Ordering numbers involves arranging a set of numbers in a specific sequence based on their value. The three main ways to order numbers are:

- Ascending Order: Numbers are arranged from the smallest to the largest.
- Descending Order: Numbers are arranged from the largest to the smallest.
- Comparing Numbers: Numbers are compared to determine which is greater than, less than, or equal to another number.

To put numbers in ascending order, start by finding the smallest number in the set. Then, find the next smallest number and continue this process until all numbers are arranged from least to greatest.

For example, if given the numbers 4, 1, 6, 3, and 2, the numbers in ascending order would be 1, 2, 3, 4, 6.

To put numbers in descending order, start by finding the largest number in the set. Then, find the next largest number and continue this process until all numbers are arranged from greatest to least.

For example, if given the numbers 8, 11, 5, 9, and 7, the numbers in descending order would be 11, 9, 8, 7, 5.

When comparing numbers, symbols such as "<" (less than), ">" (greater than), and "=" (equal to) are used to show the relationship between two numbers.

For example, 5 < 8 means "5 is less than 8," and 10 > 3 means "10 is greater than 3."

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Counting and Cardinality

Know number names and the count sequence.

Count to 100 by ones and by tens. [K-CC1]

Count forward beginning from a given number within the known sequence (instead of having to begin at 1). [K-CC2]

Count to tell the number of objects.

Understand the relationship between numbers and quantities; connect counting to cardinality. [K-CC4]

Understand that each successive number name refers to a quantity that is one larger. [K-CC4c]

Compare numbers.

Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to ten objects.) [K-CC6]

Operations and Algebraic Thinking

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (Drawings need not show details, but should show the mathematics in the problem. This applies wherever drawings are mentioned in the Standards.) [K-OA1]

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. [K-OA2]

Fluently add and subtract within 5. [K-OA5]