Florida B.E.S.T. MA.8.AR.2.3
The Standard
Given an equation in the form of x²=p and x³=q, where p is a whole number and q is an integer, determine the real solutions.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find all real numbers whose square or cube equals a given value. They use square and cube roots, including both square-root solutions and negative cube roots.
What Mastery Looks Like
- Students identify x = 6 and x = -6 for x² = 36, and only x = 0 for x² = 0. They find exact roots such as x = ±√20 and x = -5 for x³ = -125.
Common Misconceptions
- Students often give only the positive solution for a square equation, forgetting the negative value. They may write two solutions for a cube equation or think a negative number cannot have a real cube root.
How to Assess It
- Exit ticket: Find all real solutions to x² = 81, x² = 12, and x³ = -64. Ask students to explain why the numbers of solutions differ.
Lesson moves
Ways to Teach It
Use square tiles and linking cubes to model 25 and 27, then place every algebraic solution on a floor number line.
Ask students to explain why x² = 49 has two real solutions but x³ = 49 has only one.
Play a card match: pair equation cards, such as x³ = -216, with solution cards, such as x = -6.
Use a square garden and cube tank to find dimensions, then discuss when negative roots do not fit the real-world context.
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