze, and display data to draw
1st Grade Standards, Supporting Skills, and Examples
Students are able to collect and record data from various sources or situations including
surveys.
Example: Would you rather be able to fly or be invisible?
Students are able to display data in pictographs with units of one and bar graphs with
intervals of one. (1.S.1.1.)
Examples: Modes of transportation to school, pets owned by students, articles of clothing.
Students are able to answer questions from organized data. (1.S.1.2.)
Example: What observation can you make about the data in this graph?
Write a sentence to describe the data in this graph?
Indicator 2: Apply the concepts of probability to predict events/outcomes and solve
problems.
1st Grade Standard, Supporting Skills, and Examples
Students are able to recognize whether the outcome of a simple event is possible or
impossible. (1.S.2.1.)
Examples: spinners, number cubes, everyday events
The spinner is half blue and half yellow. Can you land on green?
You have green and yellow cubes in a bag. Can you pull out a green cube?
First Grade Statistics & Probability Performance Descriptors
First grade students performing at the advanced level:
Advanced
 Represent data sets in more than one way.
 Determine whether an outcome is certain or impossible.
First grade students performing at the proficient level:
 Collect and record data.
 Display data in pictographs and bar graphs and answer related
Proficient
questions.
 Recognize the outcome of a simple event as possible or
impossible.
First grade students performing at the basic level:
Basic
 Collect data.
 Answer questions about more/less from collected data.
Second Grade Algebra
Indicator 1: Use procedures to transform algebraic expressions.
2nd Grade Standards, Supporting Skills, and Examples
Students are able to apply the commutative property of addition and the zero property of
addition and subtraction.
Examples: 4 + 3 =  + 4 (commutative property)
7 + 0 = 7, 7- 0= 7 (zero property)
Students are able to recognize the inverse relationship between addition and subtraction
and use it to solve related problems.
Example: 3 + 5 = 8, so 8 – 5 =
Indicator 2: Use a variety of algebraic concepts and methods to solve equations and
inequalities.
2nd Grade Standards, Supporting Skills, and Examples
Students are able to use concepts of equal to, greater than, and less than to compare
numbers (0-100). (2.A.2.1.)
 For numbers 0 - 100, identify 10 more/10 less.
 Write the words less than, greater than, or equal between two numbers to create a true
statement.
Example: 50 is less than 78
 Identify numbers that are greater than or less than a given number.
Students are able to solve open addition and subtraction sentences with one unknown using
numbers equal to or less than 20. (2.A.2.2.)
Examples:
10 =  + 8
+6=8+1
=7–3
10 –  = 4
Students are able to balance addition and subtraction equations using combinations to 20.
(2.A.2.3.)
Example: 9 + 6 = 10 + 
 Describe strategies used in adding and subtracting.
 Use the commutative property to solve related equations.
Indicator 3: Interpret and develop mathematical models.
2nd Grade Standards, Supporting Skills, and Examples
Students are able to write and solve number sentences from word problems. (2.A.3.1.)
 Represent problem situations and solve using concrete objects, pictures, or numbers.
 Explain how one arrives at solutions to problems.
 Select appropriate operation(s).
 Create word problems for number sentences.
 Estimate to determine if a given answer is reasonable.
Examples: Write and solve number sentences that go with these story problems.
1) Mary made 9 bracelets. She bought 4 more bracelets. How many bracelets does she
have in all?
2) Bob caught 18 fish. He ate 9 for supper. How many are left?
3) Deb had 5 cubes. She got some more. Now she has 10. How many did she get?
Indicator 4: Describe and use the properties and behaviors of relations, functions and
inverses.
2nd Grade Standards, Supporting Skills, and Examples
Students are able to find and extend growing patterns using symbols, objects, and
numbers. (2.A.4.1.)

