Florida B.E.S.T. MA.912.AR.1.4
The Standard
Divide a polynomial expression by a monomial expression with rational number coefficients.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students split a quotient across every term in the numerator. They divide rational coefficients and subtract exponents on like bases. They simplify the result and check it by multiplication.
What Mastery Looks Like
- A student correctly handles signs, fractional coefficients, and variables in every term. The student can multiply the quotient by the divisor to recover the original numerator.
Common Misconceptions
- Students may divide only the first term instead of every term. Some cancel variables across sums or divide exponents instead of subtracting them. Negative signs and fraction arithmetic also cause errors.
How to Assess It
- Exit ticket: Simplify [(3/4)x³y − (1/2)x²y² + (5/8)xy] ÷ [(1/4)xy]. Show the division for each term, then verify by multiplication.
Lesson moves
Ways to Teach It
Give students color-coded term cards for a polynomial and divisor, then have them build and simplify one quotient card per term.
Ask students to explain why each numerator term must be divided, using the distributive property and a worked example.
Run a matching game where students pair quotient cards with products that return the original numerator.
Give a rectangle's polynomial area and monomial width, then ask students to find and verify its length.
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Printable MA.912.AR.1.4 Worksheet
A ready-to-print activity worksheet aligned to MA.912.AR.1.4, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- MA.912.AR.1.5
Divide polynomial expressions using long division, synthetic division or algebraic manipulation.
- MA.912.AR.1.3
Add, subtract and multiply polynomial expressions with rational number coefficients.
- MA.8.AR.1.2
Apply properties of operations to multiply two linear expressions with rational coefficients.
- MA.912.AR.1.7
Rewrite a polynomial expression as a product of polynomials over the real number system.
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