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National STEM Standards - Mathematics Grade K

	CONTENT AREA / ORGANIZATION					STEM.M.	MATHEMATICS: National Council of Teachers of Mathematics (NCTM)
		STRAND / STANDARD				NCTM.1.	Number and Operations
			STANDARD / BENCHMARK			1.1.	Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
				BENCHMARK / INDICATOR		1.1.1.	Count with understanding and recognize ''how many'' in sets of objects. (materials correlated to this standard)
				BENCHMARK / INDICATOR		1.1.2.	Use multiple models to develop initial understandings of place value and the base-ten number system. (materials correlated to this standard)
				BENCHMARK / INDICATOR		1.1.3.	Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections. (materials correlated to this standard)
				BENCHMARK / INDICATOR		1.1.4.	Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers. (materials correlated to this standard)
				BENCHMARK / INDICATOR		1.1.5.	Connect number words and numerals to the quantities they represent, using various physical models and representations. (materials correlated to this standard)
				BENCHMARK / INDICATOR		1.1.6.	Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2. (materials correlated to this standard)
			STANDARD / BENCHMARK			1.2.	Understand meanings of operations and how they relate to one another.
				BENCHMARK / INDICATOR		1.2.1.	Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
				BENCHMARK / INDICATOR		1.2.2.	Understand the effects of adding and subtracting whole numbers.
				BENCHMARK / INDICATOR		1.2.3.	Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally. (materials correlated to this standard)
			STANDARD / BENCHMARK			1.3.	Compute fluently and make reasonable estimates.
				BENCHMARK / INDICATOR		1.3.1.	Develop and use strategies for whole-number computations, with a focus on addition and subtraction. (materials correlated to this standard)
				BENCHMARK / INDICATOR		1.3.2.	Develop fluency with basic number combinations for addition and subtraction. (materials correlated to this standard)
				BENCHMARK / INDICATOR		1.3.3.	Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators. (materials correlated to this standard)
		STRAND / STANDARD				NCTM.2.	Algebra
			STANDARD / BENCHMARK			2.1.	Understand patterns, relations, and functions.
				BENCHMARK / INDICATOR		2.1.1.	Sort, classify, and order objects by size, number, and other properties. (materials correlated to this standard)
				BENCHMARK / INDICATOR		2.1.2.	Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another. (materials correlated to this standard)
				BENCHMARK / INDICATOR		2.1.3.	Analyze how both repeating and growing patterns are generated. (materials correlated to this standard)
			STANDARD / BENCHMARK			2.2.	Represent and analyze mathematical situations and structures using algebraic symbols.
				BENCHMARK / INDICATOR		2.2.1.	Illustrate general principles and properties of operations, such as commutativity, using specific numbers.
				BENCHMARK / INDICATOR		2.2.2.	Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
			STANDARD / BENCHMARK			2.3.	Use mathematical models to represent and understand quantitative relationships.
				BENCHMARK / INDICATOR		2.3.1.	Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols. (materials correlated to this standard)
			STANDARD / BENCHMARK			2.4.	Analyze change in various contexts.
				BENCHMARK / INDICATOR		2.4.1.	Describe qualitative change, such as a student's growing taller.
				BENCHMARK / INDICATOR		2.4.2.	Describe quantitative change, such as a student's growing two inches in one year.
		STRAND / STANDARD				NCTM.3.	Geometry
			STANDARD / BENCHMARK			3.1.	Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
				BENCHMARK / INDICATOR		3.1.1.	Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes. (materials correlated to this standard)
				BENCHMARK / INDICATOR		3.1.2.	Describe attributes and parts of two- and three-dimensional shapes. (materials correlated to this standard)
				BENCHMARK / INDICATOR		3.1.3.	Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes. (materials correlated to this standard)
			STANDARD / BENCHMARK			3.2.	Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
				BENCHMARK / INDICATOR		3.2.1.	Describe, name, and interpret relative positions in space and apply ideas about relative position. (materials correlated to this standard)
				BENCHMARK / INDICATOR		3.2.2.	Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance. (materials correlated to this standard)
				BENCHMARK / INDICATOR		3.2.3.	Find and name locations with simple relationships such as ''near to'' and in coordinate systems such as maps. (materials correlated to this standard)
			STANDARD / BENCHMARK			3.3.	Apply transformations and use symmetry to analyze mathematical situations.
