Maryland Math A.CED.A.1.b

MathGrades 9–12CREATING EQUATIONS

The Standard

A.CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Create polynomial equations given roots.

Maryland College and Career Ready Standards for Mathematics (2025) · Create equations that describe numbers or relationships.

Teacher's field guide

What Students Need to Do: Students turn each given root into a factor that equals zero at that value. They multiply the factors and set the polynomial equal to zero.
What Mastery Looks Like: Given roots 2 and -3, a student writes (x-2)(x+3)=0 and expands it to x²+x-6=0. They check both roots by substitution.
Common Misconceptions: Students may use x+3 for a root of 3, reversing the sign. Some write a polynomial expression but forget to set it equal to zero.
How to Assess It: Exit ticket: Write a polynomial equation with roots -2 and 5 in factored and expanded form. Substitute both roots to check.

Lesson moves

Hand out root cards and factor cards; students match each root to a factor, then build an equation from two matches.
Ask students to explain why a root of -4 gives the factor x+4, not x-4.
Play a card match with pairs of roots, factored equations, and expanded equations; students check matches by substitution.
A ball starts on the ground and lands after 4 seconds; ask students to write a possible height equation.

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