National STEM Standards Kindergarten Math Activities

STEM.M. MATHEMATICS: National Council of Teachers of Mathematics (NCTM)

NCTM.1. Number and Operations

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

1.1.1. Count with understanding and recognize ''how many'' in sets of objects.

1.1.2. Use multiple models to develop initial understandings of place value and the base-ten number system.

1.1.3. Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.

1.1.4. Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.

1.1.5. Connect number words and numerals to the quantities they represent, using various physical models and representations.

1.1.6. Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2.

1.2. Understand meanings of operations and how they relate to one another.

1.2.1. Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.

1.2.2. Understand the effects of adding and subtracting whole numbers.

1.3. Compute fluently and make reasonable estimates.

1.3.1. Develop and use strategies for whole-number computations, with a focus on addition and subtraction.

1.3.2. Develop fluency with basic number combinations for addition and subtraction.

NCTM.2. Algebra

2.1. Understand patterns, relations, and functions.

2.1.1. Sort, classify, and order objects by size, number, and other properties.

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.

2.1.3. Analyze how both repeating and growing patterns are generated.

2.2. Represent and analyze mathematical situations and structures using algebraic symbols.

2.2.1. Illustrate general principles and properties of operations, such as commutativity, using specific numbers.

2.2.2. Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.

2.3. Use mathematical models to represent and understand quantitative relationships.

2.3.1. Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.

NCTM.3. Geometry

3.1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

3.1.1. Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes.

3.1.2. Describe attributes and parts of two- and three-dimensional shapes.

3.2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

3.2.1. Describe, name, and interpret relative positions in space and apply ideas about relative position.

3.2.2. Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance.

3.2.3. Find and name locations with simple relationships such as ''near to'' and in coordinate systems such as maps.

3.3. Apply transformations and use symmetry to analyze mathematical situations.

3.3.2. Recognize and create shapes that have symmetry.

3.4. Use visualization, spatial reasoning, and geometric modeling to solve problems.

3.4.4. Recognize geometric shapes and structures in the environment and specify their location.

NCTM.4. Measurement

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

4.1.1. Recognize the attributes of length, volume, weight, area, and time.

4.1.2. Compare and order objects according to these attributes.

4.1.3. Understand how to measure using nonstandard and standard units.

4.1.4. Select an appropriate unit and tool for the attribute being measured.

4.2. Apply appropriate techniques, tools, and formulas to determine measurements.

4.2.3. Use tools to measure.

NCTM.11. Kindergarten Curriculum Focal Points

11.1. Number and Operation: Representing, comparing, and ordering whole numbers and joining and separating sets

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.

11.2. Geometry: Describing shapes and space

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.

11.3. Measurement: Ordering objects by measurable attributes

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.

NCTM.12. Connections to the Kindergarten Focal Points

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.