Math Relearning/Number Sense

Note: These paragraphs are more like topic sentences, so they won't necessarily make sense on their own. They're placeholders I'll fill out later.

Sequence
Numbers form a sequence ordered by magnitude.

We represent this sequence on a diagram called the number line.

We'll start with the number 1. You can think of it as a unit of distance on the number line. If we move the same distance repeatedly, we'll arrive at other numbers: 2, 3, etc. We call these the counting numbers.

Assignment
Numbers can be associated with objects, both concrete and abstract.

The sequential nature of numbers and their ability to be assigned to objects gives us our three main uses for numbers: quantifying, ordering, and naming.

The fact that these associations can be made and broken freely means that numbers are abstract.

Decomposition
Numbers can be split apart into smaller numbers and grouped together to form larger ones.

In this way numbers have relationships with each other. You could also say numbers have behavior and that each number has its own character.

Place value
Our numeration system uses place value to represent a number by means of the regular groupings within it.

Let's add the number 0 to our sequence. Its simplest use is to hold a place in a numeral that has more than one digit. When we include 0 with the counting numbers, we call the new set the whole numbers.

Classification
Numbers can be grouped into categories or sets by various criteria.

For example, the whole numbers are one set, and numbers in that set can be further classified as even or odd.