If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.
You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!

7-N-1-1

Page history last edited by Brenda Butz 6 years, 3 months ago

7.N.1.1 Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal.

In a Nutshell

Rational numbers are those that can be written as where both a and b are integers and b≠0. All rational numbers can be expanded by division. Resulting decimal expansions either terminate $left parenthesis i full stop e full stop comma \ two fifths equals 0.4 right parenthesis$ or repeat $left parenthesis i full stop e full stop comma \ one third equals zero full stop macron over 3 right parenthesis$ . Decimals that do not terminate or repeat cannot be written as a rational number and are referred to as irrational. An integer can be written as a fraction simply by giving it a denominator of one, so any integer is a rational number.

Student Actions	Teacher Actions
Develop a deep understanding of when a number can or cannot be described as a ratio of two integers by working with a variety of numbers and trying to express them as ratios. Develop accurate and appropriate procedural fluency by developing fluency with division in order to apply to changing rationals into decimals.	Implement tasks that allow students to decide which representations to use in making sense of the problems. Facilitate mathematical discourse by having students look for a pattern in rational numbers. Use this pattern to create a shared understanding of a rational number. Build procedural fluency from conceptual understanding by introducing and reinforcing correct terminology/vocabulary (rational, ratio, integer, terminating and repeating decimals).
Key Understandings	Misconceptions
Know the definition and give examples of rational numbers, integers, terminating decimals, and repeating decimals. Know the definition and give examples of non-repeating and non-terminating decimals. Identifying rational versus irrational numbers. Can write repeating decimals using bar notation.	Students may believe that terminating decimals are equivalent to repeating decimals with similar numbers ex. 0.333… may be written as 333/1000. Students may believe that repeating decimals are not repeating because calculators round the last digit in the viewing window. Students may think pi is rational because of the frequency of representing pi as its approximate 3.14.