				BENCHMARK / INDICATOR		3.3.1.	Recognize and apply slides, flips, and turns.
				BENCHMARK / INDICATOR		3.3.2.	Recognize and create shapes that have symmetry. (materials correlated to this standard)
			STANDARD / BENCHMARK			3.4.	Use visualization, spatial reasoning, and geometric modeling to solve problems.
				BENCHMARK / INDICATOR		3.4.1.	Create mental images of geometric shapes using spatial memory and spatial visualization. (materials correlated to this standard)
				BENCHMARK / INDICATOR		3.4.2.	Recognize and represent shapes from different perspectives.
				BENCHMARK / INDICATOR		3.4.3.	Relate ideas in geometry to ideas in number and measurement. (materials correlated to this standard)
				BENCHMARK / INDICATOR		3.4.4.	Recognize geometric shapes and structures in the environment and specify their location. (materials correlated to this standard)
		STRAND / STANDARD				NCTM.4.	Measurement
			STANDARD / BENCHMARK			4.1.	Understand measurable attributes of objects and the units, systems, and processes of measurement.
				BENCHMARK / INDICATOR		4.1.1.	Recognize the attributes of length, volume, weight, area, and time. (materials correlated to this standard)
				BENCHMARK / INDICATOR		4.1.2.	Compare and order objects according to these attributes. (materials correlated to this standard)
				BENCHMARK / INDICATOR		4.1.3.	Understand how to measure using nonstandard and standard units. (materials correlated to this standard)
				BENCHMARK / INDICATOR		4.1.4.	Select an appropriate unit and tool for the attribute being measured. (materials correlated to this standard)
			STANDARD / BENCHMARK			4.2.	Apply appropriate techniques, tools, and formulas to determine measurements.
				BENCHMARK / INDICATOR		4.2.1.	Measure with multiple copies of units of the same size, such as paper clips laid end to end. (materials correlated to this standard)
				BENCHMARK / INDICATOR		4.2.2.	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.
				BENCHMARK / INDICATOR		4.2.3.	Use tools to measure. (materials correlated to this standard)
				BENCHMARK / INDICATOR		4.2.4.	Develop common referents for measures to make comparisons and estimates.
		STRAND / STANDARD				NCTM.5.	Data Analysis and Probability
			STANDARD / BENCHMARK			5.1.	Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
				BENCHMARK / INDICATOR		5.1.1.	Pose questions and gather data about themselves and their surroundings. (materials correlated to this standard)
				BENCHMARK / INDICATOR		5.1.2.	Sort and classify objects according to their attributes and organize data about the objects.
				BENCHMARK / INDICATOR		5.1.3.	Represent data using concrete objects, pictures, and graphs.
			STANDARD / BENCHMARK			5.2.	Select and use appropriate statistical methods to analyze data.
				BENCHMARK / INDICATOR		5.2.1.	Describe parts of the data and the set of data as a whole to determine what the data show. (materials correlated to this standard)
			STANDARD / BENCHMARK			5.3.	Develop and evaluate inferences and predictions that are based on data.
				BENCHMARK / INDICATOR		5.3.1.	Discuss events related to students'' experiences as likely or unlikely.
		STRAND / STANDARD				NCTM.6.	Problem Solving
			STANDARD / BENCHMARK			6.1.	Build new mathematical knowledge through problem solving.
			STANDARD / BENCHMARK			6.2.	Solve problems that arise in mathematics and in other contexts. (materials correlated to this standard)
			STANDARD / BENCHMARK			6.3.	Apply and adapt a variety of appropriate strategies to solve problems. (materials correlated to this standard)
			STANDARD / BENCHMARK			6.4.	Monitor and reflect on the process of mathematical problem solving.
		STRAND / STANDARD				NCTM.7.	Reasoning and Proof
			STANDARD / BENCHMARK			7.1.	Recognize reasoning and proof as fundamental aspects of mathematics. (materials correlated to this standard)
			STANDARD / BENCHMARK			7.2.	Make and investigate mathematical conjectures.
