Comparison of National Standards to Nebraska Standards

Content Standards for Pre Kindergarten through Grade Two

Number Relationships and Operations

NCTM

Nebraska

Standard

Instructional programs from prekindergarten through grade 12 should enable all students to–

Expectations

In prekindergarten through grade 2 all students should-

By the end of first grade, students will

Understand numbers, ways of representing numbers, relationships among numbers, and number systems

• count with understanding and recognize "how many" in sets of objects;

• use multiple models to develop initial understandings of place value and the base-ten number system;

• develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections;

• develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers;

• connect number words and numerals to the quantities they represent, using various physical models and representations;

• understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2.

1.1 NUMERATION / NUMBER SENSE

1.1.1 communicate the sequential nature of the number system

Student demonstration:

Recognize and write numerals from 0-100.
Count forward by 1’s, 2’s, 5’s and 10’s up to 100.
Count backward from 10 to 0 by 1’s.

1.1.2 communicate the mathematical relations of the number system.

Student demonstration:

Count objects to demonstrate one-to-one correspondence.
Use comparison vocabulary, such as bigger, smaller, more, less, equal, higher, and lower.
Identify ordinal positions of first, second, third, …through tenth.
Identify and represent wholes into equal parts for the fractions of one-half and one-forth.

1.1.3 recognize numbers and applications in everyday situations.

Student demonstrations:

Identify how numbers are used in counting situations, such as setting the table and passing out candy treats.
Identify how numbers are used for identification, such as room numbers and phone numbers.
Recognize and demonstrate the value of a collection of pennies, nickels, dimes, and quarters whose value is 100 cents or less.
Demonstrate the number system of base ten using one dime to ten pennies and ten dimes to one dollar.
By the end of first grade, students will demonstrate the value of numbers (0-20) using concrete objects

Understand meanings of operations and how they related to one another

understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations;

• understand the effects of adding and subtracting whole numbers;

• understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.

1.2 COMPUTATION / ESTIMATION

1.2.1 demonstrate the concepts of addition and subtraction up to 10.

Student demonstration

Communicate the basic facts and show their value using concrete objects.
Recognize the symbols + and - as representing the operations of addition and subtraction.
Recognize the symbol = represent equal quantities.
Solve problems involving one-step solutions, using addition and subtraction facts.

Compute fluently and make reasonable estimates

• develop and use strategies for whole-number computations, with a focus on addition and subtraction;

• develop fluency with basic number combinations for addition and subtraction;

• use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

1.2.2 demonstrate the reasonableness of proposed solutions to mathematical problems.

Student demonstration:

Make estimations and comparisons to actual results.

Algebra
NCTM		Nebraska
Standard Instructional programs from prekindergarten through grade 12 should enable all students to–	Expectations In prekindergarten through grade 2 all students should-	By the end of first grade, students will
Understand patterns, relations, and functions	• sort, classify, and order objects by size, number, and other properties; • recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another; • analyze how both repeating and growing patterns are generated.	1.6 ALGBRAIC CONCEPTS 1.6.1 identify, describe, extend, and create a variety of patterns, such as objects, sounds, movements, shapes, numbers, and colors. 1.6.2 sort and classify objects according to one or more attributes, such as size, shape, color, and thickness. 1.6.3 identify and describe patterns in their environment.
Represent and analyze mathematical situations and structures using algebraic symbols	• illustrate general principles and properties of operations, such as commutativity, using specific numbers; • use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
Use mathematical models to represent and understand quantitative relationships	• model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.
Analyze change in various contexts	• describe qualitative change, such as a student's growing taller; • describe quantitative change, such as a student's growing two inches in one year.

Geometry
NCTM		Nebraska
Standard Instructional programs from prekindergarten through grade 12 should enable all students to–	Expectations In prekindergarten through grade 2 all students should-	By the end of first grade, students will
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships	• recognize, name, build, draw, compare, and sort two- and three-dimensional shapes; • describe attributes and parts of two- and three-dimensional shapes; • investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.	1.4 GEOMETRY / SPATIAL CONCEPTS 1.4.2 identify, describe, and create circles, squares, triangles, and rectangles. Student demonstrations: Construct congruent shapes and designs using manipulative.
Specify locations and describe spatial relationships using coordinate geometry and other representational systems	• describe, name, and interpret relative positions in space and apply ideas about relative position; • describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance; • find and name locations with simple relationships such as "near to" and in coordinate systems such as maps.	1.4.1 compare relative positions and spatial relationships, such as left/right, above/below, over/under, up/down, and near/far
Apply transformations and use symmetry to annayze mathematical situations	• recognize and apply slides, flips, and turns; • recognize and create shapes that have symmetry.
Use visualization, spatial reasoning, and geometric modeling to solve problems	• create mental images of geometric shapes using spatial memory and spatial visualization; • recognize and represent shapes from different perspectives; • relate ideas in geometry to ideas in number and measurement; • recognize geometric shapes and structures in the environment and specify their location.	1.4.2 Student demonstrations Construct congruent shapes and designs using manipulative. Identify and describe common geometric shapes in their environment.

Measurement
NCTM		Nebraska
Standard Instructional programs from prekindergarten through grade 12 should enable all students to–	Expectations In prekindergarten through grade 2 all students should-	By the end of first grade, students will
Understand measurable attributes of objects and the units, systems, and processes of measurement	• recognize the attributes of length, volume, weight, area, and time; • compare and order objects according to these attributes; • understand how to measure using nonstandard and standard units; • select an appropriate unit and tool for the attribute being measured.	1.3.1 compare two or more items or sets using direct comparisons or nonstandard units of measure for the following attributes: length (shorter/longer), height (taller/shorter), weight (heavier/lighter), temperature (hotter/colder). Nonstandard units examples are length of a human foot, hand span, new pencil, a toothpick, block, etc. 1.3.2 recognize tools of measurement and their appropriate use, such as clocks, calendar, ruler, balance scale, and thermometer. 1.3.3 tell time to the half-hour using an analog and digital clock. 1.3.4 identify the different units of measurement used in their environment, such as cents, dollars, pounds, gallons, liters, meters, miles, minutes, and hours. 1.3.5 demonstrate an understanding of orientation in time for past, present, future, earlier and later.
Apply appropriate techniques, tools, and formulas to determine measurements	• measure with multiple copies of units of the same size, such as paper clips laid end to end; • use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meterstick; • use tools to measure; • develop common referents for measures to make comparisons and estimates.

Data Analysis and Probability
NCTM		Nebraska
Standard Instructional programs from prekindergarten through grade 12 should enable all students to–	Expectations In prekindergarten through grade 2 all students should-	By the end of first grade, students will
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them	• pose questions and gather data about themselves and their surroundings; • sort and classify objects according to their attributes and organize data about the objects; • represent data using concrete objects, pictures, and graphs.	1.5 DATA ANALYSIS, PROBABILITY, AND STATISTICAL CONCEPTS 1.5.1 count and collect information about objects and events in their environment, such as what is your favorite candy bar, who has a brother, how many pets, and who is going to the library. 1.5.2 organize and display collected information using objects and pictures. 1.5.4 describe the steps used in collecting and analyzing information.
Select and use appropriate statistical methods to analyze data	• describe parts of the data and the set of data as a whole to determine what the data show.	1.5.3 make comparisons from displayed data, such as more, less, and fewer.
Develop and evaluate inferences and predictions that are based on data	• discuss events related to students' experiences as likely or unlikely.
Understand and apply basic concepts of probability