Comparison of National Standards to Nebraska Standards

Content Standards for Grade Three through Five

Number and Operations

NCTM

Nebraska

Standard

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

Expectations

In grades 3—5 all students should–

By the end of fourth grade, students will

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

• understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals;

• recognize equivalent representations for the same number and generate them by decomposing and composing numbers;

• develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;

• use models, benchmarks, and equivalent forms to judge the size of fractions;

• recognize and generate equivalent forms of commonly used fractions, decimals, and percents;

• explore numbers less than 0 by extending the number line and through familiar applications;

• describe classes of numbers (e.g., odds, primes, squares, and multiples) according to characteristics such as the nature of their factors.

4.1 NUMERATION/NUMBER SENSE

4.1.1 demonstrate an understanding of place value through the millions and decimals to the hundredths place.

Student demonstrations:

  • Read and write numerals (in digits and words) to the one millions place and decimals to the hundredths place.
  • Order and compare numbers to the one millions place and decimals to the hundredths place using the symbols <,>, and =.
  • Round whole numbers to the nearest named place, such as rounding 1.234 to the nearest hundred would be 1.200.

4.1.2 represent numbers in equivalent forms.

Student demonstration:

  • Write numbers in expanded form, such as 432=4x100 + 3x10 + 2x1.
  • Represent equivalent fractions and decimals for common fractions with denominators of 2, 4, 5, 8, and 10 using concrete objects.

4.1.3 describe and apply relationships between numbers by order, comparison, and across the operation, such as subtraction as the opposite of addition and multiplication as repeated addition.

Student demonstration:

  • Order and compare common fractions and decimals using the symbols <, >, and =.
  • Illustrate mathematical concepts by using objects and drawing pictures or diagrams.
  • Solve the check a mathematical problem by using the related facts.

4.1.4 identify and demonstrate positive and negative numbers and zero.

Student demonstration:

  • Demonstrate simple concepts of positive and negative numbers, such as using a thermometer for temperature or distance to the right or left of zero on a number line.

4.1.5 make change and count out in amounts up to $20.00.

Understand meanings of operations and how they relate to one another

• understand various meanings of multiplication and division;

• understand the effects of multiplying and dividing whole numbers;

• identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems;

• understand and use properties of operations, such as the distributivity of multiplication over addition.

 

Compute fluently and make reasonable estimates

• develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 3050;

• develop fluency in adding, subtracting, multiplying, and dividing whole numbers;

• develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results;

• develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience;

• use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals;

• select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

4.2 COMPUTATION / ESTIMATION

4.2.1 estimate and accurately calculate without and with calculators and solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.

Student demonstrations:

  • Demonstrate with accuracy and reasonable speed the basic facts of addition (1-20), subtraction (1-20), multiplication (1-144), and division (1-144).
  • Add and subtract accurately five-digit numbers including columns fo numbers.
  • Multiply up to three-digit number by two-digit number.
  • Divide up to three-digit number by one-digit divisor.

4.2.2 estimate and accurately calculate without and with calculators and solve problems involving addition and subtraction of decimals and understand the relationships among these two operations.

4.2.3 estimate and accurately calculate with out calculators and solve problems involving addition and subtraction of fractions and understand the relationship among these two operations.

 

Algebra for Grades 3-5

NCTM

Nebraska

Standard

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

Expectations

In grades 3—5 all students should–

By the end of fourth grade, students will

Understand patterns, relations, and functions

• describe, extend, and make generalizations about geometric and numeric patterns;

• represent and analyze patterns and functions, using words, tables, and graphs.

4.6 ALGEBRAIC CONCEPTS

4.6.2 identify, describe, and extend arithmetic patterns, using concrete materials and tables

Represent and analyze mathematical situations and structures using algebraic symbols

• identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers;

• represent the idea of a variable as an unknown quantity using a letter or a symbol;

• express mathematical relationships using equations.

4.6.1 use and interpret variables, mathematical symbols and properties to write and simplify expressions and sentences.

Student demonstrations:

  • Use letters, boxes, or other symbols to stand for any number, measured quantity, or object in simple situations to demonstrate the beginning concept of a variable and writing formulas.

Identify and use various indicators of multiplication (parenthesis, x, *) and division (/)

Use mathematical models to represent and understand quantitative relationships

• model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

 

Analyze change in various contexts

• investigate how a change in one variable relates to a change in a second variable;

• identify and describe situations with constant or varying rates of change and compare them.

 

 

Geometry Standard for Grades 3—5
NCTM  Nebraska
Standard Instructional programs from prekindergarten through grade 12 should enable all students to– ExpectationsIn grades 3—5 all students should– By the end of fourth grade, students will
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometricrelationships • identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes; • classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids; • investigate, describe, and reason about the results of subdividing, combining, and transforming shapes; • explore congruence and similarity; • make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions.

