NS.1.1

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

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Formative Assessments
Formative Assessments
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CPALMS: Students are given several terminating and repeating decimals and asked to convert them to fractions.

Decimal to Fraction Conversion

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CPALMS: Students are given a fraction to convert to a decimal and are asked to determine if the decimal repeats.

Fraction to Decimal Conversion

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CPALMS: Students are asked to identify rational numbers from a list of real numbers, explain how to identify rational numbers, and to identify the number system that contains numbers that are not rational.

Rational Numbers

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Assessment Questions
Assessment Questions
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Videos of Expert Instruction
Videos of Expert Instruction
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Although the Greeks initially thought all numeric quantities could be represented by the ratio of two integers, i.e. rational numbers, we now know that not all numbers are rational. How do we know this?
Irrational Numbers
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Hook/Performance Tasks
Hook/Performance Tasks
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Illustrative Mathematics: Students are give three rational numbers and asked to represent each in fraction form.

Converting Decimal Representations of Rational Numbers to Fraction Representations

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Illustrative Mathematics: The purpose of this task is to understand, in some concrete cases, why terminating decimal numbers can also be written as repeating decimals where the repeating part is all 9's.

Repeating or Terminating?

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Illustrative Mathematics: The purpose of this task is to study some concrete examples of repeating decimals and find a way to convert them to fractions.

Converting Repeating Decimals to Fractions

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Illustrative Mathematics: Students are to decide whether each of the given numbers is rational or irrational and explain how they know. It assumes that students are able to express a given repeating decimal as a fraction.

Identifying Rational Numbers