Virginia SOL 6.NS.3.c
The Standard
Justify if a number between 0 and 400 is a perfect square through modeling or mathematical reasoning.
Virginia Standards of Learning for Mathematics · The student will recognize and represent patterns with whole number exponents and perfect squares.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide whether a whole number can be written as one whole number multiplied by itself. They justify the decision using square arrays, factor pairs, exponents, or nearby known squares.
What Mastery Looks Like
- Students identify perfect squares and support each decision with equal factors, an exponent equation, or a square array. They can also place a number between consecutive squares to show it is not a square.
Common Misconceptions
- Students may think every even number is a square or confuse squaring with multiplying by two. They may use a number’s last digit as proof instead of checking equal factors.
How to Assess It
- Ask: “Is 196 a perfect square? Prove your answer with an equation, factor reasoning, or a square model.”
Lesson moves
Ways to Teach It
Use color tiles to build arrays for 36, 40, and 49, then identify which can form squares with equal side lengths.
Ask, “Is 225 a perfect square?” Students write two proofs, one using factors and one using a nearby-square argument.
Play Perfect Square Sort: teams place number cards under square or not square, then earn points by defending each choice.
A square patio has area 324 square feet; students find its side length and explain why that length works.
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Printable 6.NS.3.c Worksheet
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Related Standards
- 5.NS.2.a
Given a whole number up to 100, create a concrete or pictorial representation to demonstrate whether the number is prime or composite, and justify reasoning.
- 6.NS.3.b
Recognize and represent patterns of perfect squares not to exceed 202 , by using concrete and pictorial models.
- 7.NS.3.a
Determine the positive square root of a perfect square from 0 to 400.*
- 8.NS.1.a
Estimate and identify the two consecutive natural numbers between which the positive square root of a given number lies and justify which natural number is the ...
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