<?xml version="1.0" encoding="UTF-8"?>
<xsd:schema xmlns:xsd="http://www.w3.org/2001/XMLSchema" elementFormDefault="qualified" attributeFormDefault="unqualified" version="0.6.50">
	<xsd:annotation>
		<xsd:documentation>
		**********************************************************************  Schema Overview  **************************************************************
			Definition: 			Controlled vocabulary schema for DLESE metadata frameworks
			Framework use: 		ADN-I (item)
			Source org:			National Council of Teachers of Mathematics (NCTM); http://standards.nctm.org/index.htm/
			Vocab values:		http://standards.nctm.org/document/index.htm
			Vocab last update:	Unknown
			DPC last update:		2006-07-17 missing some words in copying; 2003-3-10
			Notes: 						
		</xsd:documentation>
	</xsd:annotation>
	<xsd:annotation>
		<xsd:documentation>*** LICENSE INFORMATION *****
		Copyright 2002, 2003 DLESE Program Center
		University Corporation for Atmospheric Research (UCAR)
		P.O. Box 3000, Boulder, CO 80307, United States of America
		email: support@dlese.org. 
These schemas are free software; you can redistribute them and/or modify them under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.  These schemas are distributed in the hope that they will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this project; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA  
		</xsd:documentation>
	</xsd:annotation>
	<xsd:annotation>
		<xsd:documentation>*********************** Hisotry of Change *****************************
2003-03-10: Changed and m-dash to a comma; see comments below.
2006-07-17: Updated word prob to problems; update word meaningsof to meanings of
2006-07-19: Updated operations, ways to operations:Understand numbers, ways
		</xsd:documentation>
	</xsd:annotation>
	<xsd:annotation>
		<xsd:documentation>***********************  Simple Types (alpha order) *************************************</xsd:documentation>
	</xsd:annotation>
	<xsd:simpleType name="NCTMmathContentStandardsType">
		<xsd:annotation>
			<xsd:documentation>
				***************************************  NCTMmathContentStandardsType  ***************************************
				Lists the values that will appear in the metadata record
			</xsd:documentation>
		</xsd:annotation>
		<xsd:restriction base="xsd:string">
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Count with understanding and recognize 'how many' in sets of objects"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Use multiple models to develop initial understandings of place value and the base-ten number system"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Connect number words and numerals to the quantities they represent, using various physical models and representations"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Understand meanings of operations and how they relate to one another:Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Understand meanings of operations and how they relate to one another:Understand the effects of adding and subtracting whole numbers"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Understand meanings of operations and how they relate to one another:Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Compute fluently and make reasonable estimates:Develop and use strategies for whole-number computations, with a focus on addition and subtraction"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Compute fluently and make reasonable estimates:Develop fluency with basic number combinations for addition and subtraction"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Number and operations:Compute fluently and make reasonable estimates:Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Algebra:Understand patterns, relations, and functions:Sort, classify, and order objects by size, number, and other properties"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Algebra:Understand patterns, relations, and functions:Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Algebra:Understand patterns, relations, and functions:Analyze how both repeating and growing patterns are generated"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Illustrate general principles and properties of operations, such as commutativity, using specific numbers"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Algebra: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"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Algebra:Analyze change in various contexts:Describe qualitative change, such as a student's growing taller"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Algebra:Analyze change in various contexts:Describe quantitative change, such as a student's growing two inches in one year"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry: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"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Describe attributes and parts of two- and three-dimensional shapes"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry: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"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Find and name locations with simple relationships such as 'near to' and in coordinate systems such as maps"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Recognize and apply slides, flips, and turns"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Recognize and create shapes that have symmetry"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Create mental images of geometric shapes using spatial memory and spatial visualization"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Recognize and represent shapes from different perspectives"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Relate ideas in geometry to ideas in number and measurement"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Recognize geometric shapes and structures in the environment and specify their location"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Recognize the attributes of length, volume, weight, area, and time"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Compare and order objects according to these attributes"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand how to measure using nonstandard and standard units"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Select an appropriate unit and tool for the attribute being measured"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Measurement: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"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements: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"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Use tools to measure"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop common referents for measures to make comparisons and estimates"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Data analysis and probability: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"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Sort and classify objects according to their attributes and organize data about the objects"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Represent data using concrete objects, pictures, and graphs"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Data analysis and probability: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"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Discuss events related to students' experiences as likely or unlikely"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Data analysis and probability:Understand and apply basic concepts of probability"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Problem solving:Build new mathematical knowledge through problem solving"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Problem solving:Solve problems that arise in mathematics and in other contexts"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Problem solving:Monitor and reflect on the process of mathematical problem solving"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Reasoning and proof:Make and investigate mathematical conjectures"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Reasoning and proof:Develop and evaluate mathematical arguments and proofs"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Reasoning and proof:Select and use various types of reasoning and methods of proof"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Communication:Organize and consolidate their mathematical thinking through communication"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Communication:Analyze and evaluate the mathematical thinking and strategies of others"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Connections:Recognize and use connections among mathematical ideas"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Connections:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Connections:Recognize and apply mathematics in contexts outside of mathematics"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Representation:Create and use representations to organize, record, and communicate mathematical ideas"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Representation:Select, apply, and translate among mathematical representations to solve problems"/>
