Florida B.E.S.T. MA.912.AR.1.10
The Standard
Solve mathematical and real-world problems involving addition, subtraction, multiplication or division of rational algebraic expressions.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students factor polynomials, identify excluded values, and use common denominators to add or subtract rational expressions. They multiply or divide by factoring and canceling factors, then use the simplified expression to solve a stated problem.
What Mastery Looks Like
- A student chooses the correct operation, shows valid factor cancellation, and states values that make any original denominator zero. The student simplifies the result and explains its meaning in context, including reasonable units.
Common Misconceptions
- Students often cancel terms across addition, add denominators, or forget to multiply by the reciprocal when dividing. They may omit restrictions from the original expressions or accept context answers that make a denominator zero.
How to Assess It
- Exit ticket: Pump A fills a tank in x hours and Pump B in x + 2 hours. Their joint rate is 3/4 tank per hour. Write an equation, solve for x, and reject any invalid solution.
Lesson moves
Ways to Teach It
Give pairs factor cards for x, x + 2, and x − 2; have them build the common denominator for two rational expressions.
Display (x + 2)/x = 2 and ask students to explain why the cancellation is invalid, then correct the simplification.
Run a card sort matching eight rational expressions to simplified forms and excluded-value cards, with partners checking each match by substitution.
Have students combine two pumps' rates, 1/x and 1/(x + 2), then find x when their joint rate is 3/4 tank hourly.
Free download
Printable MA.912.AR.1.10 Worksheet
A ready-to-print activity worksheet aligned to MA.912.AR.1.10, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetKeep exploring
Related Standards
- MA.912.AR.1.6
Solve mathematical and real-world problems involving addition, subtraction, multiplication or division of polynomials.
- MA.8.NSO.1.7
Solve multi-step mathematical and real-world problems involving the order of operations with rational numbers including exponents and radicals.
- MA.5.AR.1.2
Solve real-world problems involving the addition, subtraction or multiplication of fractions, including mixed numbers and fractions greater than 1.
- MA.912.AR.1.9
Apply previous understanding of rational number operations to add, subtract, multiply and divide rational algebraic expressions.
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.