Maryland Math 8.NOS.B.4

8.NOS.B.4 is a cluster heading. These are the individual standards under it.

• 8.NOS.B.4.a

  Use square and cube roots symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number.

• 8.NOS.B.4.b

  Evaluate square roots of perfect squares from 1 to 100 and cube roots of perfect cubes from 1 to 125 by inspection.

01

What Students Need to Do

Students use root symbols to write solutions to square and cube equations with positive whole numbers or fractions. They find square roots of perfect squares through 100 and cube roots of perfect cubes through 125 without a calculator.

02

What Mastery Looks Like

A student writes x = ±√p for x² = p, but only x = ∛p for x³ = p. They know √81 = 9 and ∛125 = 5 by checking the square or cube.

03

Common Misconceptions

Students may give only the positive solution to x² = 36, or say √36 = ±6. Some confuse squares and cubes, giving 8 for ∛64, or miss that (1/2)³ = 1/8.

04

How to Assess It

Ask students to solve x² = 9/16 and x³ = 27 using root symbols, then evaluate √81 and ∛125 without a calculator.

1. 01

   Arrange 36 square tiles into a square and 27 unit cubes into a cube, then label each side length with a root symbol.

2. 02

   Ask, 'Why does x² = 49 have two solutions while √49 names one number?' Have partners check both solutions by squaring.

3. 03

   Play a matching game with equation cards such as x² = 9/16 and x³ = 1/8, paired with cards showing their root-form solutions.

4. 04

   Give students a 49-square-foot square garden and a 64-cubic-foot cube-shaped box; have them find each side length and name the root used.

• 7.AT.C.8

  Use variables to represent quantities and write and solve equations to model and reason about relationships in context.

• 6.AT.C.8.c

  Represent solutions of such equations on a number line.