Standards: Grades K-2

Kindergarten

• Counting & Cardinality
• Operations & Algebraic Thinking
• Number & Operations in Base Ten
• Measurement & Data
• Geometry

Grade 1

• Operations & Algebraic Thinking
• Number & Operations in Base Ten
• Measurement & Data
• Geometry

Grade 2

• Operations & Algebraic Thinking
• Number & Operations in Base Ten
• Measurement & Data
• Geometry

Number & Operations

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

• count with understanding and recognize "how many" in sets of objects;
• use multiple models to develop initial understandings of place value and the base-ten number system;
• develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections;
• develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers;
• connect number words and numerals to the quantities they represent, using various physical models and representations;
• understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2.

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;
• understand the effects of adding and subtracting whole numbers;
• understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.

Compute fluently and make reasonable estimates

• develop and use strategies for whole-number computations, with a focus on addition and subtraction;
• develop fluency with basic number combinations for addition and subtraction;
• use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

Algebra

Understand patterns, relations, and functions

• sort, classify, and order objects by size, number, and other properties;
• recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another;
• analyze how both repeating and growing patterns are generated.

Represent and analyze mathematical situations and structures using algebraic symbols

• illustrate general principles and properties of operations, such as commutativity, using specific numbers;
• use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.

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.

Analyze change in various contexts

• describe qualitative change, such as a student's growing taller;
• describe quantitative change, such as a student's growing two inches in one year.

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;
• describe attributes and parts of two- and three-dimensional shapes;
• investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.

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;
• describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance;
• find and name locations with simple relationships such as "near to" and in coordinate systems such as maps.

Apply transformations and use symmetry to analyze mathematical situations

• recognize and apply slides, flips, and turns;
• recognize and create shapes that have symmetry.

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

• create mental images of geometric shapes using spatial memory and spatial visualization;
• recognize and represent shapes from different perspectives;
• relate ideas in geometry to ideas in number and measurement;
• recognize geometric shapes and structures in the environment and specify their location.

Measurement

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

• recognize the attributes of length, volume, weight, area, and time;
• compare and order objects according to these attributes;
• understand how to measure using nonstandard and standard units;
• select an appropriate unit and tool for the attribute being measured.

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;
• use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meter stick;
• use tools to measure;
• develop common referents for measures to make comparisons and estimates.

Data Analysis & 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;
• sort and classify objects according to their attributes and organize data about the objects;
• represent data using concrete objects, pictures, and graphs.

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.

Develop and evaluate inferences and predictions that are based on data

• discuss events related to students' experiences as likely or unlikely.