Mississippi Math A-REI.4b

MathGrades 9–12Seeing Structure in Expressions

The Standard

A-REI.4: Solve quadratic equations in one variable.

Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Solve Equations and Inequalities in One Variable

Teacher's field guide

What This Standard Means

What Students Need to Do: Students choose a method that fits the equation: inspection, square roots, factoring, completing the square, or the quadratic formula. They find all roots and recognize when the roots are complex.
What Mastery Looks Like: Students solve x² = 49 with both answers, 7 and -7. They factor when it works, use another method when it does not, and write complex roots instead of saying there is no solution.
Common Misconceptions: Students often miss the negative root when taking a square root. They may add a number to only one side while completing the square, or mistake a negative discriminant for no solutions at all.
How to Assess It: Exit ticket: Solve x² + 6x + 13 = 0 by completing the square. Use the discriminant to explain whether the roots are real or complex.

Lesson moves

Ways to Teach It

Arrange algebra tiles for x² + 6x + 9 into a square, then use the square to solve x² + 6x + 9 = 16.
Ask: Which method would you use for 4x² = 36 and x² + 5x + 6 = 0, and why?
Give pairs equation cards and method cards; students match them, solve each equation, and check their answers by substitution.
Give h(t) = -5t² + 20t for a tossed ball; students find when it reaches 15 meters and explain both times.

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