			<xsd:enumeration value="NCTM:Pre-K-2:Representation:Use representations to model and interpret physical, social, and mathematical phenomena"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations: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"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Recognize equivalent representations for the same number and generate them by decomposing and composing numbers"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems: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"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Use models, benchmarks, and equivalent forms to judge the size of fractions"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Recognize and generate equivalent forms of commonly used fractions, decimals, and percents"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Explore numbers less than 0 by extending the number line and through familiar applications"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Describe classes of numbers according to characteristics such as the nature of their factors"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Understand meanings of operations and how they relate to one another:Understand various meanings of multiplication and division"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Understand meanings of operations and how they relate to one another:Understand the effects of multiplying and dividing whole numbers"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Understand meanings of operations and how they relate to one another:Identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Understand meanings of operations and how they relate to one another:Understand and use properties of operations, such as the distributivity of multiplication over addition"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations: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 30 x 50"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Compute fluently and make reasonable estimates:Develop fluency in adding, subtracting, multiplying, and dividing whole numbers"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Compute fluently and make reasonable estimates:Develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Compute fluently and make reasonable estimates:Develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Compute fluently and make reasonable estimates:Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals"/>
			<xsd:enumeration value="NCTM:3-5:Number and operations:Compute fluently and make reasonable estimates: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"/>
			<xsd:enumeration value="NCTM:3-5:Algebra:Understand patterns, relations, and functions:Describe, extend, and make generalizations about geometric and numeric patterns"/>
			<xsd:enumeration value="NCTM:3-5:Algebra:Understand patterns, relations, and functions:Represent and analyze patterns and functions, using words, tables, and graphs"/>
			<xsd:enumeration value="NCTM:3-5:Algebra: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"/>
			<xsd:enumeration value="NCTM:3-5:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Represent the idea of a variable as an unknown quantity using a letter or a symbol"/>
			<xsd:enumeration value="NCTM:3-5:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Express mathematical relationships using equations"/>
			<xsd:enumeration value="NCTM:3-5:Algebra: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"/>
			<xsd:enumeration value="NCTM:3-5:Algebra:Analyze change in various contexts:Investigate how a change in one variable relates to a change in a second variable"/>
			<xsd:enumeration value="NCTM:3-5:Algebra:Analyze change in various contexts:Identify and describe situations with constant or varying rates of change and compare them"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about:Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about:Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about:Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about:Explore congruence and similarity"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about:Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Describe location and movement using common language and geometric vocabulary"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Make and use coordinate systems to specify locations and to describe paths"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Find the distance between points along horizontal and vertical lines of a coordinate system"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Predict and describe the results of sliding, flipping, and turning two-dimensional shapes"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Describe a motion or a series of motions that will show that two shapes are congruent"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Build and draw geometric objects"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Create and describe mental images of objects, patterns, and paths"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Identify and build a three-dimensional object from two-dimensional representations of that object"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Identify and draw a two-dimensional representation of a three-dimensional object"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use geometric models to solve problems in other areas of mathematics, such as number and measurement"/>
			<xsd:enumeration value="NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life"/>
			<xsd:enumeration value="NCTM:3-5:Measurement: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"/>
			<xsd:enumeration value="NCTM:3-5:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems"/>
			<xsd:enumeration value="NCTM:3-5:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Carry out simple unit conversions, such as from centimeters to meters, within a system of measurement"/>
			<xsd:enumeration value="NCTM:3-5:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand that measurements are approximations and how differences in units affect precision"/>
			<xsd:enumeration value="NCTM:3-5:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way"/>
			<xsd:enumeration value="NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes"/>
			<xsd:enumeration value="NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles"/>
			<xsd:enumeration value="NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Select and use benchmarks to estimate measurements"/>
			<xsd:enumeration value="NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms"/>
			<xsd:enumeration value="NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop strategies to determine the surface areas and volumes of rectangular solids"/>
			<xsd:enumeration value="NCTM:3-5:Data analysis and probability: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"/>
			<xsd:enumeration value="NCTM:3-5:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Collect data using observations, surveys, and experiments"/>
			<xsd:enumeration value="NCTM:3-5:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Represent data using tables and graphs such as line plots, bar graphs, and line graphs"/>
			<xsd:enumeration value="NCTM:3-5:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Recognize the differences in representing categorical and numerical data"/>
			<xsd:enumeration value="NCTM:3-5:Data analysis and probability: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"/>
			<xsd:enumeration value="NCTM:3-5:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set"/>
