| Mathematics
The Nebraska K-12 Mathematics Standards are intended to reflect what students should know and be able to do by the end of grades 1, 4, 8, and 12. In addition to identifying grade-level specific standards, the content standards are further divided into six topic strands: Numeration/Number Sense; Computation/Estimation; Measurement; Geometry/Spatial Concepts; Data Analysis, Probability, and Statistical Concepts; and Algebraic Concepts. Topic strands are identified to help organize the standards. They should not to be confused with secondary course titles.
The Nebraska K-12 Mathematics Standards document is not a curriculum guide, defining what is taught at each grade level or prescribing how content should be taught. Standards are to guide local school districts and communities as they work together to set high expectations for ALL students and plan instruction that enables students to meet those expectations. ALL students must be equipped with the skills and knowledge that will permit them to enter an ever-changing job market. Teachers should relate mathematical concepts to their students' personal lives and help them apply concepts in real-life situations.
The following conceptual threads are assumed to be woven throughout the Mathematics Standards:
Problem Solving - The problem-solving process helps students learn mathematical concepts through clarification, formulation, representation, analysis, and communication. Problems can involve real situations or explore and extend mathematical ideas. To be successful, students must use a variety of methods and tools to do computations, including paper and pencil, mental arithmetic, memorization, estimation, and calculators. Technology should not be a substitute for a student's understanding of the basic facts.
Mathematical Communication - Mathematics is a language used to communicate ideas. Students should be asked to illustrate, demonstrate, describe and report their problem-solving strategies and processes. Students should use the correct concepts, skills, symbols, and vocabulary. Students should have the tools needed to collect, analyze and report data, conduct research, and explore mathematics. Graphing utilities, spreadsheets, calculators, computers, and other forms of technology allow all students to succeed. Technology must be an integral part of teaching and learning.
Mathematical Reasoning - Persuasive arguments, evaluating the arguments of others and estimation skills are important uses of mathematical reasoning used to verify reasonableness of answers.
Mathematical Connections - Using mathematical ideas in other disciplines and real life creates connections that make mathematics useful. Exploring connections helps students build concepts on past experiences.
Grade 4
The Grade 2-4 Mathematics Standards are intended to reflect what students should know and be able to do by the end of grade four.
The Intermediate 1 level of the Stanford Achievement Test, Ninth Edition (SAT-9) assesses students in either the spring of Grade 4 or the fall of Grade 5.
According the Reviewer's Edition of the assessment, there are two sections of Mathematics:
* Mathematics: Procedures
* Mathematics: Problem Solving
"At all levels, the emphasis in Stanford 9 mathematics is on assessing skills and concepts within the contexts that require those skills and concepts outside of the classroom. This assessment of student proficiency in a modern mathematics curriculum encourages students to value mathematics and supports sound instructional practice in the mathematics classroom."
In this course students explore the world of numbers, algorithms, patterns, shapes, data, and spatial sense. Students engage in activities involving operations with whole numbers, decimals, and fractions, measurement, estimation, making sense of real-world data (collecting, discussing, and making conclusions about data), conceptualizing and converting numbers in various forms, and justifying mathematics solutions by articulating the reasons behind the solutions. Course work includes using manipulatives to represent number sentences and other primitive algebraic concepts. The course emphasizes the need for students to make mathematical connections and to use mathematics principles to communicate, reason, and solve problems.
Algebraic Concepts
The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. This unit includes studying number systems, operations, and forms. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties.
Data Interpretation
The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. The Data Interpretation Unit includes data collection and classification, organization and display of data, logical reasoning and problem solving.
This unit includes presenting data in graphical forms and interpreting data given in graphical forms.
Decimals
The Decimals Unit includes Competencies/Objectives which focus on number sense and operations with decimals. The Decimals Unit includes comparison, computing, money, estimation, problem solving and reasoning.
This unit includes comparing decimals, performing operations with decimals, converting decimals to other number forms, using manipulatives to demonstrate decimals, and solving problems with decimals in real-world contexts.
Fractions
The Fractions Unit includes Competencies/Objectives which focus on number sense and operations with fractions. The Fractions Unit includes comparison, ordering, fractions parts, estimation, reasoning and problem solving.
This unit includes comparing fractions, performing computations with fractions, converting fractions to other number forms, using manipulatives to demonstrate fractions, and solving problems with fractions in real-world contexts.
Geometry
The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. The Geometry Unit includes properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving.
This unit includes exploring geometric concepts from multiple perspectives.
Integers
The Integers Unit includes Competencies/Objectives which focus on number sense and operations with integers. This unit includes comparing integers, performing operations with integers, converting integers to other number forms, using manipulatives to demonstrate integers, and solving problems with integers in real-world contexts.
Mathematics Processes
The Mathematics Processes Unit focuses on mathematical connections, communication, modeling, concepts and procedures.
Measurement
The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. The Measurement Unit includes concepts of length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns and problem solving.
This unit includes experimenting with formal, informal, customary, and metric units of measurement, and distinguishing between situations which call for exact measurement and those which call for estimation.
Number Theory
The Number Theory Unit focuses on manipulating number forms and classifications. Students make connections between number forms and their real-world applications.
This unit includes manipulating number forms and classifications. Students make connections between number forms and their real-world applications.
Numeration
The Numeration Unit focuses on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships.
This unit includes exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships.
Probability/Statistics
The Probability/Statistics Unit focuses on data analysis and probability concepts. This unit includes collecting, analyzing, and making sense of real-world data (including overlapping data, inconclusive data, etc.).
Problem Solving
The Problem Solving Unit focuses on the problem solving effort. This unit includes analyzing problems, evaluating solutions, problem exploration, and strategies.
Real Numbers and the Coordinate Plane
This unit includes graphing equations, and making connections between algebraic concepts and their geometric correspondences.
Whole Numbers
The Whole Numbers Unit includes performing operations with whole numbers, using manipulatives to demonstrate whole number concepts, and solving problems with whole numbers in real-world contexts.
This unit includes performing operations with whole numbers, using manipulatives to demonstrate whole number concepts, and solving problems with whole numbers in real-world contexts.
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