Virginia SOL 7.NS.3.b
The Standard
Describe the relationship between square roots and perfect squares.*
Virginia Standards of Learning for Mathematics · The student will recognize and describe the relationship between square roots and perfect squares.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students connect squaring a whole number with finding the square root of its perfect square. They describe these operations as inverses using words, symbols, and square models.
What Mastery Looks Like
- Students identify perfect squares and find their nonnegative square roots. They use equations such as 8² = 64 and √64 = 8 to explain that the operations reverse each other.
Common Misconceptions
- Students may think finding a square root means dividing by 2. They may also assume every whole number has a whole-number square root or confuse √36 with solutions to x² = 36.
How to Assess It
- Exit ticket: Complete 11² = ___ and √121 = ___. Then explain how the two equations are related.
Lesson moves
Ways to Teach It
Give students square tiles to build square arrays, then record each side length, total area, multiplication equation, and square root equation.
Ask students to explain in writing why 49 is a perfect square and why √49 equals 7.
Use matching cards with square models, exponential equations, perfect squares, and square root equations for students to pair.
Present square garden areas such as 81 square feet, then have students find and justify each garden's side length.
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Printable 7.NS.3.b Worksheet
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Related Standards
- 6.NS.3.c
Justify if a number between 0 and 400 is a perfect square through modeling or mathematical reasoning.
- 6.NS.3
The student will recognize and represent patterns with whole number exponents and perfect squares.
- 7.NS.3
The student will recognize and describe the relationship between square roots and perfect squares.
- 7.NS.3.a
Determine the positive square root of a perfect square from 0 to 400.*
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