			<xsd:enumeration value="NCTM:3-5:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Compare different representations of the same data and evaluate how well each representation shows important aspects of the data"/>
			<xsd:enumeration value="NCTM:3-5:Data analysis and probability: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"/>
			<xsd:enumeration value="NCTM:3-5:Data analysis and probability: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"/>
			<xsd:enumeration value="NCTM:3-5:Data analysis and probability:Understand and apply basic concepts of probability:Predict the probability of outcomes of simple experiments and test the predictions"/>
			<xsd:enumeration value="NCTM:3-5:Data analysis and probability:Understand and apply basic concepts of probability:Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1"/>
			<xsd:enumeration value="NCTM:3-5:Problem solving:Build new mathematical knowledge through problem solving"/>
			<xsd:enumeration value="NCTM:3-5:Problem solving:Solve problems that arise in mathematics and in other contexts"/>
			<xsd:enumeration value="NCTM:3-5:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems"/>
			<xsd:enumeration value="NCTM:3-5:Problem solving:Monitor and reflect on the process of mathematical problem solving"/>
			<xsd:enumeration value="NCTM:3-5:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics"/>
			<xsd:enumeration value="NCTM:3-5:Reasoning and proof:Make and investigate mathematical conjectures"/>
			<xsd:enumeration value="NCTM:3-5:Reasoning and proof:Develop and evaluate mathematical arguments and proofs"/>
			<xsd:enumeration value="NCTM:3-5:Reasoning and proof:Select and use various types of reasoning and methods of proof"/>
			<xsd:enumeration value="NCTM:3-5:Communication:Organize and consolidate their mathematical thinking through communication"/>
			<xsd:enumeration value="NCTM:3-5:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others"/>
			<xsd:enumeration value="NCTM:3-5:Communication:Analyze and evaluate the mathematical thinking and strategies of others"/>
			<xsd:enumeration value="NCTM:3-5:Communication:Use the language of mathematics to express mathematical ideas precisely"/>
			<xsd:enumeration value="NCTM:3-5:Connections:Recognize and use connections among mathematical ideas"/>
			<xsd:enumeration value="NCTM:3-5:Connections:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole"/>
			<xsd:enumeration value="NCTM:3-5:Connections:Recognize and apply mathematics in contexts outside of mathematics"/>
			<xsd:enumeration value="NCTM:3-5:Representation:Create and use representations to organize, record, and communicate mathematical ideas"/>
			<xsd:enumeration value="NCTM:3-5:Representation:Select, apply, and translate among mathematical representations to solve problems"/>
			<xsd:enumeration value="NCTM:3-5:Representation:Use representations to model and interpret physical, social, and mathematical phenomena"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Work flexibly with fractions, decimals, and percents to solve problems"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop meaning for percents greater than 100 and less than 1"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Understand and use ratios and proportions to represent quantitative relationships"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Use factors, multiples, prime factorization, and relatively prime numbers to solve problems"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop meaning for integers and represent and compare quantities with them"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Understand meanings of operations and how they relate to one another:Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Understand meanings of operations and how they relate to one another:Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Understand meanings of operations and how they relate to one another:Understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Compute fluently and make reasonable estimates:Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Compute fluently and make reasonable estimates:Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Compute fluently and make reasonable estimates:Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results"/>
			<xsd:enumeration value="NCTM:6-8:Number and operations:Compute fluently and make reasonable estimates:Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios"/>
			<xsd:enumeration value="NCTM:6-8:Algebra:Understand patterns, relations, and functions:Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules"/>
			<xsd:enumeration value="NCTM:6-8:Algebra:Understand patterns, relations, and functions:Relate and compare different forms of representation for a relationship"/>
			<xsd:enumeration value="NCTM:6-8:Algebra:Understand patterns, relations, and functions:Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations"/>
			<xsd:enumeration value="NCTM:6-8:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Develop an initial conceptual understanding of different uses of variables"/>
			<xsd:enumeration value="NCTM:6-8:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope"/>
			<xsd:enumeration value="NCTM:6-8:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships"/>
			<xsd:enumeration value="NCTM:6-8:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations"/>
			<xsd:enumeration value="NCTM:6-8:Algebra:Use mathematical models to represent and understand quantitative relationships:Model and solve contextualized problems using various representations, such as graphs, tables, and equations"/>
			<xsd:enumeration value="NCTM:6-8:Algebra:Analyze change in various contexts:Use graphs to analyze the nature of changes in quantities in linear relationships"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Use coordinate geometry to represent and examine the properties of geometric shapes"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Examine the congruence, similarity, and line or rotational symmetry of objects using transformations"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Draw geometric objects with specified properties, such as side lengths or angle measures"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use visual tools such as networks to represent and solve problems"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use geometric models to represent and explain numerical and algebraic relationships"/>
			<xsd:enumeration value="NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life"/>
			<xsd:enumeration value="NCTM:6-8:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand both metric and customary systems of measurement"/>
			<xsd:enumeration value="NCTM:6-8:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand relationships among units and convert from one unit to another within the same system"/>
			<xsd:enumeration value="NCTM:6-8:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume"/>
			<xsd:enumeration value="NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Use common benchmarks to select appropriate methods for estimating measurements"/>
			<xsd:enumeration value="NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision"/>
			<xsd:enumeration value="NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes"/>
			<xsd:enumeration value="NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders"/>
			<xsd:enumeration value="NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Solve problems involving scale factors, using ratio and proportion"/>
			<xsd:enumeration value="NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Solve simple problems involving rates and derived measurements for such attributes as velocity and density"/>
			<xsd:enumeration value="NCTM:6-8:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population"/>
			<xsd:enumeration value="NCTM:6-8:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots"/>
			<xsd:enumeration value="NCTM:6-8:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Find, use, and interpret measures of center and spread, including mean and interquartile range"/>
			<xsd:enumeration value="NCTM:6-8:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots"/>
			<xsd:enumeration value="NCTM:6-8:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken"/>
			<xsd:enumeration value="NCTM:6-8:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit"/>