Identify even and odd numbers.
Example: If there are 10 children, can you make 2 even teams?
 Show why a given number is even or odd using different models,
 Recognize and extend basic number patterns using a 0-99 or 1-100 chart.
Students are able to determine likenesses and differences between sets. (2.A.4.2.)
Example: Use Venn diagrams
Second Grade Measurement Performance Descriptors
Advanced
Proficient
Basic
Second grade students performing at the advanced level:
 Create growing patterns.
 Solve open addition and subtraction sentences using 2- digit numbers.
 Balance addition and subtraction equations using combinations to 50.
Second grade students performing at the proficient level:
 Apply the commutative property of addition and the zero property of
subtraction and addition.
 Use the inverse relationship between addition and subtraction to solve
problems.
 Compare numbers (0-100).
 Solve open addition and subtraction sentences using numbers equal to or
less than 20.
 Balance addition and subtraction equations using combinations to 20.
 Write and solve number sentences from word problems.
 Find and extend growing patterns.
 Determine likenesses and differences between sets.
Second grade students performing at the basic level:
 Solve open addition and subtraction sentences using two digit numbers.
 Balance addition and subtraction equations using combinations to 10.
 Compare numbers 0-50.
Second Grade Geometry
Indicator 1: Use deductive and inductive reasoning to recognize and apply properties of
geometric figures.
Indicator 2: Use properties of geometric figures to solve problems from a variety of
perspectives.
2nd Grade Standards, Supporting Skills, and Examples
Students are able to identify geometric figures regardless of position
and orientation in space. (2.G.2.1.)
Example:
and
are both triangles.
Students are able to compare two-dimensional (plane) figures to determine if objects are
congruent.
Students are able to identify and construct shapes and designs that have symmetry.
Second Grade Geometry Performance Descriptors
Advanced
Proficient
Basic
Second grade students performing at the advanced level:
 Construct and compare geometric figures that meet given criteria.
 Predict results of a flip, slide, or turn.
Second grade students performing at the proficient level:
 Use terms to identify and describe plane and solid figures: side,
corner/vertex, and face.
 Construct and draw two- and three dimensional figures.
 Investigate and predict the resulting shape of putting together and
taking apart two-dimensional shapes.
 Identify geometric figures regardless of position and orientation in
space.
 Compare two-dimensional figures to determine congruency.
 Identify and construct shapes and designs that have symmetry.
Second grade students performing at the basic level:
 Identify plane figures based on attributes.
 Construct and draw circles, squares, triangles, and rectangles.
 Identify a line of symmetry in plane figures.
Second Grade Measurement
Indicator 1: Apply measurement concepts in practical applications.
2nd Grade Standards, Supporting Skills, and Examples
Students are able to tell time to the minute using digital and analog
clocks and relate time to daily events. (2.M.1.1)
Students are able to use the calendar to solve problems. (2.M.1.2)
Students are able to determine the value of a collection of like and unlike coins with a value
up to $1.00. (2.M.1.3)
Students are able to represent and write the value of money using the “¢” sign and in decimal
form using the “$” sign. (2.M.1.4)
Students are able to use whole number approximations for capacity
using non-standard units of measure. (2.M.1.5)
Examples:
The jar holds about how many marbles?
How many small jars of water will it take to fill a big jar?
Students are able to solve everyday problems by measuring length to the nearest inch or foot.
(2.M.1.6)

Compare the effects of measurement using units of different sizes.

Communicate the need for using a standard unit.
Examples:
How long is your shoe?
How tall is your chair?
Students are able to locate and name concrete objects that are about the same length, height,
weight, capacity, and temperature as a given concrete object. (2.M.1.7)
Students are able to estimate and measure the area of a shape and compare the estimate to
actual results.
Second Grade Measurement Performance Descriptors
Advanced
Proficient
Second grade students performing at the advanced level:
 Tells time using 5 minute intervals.
 Count and compare a collection of coins and bills up to $5.00.
Second grade students performing at the proficient level:
 Tell time to the minute and relate time to daily events.
 Use the calendar to solve problems.
 Determine the value of a collection of coins to $1.00.
 Represent and write the value of money.
 Use the whole number approximations for capacity using non-standard
units.
 Solve everyday problems by measuring length to the nearest inch or foot.


Locate and name concrete objects of comparable dimensions.
Estimate and measure the area of a shape.
Second grade students performing at the basic level:
Basic
 Tell time to the half-hour.
 Counts mixed collections of pennies, dimes, and
nickels to 25¢.
Second Grade Number Sense
Indicator 1: Analyze the structural
characteristics of the real number system and its
various subsystems. Analyze the concept of
value, magnitude, and relative magnitude of
real numbers.
2nd Grade Standards, Supporting Skills, and
Examples
Students are able to read, write, count, and sequence numerals to 100. (2.N.1.1.)

Say the forward and backward number word sequences in the range 0-100.

Say the number before and after a given number in the range 0-100.

Count objects using one-to-one correspondence.

Keep track of objects counted.

Say the forward skip counting sequences in the range 0-100 for twos, fives, and tens.

