NY Next Generation Math NY-7.NS.2.d

Math7th GradeApply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

The Standard

Convert a fraction to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students convert fractions to decimals with long division. They identify whether the decimal terminates or develops a repeating pattern.
What Mastery Looks Like: The student divides 3 by 8 to obtain 0.375 and 2 by 3 to obtain 0.666 repeating. The student marks the repeating digit or block clearly.
Common Misconceptions: Students may stop a nonterminating division without identifying the repeating pattern. They may place the decimal point incorrectly or call a rounded decimal exact.
How to Assess It: Ask students to convert 5/12 and 7/20 by long division, identify which repeats or terminates, and mark the repeating block.

Lesson moves

Use long-division remainder cards to track when a remainder reaches zero or begins repeating.
Ask students why a repeated remainder creates a repeated decimal digit pattern.
Play terminate-or-repeat sort after completing fraction-to-decimal long divisions.
Convert fractional measurements or rates to decimal form and state whether each result terminates or repeats.

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