			<xsd:enumeration value="NCTM:6-8:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Use conjectures to formulate new questions and plan new studies to answer them"/>
			<xsd:enumeration value="NCTM:6-8:Data analysis and probability:Understand and apply basic concepts of probability:Understand and use appropriate terminology to describe complementary and mutually exclusive events"/>
			<xsd:enumeration value="NCTM:6-8:Data analysis and probability:Understand and apply basic concepts of probability:Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations"/>
			<xsd:enumeration value="NCTM:6-8:Data analysis and probability:Understand and apply basic concepts of probability:Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models"/>
			<xsd:enumeration value="NCTM:6-8:Problem solving:Build new mathematical knowledge through problem solving"/>
			<xsd:enumeration value="NCTM:6-8:Problem solving:Solve problems that arise in mathematics and in other contexts"/>
			<xsd:enumeration value="NCTM:6-8:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems"/>
			<xsd:enumeration value="NCTM:6-8:Problem solving:Monitor and reflect on the process of mathematical problem solving"/>
			<xsd:enumeration value="NCTM:6-8:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics"/>
			<xsd:enumeration value="NCTM:6-8:Reasoning and proof:Make and investigate mathematical conjectures"/>
			<xsd:enumeration value="NCTM:6-8:Reasoning and proof:Develop and evaluate mathematical arguments and proofs"/>
			<xsd:enumeration value="NCTM:6-8:Reasoning and proof:Select and use various types of reasoning and methods of proof"/>
			<xsd:enumeration value="NCTM:6-8:Communication:Organize and consolidate their mathematical thinking through communication"/>
			<xsd:enumeration value="NCTM:6-8:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others"/>
			<xsd:enumeration value="NCTM:6-8:Communication:Analyze and evaluate the mathematical thinking and strategies of others"/>
			<xsd:enumeration value="NCTM:6-8:Communication:Use the language of mathematics to express mathematical ideas precisely"/>
			<xsd:enumeration value="NCTM:6-8:Connections:Recognize and use connections among mathematical ideas"/>
			<xsd:enumeration value="NCTM:6-8:Connections:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole"/>
			<xsd:enumeration value="NCTM:6-8:Connections:Recognize and apply mathematics in contexts outside of mathematics"/>
			<xsd:enumeration value="NCTM:6-8:Representation:Create and use representations to organize, record, and communicate mathematical ideas"/>
			<xsd:enumeration value="NCTM:6-8:Representation:Select, apply, and translate among mathematical representations to solve problems"/>
			<xsd:enumeration value="NCTM:6-8:Representation:Use representations to model and interpret physical, social, and mathematical phenomena"/>
			<xsd:enumeration value="NCTM:9-12:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Understand numbers:Develop a deeper understanding of very large and very small numbers and of various representations of them"/>
			<xsd:enumeration value="NCTM:9-12:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions"/>
			<xsd:enumeration value="NCTM:9-12:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Understand vectors and matrices as systems that have some of the properties of the real-number system"/>
			<xsd:enumeration value="NCTM:9-12:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Use number-theory arguments to justify relationships involving whole numbers"/>
			<xsd:enumeration value="NCTM:9-12:Number and operations:Understand meanings of operations and how they relate to one another:Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities"/>
			<xsd:enumeration value="NCTM:9-12:Number and operations:Understand meanings of operations and how they relate to one another:Develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices"/>
			<xsd:enumeration value="NCTM:9-12:Number and operations:Understand meanings of operations and how they relate to one another:Develop an understanding of permutations and combinations as counting techniques"/>
			<xsd:enumeration value="NCTM:9-12:Number and operations:Compute fluently and make reasonable estimates:Develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases"/>
			<xsd:enumeration value="NCTM:9-12:Number and operations:Compute fluently and make reasonable estimates:Judge the reasonableness of numerical computations and their results"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Understand patterns, relations, and functions:Generalize patterns using explicitly defined and recursively defined functions"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Understand patterns, relations, and functions:Understand relations and functions and select, convert flexibly among, and use various representations for them"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Understand patterns, relations, and functions:Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Understand patterns, relations, and functions:Understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Understand patterns, relations, and functions:Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Understand patterns, relations, and functions:Interpret representations of functions of two variables"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations"/>
			<!--In the next benchmark the m-dash symbol between 'fluency' and 'mentally' was changed to a comma in order to validate the schema file. This does not really change the meaning of the standard-->
			<xsd:enumeration value="NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency, mentally or with paper and pencil in simple cases and using technology in all cases"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Use symbolic algebra to represent and explain mathematical relationships"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Use a variety of symbolic representations, including recursive and parametric equations, for functions and relations"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Use mathematical models to represent and understand quantitative relationships:Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Use mathematical models to represent and understand quantitative relationships:Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Use mathematical models to represent and understand quantitative relationships:Draw reasonable conclusions about a situation being modeled"/>
			<xsd:enumeration value="NCTM:9-12:Algebra:Analyze change in various contexts:Approximate and interpret rates of change from graphical and numerical data"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Analyze properties and determine attributes of two- and three-dimensional objects"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Analyze characteristics:Use trigonometric relationships to determine lengths and angle measures"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Use various representations to help understand the effects of simple transformations and their compositions"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use vertex-edge graphs to model and solve problems"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use geometric models to gain insights into, and answer questions in, other areas of mathematics"/>
			<xsd:enumeration value="NCTM:9-12:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture"/>
			<xsd:enumeration value="NCTM:9-12:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Make decisions about units and scales that are appropriate for problem situations involving measurement"/>
			<xsd:enumeration value="NCTM:9-12:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Analyze precision, accuracy, and approximate error in measurement situations"/>
			<xsd:enumeration value="NCTM:9-12:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders"/>
			<xsd:enumeration value="NCTM:9-12:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations"/>
