Virginia SOL 8.NS.1

8.NS.1 is a Standards of Learning standard. These are the knowledge and skills expectations under it.

• 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 ...

• 8.NS.1.b

  Use rational approximations (to the nearest hundredth) of irrational numbers to compare, order, and locate values on a number line. Radicals may include both po...

• 8.NS.1.c

  Use multiple strategies (e.g., benchmarks, number line, equivalency) to compare and order no more than five real numbers expressed as integers, fractions (prope...

01

What Students Need to Do

Students estimate nonperfect square roots, place them between neighboring natural numbers, and decide which natural number is closer. They rewrite irrational values to the nearest hundredth and compare numbers written in several forms. They order up to five values and justify the order with benchmarks, equivalent forms, or a number line.

02

What Mastery Looks Like

A student accurately orders up to five values in different forms, including positive and negative irrational numbers. The student gives hundredth approximations, bounds square roots with neighboring natural numbers, and explains comparisons using equivalent values or a number line.

03

Common Misconceptions

Students may treat √n as n ÷ 2 or choose bounds without checking nearby perfect squares. They may think -√10 is greater than -3 because 3.16 is greater than 3. They may compare visible digits without rewriting fractions, percents, and scientific notation as equivalent decimals.

04

How to Assess It

Exit ticket: Order -√10, -3.1, -300%, π, and 3.2 from least to greatest, then bound √70 and identify its nearest natural number. Require hundredth approximations and one written justification.

1. 01

   Give pairs value cards and decimal cards, then have students match them and clip the matches onto a classroom number-line clothesline.

2. 02

   Ask whether √70 is closer to 8 or 9, then have students write a claim using neighboring squares and a hundredth estimate.

3. 03

   Run a sorting relay where teams order five mixed-format number cards, then earn a point only after explaining one comparison.

4. 04

   Compare hiking distances of √2 miles, 140% of one mile, 1.38 miles, 7/5 mile, and 1.39 × 10^0 miles, then rank them.

• 8.NS.2

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

• 2.NS.2

  The student will demonstrate an understanding of the ten-to-one relationships of the base 10 number system to represent, compare, and order whole numbers up to ...

• 7.NS.2

  The student will reason and use multiple strategies to compare and order rational numbers.

• 6.NS.2

  The student will reason and use multiple strategies to represent, compare, and order integers.