Florida B.E.S.T. MA.912.AR.1.3

MathGrades 9–12Interpret and rewrite algebraic expressions and equations in equivalent forms.

The Standard

Add, subtract and multiply polynomial expressions with rational number coefficients.

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

Teacher's field guide

What Students Need to Do: Students combine like terms when adding and subtracting polynomials. They apply the distributive property when subtracting or multiplying, then simplify rational number coefficients.
What Mastery Looks Like: Students correctly simplify sums, differences, and products, including expressions with fractions, decimals, and negative coefficients. They organize work clearly and write terms in descending degree.
Common Misconceptions: Students combine terms with different variable parts, such as 3x and 2x². They often miss a negative sign when subtracting or add exponents during addition.
How to Assess It: Give students: Simplify (1/2x² - 3x + 1) - (1/4x² + x - 2), then multiply (2x - 3)(x + 1). Ask them to show each step.

Lesson moves

Use algebra tiles with fraction labels to model a polynomial sum, combine like tiles, and record the symbolic result.
Ask students to explain why 2x and 2x² cannot be combined, but 2x multiplied by x equals 2x².
Play a card-matching game where students pair polynomial operation cards with their simplified forms.
Find the area of a rectangular garden with side lengths 1.5x + 2 and 2x - 1, then interpret the product.

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