			<xsd:enumeration value="NCTM:9-12:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Use unit analysis to check measurement computations"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Understand histograms, parallel box plots, and scatterplots and use them to display data"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Compute basic statistics and understand the distinction between a statistic and a parameter"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Select and use appropriate statistical methods to analyze data:For univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Select and use appropriate statistical methods to analyze data:For bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Display and discuss bivariate data where at least one variable is categorical"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Recognize how linear transformations of univariate data affect shape, center, and spread"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Understand how basic statistical techniques are used to monitor process characteristics in the workplace"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Use simulations to construct empirical probability distributions"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Compute and interpret the expected value of random variables in simple cases"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Understand the concepts of conditional probability and independent events"/>
			<xsd:enumeration value="NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Understand how to compute the probability of a compound event"/>
			<xsd:enumeration value="NCTM:9-12:Problem solving:Build new mathematical knowledge through problem solving"/>
			<xsd:enumeration value="NCTM:9-12:Problem solving:Solve problems that arise in mathematics and in other contexts"/>
			<xsd:enumeration value="NCTM:9-12:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems"/>
			<xsd:enumeration value="NCTM:9-12:Problem solving:Monitor and reflect on the process of mathematical problem solving"/>
			<xsd:enumeration value="NCTM:9-12:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics"/>
			<xsd:enumeration value="NCTM:9-12:Reasoning and proof:Make and investigate mathematical conjectures"/>
			<xsd:enumeration value="NCTM:9-12:Reasoning and proof:Develop and evaluate mathematical arguments and proofs"/>
			<xsd:enumeration value="NCTM:9-12:Reasoning and proof:Select and use various types of reasoning and methods of proof"/>
			<xsd:enumeration value="NCTM:9-12:Communication:Organize and consolidate their mathematical thinking through communication"/>
			<xsd:enumeration value="NCTM:9-12:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others"/>
			<xsd:enumeration value="NCTM:9-12:Communication:Analyze and evaluate the mathematical thinking and strategies of others"/>
			<xsd:enumeration value="NCTM:9-12:Communication:Use the language of mathematics to express mathematical ideas precisely"/>
			<xsd:enumeration value="NCTM:9-12:Connection:Recognize and use connections among mathematical ideas"/>
			<xsd:enumeration value="NCTM:9-12:Connection:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole"/>
			<xsd:enumeration value="NCTM:9-12:Connection:Recognize and apply mathematics in contexts outside of mathematics"/>
			<xsd:enumeration value="NCTM:9-12:Representation:Create and use representations to organize, record, and communicate mathematical ideas"/>
			<xsd:enumeration value="NCTM:9-12:Representation:Select, apply, and translate among mathematical representations to solve problems"/>
			<xsd:enumeration value="NCTM:9-12:Representation:Use representations to model and interpret physical, social, and mathematical phenomena"/>
		</xsd:restriction>
	</xsd:simpleType>
	<xsd:simpleType name="NCTMmathContentStandardsLeafType">
		<xsd:annotation>
			<xsd:documentation>
				***************************************  NCTMmathContentStandardsLeafType  ***************************************
				Lists leaf values
			</xsd:documentation>
		</xsd:annotation>
		<xsd:restriction base="xsd:string">
			<xsd:enumeration value="Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Count with understanding and recognize 'how many' in sets of objects"/>
			<xsd:enumeration value="Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Use multiple models to develop initial understandings of place value and the base-ten number system"/>
			<xsd:enumeration value="Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections"/>
			<xsd:enumeration value="Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers"/>
			<xsd:enumeration value="Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Connect number words and numerals to the quantities they represent, using various physical models and representations"/>
			<xsd:enumeration value="Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2"/>
			<xsd:enumeration value="Understand meanings of operations and how they relate to one another:Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations"/>
			<xsd:enumeration value="Understand meanings of operations and how they relate to one another:Understand the effects of adding and subtracting whole numbers"/>
			<xsd:enumeration value="Understand meanings of operations and how they relate to one another:Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally"/>
			<xsd:enumeration value="Compute fluently and make reasonable estimates:Develop and use strategies for whole-number computations, with a focus on addition and subtraction"/>
			<xsd:enumeration value="Compute fluently and make reasonable estimates:Develop fluency with basic number combinations for addition and subtraction"/>
			<xsd:enumeration value="Compute fluently and make reasonable estimates:Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators"/>
			<xsd:enumeration value="Sort, classify, and order objects by size, number, and other properties"/>
			<xsd:enumeration value="Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another"/>
			<xsd:enumeration value="Analyze how both repeating and growing patterns are generated"/>
			<xsd:enumeration value="Illustrate general principles and properties of operations, such as commutativity, using specific numbers"/>
			<xsd:enumeration value="Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations"/>
			<xsd:enumeration value="Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols"/>
			<xsd:enumeration value="Describe qualitative change, such as a student's growing taller"/>
			<xsd:enumeration value="Describe quantitative change, such as a student's growing two inches in one year"/>
			<xsd:enumeration value="Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes"/>
			<xsd:enumeration value="Describe attributes and parts of two- and three-dimensional shapes"/>
			<xsd:enumeration value="Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes"/>
			<xsd:enumeration value="Describe, name, and interpret relative positions in space and apply ideas about relative position"/>
			<xsd:enumeration value="Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance"/>
			<xsd:enumeration value="Find and name locations with simple relationships such as 'near to' and in coordinate systems such as maps"/>
			<xsd:enumeration value="Recognize and apply slides, flips, and turns"/>
			<xsd:enumeration value="Recognize and create shapes that have symmetry"/>
			<xsd:enumeration value="Create mental images of geometric shapes using spatial memory and spatial visualization"/>
			<xsd:enumeration value="Recognize and represent shapes from different perspectives"/>
			<xsd:enumeration value="Relate ideas in geometry to ideas in number and measurement"/>
			<xsd:enumeration value="Recognize geometric shapes and structures in the environment and specify their location"/>
			<xsd:enumeration value="Recognize the attributes of length, volume, weight, area, and time"/>
			<xsd:enumeration value="Compare and order objects according to these attributes"/>
			<xsd:enumeration value="Understand how to measure using nonstandard and standard units"/>
			<xsd:enumeration value="Select an appropriate unit and tool for the attribute being measured"/>
			<xsd:enumeration value="Measure with multiple copies of units of the same size, such as paper clips laid end to end"/>
			<xsd:enumeration value="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"/>
			<xsd:enumeration value="Use tools to measure"/>
			<xsd:enumeration value="Develop common referents for measures to make comparisons and estimates"/>
			<xsd:enumeration value="Pose questions and gather data about themselves and their surroundings"/>
			<xsd:enumeration value="Sort and classify objects according to their attributes and organize data about the objects"/>
			<xsd:enumeration value="Represent data using concrete objects, pictures, and graphs"/>
			<xsd:enumeration value="Describe parts of the data and the set of data as a whole to determine what the data show"/>
