Math Relearning/Number Sense - Revision history

Andy Culbertson: Added commenting.

2016-06-27T05:17:21Z

Added commenting.

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Andy Culbertson: Removed the Numeration Systems section. Added the Complete category. Fixed a footnote.

2015-09-29T01:47:28Z

Removed the Numeration Systems section. Added the Complete category. Fixed a footnote.

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	== Classification ==		== Classification ==

	Just as numbers often represent sets of objects, numbers themselves can be grouped into sets. This grouping is based on various criteria.<ref>Chapin and Johnson, 1-2</ref>		Just as numbers often represent sets of objects, numbers themselves can be grouped into sets. This grouping is based on various criteria.<ref>Chapin and Johnson 2006, 1-2</ref>

	For example, the most basic major set of numbers we work with is the whole numbers. The whole numbers are a number system, not to be confused with the numeration systems in the next section. The whole numbers consist of the natural numbers and 0. The natural, or counting, numbers are 1, 2, 3, and so on.<ref>''Wikipedia'', s.v. “Number,” last modified August 4, 2014, http://en.wikipedia.org/wiki/Number</ref> The whole numbers have the characteristic of representing countable quantities of whole units of whatever you're counting. There are numbers in other sets that represent part of a unit, and I'll start talking about those in the fractions chapter.		For example, the most basic major set of numbers we work with is the whole numbers. The whole numbers are a number system, not to be confused with the numeration systems in the next section. The whole numbers consist of the natural numbers and 0. The natural, or counting, numbers are 1, 2, 3, and so on.<ref>''Wikipedia'', s.v. “Number,” last modified August 4, 2014, http://en.wikipedia.org/wiki/Number</ref> The whole numbers have the characteristic of representing countable quantities of whole units of whatever you're counting. There are numbers in other sets that represent part of a unit, and I'll start talking about those in the fractions chapter.

	As another example, whole numbers can be further classified as even or odd. You can find out if a number is even by forming pairs of items in a collection of that quantity. If you have one item left over, the number is odd. If all the items can form pairs, the number is even. So you could say an even number has the trait of being completely pairable within itself.<ref>Chapin and Johnson 2006, 9-10</ref>		As another example, whole numbers can be further classified as even or odd. You can find out if a number is even by forming pairs of items in a collection of that quantity. If you have one item left over, the number is odd. If all the items can form pairs, the number is even. So you could say an even number has the trait of being completely pairable within itself.<ref>Chapin and Johnson 2006, 9-10</ref>

	~~== Numeration systems ==~~

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

	== Footnotes ==		== Footnotes ==
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Andy Culbertson: Reorganized the material and filled out the placeholder content for every section except "Numeration systems."

2014-08-11T02:19:00Z

Reorganized the material and filled out the placeholder content for every section except "Numeration systems."

Show changes

Andy Culbertson: Added the article.

2014-06-21T03:24:50Z

Added the article.

New page

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.

[[Category:Math Relearning]]