Counting Principles

Rules and methods that explain how to count objects accurately, including concepts like one-to-one correspondence (counting each item only once), stable order (saying numbers in the correct sequence), and cardinality (the final number counted represents the total quantity in a group). Systematic counting by 1’s forward and backward, and skip counting by 2’s, 5’s, and 10’s are two other counting principles.

Number Identification

The ability to: (1) Identify a particular number symbol and name a number when shown its symbol; (2) Recognize, work with, and make connections between different representations of a system of numbers, including word and expanded forms; (3) Accurately recognize and interpret both the time displayed on an analog or digital clock.

Operations with Whole Numbers

The ability to accurately perform grade-level appropriate operations with whole numbers, including basic facts, when calculations involve story problems or written equations.  

Number Comparisons/Inequalities

The ability to identify which numbers are worth more or less than each other, compare the number of objects in a set (from charts and tables), compare magnitudes (using language like ‘bigger than’ or ‘smaller than '), and compare values using appropriate symbols (<, >, =).

Whole & Decimal Number Place Value/Decimal Operations

The ability to identify the value of individual digits within a dollar amount, using their understanding of place value (ones, tens, hundreds) to determine how much each coin or bill represents in a given sum of money, and solve problems with actual and estimated results.

Spatial Reasoning/Geometry

The ability to 1) Classify and compare objects by attribute, length, and position; 2) Understand and reason with the relationship between plane and solid figures; and 3) Identify rules for and extend geometric patterns.

Part/Whole Relationships

The ability to demonstrate grade-level proficiency in dividing whole objects into equal parts, understanding the concept of fractions as parts of a whole, and recognizing and representing fractions such as one-half, one-fourth, and one-third.

Counting Principles

Rules and methods that explain how to count objects accurately. In upper elementary and middle school, this includes concepts like multiples (skip counting by an integer), stable order (saying numbers in the correct sequence), and the fundamental counting principle. This principle states that if one event can occur in "m" ways and a second independent event can occur in "n" ways, then the total number of possible outcomes for both events is "m * n".

Number Identification

The ability to recognize and correctly name different numerical values. In upper elementary and middle school, this includes concepts like positive and negative integers, more complex concepts like prime and composite numbers, and interpreting numerical data displayed in tables, graphs, and charts.

Operations with Whole Numbers

The ability to accurately perform grade-level appropriate operations with whole numbers (including basic facts), apply the order of operations (PEMDAS), make calculations using data sets, and solve multi-step calculations when presented as story problems, written equations, and equations with variables.

Number Comparisons/Inequalities

The ability to reason with comparisons between two numbers, values, or expressions. Inequalities can: 1) Include variables or unknown amounts; 2) Be represented on a number line or coordinate plane; and 3) Have single or multiple correct answers.

Whole & Decimal Number Place Value/Decimal Operations

The ability to accurately solve exercises involves identifying each digit's value in a number based on its position (place value) and solving problems that include whole and decimal numbers.

Spatial Reasoning/Geometry

The ability to 1) Reason with nets to relate plane and solid figures; 2) Reason with congruence and similarity; 3) Solve for geometric measurements with whole numbers, such as area, volume, and perimeter; and 4) accurately plot points in the first quadrant of a coordinate plane.

Part/Whole Relationships

The ability to recognize and reason with fractions and percents, including the ability to add, subtract, multiply, and divide fractions, with a focus on finding common denominators, using visual models to understand the concepts, and applying these operations to real-world problems.