			<xsd:enumeration value="Discuss events related to students' experiences as likely or unlikely"/>
			<xsd:enumeration value="Understand and apply basic concepts of probability"/>
			<xsd:enumeration value="Build new mathematical knowledge through problem solving"/>
			<xsd:enumeration value="Solve problems that arise in mathematics and in other contexts"/>
			<xsd:enumeration value="Apply and adapt a variety of appropriate strategies to solve problems"/>
			<xsd:enumeration value="Monitor and reflect on the process of mathematical problem solving"/>
			<xsd:enumeration value="Recognize reasoning and proof as fundamental aspects of mathematics"/>
			<xsd:enumeration value="Make and investigate mathematical conjectures"/>
			<xsd:enumeration value="Develop and evaluate mathematical arguments and proofs"/>
			<xsd:enumeration value="Select and use various types of reasoning and methods of proof"/>
			<xsd:enumeration value="Organize and consolidate their mathematical thinking through communication"/>
			<xsd:enumeration value="Communicate their mathematical thinking coherently and clearly to peers, teachers, and others"/>
			<xsd:enumeration value="Analyze and evaluate the mathematical thinking and strategies of others"/>
			<xsd:enumeration value="Recognize and use connections among mathematical ideas"/>
			<xsd:enumeration value="Understand how mathematical ideas interconnect and build on one another to produce a coherent whole"/>
			<xsd:enumeration value="Recognize and apply mathematics in contexts outside of mathematics"/>
			<xsd:enumeration value="Create and use representations to organize, record, and communicate mathematical ideas"/>
			<xsd:enumeration value="Select, apply, and translate among mathematical representations to solve problems"/>
			<xsd:enumeration value="Use representations to model and interpret physical, social, and mathematical phenomena"/>
			<xsd:enumeration value="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"/>
			<xsd:enumeration value="Recognize equivalent representations for the same number and generate them by decomposing and composing numbers"/>
			<xsd:enumeration value="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"/>
			<xsd:enumeration value="Use models, benchmarks, and equivalent forms to judge the size of fractions"/>
			<xsd:enumeration value="Recognize and generate equivalent forms of commonly used fractions, decimals, and percents"/>
			<xsd:enumeration value="Explore numbers less than 0 by extending the number line and through familiar applications"/>
			<xsd:enumeration value="Describe classes of numbers according to characteristics such as the nature of their factors"/>
			<xsd:enumeration value="Understand various meanings of multiplication and division"/>
			<xsd:enumeration value="Understand the effects of multiplying and dividing whole numbers"/>
			<xsd:enumeration value="Identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems"/>
			<xsd:enumeration value="Understand and use properties of operations, such as the distributivity of multiplication over addition"/>
			<xsd:enumeration value="Develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 x 50"/>
			<xsd:enumeration value="Develop fluency in adding, subtracting, multiplying, and dividing whole numbers"/>
			<xsd:enumeration value="Develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results"/>
			<xsd:enumeration value="Develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience"/>
			<xsd:enumeration value="Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals"/>
			<xsd:enumeration value="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"/>
			<xsd:enumeration value="Describe, extend, and make generalizations about geometric and numeric patterns"/>
			<xsd:enumeration value="Represent and analyze patterns and functions, using words, tables, and graphs"/>
			<xsd:enumeration value="Identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers"/>
			<xsd:enumeration value="Represent the idea of a variable as an unknown quantity using a letter or a symbol"/>
			<xsd:enumeration value="Express mathematical relationships using equations"/>
			<xsd:enumeration value="Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions"/>
			<xsd:enumeration value="Investigate how a change in one variable relates to a change in a second variable"/>
			<xsd:enumeration value="Identify and describe situations with constant or varying rates of change and compare them"/>
			<xsd:enumeration value="Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes"/>
			<xsd:enumeration value="Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids"/>
			<xsd:enumeration value="Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes"/>
			<xsd:enumeration value="Explore congruence and similarity"/>
			<xsd:enumeration value="Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions"/>
			<xsd:enumeration value="Describe location and movement using common language and geometric vocabulary"/>
			<xsd:enumeration value="Make and use coordinate systems to specify locations and to describe paths"/>
			<xsd:enumeration value="Find the distance between points along horizontal and vertical lines of a coordinate system"/>
			<xsd:enumeration value="Predict and describe the results of sliding, flipping, and turning two-dimensional shapes"/>
			<xsd:enumeration value="Describe a motion or a series of motions that will show that two shapes are congruent"/>
			<xsd:enumeration value="Identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs"/>
			<xsd:enumeration value="Build and draw geometric objects"/>
			<xsd:enumeration value="Create and describe mental images of objects, patterns, and paths"/>
			<xsd:enumeration value="Identify and build a three-dimensional object from two-dimensional representations of that object"/>
			<xsd:enumeration value="Identify and draw a two-dimensional representation of a three-dimensional object"/>
			<xsd:enumeration value="Use geometric models to solve problems in other areas of mathematics, such as number and measurement"/>
			<xsd:enumeration value="Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life"/>
			<xsd:enumeration value="Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute"/>
			<xsd:enumeration value="Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems"/>
			<xsd:enumeration value="Carry out simple unit conversions, such as from centimeters to meters, within a system of measurement"/>
			<xsd:enumeration value="Understand that measurements are approximations and how differences in units affect precision"/>
			<xsd:enumeration value="Explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way"/>
			<xsd:enumeration value="Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes"/>
			<xsd:enumeration value="Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles"/>
			<xsd:enumeration value="Select and use benchmarks to estimate measurements"/>
			<xsd:enumeration value="Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms"/>
			<xsd:enumeration value="Develop strategies to determine the surface areas and volumes of rectangular solids"/>
			<xsd:enumeration value="Design investigations to address a question and consider how data-collection methods affect the nature of the data set"/>
			<xsd:enumeration value="Collect data using observations, surveys, and experiments"/>
			<xsd:enumeration value="Represent data using tables and graphs such as line plots, bar graphs, and line graphs"/>
			<xsd:enumeration value="Recognize the differences in representing categorical and numerical data"/>
			<xsd:enumeration value="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"/>
			<xsd:enumeration value="Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set"/>
			<xsd:enumeration value="Compare different representations of the same data and evaluate how well each representation shows important aspects of the data"/>
			<xsd:enumeration value="Propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions"/>
			<xsd:enumeration value="Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible"/>
			<xsd:enumeration value="Predict the probability of outcomes of simple experiments and test the predictions"/>
			<xsd:enumeration value="Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1"/>
			<xsd:enumeration value="Build new mathematical knowledge through problem solving"/>
			<xsd:enumeration value="Solve problems that arise in mathematics and in other contexts"/>
			<xsd:enumeration value="Apply and adapt a variety of appropriate strategies to solve problems"/>
