Maryland Math 7.NOS.A.3

7.NOS.A.3 is a cluster heading. These are the individual standards under it.

• 7.NOS.A.3.a

  Apply properties of operations to efficiently compute with rational numbers and convert between forms when appropriate to support problem solving.

• 7.NOS.A.3.b

  Evaluate the reasonableness of solutions using estimation, mental math, and understanding of the context.

01

What Students Need to Do

Students solve problems with several steps using positive and negative fractions, decimals, and percents. They choose useful forms, use all four operations, and estimate to check their answers.

02

What Mastery Looks Like

A student can turn a percent into a decimal, regroup numbers to make a calculation easier, and keep track of negative signs. They can explain whether their answer makes sense in the story.

03

Common Misconceptions

Students may treat subtracting a negative as subtracting a positive. They may use 20 instead of 0.20 for 20%, add fractions without common denominators, or ignore what a negative balance means.

04

How to Assess It

A group account starts at -$12.50. Add half of a $30 payment, subtract a 20% fee on that payment, then split the balance between two people. Ask students to estimate first, then find each share.

1. 01

   Give pairs play money and debt cards; start at -$5, add three $1.50 deposits, then split the remaining debt between two people.

2. 02

   Ask students to write two ways to compute -2.5 + 3/4 + 2.5 and explain which order is faster.

3. 03

   Draw a signed fraction, decimal, and percent card; arrange them with two operation cards, then estimate and solve the expression.

4. 04

   Use a grocery receipt to find a bill after a 15% discount and 6% sales tax, then split it three ways.

• 7.NOS.A.1.d

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

• 4.AT.A.4

  Solve multistep problems in context involving whole numbers and having whole number answers using the four operations, including problems in which remainders mu...

• 7.NOS.A.2.e

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