Virginia SOL 8.NS.1.a
The Standard
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 better approximation. Numbers are limited to natural numbers from 1 to 400.
Virginia Standards of Learning for Mathematics · The student will compare and order real numbers and determine the relationships between real numbers.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use known perfect squares to bracket a square root between consecutive natural numbers. They choose the closer natural number and support the choice with squared values or distances from nearby perfect squares.
What Mastery Looks Like
- Given 157, a student identifies 12 and 13 because 12² = 144 and 13² = 169. The student selects 13 and explains that 157 is closer to 169 than to 144.
Common Misconceptions
- Students may divide the given number by 2 or give the nearby perfect squares as the bounds. They may bracket the root correctly but choose an approximation without comparing distances from the nearby perfect squares.
How to Assess It
- Exit ticket: Without a calculator, place √157 between two consecutive natural numbers. Choose the better natural-number approximation and justify it using two perfect squares.
Lesson moves
Ways to Teach It
Lay cards labeled 1² through 20² on a floor line, then have students place number cards and name the nearest natural-number root.
Ask, “Is √70 better approximated by 8 or 9?” Students write a claim using 64 and 81, then compare reasons.
Play partner matching by pairing each radicand card with its two natural-number bounds and a nearest-natural-number answer card.
A square patio has area 150 square feet; estimate its side length to the nearest foot and justify with nearby square areas.
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Printable 8.NS.1.a Worksheet
A ready-to-print activity worksheet aligned to 8.NS.1.a, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 2.NS.2.g
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- 6.NS.3.c
Justify if a number between 0 and 400 is a perfect square through modeling or mathematical reasoning.
- 8.NS.1.b
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- 7.NS.3.a
Determine the positive square root of a perfect square from 0 to 400.*
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