Level I: Primary (Grades K-2)

*Understands that numbers are symbols used to represent quantities or attributes of real-world objects

*Counts whole numbers (i.e., both cardinal and ordinal numbers)

*Understands symbolic, concrete, and pictorial representations of numbers (e.g., written numerals, objects in sets, number lines)

*Understands basic whole number relationships (e.g., 4 is less than 10, 30 is 3 tens)

Level II: Upper Elementary (Grades 3-5)

*Understands the basic difference between odd and even numbers

*Understands the basic meaning of place value

*Uses models (e.g., number lines, two-dimensional and three-dimensional regions) to identify, order, and compare numbers

Level I: Primary (Grades K-2)

*Adds and subtracts whole numbers

*Solves real-world problems involving addition and subtraction of whole numbers

*Understands common terms used with estimation (e.g., "about," "near," "closer to," "between," "a little less than") Level II: Upper Elementary (Grades 3-5)

*Solves real-world problems involving number operations (e.g., computations with dollars and cents)

Level I: Primary (Grades K-2)

*Understands the basic measures length, width, height, weight, and temperature

*Understands the concept of time and how it is measured

*Knows processes for telling time, counting money, and measuring length, weight, and temperature, using basic standard and non-standard units

Level II: Upper Elementary (Grades 3-5)

*Understands the basic measures perimeter, area, volume, capacity, mass

*Selects and uses appropriate tools for given measurement situations (e.g., rulers for length, measuring cups for capacity)

*Knows approximate size of basic standard units (e.g., centimeters, feet, grams) and relationships between them (e.g., between inches and feet)

*Understands that measurement is not exact (i.e., measurements may give slightly different numbers when measured multiple times)

*Uses specific strategies to estimate quantities and measurements (e.g., estimating the whole by estimating the parts)

*Selects and uses appropriate units of measurement, according to type and size of unit

Level I: Primary (Grades K-2)

*Understands that observations about objects or events can be organized and displayed in simple graphs

Level II: Upper Elementary (Grades 3-5)

*Understands that data represent specific pieces of information about real-world objects or activities

*Understands that spreading data out on a number line helps to see what the extremes are, where the data points pile up, and where the gaps are

*Organizes and displays data in simple bar graphs, pie charts, and line graphs

*Reads and interprets simple bar graphs, pie charts, and line graphs

*Understands that data come in many different forms and that collecting, organizing, and displaying data can be done in many ways

*Understands the basic concept of a sample (e.g., a large sample leads to more reliable information; a small part of something may have unique characteristics but not be an accurate representation of the whole)

Level I: Primary (Grades K-2)

*Understands that some events are more likely to happen than others

*Understands that some events can be predicted fairly well but others cannot because we do not always know everything that may affect an event

Level II: Upper Elementary (Grades 3-5)

*Understands that the word "chance" refers to the likelihood of an event

*Recognizes events that are sure to happen, events that are sure not to happen, and events that may or may not happen (e.g., in terms of "certain," "uncertain," "likely," "unlikely")

*Understands that when predictions are based on what is known about the past, one must assume that conditions stay the same from the past event to the predicted future event

Level II: Upper Elementary (Grades 3-5)

 *Understands that numbers and the operations performed on them can be used to describe things in the real world and predict what might occur