4.4 GEOMETRY / SPATIAL CONCEPTS

4.4.1 identify, describe, and create two-and three- dimensional geometric shapes.4.4.2 identify and draw points, lines, line segments, rays, and angles.Student demonstrations:

  • Identify properties of parallel and perpendicular lines and line segments.
4.4.3 analyze, compare, and solve problems with geometric figures using congruence, symmetry, similarity, and simple transformations.
Specify locations and describe spatial relationships using coordinate geometry and other representational systems • describe location and movement using common language and geometric vocabulary; • make and use coordinate systems to specify locations and to describe paths; • find the distance between points along horizontal and vertical lines of a coordinate system.  
Apply transformations and use symmetry to analyze mathematical situations • predict and describe the results of sliding, flipping, and turning two-dimensional shapes; • describe a motion or a series of motions that will show that two shapes are congruent; • identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs.  
Use visualization, spatial reasoning, and geometric modeling to solve problems • build and draw geometric objects; • create and describe mental images of objects, patterns, and paths; • identify and build a three-dimensional object from two-dimensional representations of that object; • identify and build a two-dimensional representation of a three-dimensional object; • use geometric models to solve problems in other areas of mathematics, such as number and measurement; • recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life.  

 

Measurement Standard for Grades 3—5

NCTM

Nebraska

Standard

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

Expectations

In grades 3—5 all students should–

By the end of fourth grade, students will

Understand measurable attributes of objects and the units, systems, and processes of measurement

• understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute;

• understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems;

• carry out simple unit conversions, such as from centimeters to meters, within a system of measurement;

• understand that measurements are approximations and how differences in units affect precision;

• explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way.

 

Apply appropriate techniques, tools, and formulas to determine measurements

• develop strategies for estimating the perimeters, areas, and volumes of irregular shapes;

• select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles;

• select and use benchmarks to estimate measurements;

• develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms;

• develop strategies to determine the surface areas and volumes of rectangular solids.

4.3 MEASUREMENT

4.3.1 estimate, measure, and solve problems using metric units for linear measure, area, mass/weight, and capacity.

Student demonstrations:

  • Demonstrate an understanding of metric units of measure.
  • Use the appropriate units of measurement.
  • Estimate and accurately measure length to the nearest meter or centimeter and calculate area.
  • Estimate and accurately measure mass/weight to the nearest gram.
  • Estimate and accurately measure capacity to the nearest millimeter.
  • Measure and read temperate accurately to the nearest degree using Celsius thermometer.

4.3.2 estimate, measure, and solve problems using standard units for linear measure, area, mass/weight, and capacity.

Student demonstrations:

  • Demonstrate an understanding of standard units of measure.
  • Use the appropriate units of measurement.
  • Estimate and accurately measure length tot he nearest yard, foot, inch, and
  • quarter inch and calculate area.
  • Estimate and accurately measure mass/weight to the nearest ounce and pound.
  • Estimate and accurately measure capacity to the nearest fluid ounce.

Measure and read temperature accurately to the nearest degree using Fahrenheit thermometer

4.3.3 tell correct time to the minute on an analog clock.

Student demonstration:

  • Figure elapsed time to the nearest quarter hour.

 

Data Analysis and Probability Standard for Grades 3—5

NCTM

Nebraska

Standard

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

Expectations

In grades 3—5 all students should–

By the end of fourth grade, students will

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

• design investigations to address a question and consider how data-collection methods affect the nature of the data set;

• collect data using observations, surveys, and experiments;

• represent data using tables and graphs such as line plots, bar graphs, and line graphs;

• recognize the differences in representing categorical and numerical data.

4.5 DATA ANALYSIS, PROBABILITY, AND STATISTICAL CONCEPTS

4.5.1 By the end of the fourth grade, students will collect, organize, represent, and interpret numerical and categorical data and clearly communicate the findings.

Student demonstration:

  • Collect, construct, and interpret data in line plots, tables, charts, and graphs, such as pie graphs, bar graphs, and pictographs.
  • Draw valid conclusions from displayed data.
  • Investigate and represent possible outcomes for a simple probability situation in an organized way, such as tables, grids, and tree diagrams.

Select and use appropriate statistical methods to analyze data

• describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed;

• use measures of center, focusing on the median, and understand what each does and does not indicate about the data set;

• compare different representations of the same data and evaluate how well each representation shows important aspects of the data.

 

Develop and evaluate inferences and predictions that are based on data.

• propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions.

 

Understand and apply basic concepts of probability

• describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible;

• predict the probability of outcomes of simple experiments and test the predictions;

• understand that the measure of the likelihood of an event can be represented by a number from 0 to 1