Maryland Math 7.NOS.A.2.b
The Standard
- 7.NOS.A.2
- Multiply and divide rational numbers using multiple strategies and representations.
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 divisor is not zero.
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 use a total change and a rate to work out what a signed quotient means. They write the same negative fraction with the minus sign in front, in the numerator, or in the denominator.
What Mastery Looks Like
- They explain why −$4.50 divided by −$0.75 per day gives 6 days. They show that −(3/4), (−3)/4, and 3/(−4) have the same value.
Common Misconceptions
- Students may think 3/(−4) is positive because the numerator is positive. They may put a negative sign in both the numerator and denominator, which makes the fraction positive. Some confuse a negative rate with a negative number of days.
How to Assess It
- Exit ticket: A balance changes by −$4.50 at a rate of −$0.75 per day. How many days pass? Then rewrite −(3/4) with the minus sign in the numerator and again in the denominator.
Lesson moves
Ways to Teach It
Give students three half-unit paper strips labeled −1/2; have them combine the strips and explain why −3/2 divided by −1/2 equals 3.
Ask, "Why are −(3/4), (−3)/4, and 3/(−4) equal?" Have students support their answers with calculations.
Deal cards showing −(3/4), (−3)/4, 3/(−4), 3/4, and −0.75; students sort equal values and explain the odd card.
Show a bank statement with a $4.50 loss over six days; students find the daily change and explain its negative sign.
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