			<xsd:enumeration value="Monitor and reflect on the process of mathematical problem solving"/>
			<xsd:enumeration value="Recognize reasoning and proof as fundamental aspects of mathematics"/>
			<xsd:enumeration value="Make and investigate mathematical conjectures"/>
			<xsd:enumeration value="Develop and evaluate mathematical arguments and proofs"/>
			<xsd:enumeration value="Select and use various types of reasoning and methods of proof"/>
			<xsd:enumeration value="Organize and consolidate their mathematical thinking through communication"/>
			<xsd:enumeration value="Communicate their mathematical thinking coherently and clearly to peers, teachers, and others"/>
			<xsd:enumeration value="Analyze and evaluate the mathematical thinking and strategies of others"/>
			<xsd:enumeration value="Use the language of mathematics to express mathematical ideas precisely"/>
			<xsd:enumeration value="Recognize and use connections among mathematical ideas"/>
			<xsd:enumeration value="Understand how mathematical ideas interconnect and build on one another to produce a coherent whole"/>
			<xsd:enumeration value="Recognize and apply mathematics in contexts outside of mathematics"/>
			<xsd:enumeration value="Create and use representations to organize, record, and communicate mathematical ideas"/>
			<xsd:enumeration value="Select, apply, and translate among mathematical representations to solve prob"/>
			<xsd:enumeration value="Use representations to model and interpret physical, social, and mathematical phenomena"/>
			<xsd:enumeration value="Work flexibly with fractions, decimals, and percents to solve problems"/>
			<xsd:enumeration value="Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line"/>
			<xsd:enumeration value="Develop meaning for percents greater than 100 and less than 1"/>
			<xsd:enumeration value="Understand and use ratios and proportions to represent quantitative relationships"/>
			<xsd:enumeration value="Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation"/>
			<xsd:enumeration value="Use factors, multiples, prime factorization, and relatively prime numbers to solve problems"/>
			<xsd:enumeration value="Develop meaning for integers and represent and compare quantities with them"/>
			<xsd:enumeration value="Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers"/>
			<xsd:enumeration value="Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals"/>
			<xsd:enumeration value="Understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems"/>
			<xsd:enumeration value="Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods"/>
			<xsd:enumeration value="Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use"/>
			<xsd:enumeration value="Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results"/>
			<xsd:enumeration value="Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios"/>
			<xsd:enumeration value="Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules"/>
			<xsd:enumeration value="Relate and compare different forms of representation for a relationship"/>
			<xsd:enumeration value="Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations"/>
			<xsd:enumeration value="Develop an initial conceptual understanding of different uses of variables"/>
			<xsd:enumeration value="Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope"/>
			<xsd:enumeration value="Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships"/>
			<xsd:enumeration value="Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations"/>
			<xsd:enumeration value="Model and solve contextualized problems using various representations, such as graphs, tables, and equations"/>
			<xsd:enumeration value="Use graphs to analyze the nature of changes in quantities in linear relationships"/>
			<xsd:enumeration value="Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties"/>
			<xsd:enumeration value="Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects"/>
			<xsd:enumeration value="Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship"/>
			<xsd:enumeration value="Use coordinate geometry to represent and examine the properties of geometric shapes"/>
			<xsd:enumeration value="Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides"/>
			<xsd:enumeration value="Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling"/>
			<xsd:enumeration value="Examine the congruence, similarity, and line or rotational symmetry of objects using transformations"/>
			<xsd:enumeration value="Draw geometric objects with specified properties, such as side lengths or angle measures"/>
			<xsd:enumeration value="Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume"/>
			<xsd:enumeration value="Use visual tools such as networks to represent and solve problems"/>
			<xsd:enumeration value="Use geometric models to represent and explain numerical and algebraic relationships"/>
			<xsd:enumeration value="Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life"/>
			<xsd:enumeration value="Understand both metric and customary systems of measurement"/>
			<xsd:enumeration value="Understand relationships among units and convert from one unit to another within the same system"/>
			<xsd:enumeration value="Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume"/>
			<xsd:enumeration value="Use common benchmarks to select appropriate methods for estimating measurements"/>
			<xsd:enumeration value="Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision"/>
			<xsd:enumeration value="Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes"/>
			<xsd:enumeration value="Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders"/>
			<xsd:enumeration value="Solve problems involving scale factors, using ratio and proportion"/>
			<xsd:enumeration value="Solve simple problems involving rates and derived measurements for such attributes as velocity and density"/>
			<xsd:enumeration value="Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population"/>
			<xsd:enumeration value="Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots"/>
			<xsd:enumeration value="Find, use, and interpret measures of center and spread, including mean and interquartile range"/>
			<xsd:enumeration value="Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots"/>
			<xsd:enumeration value="Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken"/>
			<xsd:enumeration value="Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit"/>
			<xsd:enumeration value="Use conjectures to formulate new questions and plan new studies to answer them"/>
			<xsd:enumeration value="Understand and use appropriate terminology to describe complementary and mutually exclusive events"/>
			<xsd:enumeration value="Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations"/>
			<xsd:enumeration value="Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models"/>
			<xsd:enumeration value="Build new mathematical knowledge through problem solving"/>
			<xsd:enumeration value="Solve problems that arise in mathematics and in other contexts"/>
			<xsd:enumeration value="Apply and adapt a variety of appropriate strategies to solve problems"/>
			<xsd:enumeration value="Monitor and reflect on the process of mathematical problem solving"/>
			<xsd:enumeration value="Recognize reasoning and proof as fundamental aspects of mathematics"/>
			<xsd:enumeration value="Make and investigate mathematical conjectures"/>
			<xsd:enumeration value="Develop and evaluate mathematical arguments and proofs"/>
			<xsd:enumeration value="Select and use various types of reasoning and methods of proof"/>
			<xsd:enumeration value="Organize and consolidate their mathematical thinking through communication"/>
			<xsd:enumeration value="Communicate their mathematical thinking coherently and clearly to peers, teachers, and others"/>
			<xsd:enumeration value="Analyze and evaluate the mathematical thinking and strategies of others"/>
			<xsd:enumeration value="Use the language of mathematics to express mathematical ideas precisely"/>
			<xsd:enumeration value="Recognize and use connections among mathematical ideas"/>
			<xsd:enumeration value="Understand how mathematical ideas interconnect and build on one another to produce a coherent whole"/>
			<xsd:enumeration value="Recognize and apply mathematics in contexts outside of mathematics"/>
			<xsd:enumeration value="Create and use representations to organize, record, and communicate mathematical ideas"/>
