CCSS.Math.Content.8.EE.A.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. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Common Core State Standards for Mathematics · Expressions and Equations
What this standard means
Students need to connect powers with their inverse operations. If x² = 49, they should write x = ±√49 and know the answers are 7 and -7. If x³ = 27, they should write x = ∛27 and get 3. They also need to know common perfect squares and cubes, and recognize that √2 cannot be written as a fraction.
Mastery means students choose the right root symbol, include both positive and negative answers for square root equations, and evaluate familiar roots quickly. Students often forget the negative square root, confuse square and cube roots, or think every radical has a neat whole number answer.
Ways to teach it
- Use square tiles and unit cubes to build models for 16, 25, 8, and 27, then match each model to its root equation.
- Ask students to explain why x² = 36 has two solutions, but x³ = 8 has one solution.
- Give a five-question exit ticket with √64, ∛125, x² = 81, x³ = 64, and whether √2 is rational.
- Have students estimate the side length of a square table with area 2 square meters, then discuss why the answer is not a fraction.
Plan a lesson for CCSS.Math.Content.8.EE.A.2
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