Maryland Math 7.NOS.A.2

7.NOS.A.2 is a cluster heading. These are the individual standards under it.

• 7.NOS.A.2.a

  Model multiplication of rational numbers using number lines, arrays, or area models to show how properties of operations (e.g., the distributive property) lead ...

• 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...

• 7.NOS.A.2.c

  Use properties of operations to multiply and divide rational numbers flexibly and efficiently.

• 7.NOS.A.2.d

  Analyze the decimal representation of a quotient resulting from dividing rational numbers to determine whether it terminates or repeats and use this pattern to ...

• 7.NOS.A.2.e

  Model and solve multistep contextual problems involving multiplication and division of rational numbers, using efficient and flexible strategies.

01

What Students Need to Do

Students use models and properties to multiply signed numbers and explain the sign of a product. They divide signed fractions, interpret negative quotients, and solve multistep problems. They track remainders to explain why a rational decimal stops or repeats.

02

What Mastery Looks Like

Students use 0 = (-1) × (1 + (-1)) to show why (-1) × (-1) = 1. They solve a multistep problem and show that -(3/4), (-3)/4, and 3/(-4) have the same value. They explain that division reaches a remainder of zero or repeats a remainder, so a rational decimal terminates or repeats.

03

Common Misconceptions

Students may know that two negatives make a positive but cannot explain why. Some put a negative sign on both the numerator and denominator and expect a negative quotient. Others assume a long decimal is irrational without checking whether its digits repeat.

04

How to Assess It

Exit ticket: Calculate (-3/4) ÷ (1/2), write the quotient with its negative sign in two positions, and state whether its decimal terminates.

1. 01

   Build three zero pairs with red negative and blue positive counters, then remove the red counters to model (-1) × (-3).

2. 02

   Ask students to expand 0 = (-1) × (1 + (-1)) and explain what (-1) × (-1) must equal.

3. 03

   Play a remainder race: divide 1 by 6 and 3 by 8, record each remainder, and explain why one decimal repeats.

4. 04

   A diver descends 2.5 meters per minute for 4 minutes, then rises 6 meters over 3 minutes; find the final depth and rising rate.

• 5.NOS.B.7.c

  Use strategies based on place value (e.g., partial products, partial quotients) to multiply and divide.

• 7.NOS.A.1

  Add and subtract rational numbers using multiple strategies and representations.