			STANDARD / BENCHMARK			7.3.	Develop and evaluate mathematical arguments and proofs. (materials correlated to this standard)
			STANDARD / BENCHMARK			7.4.	Select and use various types of reasoning and methods of proof. (materials correlated to this standard)
		STRAND / STANDARD				NCTM.8.	Communication
			STANDARD / BENCHMARK			8.1.	Organize and consolidate their mathematical thinking through communication.
			STANDARD / BENCHMARK			8.2.	Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. (materials correlated to this standard)
			STANDARD / BENCHMARK			8.3.	Analyze and evaluate the mathematical thinking and strategies of others. (materials correlated to this standard)
			STANDARD / BENCHMARK			8.4.	Use the language of mathematics to express mathematical ideas precisely. (materials correlated to this standard)
		STRAND / STANDARD				NCTM.9.	Connections
			STANDARD / BENCHMARK			9.1.	Recognize and use connections among mathematical ideas.
			STANDARD / BENCHMARK			9.2.	Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
			STANDARD / BENCHMARK			9.3.	Recognize and apply mathematics in contexts outside of mathematics. (materials correlated to this standard)
		STRAND / STANDARD				NCTM.10.	Representation
			STANDARD / BENCHMARK			10.1.	Create and use representations to organize, record, and communicate mathematical ideas. (materials correlated to this standard)
			STANDARD / BENCHMARK			10.2.	Select, apply, and translate among mathematical representations to solve problems. (materials correlated to this standard)
			STANDARD / BENCHMARK			10.3.	Use representations to model and interpret physical, social, and mathematical phenomena. (materials correlated to this standard)
		STRAND / STANDARD				NCTM.11.	Kindergarten Curriculum Focal Points
			STANDARD / BENCHMARK			11.1.	Number and Operation: Representing, comparing, and ordering whole numbers and joining and separating sets
				BENCHMARK / INDICATOR		11.1.1.	Children use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set, creating a set with a given number of objects, comparing and ordering sets or numerals by using both cardinal and ordinal meanings, and modeling simple joining and separating situations with objects. They choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the number in a small set, counting and producing sets of given sizes, counting the number in combined sets, and counting backward. (materials correlated to this standard)
			STANDARD / BENCHMARK			11.2.	Geometry: Describing shapes and space
				BENCHMARK / INDICATOR		11.2.1.	Children interpret the physical world with geometric ideas (e.g., shape, orientation, spatial relations) and describe it with corresponding vocabulary. They identify, name, and describe a variety of shapes, such as squares, triangles, circles, rectangles, (regular) hexagons, and (isosceles) trapezoids presented in a variety of ways (e.g., with different sizes or orientations), as well as such three-dimensional shapes as spheres, cubes, and cylinders. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes. (materials correlated to this standard)
			STANDARD / BENCHMARK			11.3.	Measurement: Ordering objects by measurable attributes
				BENCHMARK / INDICATOR		11.3.1.	Children use measurable attributes, such as length or weight, to solve problems by comparing and ordering objects. They compare the lengths of two objects both directly (by comparing them with each other) and indirectly (by comparing both with a third object), and they order several objects according to length. (materials correlated to this standard)
		STRAND / STANDARD				NCTM.12.	Connections to the Kindergarten Focal Points
			STANDARD / BENCHMARK			12.1.	Data Analysis: Children sort objects and use one or more attributes to solve problems. For example, they might sort solids that roll easily from those that do not. Or they might collect data and use counting to answer such questions as, ''What is our favorite snack?'' They re-sort objects by using new attributes (e.g., after sorting solids according to which ones roll, they might re-sort the solids according to which ones stack easily).
			STANDARD / BENCHMARK			12.2.	Geometry: Children integrate their understandings of geometry, measurement, and number. For example, they understand, discuss, and create simple navigational directions (e.g., ''Walk forward 10 steps, turn right, and walk forward 5 steps'').
			STANDARD / BENCHMARK			12.3.	Algebra: Children identify, duplicate, and extend simple number patterns and sequential and growing patterns (e.g., patterns made with shapes) as preparation for creating rules that describe relationships. (materials correlated to this standard)