Virginia SOL 7.PFA.2

7.PFA.2 is a Standards of Learning standard. These are the knowledge and skills expectations under it.

• 7.PFA.2.a

  Use the order of operations and apply the properties of real numbers to simplify numerical expressions. Exponents are limited to 1, 2, 3, or 4 and bases are lim...

• 7.PFA.2.b

  Represent equivalent algebraic expressions in one variable using concrete manipulatives and pictorial representations (e.g., colored chips, algebra tiles).

• 7.PFA.2.c

  Simplify and generate equivalent algebraic expressions in one variable by applying the order of operations and properties of real numbers. Expressions may requi...

• 7.PFA.2.d

  Use the order of operations and apply the properties of real numbers to evaluate algebraic expressions for given replacement values of the variables. Exponents ...

01

What Students Need to Do

Students simplify numerical expressions using the correct order of operations and properties of real numbers. They model and rewrite one-variable expressions by distributing and combining like terms. They substitute given values, including negative rational numbers, and evaluate accurately.

02

What Mastery Looks Like

Students simplify expressions accurately and show each step in the correct order. They use tiles, drawings, or properties to prove two expressions are equivalent. They substitute positive or negative rational values using parentheses and calculate the result correctly.

03

Common Misconceptions

Students often combine unlike terms, such as 3x + 4 = 7x. They may lose a negative sign when distributing or fail to place negative replacement values in parentheses. Some apply exponents after multiplication or treat absolute value bars like grouping symbols.

04

How to Assess It

Give this exit ticket: simplify [18 ÷ 3 + 2³] - |-4|, rewrite 2(x - 3) + x, then evaluate 3x - 2y + √49 for x = -1/2 and y = 2. Require students to label one property or operation used in each part.

1. 01

   Build 2(x + 3) - x with algebra tiles, remove matching pieces, draw the final model, and write its simplified expression.

2. 02

   Ask, “Are 3(x - 2) + x and 4x - 6 equivalent?” Students defend their answer with a property and two replacement values.

3. 03

   Run a card match with numerical expressions, algebraic expressions, simplified forms, and values, then have pairs explain every match.

4. 04

   Model a phone bill as 12 + 3m + 2m, simplify the expression, and evaluate the cost for several monthly data amounts.

• 8.PFA.1

  The student will represent, simplify, and generate equivalent algebraic expressions in one variable. 

• 5.CE.4

  The student will simplify numerical expressions with whole numbers using the order of operations.

• 8.PFA.1.b

  Simplify and generate equivalent algebraic expressions in one variable by applying the order of operations and properties of real numbers. Expressions may need ...