Virginia SOL 7.NS.3

7.NS.3 is a Standards of Learning standard. These are the knowledge and skills expectations under it.

• 7.NS.3.a

  Determine the positive square root of a perfect square from 0 to 400.*

• 7.NS.3.b

  Describe the relationship between square roots and perfect squares.*

01

What Students Need to Do

Students connect perfect squares to their positive square roots. They determine the positive square root of each perfect square from 0 through 400 and explain the inverse relationship.

02

What Mastery Looks Like

Students quickly find the positive square root of any perfect square from 0 through 400. They explain that squaring a whole number and taking its positive square root undo each other.

03

Common Misconceptions

Students may confuse a square root with dividing by 2, or say that the square root of 36 is 18. They may also list both 6 and negative 6 when asked for the positive square root.

04

How to Assess It

Exit ticket: Find the positive square roots of 0, 81, and 324, then explain how 18² relates to √324.

1. 01

   Have students arrange square tiles into larger squares, then record each total number of tiles and its side length.

2. 02

   Ask students to explain in writing why 13² = 169 means √169 = 13.

3. 03

   Play a card-matching game using whole numbers, their squares, and matching positive square root expressions.

4. 04

   Give students square patio areas, such as 64 or 225 square feet, and have them find each patio’s side length.

• 8.NS.2

  The student will investigate and describe the relationship between the subsets of the real number system.

• 6.NS.3

  The student will recognize and represent patterns with whole number exponents and perfect squares.