Virginia SOL 7.PFA.2.a
The Standard
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 limited to positive integers. Expressions should not include braces { } but may include brackets [ ] and absolute value bars | |. Square roots are limited to perfect squares.*
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 simplify expressions containing whole-number powers, brackets, absolute values, and square roots of perfect squares. They choose a valid calculation order and use number properties to make steps clearer or faster.
What Mastery Looks Like
- Students reach the correct value and show steps in a valid sequence. They can use regrouping, distribution, or another number property without changing the expression’s value.
Common Misconceptions
- Students may work strictly from left to right, ignoring multiplication, division, and grouping symbols. They may read 3² as 3 × 2, treat absolute value bars as parentheses, or confuse √49 with 49 ÷ 2.
How to Assess It
- Give: Simplify 3[8 − 2²] + |5 − 11| + √36, showing each step. Ask students to label one property or rule they used.
Lesson moves
Ways to Teach It
Give pairs operation cards for an expression, then have them arrange the cards to show the correct calculation order.
Display two worked solutions to 4[7 − 2²] + |−3| and ask students to explain which is correct.
Play an expression relay where teams simplify one step at a time and earn a point only when each step is justified.
Use a store receipt with discounts, quantities, and fees, then write and simplify one expression for the final cost.
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Printable 7.PFA.2.a Worksheet
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