Maryland Math 7.NOS.A.2.d
The Standard
- 7.NOS.A.2
- Multiply and divide rational numbers using multiple strategies and representations.
Analyze the decimal representation of a quotient resulting from dividing rational numbers to determine whether it terminates or repeats and use this pattern to explain why all rational numbers have decimal forms that either terminate or repeat.
Maryland College and Career Ready Standards for Mathematics (2025) · USE STRUCTURE AND REPRESENTATIONS TO REASON WITH RATIONAL NUMBERS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students divide rational numbers and track the remainders. They decide whether the decimal stops or repeats. They explain how the remainders determine what happens next.
What Mastery Looks Like
- A student can show that 5 ÷ 12 has a repeated remainder, so its digits repeat. They can explain that division either reaches a zero remainder or returns to an earlier remainder.
Common Misconceptions
- Students may treat a rounded answer, such as 0.17 for 1 ÷ 6, as an exact terminating decimal. They may also think a repeating pattern must start with the first decimal digit.
How to Assess It
- Exit ticket: Use long division to find the first five decimal digits of 5 ÷ 12. Circle a remainder that repeats and explain what it tells you about the decimal.
Lesson moves
Ways to Teach It
Give pairs place-value disks through thousandths; have them share one whole among eight groups, trading leftovers for smaller disks.
Show the long division for 1 ÷ 6 and ask, “How does the repeated remainder explain the repeated 6?”
Give pairs cards labeled 3/8, 2/3, 7/20, and 5/12; have them sort the cards, then check by long division.
Split $1 equally among four people, then six; compare the exact dollar amounts with what can be paid using cents.
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Related Standards
- 7.NOS.A.2
Multiply and divide rational numbers using multiple strategies and representations.
- 7.NOS.A.2.b
Interpret quotients of rational numbers in context and represent division of signed numbers in different forms, such as −(p/q) = (−p)/q = p/(−q) when the diviso...
- 3.NOS.B.3
Represent and interpret whole-number quotients (0-10) as dividing an amount into known number of groups (partitive) or as dividing an amount into groups of know...
- 8.NOS.A.1
Identify a number as irrational when its decimal expansion neither terminates nor repeats, and explain that irrational numbers cannot be expressed as the ratio ...
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