Count objects by groups of twos, fives and tens to 100.

Associate verbal names, written word names, and standard numerals with whole
numbers to 100.
 Use words, models, and expanded notation to write numbers as
tens and ones to 100.
Students are able to identify and represent fractions as parts of a group or parts of whole.
(1/2, 1/3, 1/4) (2.N.1.2.)
Example: Circle half of the cookies.
Indicator 2: Apply number operations with real
numbers and other number systems.
2nd Grade Standards, Supporting Skills, and
Examples
Students are able to solve two-digit addition and
subtraction problems written in horizontal and
vertical formats using a variety of strategies.
(2.N.2.1.)
Strategy Examples:
Doubles
One more, one less
Breaking apart
numbers
Commutative property
Mental math
Estimation
Compensation
Near-doubles
Making fives
Making tens
Incrementing (jump
strategies)
Using landmark
numbers (rounding)
Relating to money
Inverse operations
Students are able to apply with fluency sums to 10 and related subtraction facts.




Can identify the whole when given two parts
Can identify the unknown part when given the whole and one part
Uses known combinations to solve more difficult combinations
Either automatically knows each combination or has one quick strategy for figuring it
out.
Students are able to represent equivalent forms of the same number through the use of
physical models, pictures and numerical expressions. (numbers to 100).
Examples: 45 can be represented as:
20 + 20 + 5
4 tens and 5 ones
45 ones
Indicator 3: Develop conjectures, predictions, or
estimations to solve problems and verify or
justify the results.
2nd Grade Standards, Supporting Skills, and
Examples
Students are able to solve addition and subtraction problems up to
100 in context. (2.N.3.1.)
 Represent problem situations and solve using concrete objects,
pictures, numbers, tables, or charts.
 Explain the strategies used to arrive at a solution to a problem.
 Select appropriate operation(s).
 Estimate to determine if a given answer is reasonable.
Second Grade Number Sense Performance Descriptors
Advanced
Second grade students performing at the advanced level:
 Order and compare whole numbers less than 1,000..
 Apply with fluency sums to 20 and related
subtraction facts.
Proficient
Basic
Second grade students performing at the proficient level:
 Read, write, count and sequence numerals to 100.
 Identify and represent fractions as parts of a group or parts of a
whole.
 Solve two-digit addition and subtraction problems using multiple
strategies.
 Apply with fluency sums to 10 and related subtraction facts.
 Represent equivalent forms of the same number to 100.
 Solve addition and subtraction problems up to 100 in context.
Second grade students performing at the basic level:
 Read, write, count and sequence numerals to 50.

Uses counting strategies for sums to 10 and related subtraction facts.
Second Grade Statistics & Probability
Indicator 1: Use statistical models to gather,
analyze, and display data to draw conclusions.
2nd Grade Standards, Supporting Skills, and
Examples
Students are able to use interviews, surveys, and observations to
gather data. (2.S.1.1.)
Examples:
Observe the sky conditions for 5 days and record data.
Conduct a survey on animals in our neighborhood.
Students are able to represent data sets in more than one way.
(2.S.1.2.)
Examples: pictographs, bar graphs, frequency tables, Venn diagrams.
Students are able to ask and answer questions about and generate
explanations of data given in tables and graphs. (2.S.1.3.)
 Identify features of data sets in terms of most often, least often.
Indicator 2: Apply the concepts of probability to
predict events/outcomes and solve problems.
2nd Grade Standards, Supporting Skills, and
Examples
Students are able to list possible outcomes of a simple event and
make predictions about which outcome is more or less likely to
occur. (2.S.2.1.)
Examples:
The spinner is
1
2
blue,
1
4
yellow, and
1
4
green. On which color are
you most likely land?
You have 7 green and 3 yellow cubes in a bag. Which color cube
would you be least likely to pull out?
Second Grade Statistics & Probability Performance Descriptors
Second grade students performing at the advanced level:
Advanced
Proficient
Basic
 Compare data found in tables or graphs.
 Generate questions for data in a table or graph.
Second grade students performing at the proficient level:
 Use interviews, surveys, and observations to gather data.
 Represent data sets in more than one way.
 Answer questions and provide explanations for data in tables or
graphs.
 Make predictions and list possible outcomes that are more or less
likely to occur.
Second grade students performing at the basic level:
 Represent data using bar graphs.
 Make observations about data displayed in bar graphs.