## GRADE 6 STANDARDS

ESSENTIAL UNDERSTANDINGS OF THE NUMBER SYSTEM

- Rational numbers are a natural extension of the way that we use numbers.
- Rational numbers are a set of numbers that includes whole numbers and integers as well as numbers that can be written as the quotient of two integers,
*a*divided by*b*, where*b*is not zero. - Rational numbers allow us to solve problems that are not possible to solve with just whole numbers or integers.
- Rational numbers have multiple interpretations, and making sense of them depends on identifying the unit.
- The concept of
*unit*is fundamental to the interpretation of rational numbers. - One interpretation of a rational number is as a part-whole relationship.
- One interpretation of a rational number is as a measure.
- One interpretation of a rational number is as a quotient.
- One interpretation of a rational number is as a ratio.
- One interpretation of a rational number is as a operator.
- Whole number conceptions of
*unit*become more complex when extended to rational numbers.

- The concept of
- Any rational number can be expressed as a fraction in an infinite number of ways.
- Between any two rational numbers there are infinitely many rational numbers.
- A rational number can be expressed as a decimal.
- The interpretation of the operations on rational numbers are essentially the same as those on whole numbers, but some interpretations require adaptation, and the algorithms are different.
- Estimation and mental math are more complex with rational numbers than with whole numbers.