What is essential for grades 3-5 to know about rational numbers to be effective in the classroom?
Big Idea #1: Extending from whole numbers to rational numbers creates a more powerful and complicated number system.
Essential Understandings:
1a- Rational numbers are a natural extension of the way we use numbers.
1b- Rational numbers are a set of numbers that include the whole numbers and integers as well as numbers that can be written as
quotient of two integers, a/b, where b is not zero.
1c- Rational numbers allow us to solve problems that are not possible to solve with just whole numbers or integers.
Big Idea #2: Rational numbers have multiple representations, and making sense of them depends on identifying the unit.
Essential Understandings:
2a- The concept of unit is fundamental to the interpretation of rational numbers.
2b- One interpretation of a rational number is a part-whole relationship.
2c- One interpretation of a rational number is a measure.
2d- One interpretation of a rational number is a quotient.
2e- One interpretation of a rational number is a ratio.
2f- One interpretation of a rational number is an operator.
2g- Whole number conceptions of unit become more complex when extended to rational numbers.
Big Idea #3: Any rational number can be represented in infinitely many equivalent symbolic forms.
Essential Understandings:
3a- Any rational number can be expressed as a fraction in an infinite number of ways.
3b- Between any two rational numbers there are infinitely many rational numbers.
3c- A rational number can be expressed as a decimal.
Big Idea #4: Computation with rational numbers is an extension of computation with whole numbers but introduces some new ideas
and processes.
Essential Understandings:
4a-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.
4b- Estimation and mental math are more complex with rational numbers than with whole numbers.
*for this weebly, rational numbers can be expressed in a fraction form
Big Idea #1: Extending from whole numbers to rational numbers creates a more powerful and complicated number system.
Essential Understandings:
1a- Rational numbers are a natural extension of the way we use numbers.
1b- Rational numbers are a set of numbers that include the whole numbers and integers as well as numbers that can be written as
quotient of two integers, a/b, where b is not zero.
1c- Rational numbers allow us to solve problems that are not possible to solve with just whole numbers or integers.
Big Idea #2: Rational numbers have multiple representations, and making sense of them depends on identifying the unit.
Essential Understandings:
2a- The concept of unit is fundamental to the interpretation of rational numbers.
2b- One interpretation of a rational number is a part-whole relationship.
2c- One interpretation of a rational number is a measure.
2d- One interpretation of a rational number is a quotient.
2e- One interpretation of a rational number is a ratio.
2f- One interpretation of a rational number is an operator.
2g- Whole number conceptions of unit become more complex when extended to rational numbers.
Big Idea #3: Any rational number can be represented in infinitely many equivalent symbolic forms.
Essential Understandings:
3a- Any rational number can be expressed as a fraction in an infinite number of ways.
3b- Between any two rational numbers there are infinitely many rational numbers.
3c- A rational number can be expressed as a decimal.
Big Idea #4: Computation with rational numbers is an extension of computation with whole numbers but introduces some new ideas
and processes.
Essential Understandings:
4a-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.
4b- Estimation and mental math are more complex with rational numbers than with whole numbers.
*for this weebly, rational numbers can be expressed in a fraction form