Number
sense encompasses several areas of mathematics that would indicate a good
"feel" for numbers and operations. There are five components
of number sense: 1) number meanings, 2) number relationships, 3) magnitudes
of numbers, 4) effects of operations, and 5) measurement referents.
Number meanings refer to both cardinal and ordinal numbers. It is not rote counting but a feel for the "numberness" of a word that expresses a quantity. When students hear the word "twenty," they should "see" a set of items in their mind.
Number relationships are formed by the composition and decomposition of numbers. For example, 20 can be thought of as 2 tens, 1 ten and 10 ones, or 20 ones. Further, 9 can be represented as one less than 10, two more than seven, or an odd number.
Magnitudes of numbers are expressed in various relationships. Fifty-two can be thought of as close to half of 100 or small compared to 500. Place value concepts help to develop students' ideas about number magnitude.
The effects of operations on numbers is important in helping students develop notions about the reasonableness of answers. Students may make comparisons about what happens when you multiply two whole numbers versus when you multiply two numbers between 0 and 1.
Measurement referents are not solely related to geometric measurements. Students should be able to judge the appropriateness of units of answers as well as the magnitude. It is impossible, for example, for someone in third-grade to be 3 meters tall or to weigh 12 kg.
In grades K4, the mathematics curriculum should include whole number concepts and skills so that students can