Virginia SOL 7.PFA.2.d
The Standard
Use the order of operations and apply the properties of real numbers to evaluate algebraic expressions for given replacement values of the variables. Exponents are limited to 1, 2, 3, or 4 and bases are limited to positive integers. Expressions should not include braces { } but may include brackets [ ] and absolute value bars | |. Square roots are limited to perfect squares. Limit the number of replacements to no more than three per expression. Replacement values may be positive or negative rational numbers.
Virginia Standards of Learning for Mathematics · The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students substitute up to three given rational values for variables, using parentheses when a value is negative. They evaluate in the correct order, including absolute value, perfect-square roots, and powers through four.
What Mastery Looks Like
- A student writes the substituted expression before calculating and preserves each operation sign. They correctly handle negative values, grouping symbols, exponents, absolute values, and square roots, then report one accurate value.
Common Misconceptions
- Students often replace x with -3 in x² but write -3², losing the grouping that makes (-3)² equal 9. They may work strictly left to right, apply an exponent across a sum, or treat absolute value bars as parentheses. Some also say √49 is ±7 rather than 7.
How to Assess It
- Exit ticket: Given a = -3/2 and b = -2, evaluate [2a² + |3b|] ÷ √9. Show the substituted expression first.
Lesson moves
Ways to Teach It
Give pairs variable cards and expression cards; students place negative values in parentheses, then arrange operation cards to show the calculation order.
Post two solutions for x² + 4 when x = -3, one using -3² and one using (-3)²; students explain which is valid.
Run a substitution relay: teams draw one value card and one expression card, solve on mini whiteboards, then check with a key.
Students evaluate C = 5(F - 32)/9 for F = 14 and F = -4, then compare the two temperatures.
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Related Standards
- 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.c
Simplify and generate equivalent algebraic expressions in one variable by applying the order of operations and properties of real numbers. Expressions may requi...
- 6.PFA.3.c
Apply properties of real numbers and properties of equality to solve a one-step equation in one variable. Coefficients are limited to integers and unit fraction...
- 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 ...
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