Georgia 7.NR.1.7
The Standard
Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number.
Georgia's K-12 Mathematics Standards · Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers).
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students divide positive and negative integers using sign rules. They write each result as a fraction of two integers and identify division by zero as undefined.
What Mastery Looks Like
- A student correctly finds quotients such as -18 ÷ 3 = -6 and 7 ÷ -2 = -7/2. They explain that both results are rational because each can be written as a fraction with a nonzero denominator.
Common Misconceptions
- Students may think dividing two integers must produce another integer, so they reject 5/2. They may misapply sign rules, confuse 0 ÷ 6 with 6 ÷ 0, or call an undefined quotient irrational.
How to Assess It
- Exit ticket: Evaluate -15 ÷ 4 and 0 ÷ -6, then explain why each answer is rational and why 8 ÷ 0 has no value.
Lesson moves
Ways to Teach It
Have students match integer division cards to signed fraction strips, then sort the results as integers or noninteger rational numbers.
Ask students to explain why 7 divided by negative 2 is rational but not an integer.
Play Quotient Sort: teams draw two integer cards, divide the first by the second, and place the quotient in the correct category.
Model a $15 loss shared equally by four partners, then write each partner’s share as a signed fraction and decimal.
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