Pre-K Through Grade 2 Math Standards

Number and Operations Standard for Grades Pre-K–2

 

Expectations

Instructional programs from pre-kindergarten through grade 12 should enable all students to—

In pre-kindergarten through grade 2, all students should—

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

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count with understanding and recognize “how many” in sets of objects;

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use multiple models to develop initial understandings of place value and the base-ten number system;

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develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections;

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develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers;

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connect number words and numerals to the quantities they represent, using various physical models and representations;

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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

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understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations;

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understand the effects of adding and subtracting whole numbers;

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understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.

Compute fluently and make reasonable estimates

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develop and use strategies for whole-number computations, with a focus on addition and subtraction;

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develop fluency with basic number combinations for addition and subtraction;

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use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

Algebra Standard for Grades Pre-K–2

 

Expectations

Instructional programs from pre-kindergarten through grade 12 should enable all students to—

In pre-kindergarten through grade 2, all students should—

Understand patterns, relations, and functions

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sort, classify, and order objects by size, number, and other properties;

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recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another;

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analyze how both repeating and growing patterns are generated.

Represent and analyze mathematical situations and structures using algebraic symbols

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illustrate general principles and properties of operations, such ascommutativity, using specific numbers;

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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

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

Analyze change in various contexts

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describe qualitative change, such as a student’s growing taller;

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describe quantitative change, such as a student’s growing two inches in one year.

Geometry Standard for Grades Pre-K–2

 

Expectations

Instructional programs from pre-kindergarten through grade 12 should enable all students to—

In pre-kindergarten through grade 2, all students should—

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

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recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;

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describe attributes and parts of two- and three-dimensional shapes;

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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

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describe, name, and interpret relative positions in space and apply ideas about relative position;

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describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance;

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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

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recognize and apply slides, flips, and turns;

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recognize and create shapes that have symmetry.

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

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create mental images of geometric shapes using spatial memory and spatial visualization;

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recognize and represent shapes from different perspectives;

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relate ideas in geometry to ideas in number and measurement;

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recognize geometric shapes and structures in the environment and specify their location.

Measurement Standard for Grades Pre-K–2

 

Expectations

Instructional programs from pre-kindergarten through grade 12 should enable all students to—

In pre-kindergarten through grade 2, all students should—

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

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recognize the attributes of length, volume, weight, area, and time;

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compare and order objects according to these attributes;

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understand how to measure using nonstandard and standard units;

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select an appropriate unit and tool for the attribute being measured.

Apply appropriate techniques, tools, and formulas to determine measurements

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measure with multiple copies of units of the same size, such as paper clips laid end to end;

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use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a singlemeterstick;

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use tools to measure;

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develop common referents for measures to make comparisons and estimates.

Data Analysis and Probability Standard for Grades Pre-K–2

 

Expectations

Instructional programs from pre-kindergarten through grade 12 should enable all students to—

In pre-kindergarten through grade 2, all students should—

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

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pose questions and gather data about themselves and their surroundings;

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sort and classify objects according to their attributes and organize data about the objects;

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represent data using concrete objects, pictures, and graphs.

Select and use appropriate statistical methods to analyze data

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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

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discuss events related to students’ experiences as likely or unlikely.

Understand and apply basic concepts of probability

 

Problem Solving Standard for Grades Pre-K–2

Instructional programs from pre-kindergarten through grade 12 should enable all students to—

  • build new mathematical knowledge through problem solving;
  • solve problems that arise in mathematics and in other contexts;
  • apply and adapt a variety of appropriate strategies to solve problems;
  • monitor and reflect on the process of mathematical problem solving.

Reasoning and Proof Standard for Grades Pre-K–2

Instructional programs from pre-kindergarten through grade 12 should enable all students to—

  • recognize reasoning and proof as fundamental aspects of mathematics;
  • make and investigate mathematical conjectures;
  • develop and evaluate mathematical arguments and proofs;
  • select and use various types of reasoning and methods of proof.

Communication Standard for Grades Pre-K–2

Instructional programs from pre-kindergarten through grade 12 should enable all students to—

  • organize and consolidate their mathematical thinking through communication;
  • communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
  • analyze and evaluate the mathematical thinking and strategies of others;
  • use the language of mathematics to express mathematical ideas precisely.

Connections Standard for Grades Pre-K–2

Instructional programs from pre-kindergarten through grade 12 should enable all students to—

  • recognize and use connections among mathematical ideas;
  • understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
  • recognize and apply mathematics in contexts outside of mathematics.

Representation Standard for Grades Pre-K–2

Instructional programs from pre-kindergarten through grade 12 should enable all students to—

  • create and use representations to organize, record, and communicate mathematical ideas;
  • select, apply, and translate among mathematical representations to solve problems;
  • use representations to model and interpret physical, social, and mathematical phenomena.