Florida B.E.S.T. MA.912.AR.6.2
The Standard
Explain and apply the Remainder Theorem to solve mathematical and real-world problems.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students connect division by x−a with evaluating f(a). They use the resulting value as the remainder and explain why the relationship works. They apply it to find remainders, missing values, or model outputs.
What Mastery Looks Like
- Given a polynomial and divisor x−a, students identify a, calculate f(a), and state the remainder. They can use a known remainder to find a missing coefficient or check whether division was completed correctly.
Common Misconceptions
- Students often use the wrong sign, evaluating f(a) for a divisor of x+a. They may confuse the remainder with the quotient or omit zero coefficients during synthetic division.
How to Assess It
- Give f(x)=x³−4x+1 and ask: “Use the Remainder Theorem to find the remainder when f(x) is divided by x+2. Show why.”
Lesson moves
Ways to Teach It
Give groups polynomial, divisor, and value cards to match, then have them verify each remainder with synthetic division.
Ask students to explain why dividing by x+3 requires evaluating f(−3), using an example in their explanation.
Play Remainder Relay, where teams evaluate polynomials from divisor cards and earn a point for each correct remainder and explanation.
Use C(t)=2t³−5t+100 as a cost model, then find C(8) by treating it as the remainder from division by t−8.
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Related Standards
- MA.912.AR.6.3
Explain and apply theorems for polynomials to solve mathematical and real-world problems.
- MA.912.DP.4.9
Apply the addition and multiplication rules for counting to solve mathematical and real-world problems, including problems involving probability.
- MA.5.AR.1.1
Solve multi-step real-world problems involving any combination of the four operations with whole numbers, including problems in which remainders must be interpr...
- MA.4.AR.1.1
Solve real-world problems involving multiplication and division of whole numbers including problems in which remainders must be interpreted within the context.
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