Florida B.E.S.T. MA.912.NSO.1.5

MathGrades 9–12Generate equivalent expressions and perform operations with expressions involving exponents, radicals or logarithms.

The Standard

Add, subtract, multiply and divide algebraic expressions involving radicals.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students simplify radicals before adding, subtracting, multiplying, or dividing expressions. They combine like radical terms, use distribution, and rewrite quotients without radicals in the denominator when required.
What Mastery Looks Like: Students simplify radicals and combine only like radical terms. They distribute accurately, rationalize denominators when needed, and verify equivalent forms by substituting values.
Common Misconceptions: Students combine unlike radicals, such as √2 + √3 = √5. They may distribute roots across sums, forget to simplify first, or cancel terms incorrectly when dividing.
How to Assess It: Give this exit ticket: Simplify [(3√8 − √18)(√2 + 1)] ÷ √2, and show each step.

Lesson moves

Match cards showing unsimplified radicals, simplified forms, and equivalent sums or products, then have students explain each match.
Ask students to explain why √2 + √3 cannot become √5, using a numerical estimate as evidence.
Play Radical Relay, where teams simplify one step at a time and pass the expression to the next teammate.
Use a right-triangle floor plan with radical side lengths to find exact trim length, then compare it with a decimal estimate.

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