NY Next Generation Math NY-8.EE.2
The Standard
Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Know square roots of perfect squares up to 225 and cube roots of perfect cubes up to 125. Know that the square root of a non-perfect square is irrational.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use square-root and cube-root symbols to solve equations with squared or cubed variables. They recall specified perfect roots and recognize that square roots of whole numbers that are not perfect squares are irrational.
What Mastery Looks Like
- A student solves x² = 196 as x = ±14 and x³ = 125 as x = 5. The student knows √196 = 14, ∛125 = 5, and explains why √10 is irrational.
Common Misconceptions
- Students may give only the positive solution to a square equation, attach two signs to a cube-root solution, or confuse squaring with doubling. They may also assume every radical has a rational value.
How to Assess It
- Ask students to solve x² = 144 and x³ = 64 using radical symbols. Then have them classify √20 as rational or irrational and explain why.
Lesson moves
Ways to Teach It
Arrange square tiles and unit cubes for perfect numbers, then connect side or edge lengths to square and cube roots.
Ask students why x² = 49 has two solutions while x³ = 125 has only one real solution.
Match perfect squares and cubes to radical cards, equation solutions, and irrational non-perfect square roots.
Find the side of a square from its area and the edge of a cube from its volume in design problems.
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