			<xsd:enumeration value="Select, apply, and translate among mathematical representations to solve problems"/>
			<xsd:enumeration value="Use representations to model and interpret physical, social, and mathematical phenomena"/>
			<xsd:enumeration value="Develop a deeper understanding of very large and very small numbers and of various representations of them"/>
			<xsd:enumeration value="Compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions"/>
			<xsd:enumeration value="Understand vectors and matrices as systems that have some of the properties of the real-number system"/>
			<xsd:enumeration value="Use number-theory arguments to justify relationships involving whole numbers"/>
			<xsd:enumeration value="Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities"/>
			<xsd:enumeration value="Develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices"/>
			<xsd:enumeration value="Develop an understanding of permutations and combinations as counting techniques"/>
			<xsd:enumeration value="Develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases"/>
			<xsd:enumeration value="Judge the reasonableness of numerical computations and their results"/>
			<xsd:enumeration value="Generalize patterns using explicitly defined and recursively defined functions"/>
			<xsd:enumeration value="Understand relations and functions and select, convert flexibly among, and use various representations for them"/>
			<xsd:enumeration value="Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior"/>
			<xsd:enumeration value="Understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions"/>
			<xsd:enumeration value="Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions"/>
			<xsd:enumeration value="Interpret representations of functions of two variables"/>
			<xsd:enumeration value="Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations"/>
			<!--In the next benchmark the m-dash symbol between 'fluency' and 'mentally' was changed to a comma in order to validate the schema file. This does not really change the meaning of the standard-->
			<xsd:enumeration value="Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency, mentally or with paper and pencil in simple cases and using technology in all cases"/>
			<xsd:enumeration value="Use symbolic algebra to represent and explain mathematical relationships"/>
			<xsd:enumeration value="Use a variety of symbolic representations, including recursive and parametric equations, for functions and relations"/>
			<xsd:enumeration value="Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology"/>
			<xsd:enumeration value="Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships"/>
			<xsd:enumeration value="Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts"/>
			<xsd:enumeration value="Draw reasonable conclusions about a situation being modeled"/>
			<xsd:enumeration value="Approximate and interpret rates of change from graphical and numerical data"/>
			<xsd:enumeration value="Analyze properties and determine attributes of two- and three-dimensional objects"/>
			<xsd:enumeration value="Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them"/>
			<xsd:enumeration value="Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others"/>
			<xsd:enumeration value="Use trigonometric relationships to determine lengths and angle measures"/>
			<xsd:enumeration value="Use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations"/>
			<xsd:enumeration value="Investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates"/>
			<xsd:enumeration value="Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices"/>
			<xsd:enumeration value="Use various representations to help understand the effects of simple transformations and their compositions"/>
			<xsd:enumeration value="Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools"/>
			<xsd:enumeration value="Visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections"/>
			<xsd:enumeration value="Use vertex-edge graphs to model and solve problems"/>
			<xsd:enumeration value="Use geometric models to gain insights into, and answer questions in, other areas of mathematics"/>
			<xsd:enumeration value="Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture"/>
			<xsd:enumeration value="Make decisions about units and scales that are appropriate for problem situations involving measurement"/>
			<xsd:enumeration value="Analyze precision, accuracy, and approximate error in measurement situations"/>
			<xsd:enumeration value="Understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders"/>
			<xsd:enumeration value="Apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations"/>
			<xsd:enumeration value="Use unit analysis to check measurement computations"/>
			<xsd:enumeration value="Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each"/>
			<xsd:enumeration value="Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments"/>
			<xsd:enumeration value="Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable"/>
			<xsd:enumeration value="Understand histograms, parallel box plots, and scatterplots and use them to display data"/>
			<xsd:enumeration value="Compute basic statistics and understand the distinction between a statistic and a parameter"/>
			<xsd:enumeration value="For univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics"/>
			<xsd:enumeration value="For bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools"/>
			<xsd:enumeration value="Display and discuss bivariate data where at least one variable is categorical"/>
			<xsd:enumeration value="Recognize how linear transformations of univariate data affect shape, center, and spread"/>
			<xsd:enumeration value="Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled"/>
			<xsd:enumeration value="Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions"/>
			<xsd:enumeration value="Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference"/>
			<xsd:enumeration value="Evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions"/>
			<xsd:enumeration value="Understand how basic statistical techniques are used to monitor process characteristics in the workplace"/>
			<xsd:enumeration value="Understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases"/>
			<xsd:enumeration value="Use simulations to construct empirical probability distributions"/>
			<xsd:enumeration value="Compute and interpret the expected value of random variables in simple cases"/>
			<xsd:enumeration value="Understand the concepts of conditional probability and independent events"/>
			<xsd:enumeration value="Understand how to compute the probability of a compound event"/>
			<xsd:enumeration value="Build new mathematical knowledge through problem solving"/>
			<xsd:enumeration value="Solve problems that arise in mathematics and in other contexts"/>
			<xsd:enumeration value="Apply and adapt a variety of appropriate strategies to solve problems"/>
			<xsd:enumeration value="Monitor and reflect on the process of mathematical problem solving"/>
			<xsd:enumeration value="Recognize reasoning and proof as fundamental aspects of mathematics"/>
			<xsd:enumeration value="Make and investigate mathematical conjectures"/>
			<xsd:enumeration value="Develop and evaluate mathematical arguments and proofs"/>
			<xsd:enumeration value="Select and use various types of reasoning and methods of proof"/>
			<xsd:enumeration value="Organize and consolidate their mathematical thinking through communication"/>
			<xsd:enumeration value="Communicate their mathematical thinking coherently and clearly to peers, teachers, and others"/>
			<xsd:enumeration value="Analyze and evaluate the mathematical thinking and strategies of others"/>
			<xsd:enumeration value="Use the language of mathematics to express mathematical ideas precisely"/>
			<xsd:enumeration value="Recognize and use connections among mathematical ideas"/>
			<xsd:enumeration value="Understand how mathematical ideas interconnect and build on one another to produce a coherent whole"/>
			<xsd:enumeration value="Recognize and apply mathematics in contexts outside of mathematics"/>
			<xsd:enumeration value="Create and use representations to organize, record, and communicate mathematical ideas"/>
			<xsd:enumeration value="Select, apply, and translate among mathematical representations to solve problems"/>
			<xsd:enumeration value="Use representations to model and interpret physical, social, and mathematical phenomena"/>
		</xsd:restriction>
	</xsd:simpleType>
</xsd:schema>

