# The Number System

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The Number System is the mathematical term for all of the families of numbers. Real and imaginary, rational and irrational, integers and fractions/decimals, whole numbers, and natural numbers are all part of the Number System. The names of each family of numbers are usually introduced in Pre-Algebra and reinforced in Algebra 1. Students add integers to their work with natural and whole numbers in 5th or 6th grade.

### Topics usually covered:

Students learn to identify Real vs Imaginary Numbers, Rational and Irrational Numbers, Integers, Whole Numbers, and Natural Numbers in sixth grade They also begin working with negative numbers, usually by fifth grade.

### Typical problem areas:

Beginning in 5th grade, 6th grade, or Pre-Algebra, students often struggle with addition and subtraction of integers (positive and negative numbers). Using a number line as a visual aid can be helpful to establish concepts; when numbers become too large for number lines to be feasible, students can struggle to remember procedures. Multiplying and dividing integers is simple, however, students may struggle to internalize why the rules are so simple for these operations. Operations with fractions (rational numbers) pose a challenge to many students throughout middle school. Students confuse when and when not to find common denominators, or how to deal with mixed numbers.